<?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>ra2aa.out</source>

<heading><![CDATA[
Prover9 (64) version 2026-3T, March 2026.
Process 1017388 was started by veroff on b146-09,
Tue Apr 28 13:05:07 2026
The command was "prover9 -f ra2aa.in".
]]></heading>

<proof number="1" length="15807" max_count="89">

<comments><![CDATA[
% Proof 1 at 5591.89 (+ 0.24) seconds: "aa1".
% Length of proof: 15807 (0 new hints)
% Level of proof: 339
% Maximum clause weight: 1019.000 (89 w/o degradation)
% Given clauses in run: 19488
% Given clauses in proof: 15790 (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(a(x,y,z),u,w) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("aa1")
    ]]></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) * (z * z) = x * (y * (z * z))
    ]]></literal>
    <attribute><![CDATA[
      label("NucSq_r")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="33" type="assumption">
    <literal><![CDATA[
      a(K(x,y),z,u) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("aK1")
    ]]></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(a(c1,c2,c3),c4,c5) != 1
    ]]></literal>
    <attribute><![CDATA[
      label("aa1")
    ]]></attribute>
    <attribute><![CDATA[
      answer("aa1")
    ]]></attribute>
    <justification jstring="[deny(6)].">
      <j1 rule="deny" parents="6"/>
    </justification>
  </clause>

  <clause id="65">
    <literal><![CDATA[
      (1 * x) * 1 = x
    ]]></literal>
    <justification jstring="[para(8(a,2),7(a,1))].">
      <j1 rule="para" parents="8 7"/>
    </justification>
  </clause>

  <clause id="66">
    <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="67">
    <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="69">
    <literal><![CDATA[
      x \ (y \ (y * (x * z))) = z
    ]]></literal>
    <justification jstring="[para(9(a,2),9(a,1,2))].">
      <j1 rule="para" parents="9 9"/>
    </justification>
  </clause>

  <clause id="70">
    <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="71">
    <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="73">
    <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="74">
    <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="75">
    <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="76">
    <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="77">
    <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="78">
    <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="79">
    <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="80">
    <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="81">
    <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="82">
    <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="83">
    <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="85">
    <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="86">
    <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="87">
    <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="88">
    <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="89">
    <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="90">
    <literal><![CDATA[
      (x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="91">
    <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="93">
    <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="94">
    <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="95">
    <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="96">
    <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="97">
    <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="98">
    <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="99">
    <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="100">
    <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="101">
    <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="102">
    <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="103">
    <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="104">
    <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="105">
    <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="106">
    <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="108">
    <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="109">
    <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="110">
    <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="111">
    <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="112">
    <literal><![CDATA[
      T(x,1) = 1 \ x
    ]]></literal>
    <justification jstring="[para(8(a,1),22(a,2,2))].">
      <j1 rule="para" parents="8 22"/>
    </justification>
  </clause>

  <clause id="113">
    <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="114">
    <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="115">
    <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="116">
    <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="117">
    <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="118">
    <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="120">
    <literal><![CDATA[
      x \ (R(y,z,u) * x) = R(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(27(a,2),22(a,1)),flip(a)].">
      <j1 rule="para" parents="27 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="121">
    <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="122">
    <literal><![CDATA[
      L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,v5,v6),y,z),u,w)
    ]]></literal>
    <justification jstring="[para(30(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="123">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * z))) = z * z
    ]]></literal>
    <justification jstring="[para(32(a,1),9(a,1,2))].">
      <j1 rule="para" parents="32 9"/>
    </justification>
  </clause>

  <clause id="124">
    <literal><![CDATA[
      x * ((x \ y) * (z * z)) = y * (z * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),32(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="125">
    <literal><![CDATA[
      (x / y) * (y * (z * z)) = x * (z * z)
    ]]></literal>
    <justification jstring="[para(12(a,1),32(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="128">
    <literal><![CDATA[
      (x * x) \ (y * (z * (x * x))) = T(y * z,x * x)
    ]]></literal>
    <justification jstring="[para(32(a,1),22(a,2,2)),flip(a)].">
      <j1 rule="para" parents="32 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="129">
    <literal><![CDATA[
      x * a(K(y,z),u,w) = x
    ]]></literal>
    <justification jstring="[para(33(a,2),8(a,1,2))].">
      <j1 rule="para" parents="33 8"/>
    </justification>
  </clause>

  <clause id="130">
    <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="131">
    <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="132">
    <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="133">
    <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="134">
    <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="135">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(8(a,1),35(b,1))].">
      <j1 rule="para" parents="8 35"/>
    </justification>
  </clause>

  <clause id="136">
    <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="137">
    <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="138">
    <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="139">
    <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="140">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(7(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="7 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="141">
    <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="142">
    <literal><![CDATA[
      (x * y) * 1 != x * z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(8(a,2),43(a,2)),flip(a)].">
      <j1 rule="para" parents="8 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="143">
    <literal><![CDATA[
      x \ (x * (y * z)) != y * u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(9(a,2),43(a,2)),flip(a)].">
      <j1 rule="para" parents="9 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="144">
    <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="145">
    <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="146">
    <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="147">
    <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="148">
    <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="149">
    <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="150">
    <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="151">
    <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="152">
    <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="153">
    <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="154">
    <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="155">
    <literal><![CDATA[
      L(x,y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,33,a)].">
      <j1 rule="hyper" parents="52 33"/>
    </justification>
  </clause>

  <clause id="156">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * v5 = L(L(x,u,w),y,z) * v5
    ]]></literal>
    <justification jstring="[hyper(57,a,30,a)].">
      <j1 rule="hyper" parents="57 30"/>
    </justification>
  </clause>

  <clause id="157">
    <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="158">
    <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="159">
    <literal><![CDATA[
      x * L(L(y,z,u),w,v5) = x * L(L(y,w,v5),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,30,a)].">
      <j1 rule="hyper" parents="58 30"/>
    </justification>
  </clause>

  <clause id="160">
    <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="161">
    <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="162">
    <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="163">
    <literal><![CDATA[
      (x * (x \ y)) / z = y / z
    ]]></literal>
    <justification jstring="[hyper(59,a,10,a)].">
      <j1 rule="hyper" parents="59 10"/>
    </justification>
  </clause>

  <clause id="165">
    <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="166">
    <literal><![CDATA[
      (x \ (x * y)) \ z = y \ z
    ]]></literal>
    <justification jstring="[hyper(61,a,9,a)].">
      <j1 rule="hyper" parents="61 9"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      x \ L(L(y,z,u),w,v5) = x \ L(L(y,w,v5),z,u)
    ]]></literal>
    <justification jstring="[hyper(62,a,30,a)].">
      <j1 rule="hyper" parents="62 30"/>
    </justification>
  </clause>

  <clause id="168">
    <literal><![CDATA[
      x \ (y * (y \ z)) = x \ z
    ]]></literal>
    <justification jstring="[hyper(62,a,10,a)].">
      <j1 rule="hyper" parents="62 10"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      x \ (y * 1) = x \ y
    ]]></literal>
    <justification jstring="[hyper(62,a,8,a)].">
      <j1 rule="hyper" parents="62 8"/>
    </justification>
  </clause>

  <clause id="170">
    <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="171">
    <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="172">
    <literal><![CDATA[
      (x * y) / y = 1 * x
    ]]></literal>
    <justification jstring="[hyper(63,a,11,a,b,7,a(flip))].">
      <j1 rule="hyper" parents="63 11 7"/>
    </justification>
  </clause>

  <clause id="173">
    <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="174">
    <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="175">
    <literal><![CDATA[
      x * (x \ y) = 1 * y
    ]]></literal>
    <justification jstring="[hyper(63,a,10,a,b,7,a(flip))].">
      <j1 rule="hyper" parents="63 10 7"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      (x * (x \ 1)) \ y = y
    ]]></literal>
    <justification jstring="[para(10(a,2),66(a,1,1))].">
      <j1 rule="para" parents="10 66"/>
    </justification>
  </clause>

  <clause id="178">
    <literal><![CDATA[
      ((1 / x) * x) \ y = y
    ]]></literal>
    <justification jstring="[para(12(a,2),66(a,1,1))].">
      <j1 rule="para" parents="12 66"/>
    </justification>
  </clause>

  <clause id="179">
    <literal><![CDATA[
      1 \ x != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(66(a,1),47(a,2))].">
      <j1 rule="para" parents="66 47"/>
    </justification>
  </clause>

  <clause id="180">
    <literal><![CDATA[
      K(x,x) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,16,a,b,67,a)].">
      <j1 rule="hyper" parents="63 16 67"/>
    </justification>
  </clause>

  <clause id="182">
    <literal><![CDATA[
      (x \ x) * y = y
    ]]></literal>
    <justification jstring="[para(67(a,2),7(a,1,1))].">
      <j1 rule="para" parents="67 7"/>
    </justification>
  </clause>

  <clause id="183">
    <literal><![CDATA[
      x * (y \ y) = x
    ]]></literal>
    <justification jstring="[para(67(a,2),8(a,1,2))].">
      <j1 rule="para" parents="67 8"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      x / (y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(10(a,2),78(a,1,2))].">
      <j1 rule="para" parents="10 78"/>
    </justification>
  </clause>

  <clause id="185">
    <literal><![CDATA[
      x / ((1 / y) * y) = x
    ]]></literal>
    <justification jstring="[para(12(a,2),78(a,1,2))].">
      <j1 rule="para" parents="12 78"/>
    </justification>
  </clause>

  <clause id="186">
    <literal><![CDATA[
      x / 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(78(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="78 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="187">
    <literal><![CDATA[
      T(x,R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,27,a,b,113,a(flip))].">
      <j1 rule="hyper" parents="42 27 113"/>
    </justification>
  </clause>

  <clause id="188">
    <literal><![CDATA[
      T(x,L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,25,a,b,113,a(flip))].">
      <j1 rule="hyper" parents="41 25 113"/>
    </justification>
  </clause>

  <clause id="189">
    <literal><![CDATA[
      T(x,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,23,a,b,113,a(flip))].">
      <j1 rule="hyper" parents="40 23 113"/>
    </justification>
  </clause>

  <clause id="190">
    <literal><![CDATA[
      T(T(x,y),x) = T(x,y)
    ]]></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="191">
    <literal><![CDATA[
      T(L(x,y,z),x) = L(x,y,z)
    ]]></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="192">
    <literal><![CDATA[
      T(R(x,y,z),x) = R(x,y,z)
    ]]></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="193">
    <literal><![CDATA[
      T(x,y) != y
    ]]></literal>
    <literal><![CDATA[
      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="194">
    <literal><![CDATA[
      x * K(y,y) = x
    ]]></literal>
    <justification jstring="[para(180(a,2),8(a,1,2))].">
      <j1 rule="para" parents="180 8"/>
    </justification>
  </clause>

  <clause id="195">
    <literal><![CDATA[
      x / (y \ x) = z / (y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,80,a,b,80,a(flip))].">
      <j1 rule="hyper" parents="63 80 80"/>
    </justification>
  </clause>

  <clause id="196">
    <literal><![CDATA[
      x / (y \ x) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,80,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="63 80 10"/>
    </justification>
  </clause>

  <clause id="197">
    <literal><![CDATA[
      x * (y / (z \ y)) = x * z
    ]]></literal>
    <justification jstring="[hyper(58,a,80,a)].">
      <j1 rule="hyper" parents="58 80"/>
    </justification>
  </clause>

  <clause id="198">
    <literal><![CDATA[
      (x / (y \ x)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(57,a,80,a)].">
      <j1 rule="hyper" parents="57 80"/>
    </justification>
  </clause>

  <clause id="199">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(36,a,20,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="36 20 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      ((x * y) * z) / a(x,y,z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(14(a,2),80(a,1,2))].">
      <j1 rule="para" parents="14 80"/>
    </justification>
  </clause>

  <clause id="201">
    <literal><![CDATA[
      (x * y) / K(x,y) = y * x
    ]]></literal>
    <justification jstring="[para(16(a,2),80(a,1,2))].">
      <j1 rule="para" parents="16 80"/>
    </justification>
  </clause>

  <clause id="202">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) = x * y
    ]]></literal>
    <justification jstring="[para(18(a,2),80(a,1,2))].">
      <j1 rule="para" parents="18 80"/>
    </justification>
  </clause>

  <clause id="203">
    <literal><![CDATA[
      (x * y) / T(x,y) = y
    ]]></literal>
    <justification jstring="[para(22(a,2),80(a,1,2))].">
      <j1 rule="para" parents="22 80"/>
    </justification>
  </clause>

  <clause id="204">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z \ x = y
    ]]></literal>
    <justification jstring="[para(80(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="80 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="205">
    <literal><![CDATA[
      x / (y / ((z \ x) \ y)) = z
    ]]></literal>
    <justification jstring="[para(80(a,2),80(a,1,2))].">
      <j1 rule="para" parents="80 80"/>
    </justification>
  </clause>

  <clause id="206">
    <literal><![CDATA[
      ((x / y) \ x) \ z = y \ z
    ]]></literal>
    <justification jstring="[hyper(61,a,83,a)].">
      <j1 rule="hyper" parents="61 83"/>
    </justification>
  </clause>

  <clause id="207">
    <literal><![CDATA[
      ((x / y) \ x) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(57,a,83,a)].">
      <j1 rule="hyper" parents="57 83"/>
    </justification>
  </clause>

  <clause id="208">
    <literal><![CDATA[
      ((x / (y / z)) \ x) \ y = z
    ]]></literal>
    <justification jstring="[hyper(36,a,80,a,b,83,a(flip))].">
      <j1 rule="hyper" parents="36 80 83"/>
    </justification>
  </clause>

  <clause id="209">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      u / x = z
    ]]></literal>
    <justification jstring="[para(83(a,1),39(a,1))].">
      <j1 rule="para" parents="83 39"/>
    </justification>
  </clause>

  <clause id="210">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      y / z = x
    ]]></literal>
    <justification jstring="[para(83(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="83 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="211">
    <literal><![CDATA[
      T(x,1) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,112,a,b,66,a)].">
      <j1 rule="hyper" parents="63 112 66"/>
    </justification>
  </clause>

  <clause id="212">
    <literal><![CDATA[
      K(x,1) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,211,a)].">
      <j1 rule="hyper" parents="55 211"/>
    </justification>
  </clause>

  <clause id="213">
    <literal><![CDATA[
      T(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,211,a)].">
      <j1 rule="hyper" parents="54 211"/>
    </justification>
  </clause>

  <clause id="214">
    <literal><![CDATA[
      T(x,1) != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(211(a,1),49(a,2))].">
      <j1 rule="para" parents="211 49"/>
    </justification>
  </clause>

  <clause id="215">
    <literal><![CDATA[
      T(x,y \ y) = x
    ]]></literal>
    <justification jstring="[para(67(a,2),211(a,1,2))].">
      <j1 rule="para" parents="67 211"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      T(1,x) * y = y
    ]]></literal>
    <justification jstring="[para(213(a,2),7(a,1,1))].">
      <j1 rule="para" parents="213 7"/>
    </justification>
  </clause>

  <clause id="218">
    <literal><![CDATA[
      (x \ x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(182(a,1),43(a,2))].">
      <j1 rule="para" parents="182 43"/>
    </justification>
  </clause>

  <clause id="219">
    <literal><![CDATA[
      x * (y \ y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(183(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="183 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="220">
    <literal><![CDATA[
      x * (y \ y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(183(a,1),44(a,2))].">
      <j1 rule="para" parents="183 44"/>
    </justification>
  </clause>

  <clause id="222">
    <literal><![CDATA[
      (x / x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(77(a,2),141(a,1,1))].">
      <j1 rule="para" parents="77 141"/>
    </justification>
  </clause>

  <clause id="223">
    <literal><![CDATA[
      K(x,1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(212(a,2),141(a,1,1))].">
      <j1 rule="para" parents="212 141"/>
    </justification>
  </clause>

  <clause id="225">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      1 * x = y
    ]]></literal>
    <justification jstring="[para(65(a,1),145(a,1)),flip(b)].">
      <j1 rule="para" parents="65 145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="227">
    <literal><![CDATA[
      L(x,y,1) = x
    ]]></literal>
    <justification jstring="[para(180(a,1),155(a,1,3))].">
      <j1 rule="para" parents="180 155"/>
    </justification>
  </clause>

  <clause id="228">
    <literal><![CDATA[
      L(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(227(a,1),50(a,2))].">
      <j1 rule="para" parents="227 50"/>
    </justification>
  </clause>

  <clause id="229">
    <literal><![CDATA[
      (x \ 1) * (x * x) = x
    ]]></literal>
    <justification jstring="[hyper(34,a,32,a(flip),b,71,a(flip))].">
      <j1 rule="hyper" parents="34 32 71"/>
    </justification>
  </clause>

  <clause id="230">
    <literal><![CDATA[
      (x * ((x \ 1) * y)) \ y = a(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(71(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="71 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="231">
    <literal><![CDATA[
      x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(73(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="73 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="232">
    <literal><![CDATA[
      L(x \ 1,x,y) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(73(a,1),18(a,2,2))].">
      <j1 rule="para" parents="73 18"/>
    </justification>
  </clause>

  <clause id="233">
    <literal><![CDATA[
      x * ((1 / x) * (1 / x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(34,a,32,a(flip),b,81,a(flip))].">
      <j1 rule="hyper" parents="34 32 81"/>
    </justification>
  </clause>

  <clause id="234">
    <literal><![CDATA[
      R(1 / x,x,y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(81(a,1),20(a,2,1))].">
      <j1 rule="para" parents="81 20"/>
    </justification>
  </clause>

  <clause id="235">
    <literal><![CDATA[
      L(x,1 / x,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(82(a,1),18(a,2,2))].">
      <j1 rule="para" parents="82 18"/>
    </justification>
  </clause>

  <clause id="236">
    <literal><![CDATA[
      (x \ y) * T(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,114,a,b,10,a)].">
      <j1 rule="hyper" parents="63 114 10"/>
    </justification>
  </clause>

  <clause id="237">
    <literal><![CDATA[
      x \ (y * T(z,y)) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(62,a,114,a)].">
      <j1 rule="hyper" parents="62 114"/>
    </justification>
  </clause>

  <clause id="238">
    <literal><![CDATA[
      x * (y * T(z,y)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,114,a)].">
      <j1 rule="hyper" parents="58 114"/>
    </justification>
  </clause>

  <clause id="239">
    <literal><![CDATA[
      (x * T(y,x)) * z = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(57,a,114,a)].">
      <j1 rule="hyper" parents="57 114"/>
    </justification>
  </clause>

  <clause id="240">
    <literal><![CDATA[
      T((x * y) / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,12,a(flip),b,114,a),flip(a)].">
      <j1 rule="hyper" parents="34 12 114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="241">
    <literal><![CDATA[
      (x * T(y,x)) / x = y
    ]]></literal>
    <justification jstring="[hyper(35,a,12,a,b,114,a(flip))].">
      <j1 rule="hyper" parents="35 12 114"/>
    </justification>
  </clause>

  <clause id="242">
    <literal><![CDATA[
      x \ (y * T(x,y)) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,10,a,b,114,a(flip))].">
      <j1 rule="hyper" parents="34 10 114"/>
    </justification>
  </clause>

  <clause id="243">
    <literal><![CDATA[
      x * (y * (y \ T(z,x))) = z * x
    ]]></literal>
    <justification jstring="[para(10(a,2),114(a,1,2))].">
      <j1 rule="para" parents="10 114"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z))
    ]]></literal>
    <justification jstring="[para(114(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="114 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="245">
    <literal><![CDATA[
      (x * (y * T(z,x * y))) \ (z * (x * y)) = a(x,y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(114(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="114 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * y) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(114(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="114 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="247">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[para(114(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="114 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      ((x * y) * z) / (T(x,y) * z) = R(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[para(114(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="114 20"/>
      <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),114(a,1,2))].">
      <j1 rule="para" parents="23 114"/>
    </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),114(a,1,2))].">
      <j1 rule="para" parents="25 114"/>
    </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),114(a,1,2))].">
      <j1 rule="para" parents="27 114"/>
    </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(114(a,1),34(a,1))].">
      <j1 rule="para" parents="114 34"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      x * y != z * x
    ]]></literal>
    <literal><![CDATA[
      T(z,x) = y
    ]]></literal>
    <justification jstring="[para(114(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="114 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(114(a,2),44(a,2)),flip(a)].">
      <j1 rule="para" parents="114 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      T(x,y) * x = x * T(x,y)
    ]]></literal>
    <justification jstring="[para(189(a,1),114(a,1,2))].">
      <j1 rule="para" parents="189 114"/>
    </justification>
  </clause>

  <clause id="257">
    <literal><![CDATA[
      L(x,y,z) * x = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(188(a,1),114(a,1,2))].">
      <j1 rule="para" parents="188 114"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      T(x / (x / y),x / y) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,116,a,b,83,a)].">
      <j1 rule="hyper" parents="63 116 83"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y)
    ]]></literal>
    <justification jstring="[para(20(a,2),116(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      T(T(x / y,z),y) = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(116(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="116 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      T(L(x / y,z,u),y) = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(116(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="116 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      T(R(x / y,z,u),y) = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(116(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="116 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="263">
    <literal><![CDATA[
      T(x,y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(116(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="116 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="264">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(170(a,2),145(a,1))].">
      <j1 rule="para" parents="170 145"/>
    </justification>
  </clause>

  <clause id="265">
    <literal><![CDATA[
      1 * x != y * z
    ]]></literal>
    <literal><![CDATA[
      x / z = y
    ]]></literal>
    <justification jstring="[para(171(a,1),44(a,1))].">
      <j1 rule="para" parents="171 44"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(172(a,2),140(a,1))].">
      <j1 rule="para" parents="172 140"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(172(a,2),141(a,1))].">
      <j1 rule="para" parents="172 141"/>
    </justification>
  </clause>

  <clause id="268">
    <literal><![CDATA[
      x \ (y * (y \ x)) = 1
    ]]></literal>
    <justification jstring="[hyper(34,a,10,a,b,174,a(flip))].">
      <j1 rule="hyper" parents="34 10 174"/>
    </justification>
  </clause>

  <clause id="269">
    <literal><![CDATA[
      x * 1 != y * z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(174(a,1),43(a,1))].">
      <j1 rule="para" parents="174 43"/>
    </justification>
  </clause>

  <clause id="270">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(174(a,2),146(a,1))].">
      <j1 rule="para" parents="174 146"/>
    </justification>
  </clause>

  <clause id="271">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,18,a,b,177,a),flip(a)].">
      <j1 rule="hyper" parents="63 18 177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="272">
    <literal><![CDATA[
      K(x \ 1,x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,16,a,b,177,a)].">
      <j1 rule="hyper" parents="63 16 177"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,18,a,b,178,a),flip(a)].">
      <j1 rule="hyper" parents="63 18 178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="274">
    <literal><![CDATA[
      K(x,1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,16,a,b,178,a)].">
      <j1 rule="hyper" parents="63 16 178"/>
    </justification>
  </clause>

  <clause id="275">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,20,a,b,184,a),flip(a)].">
      <j1 rule="hyper" parents="63 20 184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="276">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,20,a,b,185,a),flip(a)].">
      <j1 rule="hyper" parents="63 20 185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="277">
    <literal><![CDATA[
      K(T(x,y),x) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,190,a)].">
      <j1 rule="hyper" parents="55 190"/>
    </justification>
  </clause>

  <clause id="278">
    <literal><![CDATA[
      K(x \ y,y / x) = 1
    ]]></literal>
    <justification jstring="[para(116(a,1),277(a,1,1))].">
      <j1 rule="para" parents="116 277"/>
    </justification>
  </clause>

  <clause id="279">
    <literal><![CDATA[
      x / T(y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),203(a,1,1))].">
      <j1 rule="para" parents="10 203"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      (x * y) / T(y,T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(114(a,1),203(a,1,1))].">
      <j1 rule="para" parents="114 203"/>
    </justification>
  </clause>

  <clause id="281">
    <literal><![CDATA[
      x / (x * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,12,a,b,229,a)].">
      <j1 rule="hyper" parents="35 12 229"/>
    </justification>
  </clause>

  <clause id="282">
    <literal><![CDATA[
      (x \ 1) \ x = x * x
    ]]></literal>
    <justification jstring="[hyper(34,a,10,a,b,229,a)].">
      <j1 rule="hyper" parents="34 10 229"/>
    </justification>
  </clause>

  <clause id="283">
    <literal><![CDATA[
      T(x \ 1,x * x) = (x * x) \ x
    ]]></literal>
    <justification jstring="[para(229(a,1),22(a,2,2))].">
      <j1 rule="para" parents="229 22"/>
    </justification>
  </clause>

  <clause id="284">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(240(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="240 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="285">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * z) / y = x
    ]]></literal>
    <justification jstring="[para(240(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="240 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="286">
    <literal><![CDATA[
      T(x \ y,y / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(56,a,278,a)].">
      <j1 rule="hyper" parents="56 278"/>
    </justification>
  </clause>

  <clause id="287">
    <literal><![CDATA[
      (1 / x) * (1 / x) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[para(83(a,1),282(a,1,1)),flip(a)].">
      <j1 rule="para" parents="83 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="288">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = y \ z
    ]]></literal>
    <justification jstring="[para(114(a,1),144(a,1)),flip(b)].">
      <j1 rule="para" parents="114 144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="290">
    <literal><![CDATA[
      x * T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(203(a,1),264(a,1,1)),flip(b)].">
      <j1 rule="para" parents="203 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="291">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),266(a,1,1))].">
      <j1 rule="para" parents="10 266"/>
    </justification>
  </clause>

  <clause id="293">
    <literal><![CDATA[
      (1 * x) / y != z
    ]]></literal>
    <literal><![CDATA[
      x / y = z
    ]]></literal>
    <justification jstring="[para(171(a,1),266(a,1,1)),flip(b)].">
      <j1 rule="para" parents="171 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(114(a,2),267(a,1,1))].">
      <j1 rule="para" parents="114 267"/>
    </justification>
  </clause>

  <clause id="295">
    <literal><![CDATA[
      (x / y) \ (z * (z \ x)) = y
    ]]></literal>
    <justification jstring="[para(12(a,1),74(a,1,2,2,2))].">
      <j1 rule="para" parents="12 74"/>
    </justification>
  </clause>

  <clause id="296">
    <literal><![CDATA[
      x \ ((x * y) * L(z,y,x)) = y * z
    ]]></literal>
    <justification jstring="[para(18(a,2),74(a,1,2,2))].">
      <j1 rule="para" parents="18 74"/>
    </justification>
  </clause>

  <clause id="297">
    <literal><![CDATA[
      x \ ((y * z) * (z \ (y \ x))) = a(y,z,z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(76(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="76 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="298">
    <literal><![CDATA[
      L(x \ (y \ z),x,y) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(76(a,1),18(a,2,2))].">
      <j1 rule="para" parents="76 18"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      ((x * (x \ y)) / z) \ y = z
    ]]></literal>
    <justification jstring="[hyper(144,a,86,a)].">
      <j1 rule="hyper" parents="144 86"/>
    </justification>
  </clause>

  <clause id="301">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z = x * y
    ]]></literal>
    <justification jstring="[para(20(a,2),87(a,1,1,1))].">
      <j1 rule="para" parents="20 87"/>
    </justification>
  </clause>

  <clause id="302">
    <literal><![CDATA[
      (((x / y) / z) * (z * y)) \ x = a((x / y) / z,z,y)
    ]]></literal>
    <justification jstring="[para(88(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="88 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="303">
    <literal><![CDATA[
      R((x / y) / z,z,y) = x / (z * y)
    ]]></literal>
    <justification jstring="[para(88(a,1),20(a,2,1))].">
      <j1 rule="para" parents="88 20"/>
    </justification>
  </clause>

  <clause id="304">
    <literal><![CDATA[
      ((x / y) * y) * (x \ z) = z
    ]]></literal>
    <justification jstring="[para(80(a,1),88(a,1,1,1,1))].">
      <j1 rule="para" parents="80 88"/>
    </justification>
  </clause>

  <clause id="305">
    <literal><![CDATA[
      ((x * y) / z) * z = ((x / u) * u) * y
    ]]></literal>
    <justification jstring="[para(87(a,1),88(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="87 88"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="306">
    <literal><![CDATA[
      ((x \ y) * x) * K(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,94,a,b,10,a)].">
      <j1 rule="hyper" parents="63 94 10"/>
    </justification>
  </clause>

  <clause id="307">
    <literal><![CDATA[
      x * K(y \ x,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(10(a,1),94(a,1,1))].">
      <j1 rule="para" parents="10 94"/>
    </justification>
  </clause>

  <clause id="308">
    <literal><![CDATA[
      (x * y) / (x * K(x,y)) = R(y,x,K(x,y))
    ]]></literal>
    <justification jstring="[para(94(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="94 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="309">
    <literal><![CDATA[
      (x * y) * z != y * x
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(94(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="94 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="310">
    <literal><![CDATA[
      L(T(x,L(x,y,z) \ u),y,z) = (L(x,y,z) \ u) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a,b,115,a)].">
      <j1 rule="hyper" parents="63 25 115"/>
    </justification>
  </clause>

  <clause id="311">
    <literal><![CDATA[
      x \ T(y,y \ z) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(62,a,115,a)].">
      <j1 rule="hyper" parents="62 115"/>
    </justification>
  </clause>

  <clause id="312">
    <literal><![CDATA[
      T(x,x \ y) \ z = ((x \ y) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(61,a,115,a)].">
      <j1 rule="hyper" parents="61 115"/>
    </justification>
  </clause>

  <clause id="313">
    <literal><![CDATA[
      T(x,x \ y) * z = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(57,a,115,a)].">
      <j1 rule="hyper" parents="57 115"/>
    </justification>
  </clause>

  <clause id="314">
    <literal><![CDATA[
      T(x,y) = (x \ (x * y)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),115(a,1,2))].">
      <j1 rule="para" parents="9 115"/>
    </justification>
  </clause>

  <clause id="315">
    <literal><![CDATA[
      T(L(x,y,z),x \ u) = L((x \ u) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(115(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="115 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="316">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),130(b,1))].">
      <j1 rule="para" parents="7 130"/>
    </justification>
  </clause>

  <clause id="318">
    <literal><![CDATA[
      x / (y \ ((x / z) * z)) = y
    ]]></literal>
    <justification jstring="[hyper(291,a,162,a)].">
      <j1 rule="hyper" parents="291 162"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      (((x / y) * y) / z) \ x = z
    ]]></literal>
    <justification jstring="[hyper(36,a,80,a(flip),b,162,a),flip(a)].">
      <j1 rule="hyper" parents="36 80 162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="320">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(173(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="173 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="321">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(173(a,2),219(a,1))].">
      <j1 rule="para" parents="173 219"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(173(a,2),220(a,1))].">
      <j1 rule="para" parents="173 220"/>
    </justification>
  </clause>

  <clause id="323">
    <literal><![CDATA[
      x * (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(173(a,1),270(a,1,2))].">
      <j1 rule="para" parents="173 270"/>
    </justification>
  </clause>

  <clause id="324">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(12(a,1),321(a,1,2))].">
      <j1 rule="para" parents="12 321"/>
    </justification>
  </clause>

  <clause id="325">
    <literal><![CDATA[
      x \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(114(a,1),321(a,1,2)),flip(b)].">
      <j1 rule="para" parents="114 321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="326">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(116(a,2),321(a,1))].">
      <j1 rule="para" parents="116 321"/>
    </justification>
  </clause>

  <clause id="327">
    <literal><![CDATA[
      x \ (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(174(a,1),321(a,1,2)),flip(b)].">
      <j1 rule="para" parents="174 321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="328">
    <literal><![CDATA[
      x \ (1 * y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(175(a,1),321(a,1,2)),flip(b)].">
      <j1 rule="para" parents="175 321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="329">
    <literal><![CDATA[
      (x * y) \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(94(a,1),321(a,1,2)),flip(b)].">
      <j1 rule="para" parents="94 321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(116(a,2),322(a,1))].">
      <j1 rule="para" parents="116 322"/>
    </justification>
  </clause>

  <clause id="332">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(196(a,1),324(a,1,1)),flip(b)].">
      <j1 rule="para" parents="196 324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="333">
    <literal><![CDATA[
      ((x / y) \ x) * (y \ z) = z
    ]]></literal>
    <justification jstring="[hyper(152,a,206,a)].">
      <j1 rule="hyper" parents="152 206"/>
    </justification>
  </clause>

  <clause id="334">
    <literal><![CDATA[
      x * (((y / x) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(38,a,9,a(flip),b,206,a),flip(a)].">
      <j1 rule="hyper" parents="38 9 206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="335">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y \ u = z
    ]]></literal>
    <justification jstring="[para(207(a,2),144(a,1))].">
      <j1 rule="para" parents="207 144"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      L(T(x,x \ y),x \ y,z) = (z * (x \ y)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(236(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="236 18"/>
    </justification>
  </clause>

  <clause id="337">
    <literal><![CDATA[
      x * T(x \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,114,a,b,272,a)].">
      <j1 rule="hyper" parents="316 114 272"/>
    </justification>
  </clause>

  <clause id="338">
    <literal><![CDATA[
      K(x \ 1,x) / x = x \ 1
    ]]></literal>
    <justification jstring="[hyper(149,a,272,a(flip))].">
      <j1 rule="hyper" parents="149 272"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      (x \ 1) \ K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,272,a(flip))].">
      <j1 rule="hyper" parents="144 272"/>
    </justification>
  </clause>

  <clause id="340">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ (K(x \ 1,x) * y) = a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(272(a,2),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="272 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="341">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * K(y \ 1,y)) = L(y,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(272(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="272 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="342">
    <literal><![CDATA[
      K(x,1 / x) / (1 / x) = x
    ]]></literal>
    <justification jstring="[hyper(149,a,274,a(flip))].">
      <j1 rule="hyper" parents="149 274"/>
    </justification>
  </clause>

  <clause id="344">
    <literal><![CDATA[
      x / R(T(y,R(y,z,u) \ x),z,u) = R(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(27(a,2),279(a,1,2))].">
      <j1 rule="para" parents="27 279"/>
    </justification>
  </clause>

  <clause id="345">
    <literal><![CDATA[
      (x / y) * (y \ x) = (y \ x) * (x / y)
    ]]></literal>
    <justification jstring="[para(286(a,1),114(a,1,2))].">
      <j1 rule="para" parents="286 114"/>
    </justification>
  </clause>

  <clause id="346">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(295(a,1),148(a,1,2)),flip(a),flip(b)].">
      <j1 rule="para" parents="295 148"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      (x * (x \ y)) / z != u
    ]]></literal>
    <literal><![CDATA[
      y / z = u
    ]]></literal>
    <justification jstring="[para(295(a,1),291(a,1,2)),flip(b)].">
      <j1 rule="para" parents="295 291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="348">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) \ z = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(20(a,2),300(a,1,1))].">
      <j1 rule="para" parents="20 300"/>
    </justification>
  </clause>

  <clause id="349">
    <literal><![CDATA[
      R(x / y,y,x \ z) = z / (y * (x \ z))
    ]]></literal>
    <justification jstring="[para(304(a,1),20(a,2,1))].">
      <j1 rule="para" parents="304 20"/>
    </justification>
  </clause>

  <clause id="350">
    <literal><![CDATA[
      ((x / y) \ x) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(333(a,1),321(a,1,2)),flip(b)].">
      <j1 rule="para" parents="333 321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="351">
    <literal><![CDATA[
      x \ (x * y) = L(y,1,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),99(a,1,1))].">
      <j1 rule="para" parents="8 99"/>
    </justification>
  </clause>

  <clause id="352">
    <literal><![CDATA[
      L(x,1,y) = x
    ]]></literal>
    <justification jstring="[hyper(322,a,351,a),flip(a)].">
      <j1 rule="hyper" parents="322 351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      L(x,1,y) = z \ (z * x)
    ]]></literal>
    <justification jstring="[hyper(316,a,9,a,b,352,a),flip(a)].">
      <j1 rule="hyper" parents="316 9 352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="354">
    <literal><![CDATA[
      x * y != x * z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(8(a,1),142(a,1))].">
      <j1 rule="para" parents="8 142"/>
    </justification>
  </clause>

  <clause id="355">
    <literal><![CDATA[
      L(x \ 1,x,1 / x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(316,a,178,a(flip),b,232,a),flip(a)].">
      <j1 rule="hyper" parents="316 178 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="356">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,165,a(flip),b,232,a),flip(a)].">
      <j1 rule="hyper" parents="316 165 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="357">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,y) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,155,a(flip),b,232,a),flip(a)].">
      <j1 rule="hyper" parents="63 155 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="358">
    <literal><![CDATA[
      L(x \ 1,x,y) \ z = ((y * x) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(61,a,232,a)].">
      <j1 rule="hyper" parents="61 232"/>
    </justification>
  </clause>

  <clause id="359">
    <literal><![CDATA[
      x * L(y \ 1,y,z) = x * ((z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,232,a)].">
      <j1 rule="hyper" parents="58 232"/>
    </justification>
  </clause>

  <clause id="360">
    <literal><![CDATA[
      L(x \ 1,x,y) * z = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(57,a,232,a)].">
      <j1 rule="hyper" parents="57 232"/>
    </justification>
  </clause>

  <clause id="361">
    <literal><![CDATA[
      x / L(y \ 1,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(210,a,232,a(flip))].">
      <j1 rule="hyper" parents="210 232"/>
    </justification>
  </clause>

  <clause id="362">
    <literal><![CDATA[
      (x * y) * L(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(152,a,232,a(flip))].">
      <j1 rule="hyper" parents="152 232"/>
    </justification>
  </clause>

  <clause id="363">
    <literal><![CDATA[
      L(x \ 1,x,y / x) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),232(a,2,1))].">
      <j1 rule="para" parents="12 232"/>
    </justification>
  </clause>

  <clause id="364">
    <literal><![CDATA[
      T((x * y) \ x,z) = L(T(y \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(232(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="232 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="365">
    <literal><![CDATA[
      R((x * y) \ x,z,u) = L(R(y \ 1,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(232(a,1),29(a,1,1))].">
      <j1 rule="para" parents="232 29"/>
    </justification>
  </clause>

  <clause id="366">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(232(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="232 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="367">
    <literal><![CDATA[
      L(T(x,x \ 1),x \ 1,y) = (y * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(115(a,2),232(a,1,1))].">
      <j1 rule="para" parents="115 232"/>
    </justification>
  </clause>

  <clause id="369">
    <literal><![CDATA[
      R(1 / x,x,y) \ y = x * y
    ]]></literal>
    <justification jstring="[hyper(204,a,234,a(flip))].">
      <j1 rule="hyper" parents="204 234"/>
    </justification>
  </clause>

  <clause id="370">
    <literal><![CDATA[
      R(1 / x,x,x \ y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(10(a,1),234(a,2,2))].">
      <j1 rule="para" parents="10 234"/>
    </justification>
  </clause>

  <clause id="371">
    <literal><![CDATA[
      R(1 / (x / y),x / y,y) = y / x
    ]]></literal>
    <justification jstring="[para(12(a,1),234(a,2,2))].">
      <j1 rule="para" parents="12 234"/>
    </justification>
  </clause>

  <clause id="374">
    <literal><![CDATA[
      ((1 / x) * x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(12(a,2),265(a,1,1))].">
      <j1 rule="para" parents="12 265"/>
    </justification>
  </clause>

  <clause id="375">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(174(a,2),269(a,1))].">
      <j1 rule="para" parents="174 269"/>
    </justification>
  </clause>

  <clause id="376">
    <literal><![CDATA[
      ((x / y) * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / z = u
    ]]></literal>
    <justification jstring="[para(171(a,2),293(a,1,1))].">
      <j1 rule="para" parents="171 293"/>
    </justification>
  </clause>

  <clause id="377">
    <literal><![CDATA[
      T(x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(10(a,1),326(a,1,1,1)),flip(b)].">
      <j1 rule="para" parents="10 326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="378">
    <literal><![CDATA[
      K(x,y) / (z \ 1) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(155(a,1),361(a,1,2))].">
      <j1 rule="para" parents="155 361"/>
    </justification>
  </clause>

  <clause id="379">
    <literal><![CDATA[
      (x * y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(361(a,1),324(a,1,1)),flip(b)].">
      <j1 rule="para" parents="361 324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="381">
    <literal><![CDATA[
      L(L(x \ 1,x,y),y * x,z) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(362(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="362 18"/>
    </justification>
  </clause>

  <clause id="382">
    <literal><![CDATA[
      R(x,x \ 1,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(80(a,1),369(a,1,1,1))].">
      <j1 rule="para" parents="80 369"/>
    </justification>
  </clause>

  <clause id="383">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ (x * y) = z
    ]]></literal>
    <justification jstring="[para(11(a,1),377(a,1,1))].">
      <j1 rule="para" parents="11 377"/>
    </justification>
  </clause>

  <clause id="384">
    <literal><![CDATA[
      T(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(80(a,1),377(a,1,1))].">
      <j1 rule="para" parents="80 377"/>
    </justification>
  </clause>

  <clause id="385">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(272(a,2),96(a,1,1))].">
      <j1 rule="para" parents="272 96"/>
    </justification>
  </clause>

  <clause id="386">
    <literal><![CDATA[
      T(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(118(a,1),325(a,1))].">
      <j1 rule="para" parents="118 325"/>
    </justification>
  </clause>

  <clause id="387">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,18,a,b,177,a(flip))].">
      <j1 rule="hyper" parents="133 18 177"/>
    </justification>
  </clause>

  <clause id="388">
    <literal><![CDATA[
      x \ (y * (z * z)) = (x \ y) * (z * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,158,a(flip),b,32,a(flip))].">
      <j1 rule="hyper" parents="133 158 32"/>
    </justification>
  </clause>

  <clause id="389">
    <literal><![CDATA[
      (x \ 1) * (y * y) = x \ (y * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,71,a(flip),b,32,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 71 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="390">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      T(z,u) = u \ x
    ]]></literal>
    <justification jstring="[para(114(a,1),133(b,1)),flip(c)].">
      <j1 rule="para" parents="114 133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="391">
    <literal><![CDATA[
      R(x,1 / y,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(136,a,20,a,b,185,a(flip))].">
      <j1 rule="hyper" parents="136 20 185"/>
    </justification>
  </clause>

  <clause id="392">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(136,a,20,a,b,184,a(flip))].">
      <j1 rule="hyper" parents="136 20 184"/>
    </justification>
  </clause>

  <clause id="393">
    <literal><![CDATA[
      (x / (y * y)) / z = x / (z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(136,a,88,a(flip),b,32,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 88 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="394">
    <literal><![CDATA[
      x * (1 / (y * y)) = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(136,a,82,a(flip),b,32,a),flip(a)].">
      <j1 rule="hyper" parents="136 82 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="395">
    <literal><![CDATA[
      (x / (y * (z * z))) * y = x / (z * z)
    ]]></literal>
    <justification jstring="[hyper(136,a,12,a(flip),b,32,a),flip(a)].">
      <j1 rule="hyper" parents="136 12 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="396">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (((y * x) \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(137,a,232,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="137 232 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="397">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,31,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="138 31 20"/>
    </justification>
  </clause>

  <clause id="398">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (L(L(x,u,w),y,z) \ v5) = v5
    ]]></literal>
    <justification jstring="[hyper(138,a,30,a,b,80,a)].">
      <j1 rule="hyper" parents="138 30 80"/>
    </justification>
  </clause>

  <clause id="399">
    <literal><![CDATA[
      ((x \ y) \ y) * T(z,T(x,x \ y)) = z * T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(138,a,115,a(flip),b,203,a)].">
      <j1 rule="hyper" parents="138 115 203"/>
    </justification>
  </clause>

  <clause id="400">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,29,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="138 29 20"/>
    </justification>
  </clause>

  <clause id="401">
    <literal><![CDATA[
      T(R(x,y,z),u) * (y * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,27,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="138 27 20"/>
    </justification>
  </clause>

  <clause id="402">
    <literal><![CDATA[
      (x / y) * ((z / y) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,83,a,b,83,a)].">
      <j1 rule="hyper" parents="139 83 83"/>
    </justification>
  </clause>

  <clause id="403">
    <literal><![CDATA[
      (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,30,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="139 30 18"/>
    </justification>
  </clause>

  <clause id="404">
    <literal><![CDATA[
      (x * y) * R(L(z,y,x),u,w) = x * (y * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,29,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="139 29 18"/>
    </justification>
  </clause>

  <clause id="405">
    <literal><![CDATA[
      x * L(y,z \ x,z) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,18,a,b,165,a(flip))].">
      <j1 rule="hyper" parents="139 18 165"/>
    </justification>
  </clause>

  <clause id="406">
    <literal><![CDATA[
      (K(x,y) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,155,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="139 155 18"/>
    </justification>
  </clause>

  <clause id="407">
    <literal><![CDATA[
      T(x,T(x,y) \ z) * y = y * ((T(x,y) \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,115,a(flip),b,118,a),flip(a)].">
      <j1 rule="hyper" parents="139 115 118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="408">
    <literal><![CDATA[
      (x * y) * T(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,25,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="139 25 18"/>
    </justification>
  </clause>

  <clause id="409">
    <literal><![CDATA[
      (x * (y / (z * y))) / R(1 / z,z,y) = x
    ]]></literal>
    <justification jstring="[hyper(209,a,234,a,b,9,a)].">
      <j1 rule="hyper" parents="209 234 9"/>
    </justification>
  </clause>

  <clause id="410">
    <literal><![CDATA[
      (K(x,y) * (z * u)) / u = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(209,a,155,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="209 155 18"/>
    </justification>
  </clause>

  <clause id="411">
    <literal><![CDATA[
      (x * y) * ((1 / y) * (1 / y)) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(233(a,1),32(a,2,2))].">
      <j1 rule="para" parents="233 32"/>
    </justification>
  </clause>

  <clause id="412">
    <literal><![CDATA[
      x * (y * L(T(z,y),u,w)) = x * (L(z,u,w) * y)
    ]]></literal>
    <justification jstring="[para(25(a,2),238(a,1,2,2))].">
      <j1 rule="para" parents="25 238"/>
    </justification>
  </clause>

  <clause id="413">
    <literal><![CDATA[
      L(x \ T(y,z),x,z) = (z * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(243(a,1),18(a,2,2))].">
      <j1 rule="para" parents="243 18"/>
    </justification>
  </clause>

  <clause id="414">
    <literal><![CDATA[
      x * T(x \ (y * x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(22(a,1),250(a,1,2,1))].">
      <j1 rule="para" parents="22 250"/>
    </justification>
  </clause>

  <clause id="415">
    <literal><![CDATA[
      T(x / y,z) * y = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(116(a,1),250(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="116 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(115(a,1),250(a,1,2,1))].">
      <j1 rule="para" parents="115 250"/>
    </justification>
  </clause>

  <clause id="417">
    <literal><![CDATA[
      (L(x,y,z) * (x * u)) \ ((x * L(x,y,z)) * u) = a(L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(257(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="257 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (L(x,y,z) * (x * u)) = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(257(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="257 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      ((x * L(y,z,u)) * y) / (y * L(y,z,u)) = R(x,L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(257(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="257 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="420">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x = T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(285,a,260,a)].">
      <j1 rule="hyper" parents="285 260"/>
    </justification>
  </clause>

  <clause id="422">
    <literal><![CDATA[
      (x * T(y,z)) / x = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(285,a,284,a)].">
      <j1 rule="hyper" parents="285 284"/>
    </justification>
  </clause>

  <clause id="423">
    <literal><![CDATA[
      K(x \ 1,x) * K(x,x \ 1) = 1
    ]]></literal>
    <justification jstring="[para(272(a,2),306(a,1,1))].">
      <j1 rule="para" parents="272 306"/>
    </justification>
  </clause>

  <clause id="424">
    <literal><![CDATA[
      K(x,y) * (1 / z) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(209,a,83,a(flip),b,357,a),flip(a)].">
      <j1 rule="hyper" parents="209 83 357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="425">
    <literal><![CDATA[
      (K(x,y) \ z) \ 1 = z \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,165,a(flip),b,357,a),flip(a)].">
      <j1 rule="hyper" parents="63 165 357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="426">
    <literal><![CDATA[
      (K(x,y) \ 1) * K(x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(139,a,177,a(flip),b,357,a(flip))].">
      <j1 rule="hyper" parents="139 177 357"/>
    </justification>
  </clause>

  <clause id="427">
    <literal><![CDATA[
      (x * x) \ (y \ (x * x)) = T(y \ 1,x * x)
    ]]></literal>
    <justification jstring="[hyper(288,a,389,a),flip(a)].">
      <j1 rule="hyper" parents="288 389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="428">
    <literal><![CDATA[
      (x \ (y * y)) / (y * y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(149,a,389,a)].">
      <j1 rule="hyper" parents="149 389"/>
    </justification>
  </clause>

  <clause id="429">
    <literal><![CDATA[
      ((x * x) / y) \ 1 = y / (x * x)
    ]]></literal>
    <justification jstring="[hyper(136,a,83,a(flip),b,389,a),flip(a)].">
      <j1 rule="hyper" parents="136 83 389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="430">
    <literal><![CDATA[
      1 / (x * x) = (x * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(136,a,67,a(flip),b,389,a)].">
      <j1 rule="hyper" parents="136 67 389"/>
    </justification>
  </clause>

  <clause id="431">
    <literal><![CDATA[
      1 / (x * x) = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,281,a(flip),b,394,a),flip(a)].">
      <j1 rule="hyper" parents="133 281 394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="432">
    <literal><![CDATA[
      x * ((y * y) \ 1) = x / (y * y)
    ]]></literal>
    <justification jstring="[para(430(a,1),394(a,1,2))].">
      <j1 rule="para" parents="430 394"/>
    </justification>
  </clause>

  <clause id="433">
    <literal><![CDATA[
      (x * x) \ 1 = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,430,a(flip),b,431,a)].">
      <j1 rule="hyper" parents="63 430 431"/>
    </justification>
  </clause>

  <clause id="434">
    <literal><![CDATA[
      x * (y \ (y \ 1)) = x / (y * y)
    ]]></literal>
    <justification jstring="[para(431(a,1),394(a,1,2))].">
      <j1 rule="para" parents="431 394"/>
    </justification>
  </clause>

  <clause id="435">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,426,a,b,423,a)].">
      <j1 rule="hyper" parents="35 426 423"/>
    </justification>
  </clause>

  <clause id="436">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,338,a(flip),b,424,a),flip(a)].">
      <j1 rule="hyper" parents="316 338 424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="437">
    <literal><![CDATA[
      K(x,y) \ (K(x,y) / z) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(144,a,424,a)].">
      <j1 rule="hyper" parents="144 424"/>
    </justification>
  </clause>

  <clause id="438">
    <literal><![CDATA[
      x / (1 / (1 / x)) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(136,a,342,a(flip),b,424,a)].">
      <j1 rule="hyper" parents="136 342 424"/>
    </justification>
  </clause>

  <clause id="440">
    <literal><![CDATA[
      K(x,1 / x) \ x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,342,a(flip),b,424,a)].">
      <j1 rule="hyper" parents="133 342 424"/>
    </justification>
  </clause>

  <clause id="441">
    <literal><![CDATA[
      1 / (x / (y * y)) = (y * y) / x
    ]]></literal>
    <justification jstring="[hyper(210,a,429,a)].">
      <j1 rule="hyper" parents="210 429"/>
    </justification>
  </clause>

  <clause id="443">
    <literal><![CDATA[
      x \ (x / (y * y)) = y \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,434,a)].">
      <j1 rule="hyper" parents="144 434"/>
    </justification>
  </clause>

  <clause id="444">
    <literal><![CDATA[
      x / (y \ (y \ 1)) = x * (y * y)
    ]]></literal>
    <justification jstring="[hyper(136,a,11,a(flip),b,434,a)].">
      <j1 rule="hyper" parents="136 11 434"/>
    </justification>
  </clause>

  <clause id="445">
    <literal><![CDATA[
      (x * (y * y)) \ x = y \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,11,a(flip),b,434,a)].">
      <j1 rule="hyper" parents="133 11 434"/>
    </justification>
  </clause>

  <clause id="446">
    <literal><![CDATA[
      x / ((1 / y) * (1 / y)) = x * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[para(83(a,1),434(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="447">
    <literal><![CDATA[
      T(x * (y * y),y \ (y \ 1)) = (y \ (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(444(a,1),116(a,1,1))].">
      <j1 rule="para" parents="444 116"/>
    </justification>
  </clause>

  <clause id="448">
    <literal><![CDATA[
      (x * (y * z)) / L(T(y,z),z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(136,a,238,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="136 238 100"/>
    </justification>
  </clause>

  <clause id="449">
    <literal><![CDATA[
      (x * y) / L(z \ y,z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(136,a,160,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="136 160 100"/>
    </justification>
  </clause>

  <clause id="450">
    <literal><![CDATA[
      (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,239,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="63 239 100"/>
    </justification>
  </clause>

  <clause id="451">
    <literal><![CDATA[
      x * L(y,z,x / z) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,157,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="63 157 100"/>
    </justification>
  </clause>

  <clause id="452">
    <literal><![CDATA[
      L(x * x,y,z) = x * x
    ]]></literal>
    <justification jstring="[hyper(34,a,32,a,b,100,a),flip(a)].">
      <j1 rule="hyper" parents="34 32 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="453">
    <literal><![CDATA[
      L(x \ T(y * x,y),x,y) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,243,a(flip),b,100,a),flip(a)].">
      <j1 rule="hyper" parents="34 243 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="454">
    <literal><![CDATA[
      L(x \ (y \ ((y * x) * z)),x,y) = z
    ]]></literal>
    <justification jstring="[hyper(34,a,76,a(flip),b,100,a),flip(a)].">
      <j1 rule="hyper" parents="34 76 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="455">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(138,a,100,a(flip),b,201,a)].">
      <j1 rule="hyper" parents="138 100 201"/>
    </justification>
  </clause>

  <clause id="456">
    <literal><![CDATA[
      x \ (y * L(z,x \ y,x)) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,158,a(flip),b,100,a(flip))].">
      <j1 rule="hyper" parents="133 158 100"/>
    </justification>
  </clause>

  <clause id="457">
    <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(100(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="100 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="458">
    <literal><![CDATA[
      (x * (y * L(z,y,x))) \ (x * (y * z)) = a(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(100(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="100 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="459">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * (L(z,y,x) * u)) = L(u,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(100(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="100 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="460">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(100(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="100 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      (x * (y * z)) / (y * L(z,y,x)) = R(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(100(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="100 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      (x * y) * z != x * (y * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(100(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="100 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="464">
    <literal><![CDATA[
      K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(272(a,2),100(a,1,1))].">
      <j1 rule="para" parents="272 100"/>
    </justification>
  </clause>

  <clause id="465">
    <literal><![CDATA[
      L((1 / x) * (1 / x),y,z) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(316,a,287,a(flip),b,452,a),flip(a)].">
      <j1 rule="hyper" parents="316 287 452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="466">
    <literal><![CDATA[
      a(x,y,z * z) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,452,a)].">
      <j1 rule="hyper" parents="53 452"/>
    </justification>
  </clause>

  <clause id="467">
    <literal><![CDATA[
      L(T(x * x,y),z,u) = T(x * x,y)
    ]]></literal>
    <justification jstring="[para(452(a,1),25(a,2,1))].">
      <j1 rule="para" parents="452 25"/>
    </justification>
  </clause>

  <clause id="469">
    <literal><![CDATA[
      a(x,y,1) = 1
    ]]></literal>
    <justification jstring="[para(7(a,1),466(a,1,3))].">
      <j1 rule="para" parents="7 466"/>
    </justification>
  </clause>

  <clause id="470">
    <literal><![CDATA[
      L(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(52,a,469,a)].">
      <j1 rule="hyper" parents="52 469"/>
    </justification>
  </clause>

  <clause id="471">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,453,a(flip),b,155,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 453 155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="472">
    <literal><![CDATA[
      L(x \ (y * x),x,y) = T(y,y * x)
    ]]></literal>
    <justification jstring="[hyper(316,a,22,a,b,102,a),flip(a)].">
      <j1 rule="hyper" parents="316 22 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="473">
    <literal><![CDATA[
      L(x \ y,x,1 / x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(316,a,178,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="316 178 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(316,a,177,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="316 177 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="475">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,165,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="316 165 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="476">
    <literal><![CDATA[
      x \ L(y \ z,y,u) = x \ ((u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(133,a,102,a,b,10,a)].">
      <j1 rule="hyper" parents="133 102 10"/>
    </justification>
  </clause>

  <clause id="477">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * u) = z \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,155,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="63 155 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="478">
    <literal><![CDATA[
      (K(x,y) * z) / (u \ z) = K(x,y) * u
    ]]></literal>
    <justification jstring="[hyper(209,a,155,a(flip),b,102,a(flip))].">
      <j1 rule="hyper" parents="209 155 102"/>
    </justification>
  </clause>

  <clause id="479">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) = K(x,y) * u
    ]]></literal>
    <justification jstring="[hyper(139,a,155,a(flip),b,102,a(flip))].">
      <j1 rule="hyper" parents="139 155 102"/>
    </justification>
  </clause>

  <clause id="480">
    <literal><![CDATA[
      L(x \ y,x,z / x) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),102(a,2,1))].">
      <j1 rule="para" parents="12 102"/>
    </justification>
  </clause>

  <clause id="481">
    <literal><![CDATA[
      L(x \ y,x,z / y) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[para(12(a,1),102(a,2,2))].">
      <j1 rule="para" parents="12 102"/>
    </justification>
  </clause>

  <clause id="482">
    <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),102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="483">
    <literal><![CDATA[
      T((x * y) \ (x * z),u) = L(T(y \ z,u),y,x)
    ]]></literal>
    <justification jstring="[para(102(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="102 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="484">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,w) = L((w * x) \ (w * y),z,u)
    ]]></literal>
    <justification jstring="[para(102(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="102 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="485">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(114(a,1),102(a,2,1))].">
      <j1 rule="para" parents="114 102"/>
    </justification>
  </clause>

  <clause id="486">
    <literal><![CDATA[
      L((x * x) \ y,x * x,x \ 1) = x \ ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(229(a,1),102(a,2,1))].">
      <j1 rule="para" parents="229 102"/>
    </justification>
  </clause>

  <clause id="487">
    <literal><![CDATA[
      x / L(y \ z,y,x / z) = (x / z) * y
    ]]></literal>
    <justification jstring="[para(102(a,2),318(a,1,2))].">
      <j1 rule="para" parents="102 318"/>
    </justification>
  </clause>

  <clause id="488">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * u)
    ]]></literal>
    <justification jstring="[para(100(a,1),102(a,2,1))].">
      <j1 rule="para" parents="100 102"/>
    </justification>
  </clause>

  <clause id="489">
    <literal><![CDATA[
      L(x \ L(y,z,u),x,u * z) = ((u * z) * x) \ (u * (z * y))
    ]]></literal>
    <justification jstring="[para(100(a,1),102(a,2,2))].">
      <j1 rule="para" parents="100 102"/>
    </justification>
  </clause>

  <clause id="490">
    <literal><![CDATA[
      R(x / y,y,x \ z) \ z = y * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(133,a,304,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="133 304 109"/>
    </justification>
  </clause>

  <clause id="491">
    <literal><![CDATA[
      R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,239,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="133 239 109"/>
    </justification>
  </clause>

  <clause id="492">
    <literal><![CDATA[
      R(x,x \ y,z) \ (y * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,158,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="133 158 109"/>
    </justification>
  </clause>

  <clause id="493">
    <literal><![CDATA[
      R(x / y,y,z) \ (x * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(133,a,157,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="133 157 109"/>
    </justification>
  </clause>

  <clause id="494">
    <literal><![CDATA[
      R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,238,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="63 238 109"/>
    </justification>
  </clause>

  <clause id="495">
    <literal><![CDATA[
      R(x,y,y \ z) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,160,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="63 160 109"/>
    </justification>
  </clause>

  <clause id="496">
    <literal><![CDATA[
      R(((x * (y * z)) / z) / y,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,88,a(flip),b,109,a),flip(a)].">
      <j1 rule="hyper" parents="35 88 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="497">
    <literal><![CDATA[
      R(x,y,z * z) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,32,a(flip),b,109,a),flip(a)].">
      <j1 rule="hyper" parents="35 32 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="498">
    <literal><![CDATA[
      ((x * y) * z) / L(z,y,R(x,y,z)) = R(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(136,a,109,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="136 109 100"/>
    </justification>
  </clause>

  <clause id="499">
    <literal><![CDATA[
      ((x * y) * z) \ ((R(x,y,z) * y) * z) = a(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(109(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="109 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="500">
    <literal><![CDATA[
      (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u)
    ]]></literal>
    <justification jstring="[para(109(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="109 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="501">
    <literal><![CDATA[
      (x * y) * z != u * (y * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(109(a,1),44(a,1))].">
      <j1 rule="para" parents="109 44"/>
    </justification>
  </clause>

  <clause id="503">
    <literal><![CDATA[
      R(x,y,z * z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(497(a,1),51(a,2))].">
      <j1 rule="para" parents="497 51"/>
    </justification>
  </clause>

  <clause id="504">
    <literal><![CDATA[
      R(x,y,z \ (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(287(a,1),497(a,1,3))].">
      <j1 rule="para" parents="287 497"/>
    </justification>
  </clause>

  <clause id="505">
    <literal><![CDATA[
      (x * y) * (z \ (1 / z)) = x * (y * (z \ (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(138,a,504,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="138 504 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="506">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(316,a,185,a(flip),b,110,a),flip(a)].">
      <j1 rule="hyper" parents="316 185 110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="507">
    <literal><![CDATA[
      R(x / y,y,y \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,184,a(flip),b,110,a),flip(a)].">
      <j1 rule="hyper" parents="316 184 110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="508">
    <literal><![CDATA[
      R(x / y,y,y \ z) = (x * (y \ z)) / z
    ]]></literal>
    <justification jstring="[para(10(a,1),110(a,2,2))].">
      <j1 rule="para" parents="10 110"/>
    </justification>
  </clause>

  <clause id="509">
    <literal><![CDATA[
      R(x / (y / z),y / z,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),110(a,2,2))].">
      <j1 rule="para" parents="12 110"/>
    </justification>
  </clause>

  <clause id="510">
    <literal><![CDATA[
      T((x * y) / (z * y),u) = R(T(x / z,u),z,y)
    ]]></literal>
    <justification jstring="[para(110(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="110 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="511">
    <literal><![CDATA[
      R(x / y,y,T(z,y)) = (x * T(z,y)) / (z * y)
    ]]></literal>
    <justification jstring="[para(114(a,1),110(a,2,2))].">
      <j1 rule="para" parents="114 110"/>
    </justification>
  </clause>

  <clause id="512">
    <literal><![CDATA[
      T(R(x / y,y,z),y * z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[para(110(a,2),116(a,1,1))].">
      <j1 rule="para" parents="110 116"/>
    </justification>
  </clause>

  <clause id="513">
    <literal><![CDATA[
      R((x * y) / z,z,K(y,x)) = (y * x) / (z * K(y,x))
    ]]></literal>
    <justification jstring="[para(94(a,1),110(a,2,1))].">
      <j1 rule="para" parents="94 110"/>
    </justification>
  </clause>

  <clause id="514">
    <literal><![CDATA[
      R(x / y,y,x) \ 1 = (y * x) / (x * x)
    ]]></literal>
    <justification jstring="[para(110(a,2),429(a,1,1))].">
      <j1 rule="para" parents="110 429"/>
    </justification>
  </clause>

  <clause id="515">
    <literal><![CDATA[
      R((x * y) / z,z,L(u,y,x)) = (x * (y * u)) / (z * L(u,y,x))
    ]]></literal>
    <justification jstring="[para(100(a,1),110(a,2,1))].">
      <j1 rule="para" parents="100 110"/>
    </justification>
  </clause>

  <clause id="516">
    <literal><![CDATA[
      R(R(x,y,z) / u,u,y * z) = ((x * y) * z) / (u * (y * z))
    ]]></literal>
    <justification jstring="[para(109(a,1),110(a,2,1))].">
      <j1 rule="para" parents="109 110"/>
    </justification>
  </clause>

  <clause id="517">
    <literal><![CDATA[
      x \ y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (x \ y) = u
    ]]></literal>
    <justification jstring="[para(76(a,1),143(a,1,2)),flip(b)].">
      <j1 rule="para" parents="76 143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="518">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(12(a,1),147(a,1,2,2))].">
      <j1 rule="para" parents="12 147"/>
    </justification>
  </clause>

  <clause id="519">
    <literal><![CDATA[
      R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(94(a,1),199(a,1,2,1))].">
      <j1 rule="para" parents="94 199"/>
    </justification>
  </clause>

  <clause id="521">
    <literal><![CDATA[
      (x * y) / L(z,y / z,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),202(a,1,1,2))].">
      <j1 rule="para" parents="12 202"/>
    </justification>
  </clause>

  <clause id="522">
    <literal><![CDATA[
      (x * y) / L(T(z,z \ y),z \ y,x) = x * (z \ y)
    ]]></literal>
    <justification jstring="[para(236(a,1),202(a,1,1,2))].">
      <j1 rule="para" parents="236 202"/>
    </justification>
  </clause>

  <clause id="523">
    <literal><![CDATA[
      K(x,1 / x) \ x = L(x,1 / x,x)
    ]]></literal>
    <justification jstring="[para(274(a,2),235(a,2,1)),flip(a)].">
      <j1 rule="para" parents="274 235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="524">
    <literal><![CDATA[
      x \ L(L(y,x \ 1,x),z,u) = (x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,30,a,b,271,a)].">
      <j1 rule="hyper" parents="133 30 271"/>
    </justification>
  </clause>

  <clause id="525">
    <literal><![CDATA[
      x \ R(L(y,x \ 1,x),z,u) = (x \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,29,a,b,271,a)].">
      <j1 rule="hyper" parents="133 29 271"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      (K(x,y) \ 1) * z = K(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(133,a,155,a(flip),b,271,a),flip(a)].">
      <j1 rule="hyper" parents="133 155 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="527">
    <literal><![CDATA[
      L(T(x,y \ 1),y \ 1,y) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,238,a(flip),b,271,a),flip(a)].">
      <j1 rule="hyper" parents="63 238 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="528">
    <literal><![CDATA[
      x * K(x \ 1,x) = L(x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(272(a,2),271(a,1,2))].">
      <j1 rule="para" parents="272 271"/>
    </justification>
  </clause>

  <clause id="530">
    <literal><![CDATA[
      K(x \ 1,x) \ y = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(385(a,1),526(a,1,1)),flip(a)].">
      <j1 rule="para" parents="385 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="531">
    <literal><![CDATA[
      K(x,x \ 1) \ y = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(435(a,1),526(a,1,1)),flip(a)].">
      <j1 rule="para" parents="435 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="532">
    <literal><![CDATA[
      (1 / x) \ L(L(y,x,1 / x),z,u) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,30,a,b,273,a)].">
      <j1 rule="hyper" parents="133 30 273"/>
    </justification>
  </clause>

  <clause id="533">
    <literal><![CDATA[
      L(T(x,y),y,1 / y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,238,a(flip),b,273,a),flip(a)].">
      <j1 rule="hyper" parents="63 238 273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="534">
    <literal><![CDATA[
      R(R(x,1 / y,y),z,u) / y = R(x,z,u) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(136,a,31,a,b,276,a)].">
      <j1 rule="hyper" parents="136 31 276"/>
    </justification>
  </clause>

  <clause id="535">
    <literal><![CDATA[
      L(R(x,1 / y,y),z,u) / y = L(x,z,u) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(136,a,29,a(flip),b,276,a)].">
      <j1 rule="hyper" parents="136 29 276"/>
    </justification>
  </clause>

  <clause id="536">
    <literal><![CDATA[
      L(L(x \ (y \ z),u,w),x,y) = L((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(298(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="298 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="537">
    <literal><![CDATA[
      L(x \ L(y \ z,y,u),x,u * y) = ((u * y) * x) \ (u * z)
    ]]></literal>
    <justification jstring="[para(102(a,2),298(a,1,1,2))].">
      <j1 rule="para" parents="102 298"/>
    </justification>
  </clause>

  <clause id="538">
    <literal><![CDATA[
      x * (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(67(a,1),323(a,1,2,2))].">
      <j1 rule="para" parents="67 323"/>
    </justification>
  </clause>

  <clause id="539">
    <literal><![CDATA[
      x * (y \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(173(a,2),323(a,1,2))].">
      <j1 rule="para" parents="173 323"/>
    </justification>
  </clause>

  <clause id="540">
    <literal><![CDATA[
      x * (y / (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(196(a,2),323(a,1,2))].">
      <j1 rule="para" parents="196 323"/>
    </justification>
  </clause>

  <clause id="541">
    <literal><![CDATA[
      T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y)
    ]]></literal>
    <justification jstring="[para(363(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="363 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="542">
    <literal><![CDATA[
      L(x \ 1,x,y / x) * y = (y / x) * K(y \ (y / x),y)
    ]]></literal>
    <justification jstring="[para(363(a,2),307(a,2,1)),flip(a)].">
      <j1 rule="para" parents="363 307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="543">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(173(a,1),375(a,1,2))].">
      <j1 rule="para" parents="173 375"/>
    </justification>
  </clause>

  <clause id="544">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(22(a,2),472(a,1,1))].">
      <j1 rule="para" parents="22 472"/>
    </justification>
  </clause>

  <clause id="545">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a(flip),b,544,a)].">
      <j1 rule="hyper" parents="63 25 544"/>
    </justification>
  </clause>

  <clause id="546">
    <literal><![CDATA[
      (x * T(y,y * x)) / x = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(285,a,545,a)].">
      <j1 rule="hyper" parents="285 545"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      T((x * y) / x,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,284,a,b,545,a)].">
      <j1 rule="hyper" parents="40 284 545"/>
    </justification>
  </clause>

  <clause id="548">
    <literal><![CDATA[
      x * T(y,y * x) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,545,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 545 22"/>
    </justification>
  </clause>

  <clause id="549">
    <literal><![CDATA[
      L(T(x \ y,z),x,1 / x) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(473(a,1),25(a,2,1))].">
      <j1 rule="para" parents="473 25"/>
    </justification>
  </clause>

  <clause id="550">
    <literal><![CDATA[
      L(R(x \ y,z,u),x,1 / x) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(473(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="473 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="551">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,1 / x) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(473(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="473 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="552">
    <literal><![CDATA[
      L(T((x \ 1) \ y,z),x \ 1,x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(474(a,1),25(a,2,1))].">
      <j1 rule="para" parents="474 25"/>
    </justification>
  </clause>

  <clause id="553">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(507(a,1),27(a,2,1))].">
      <j1 rule="para" parents="507 27"/>
    </justification>
  </clause>

  <clause id="554">
    <literal><![CDATA[
      R(R(x / y,z,u),y,y \ 1) = R(x * (y \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(507(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="507 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="555">
    <literal><![CDATA[
      T(x / y,x * (y \ 1)) = x / y
    ]]></literal>
    <justification jstring="[para(507(a,1),187(a,1,2))].">
      <j1 rule="para" parents="507 187"/>
    </justification>
  </clause>

  <clause id="556">
    <literal><![CDATA[
      T(x * (y \ 1),x / y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(54,a,555,a)].">
      <j1 rule="hyper" parents="54 555"/>
    </justification>
  </clause>

  <clause id="557">
    <literal><![CDATA[
      L(x,1 / x,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,440,a(flip),b,523,a),flip(a)].">
      <j1 rule="hyper" parents="63 440 523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="558">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(334(a,1),539(a,1))].">
      <j1 rule="para" parents="334 539"/>
    </justification>
  </clause>

  <clause id="559">
    <literal><![CDATA[
      ((x * y) / x) * (y * x) = (y * x) * L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,547,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 547 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="560">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(109(a,1),120(a,1,2))].">
      <j1 rule="para" parents="109 120"/>
    </justification>
  </clause>

  <clause id="561">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * y) = y * y
    ]]></literal>
    <justification jstring="[para(229(a,1),123(a,1,2,2))].">
      <j1 rule="para" parents="229 123"/>
    </justification>
  </clause>

  <clause id="562">
    <literal><![CDATA[
      (x * y) / (y * y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(210,a,561,a)].">
      <j1 rule="hyper" parents="210 561"/>
    </justification>
  </clause>

  <clause id="563">
    <literal><![CDATA[
      R(x / y,y,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(39,a,493,a,b,561,a)].">
      <j1 rule="hyper" parents="39 493 561"/>
    </justification>
  </clause>

  <clause id="564">
    <literal><![CDATA[
      x / ((y \ x) * (y \ x)) = y * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(39,a,295,a,b,561,a)].">
      <j1 rule="hyper" parents="39 295 561"/>
    </justification>
  </clause>

  <clause id="565">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,199,a,b,561,a),flip(a)].">
      <j1 rule="hyper" parents="39 199 561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="566">
    <literal><![CDATA[
      (x / y) * (y \ 1) = x / (y * y)
    ]]></literal>
    <justification jstring="[para(561(a,1),318(a,1,2)),flip(a)].">
      <j1 rule="para" parents="561 318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="567">
    <literal><![CDATA[
      (x * (y * y)) / y = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(136,a,496,a(flip),b,563,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 496 563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="568">
    <literal><![CDATA[
      R(x,x \ y,x \ y) = y * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(80(a,1),563(a,1,1))].">
      <j1 rule="para" parents="80 563"/>
    </justification>
  </clause>

  <clause id="569">
    <literal><![CDATA[
      R(x,y,y) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(149,a,565,a)].">
      <j1 rule="hyper" parents="149 565"/>
    </justification>
  </clause>

  <clause id="570">
    <literal><![CDATA[
      (x * y) \ R(x,y,y) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(144,a,565,a)].">
      <j1 rule="hyper" parents="144 565"/>
    </justification>
  </clause>

  <clause id="571">
    <literal><![CDATA[
      L(R(x,y,y),z,u) / (y \ 1) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(136,a,29,a(flip),b,565,a)].">
      <j1 rule="hyper" parents="136 29 565"/>
    </justification>
  </clause>

  <clause id="572">
    <literal><![CDATA[
      (x \ 1) * T(y * x,x \ 1) = R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,114,a,b,565,a)].">
      <j1 rule="hyper" parents="63 114 565"/>
    </justification>
  </clause>

  <clause id="573">
    <literal><![CDATA[
      R(x,y,y \ 1) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,275,a(flip),b,565,a)].">
      <j1 rule="hyper" parents="63 275 565"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,z * x) = R(z,x,x) \ ((z * x) * y)
    ]]></literal>
    <justification jstring="[para(565(a,1),102(a,2,1))].">
      <j1 rule="para" parents="565 102"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      (x / (y \ 1)) * y = x * (y * y)
    ]]></literal>
    <justification jstring="[hyper(138,a,12,a(flip),b,562,a),flip(a)].">
      <j1 rule="hyper" parents="138 12 562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      T(x * (y \ 1),y * y) = (y * y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(562(a,1),116(a,1,1))].">
      <j1 rule="para" parents="562 116"/>
    </justification>
  </clause>

  <clause id="578">
    <literal><![CDATA[
      (1 / x) * (x \ 1) = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,431,a(flip),b,566,a),flip(a)].">
      <j1 rule="hyper" parents="316 431 566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="579">
    <literal><![CDATA[
      (x \ 1) \ (y / (x * x)) = T(y / x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(288,a,566,a),flip(a)].">
      <j1 rule="hyper" parents="288 566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="580">
    <literal><![CDATA[
      T(x / (y \ 1),y) = y \ (x * (y * y))
    ]]></literal>
    <justification jstring="[para(567(a,1),116(a,1,1))].">
      <j1 rule="para" parents="567 116"/>
    </justification>
  </clause>

  <clause id="581">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,1 / x) = (x \ (x \ 1)) \ ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(578(a,1),102(a,2,1))].">
      <j1 rule="para" parents="578 102"/>
    </justification>
  </clause>

  <clause id="582">
    <literal><![CDATA[
      ((x * x) \ y) * (x * x) = T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(254,a,124,a),flip(a)].">
      <j1 rule="hyper" parents="254 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="584">
    <literal><![CDATA[
      (x \ (y \ 1)) * (y * y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(133,a,229,a(flip),b,124,a),flip(a)].">
      <j1 rule="hyper" parents="133 229 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="585">
    <literal><![CDATA[
      x \ (y * (z * (u * u))) = (x \ (y * z)) * (u * u)
    ]]></literal>
    <justification jstring="[hyper(133,a,32,a(flip),b,124,a)].">
      <j1 rule="hyper" parents="133 32 124"/>
    </justification>
  </clause>

  <clause id="586">
    <literal><![CDATA[
      (x \ (y / (z * z))) * (z * z) = x \ y
    ]]></literal>
    <justification jstring="[hyper(133,a,12,a(flip),b,124,a),flip(a)].">
      <j1 rule="hyper" parents="133 12 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="587">
    <literal><![CDATA[
      ((x * y) \ x) * (y * y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,100,a,b,124,a),flip(a)].">
      <j1 rule="hyper" parents="34 100 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="588">
    <literal><![CDATA[
      (x \ y) / (y * y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(149,a,584,a)].">
      <j1 rule="hyper" parents="149 584"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      x / (y * (x * x)) = (x \ 1) / y
    ]]></literal>
    <justification jstring="[hyper(209,a,207,a(flip),b,584,a(flip))].">
      <j1 rule="hyper" parents="209 207 584"/>
    </justification>
  </clause>

  <clause id="590">
    <literal><![CDATA[
      (x \ (y \ 1)) / (y \ 1) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(136,a,584,a(flip),b,576,a),flip(a)].">
      <j1 rule="hyper" parents="136 584 576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="591">
    <literal><![CDATA[
      (x \ (y \ (z \ 1))) * (z * z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(133,a,584,a(flip),b,124,a),flip(a)].">
      <j1 rule="hyper" parents="133 584 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="592">
    <literal><![CDATA[
      x / (y * (z * (x * x))) = (x \ 1) / (y * z)
    ]]></literal>
    <justification jstring="[para(32(a,1),589(a,1,2))].">
      <j1 rule="para" parents="32 589"/>
    </justification>
  </clause>

  <clause id="593">
    <literal><![CDATA[
      (x \ 1) / R(y,x,x) = x / ((y * x) * x)
    ]]></literal>
    <justification jstring="[para(109(a,1),589(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="594">
    <literal><![CDATA[
      (x \ y) * ((y \ x) * (y \ x)) = L(y \ x,y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),587(a,1,1,1))].">
      <j1 rule="para" parents="10 587"/>
    </justification>
  </clause>

  <clause id="595">
    <literal><![CDATA[
      (x / (y / (z * z))) * y = x * (z * z)
    ]]></literal>
    <justification jstring="[para(12(a,1),125(a,1,2))].">
      <j1 rule="para" parents="12 125"/>
    </justification>
  </clause>

  <clause id="597">
    <literal><![CDATA[
      L(x,y,z) * (u / (w \ u)) = w * L(T(x,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,197,a,b,251,a)].">
      <j1 rule="hyper" parents="316 197 251"/>
    </justification>
  </clause>

  <clause id="598">
    <literal><![CDATA[
      x * (y * T(z,x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,100,a(flip),b,251,a)].">
      <j1 rule="hyper" parents="63 100 251"/>
    </justification>
  </clause>

  <clause id="599">
    <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="600">
    <literal><![CDATA[
      x * L(L(T(y,x),z,u),w,v5) = L(L(y,z,u),w,v5) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),251(a,1,2,1))].">
      <j1 rule="para" parents="25 251"/>
    </justification>
  </clause>

  <clause id="601">
    <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="602">
    <literal><![CDATA[
      L(x / y,z,u) * y = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(116(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="116 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="603">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(240(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="240 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="604">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(115(a,1),251(a,1,2,1))].">
      <j1 rule="para" parents="115 251"/>
    </justification>
  </clause>

  <clause id="605">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * x = x * L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(191(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="191 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="606">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * x = x * L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(192(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="192 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="607">
    <literal><![CDATA[
      (x * x) * L((x * x) \ x,y,z) = L(x \ 1,y,z) * (x * x)
    ]]></literal>
    <justification jstring="[para(283(a,1),251(a,1,2,1))].">
      <j1 rule="para" parents="283 251"/>
    </justification>
  </clause>

  <clause id="608">
    <literal><![CDATA[
      (x * y) * R(T(z,x * y),x,y) = (z * x) * y
    ]]></literal>
    <justification jstring="[hyper(316,a,109,a(flip),b,252,a),flip(a)].">
      <j1 rule="hyper" parents="316 109 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="609">
    <literal><![CDATA[
      R(x / y,z,u) * y = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(116(a,1),252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="116 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="610">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(240(a,1),252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="240 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="611">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(115(a,1),252(a,1,2,1))].">
      <j1 rule="para" parents="115 252"/>
    </justification>
  </clause>

  <clause id="612">
    <literal><![CDATA[
      R(x / (x / y),z,u) * (x / y) = (x / y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(258(a,1),252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="258 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="613">
    <literal><![CDATA[
      T(x / (y \ 1),y) = (y \ x) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(253,a,576,a,b,124,a)].">
      <j1 rule="hyper" parents="253 576 124"/>
    </justification>
  </clause>

  <clause id="614">
    <literal><![CDATA[
      T(x / y,(z / y) \ z) = y \ x
    ]]></literal>
    <justification jstring="[hyper(253,a,402,a,b,333,a)].">
      <j1 rule="hyper" parents="253 402 333"/>
    </justification>
  </clause>

  <clause id="615">
    <literal><![CDATA[
      T(R(x,y,T(x,y)),x * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(253,a,238,a(flip),b,109,a(flip))].">
      <j1 rule="hyper" parents="253 238 109"/>
    </justification>
  </clause>

  <clause id="616">
    <literal><![CDATA[
      T((x * y) / x,x * y) = L(y,x,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(253,a,100,a(flip),b,157,a(flip))].">
      <j1 rule="hyper" parents="253 100 157"/>
    </justification>
  </clause>

  <clause id="617">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,27,a,b,615,a)].">
      <j1 rule="hyper" parents="63 27 615"/>
    </justification>
  </clause>

  <clause id="618">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,x \ y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),617(a,1,1,2))].">
      <j1 rule="para" parents="10 617"/>
    </justification>
  </clause>

  <clause id="619">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / x = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(285,a,261,a)].">
      <j1 rule="hyper" parents="285 261"/>
    </justification>
  </clause>

  <clause id="620">
    <literal><![CDATA[
      T(x / (y * x),y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(234(a,1),262(a,1,1))].">
      <j1 rule="para" parents="234 262"/>
    </justification>
  </clause>

  <clause id="621">
    <literal><![CDATA[
      T((x * y) / (z * y),z) = R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[para(110(a,1),262(a,1,1))].">
      <j1 rule="para" parents="110 262"/>
    </justification>
  </clause>

  <clause id="622">
    <literal><![CDATA[
      T(x * (y \ 1),y) = R(y \ x,y,y)
    ]]></literal>
    <justification jstring="[para(563(a,1),262(a,1,1))].">
      <j1 rule="para" parents="563 262"/>
    </justification>
  </clause>

  <clause id="623">
    <literal><![CDATA[
      (x / (y * x)) * y = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,620,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 620 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="624">
    <literal><![CDATA[
      x * R(x \ y,x,x) = (y * (x \ 1)) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,622,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 622 22"/>
    </justification>
  </clause>

  <clause id="625">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x) = R(y,x,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),622(a,2,1))].">
      <j1 rule="para" parents="9 622"/>
    </justification>
  </clause>

  <clause id="626">
    <literal><![CDATA[
      T(x,y) = R(y \ (x / (y \ 1)),y,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),622(a,1,1))].">
      <j1 rule="para" parents="12 622"/>
    </justification>
  </clause>

  <clause id="627">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,573,a,b,625,a),flip(a)].">
      <j1 rule="hyper" parents="316 573 625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="628">
    <literal><![CDATA[
      ((x * y) * (x \ 1)) * x = x * R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,625,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 625 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="629">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(305(a,1),44(a,1))].">
      <j1 rule="para" parents="305 44"/>
    </justification>
  </clause>

  <clause id="630">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(305(a,1),222(a,1))].">
      <j1 rule="para" parents="305 222"/>
    </justification>
  </clause>

  <clause id="631">
    <literal><![CDATA[
      (x * (x \ y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(80(a,1),630(a,1,1,1))].">
      <j1 rule="para" parents="80 630"/>
    </justification>
  </clause>

  <clause id="632">
    <literal><![CDATA[
      (T(x,x \ y) \ z) * u = (((x \ y) \ y) \ z) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,312,a,b,11,a)].">
      <j1 rule="hyper" parents="138 312 11"/>
    </justification>
  </clause>

  <clause id="633">
    <literal><![CDATA[
      (x \ 1) * (1 / x) = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,578,a(flip),b,345,a),flip(a)].">
      <j1 rule="hyper" parents="63 578 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="634">
    <literal><![CDATA[
      (x \ 1) \ (x \ (x \ 1)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(133,a,578,a(flip),b,345,a(flip))].">
      <j1 rule="hyper" parents="133 578 345"/>
    </justification>
  </clause>

  <clause id="635">
    <literal><![CDATA[
      L(1 / x,x \ 1,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(38,a,387,a,b,633,a(flip))].">
      <j1 rule="hyper" parents="38 387 633"/>
    </justification>
  </clause>

  <clause id="636">
    <literal><![CDATA[
      L(x \ 1,x \ 1,x) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(635(a,1),261(a,1,1)),flip(a)].">
      <j1 rule="para" parents="635 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="637">
    <literal><![CDATA[
      x \ (y \ (z * (u * u))) = (x \ (y \ z)) * (u * u)
    ]]></literal>
    <justification jstring="[hyper(133,a,388,a,b,124,a)].">
      <j1 rule="hyper" parents="133 388 124"/>
    </justification>
  </clause>

  <clause id="638">
    <literal><![CDATA[
      (x \ (x \ 1)) / y = 1 / (y * (x * x))
    ]]></literal>
    <justification jstring="[para(431(a,1),393(a,1,1))].">
      <j1 rule="para" parents="431 393"/>
    </justification>
  </clause>

  <clause id="639">
    <literal><![CDATA[
      (x * y) / (z * (y * y)) = (x * (y \ 1)) / z
    ]]></literal>
    <justification jstring="[para(562(a,1),393(a,1,1)),flip(a)].">
      <j1 rule="para" parents="562 393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="640">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ z) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(631,a,406,a),flip(a)].">
      <j1 rule="hyper" parents="631 406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="641">
    <literal><![CDATA[
      x \ (K(y,z) * (u * x)) = T(K(y,z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(390,a,xx,b,406,a),flip(a)].">
      <j1 rule="hyper" parents="390 406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="642">
    <literal><![CDATA[
      K(x,y) * (T(z,K(x,y)) * u) = (z * K(x,y)) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,239,a(flip),b,406,a),flip(a)].">
      <j1 rule="hyper" parents="63 239 406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="643">
    <literal><![CDATA[
      (K(x,y) \ z) * K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(253,a,158,a(flip),b,406,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="253 158 406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="645">
    <literal><![CDATA[
      K(x,y) \ (z * (K(x,y) * u)) = u * T(z,K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(133,a,114,a(flip),b,406,a(flip))].">
      <j1 rule="hyper" parents="133 114 406"/>
    </justification>
  </clause>

  <clause id="646">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (K(y,z) * (u * x)) = K(K(y,z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,406,a(flip),b,94,a)].">
      <j1 rule="hyper" parents="133 406 94"/>
    </justification>
  </clause>

  <clause id="647">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,109,a,b,406,a(flip))].">
      <j1 rule="hyper" parents="35 109 406"/>
    </justification>
  </clause>

  <clause id="649">
    <literal><![CDATA[
      (K(x,y) * (z * (u * w))) \ (((K(x,y) * z) * u) * w) = a(K(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(406(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="406 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="650">
    <literal><![CDATA[
      (K(x,y) * (z * u)) \ (u * (K(x,y) * z)) = K(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(406(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="406 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      (K(x,y) * (z * u)) \ ((K(x,y) * z) * (u * w)) = L(w,u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(406(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="406 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="652">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,K(y,z) * u,x)
    ]]></literal>
    <justification jstring="[para(406(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="406 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="654">
    <literal><![CDATA[
      K(x,y) * z != (K(x,y) * u) * w
    ]]></literal>
    <literal><![CDATA[
      u * w = z
    ]]></literal>
    <justification jstring="[para(406(a,2),43(a,1)),flip(a)].">
      <j1 rule="para" parents="406 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="655">
    <literal><![CDATA[
      K(x,y) * ((1 / z) * u) = (K(x,y) / z) * u
    ]]></literal>
    <justification jstring="[para(424(a,1),406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="424 406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="656">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * w = K(x,y) * ((z * u) * w)
    ]]></literal>
    <justification jstring="[para(406(a,2),406(a,1,1))].">
      <j1 rule="para" parents="406 406"/>
    </justification>
  </clause>

  <clause id="658">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(647(a,1),27(a,2,1))].">
      <j1 rule="para" parents="647 27"/>
    </justification>
  </clause>

  <clause id="660">
    <literal><![CDATA[
      (K(x,y) * z) / u = K(x,y) * (z / u)
    ]]></literal>
    <justification jstring="[para(12(a,1),410(a,1,1,2))].">
      <j1 rule="para" parents="12 410"/>
    </justification>
  </clause>

  <clause id="661">
    <literal><![CDATA[
      (K(x,y) * ((z * u) * w)) / (u * w) = K(x,y) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(109(a,1),410(a,1,1,2))].">
      <j1 rule="para" parents="109 410"/>
    </justification>
  </clause>

  <clause id="662">
    <literal><![CDATA[
      ((x * y) * T(L(z,y,x),u)) / (x * y) = T((x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(18(a,2),420(a,1,1,2,1))].">
      <j1 rule="para" parents="18 420"/>
    </justification>
  </clause>

  <clause id="663">
    <literal><![CDATA[
      x * ((y * T(z,x)) / y) = ((y * z) / y) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,422,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="139 422 22"/>
    </justification>
  </clause>

  <clause id="664">
    <literal><![CDATA[
      (K(x,y) \ z) \ u = z \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(332,a,477,a),flip(a)].">
      <j1 rule="hyper" parents="332 477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="665">
    <literal><![CDATA[
      (x * K(y,z)) \ (K(y,z) * u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(114(a,1),477(a,1,1))].">
      <j1 rule="para" parents="114 477"/>
    </justification>
  </clause>

  <clause id="666">
    <literal><![CDATA[
      (x \ 1) \ (K(x \ 1,x) * y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(436(a,1),477(a,1,1))].">
      <j1 rule="para" parents="436 477"/>
    </justification>
  </clause>

  <clause id="667">
    <literal><![CDATA[
      (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(138,a,436,a(flip),b,478,a)].">
      <j1 rule="hyper" parents="138 436 478"/>
    </justification>
  </clause>

  <clause id="668">
    <literal><![CDATA[
      (K(x,y) \ z) \ z = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(253,a,479,a(flip),b,158,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="253 479 158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="669">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,x \ 1) * y) = y
    ]]></literal>
    <justification jstring="[hyper(152,a,530,a)].">
      <j1 rule="hyper" parents="152 530"/>
    </justification>
  </clause>

  <clause id="670">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * z = y
    ]]></literal>
    <justification jstring="[para(530(a,1),152(a,1))].">
      <j1 rule="para" parents="530 152"/>
    </justification>
  </clause>

  <clause id="671">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * z = y
    ]]></literal>
    <justification jstring="[para(531(a,1),152(a,1))].">
      <j1 rule="para" parents="531 152"/>
    </justification>
  </clause>

  <clause id="672">
    <literal><![CDATA[
      T(x / (y \ 1),y) / (y * y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(136,a,580,a,b,388,a(flip))].">
      <j1 rule="hyper" parents="136 580 388"/>
    </justification>
  </clause>

  <clause id="673">
    <literal><![CDATA[
      T(x,y * y) / (z * (y * y)) = ((y * y) \ x) / z
    ]]></literal>
    <justification jstring="[hyper(136,a,582,a(flip),b,125,a)].">
      <j1 rule="hyper" parents="136 582 125"/>
    </justification>
  </clause>

  <clause id="674">
    <literal><![CDATA[
      L(x \ y,x,x) * (x * x) = T(x * y,x * x)
    ]]></literal>
    <justification jstring="[para(102(a,2),582(a,1,1))].">
      <j1 rule="para" parents="102 582"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      (x \ y) / (z * z) = x \ (y / (z * z))
    ]]></literal>
    <justification jstring="[hyper(149,a,586,a)].">
      <j1 rule="hyper" parents="149 586"/>
    </justification>
  </clause>

  <clause id="676">
    <literal><![CDATA[
      (x * (y * y)) / z = x / (z / (y * y))
    ]]></literal>
    <justification jstring="[hyper(149,a,595,a)].">
      <j1 rule="hyper" parents="149 595"/>
    </justification>
  </clause>

  <clause id="677">
    <literal><![CDATA[
      (x * (y * (z * z))) / u = (x * y) / (u / (z * z))
    ]]></literal>
    <justification jstring="[hyper(136,a,32,a(flip),b,595,a)].">
      <j1 rule="hyper" parents="136 32 595"/>
    </justification>
  </clause>

  <clause id="678">
    <literal><![CDATA[
      T(K(x,y) * (z / u),u) = u \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(660(a,1),116(a,1,1))].">
      <j1 rule="para" parents="660 116"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = y \ (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(531(a,1),664(a,1,1))].">
      <j1 rule="para" parents="531 664"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      x \ (y * (x \ 1)) = T(y,x) / (x * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),672(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="681">
    <literal><![CDATA[
      T(x * y,y) / (y * y) = y \ R(x,y,y)
    ]]></literal>
    <justification jstring="[para(569(a,1),672(a,1,1,1))].">
      <j1 rule="para" parents="569 672"/>
    </justification>
  </clause>

  <clause id="682">
    <literal><![CDATA[
      (x \ 1) / (y * y) = x \ (y \ (y \ 1))
    ]]></literal>
    <justification jstring="[para(431(a,1),675(a,2,2))].">
      <j1 rule="para" parents="431 675"/>
    </justification>
  </clause>

  <clause id="683">
    <literal><![CDATA[
      (x * y) / (z * z) = x * (y / (z * z))
    ]]></literal>
    <justification jstring="[hyper(138,a,87,a(flip),b,676,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="138 87 676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="684">
    <literal><![CDATA[
      x / (y / ((1 / z) * (1 / z))) = (x * (z \ (1 / z))) / y
    ]]></literal>
    <justification jstring="[para(287(a,1),676(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="287 676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="685">
    <literal><![CDATA[
      (x \ 1) \ (y \ (x \ (x \ 1))) = T((y \ 1) / x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(390,a,682,a(flip),b,566,a),flip(a)].">
      <j1 rule="hyper" parents="390 682 566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="686">
    <literal><![CDATA[
      (x * (y / (z * z))) / u = (x * y) / (u * (z * z))
    ]]></literal>
    <justification jstring="[hyper(136,a,683,a(flip),b,395,a)].">
      <j1 rule="hyper" parents="136 683 395"/>
    </justification>
  </clause>

  <clause id="687">
    <literal><![CDATA[
      (x * y) / a(z,z \ x,y) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(136,a,158,a(flip),b,89,a)].">
      <j1 rule="hyper" parents="136 158 89"/>
    </justification>
  </clause>

  <clause id="688">
    <literal><![CDATA[
      ((x * y) * z) / ((y * z) * a(x,y,z)) = R(x,y * z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(136,a,89,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="136 89 109"/>
    </justification>
  </clause>

  <clause id="689">
    <literal><![CDATA[
      R(x,y * z,a(x,y,z)) \ ((x * y) * z) = (y * z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,89,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="133 89 109"/>
    </justification>
  </clause>

  <clause id="690">
    <literal><![CDATA[
      (x * y) * a(x,z,z \ y) = (x * z) * (z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),89(a,1,1,2))].">
      <j1 rule="para" parents="10 89"/>
    </justification>
  </clause>

  <clause id="692">
    <literal><![CDATA[
      (x * (y * z)) * a(x,z,T(y,z)) = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(114(a,1),89(a,1,1,2))].">
      <j1 rule="para" parents="114 89"/>
    </justification>
  </clause>

  <clause id="693">
    <literal><![CDATA[
      x * L(L(y,z \ x,z),u,w) = z * ((z \ x) * L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,30,a,b,101,a)].">
      <j1 rule="hyper" parents="139 30 101"/>
    </justification>
  </clause>

  <clause id="694">
    <literal><![CDATA[
      L(T(x,y \ z),y \ z,y) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[para(114(a,1),101(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="114 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="695">
    <literal><![CDATA[
      x * R(L(y,z,x / z),u,w) = (x / z) * (z * R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,29,a,b,103,a)].">
      <j1 rule="hyper" parents="139 29 103"/>
    </justification>
  </clause>

  <clause id="696">
    <literal><![CDATA[
      (x * y) / T(z * z,u) = x * (y / T(z * z,u))
    ]]></literal>
    <justification jstring="[hyper(209,a,467,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="209 467 104"/>
    </justification>
  </clause>

  <clause id="697">
    <literal><![CDATA[
      x * ((x \ y) * (z \ (1 / z))) = y * (z \ (1 / z))
    ]]></literal>
    <justification jstring="[hyper(138,a,504,a(flip),b,106,a(flip))].">
      <j1 rule="hyper" parents="138 504 106"/>
    </justification>
  </clause>

  <clause id="698">
    <literal><![CDATA[
      R(x,x \ y,y \ z) \ z = (x \ y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(106(a,2),300(a,1,1))].">
      <j1 rule="para" parents="106 300"/>
    </justification>
  </clause>

  <clause id="699">
    <literal><![CDATA[
      (x * y) * (y \ (1 / y)) = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(138,a,504,a(flip),b,108,a),flip(a)].">
      <j1 rule="hyper" parents="138 504 108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="700">
    <literal><![CDATA[
      L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(138,a,29,a(flip),b,108,a)].">
      <j1 rule="hyper" parents="138 29 108"/>
    </justification>
  </clause>

  <clause id="701">
    <literal><![CDATA[
      (x \ y) \ (1 / (x \ y)) = y \ (x * (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(133,a,699,a(flip),b,158,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 699 158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="702">
    <literal><![CDATA[
      L(R(x,y / z,z),u,w) * y = (L(x,u,w) * (y / z)) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,29,a(flip),b,111,a)].">
      <j1 rule="hyper" parents="138 29 111"/>
    </justification>
  </clause>

  <clause id="703">
    <literal><![CDATA[
      L(x,y \ 1,y) \ x = a(y,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(271(a,1),230(a,1,1))].">
      <j1 rule="para" parents="271 230"/>
    </justification>
  </clause>

  <clause id="704">
    <literal><![CDATA[
      a(x,x \ y,(x \ y) \ 1) = x \ (y * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(10(a,1),231(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="706">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(275(a,1),231(a,1,2))].">
      <j1 rule="para" parents="275 231"/>
    </justification>
  </clause>

  <clause id="707">
    <literal><![CDATA[
      a(x,y,y \ 1) = x \ R(x,y,y)
    ]]></literal>
    <justification jstring="[para(565(a,1),231(a,1,2)),flip(a)].">
      <j1 rule="para" parents="565 231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="708">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(316,a,25,a(flip),b,247,a),flip(a)].">
      <j1 rule="hyper" parents="316 25 247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="709">
    <literal><![CDATA[
      (x \ (y * y)) \ ((x \ 1) * (z * (y * y))) = L(T(z,y * y),y * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(389(a,1),247(a,1,1))].">
      <j1 rule="para" parents="389 247"/>
    </justification>
  </clause>

  <clause id="710">
    <literal><![CDATA[
      x * ((y * x) \ (y * (z * x))) = L(z,x,y) * x
    ]]></literal>
    <justification jstring="[para(247(a,2),251(a,1,2))].">
      <j1 rule="para" parents="247 251"/>
    </justification>
  </clause>

  <clause id="711">
    <literal><![CDATA[
      x * (y * L(z \ 1,z,u)) = x * (y * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(139,a,359,a,b,9,a)].">
      <j1 rule="hyper" parents="139 359 9"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,364,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="139 364 18"/>
    </justification>
  </clause>

  <clause id="713">
    <literal><![CDATA[
      x * ((x \ y) * T(z,y)) = L(z,x \ y,x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,251,a(flip),b,405,a),flip(a)].">
      <j1 rule="hyper" parents="63 251 405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="714">
    <literal><![CDATA[
      x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,251,a(flip),b,405,a(flip))].">
      <j1 rule="hyper" parents="133 251 405"/>
    </justification>
  </clause>

  <clause id="715">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,16,a,b,413,a)].">
      <j1 rule="hyper" parents="316 16 413"/>
    </justification>
  </clause>

  <clause id="716">
    <literal><![CDATA[
      (x / y) * (y * T(z,x)) = L(z,y,x / y) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,251,a(flip),b,451,a),flip(a)].">
      <j1 rule="hyper" parents="63 251 451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="717">
    <literal><![CDATA[
      L(x \ (1 / x),y,z) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[para(287(a,1),465(a,1,1))].">
      <j1 rule="para" parents="287 465"/>
    </justification>
  </clause>

  <clause id="720">
    <literal><![CDATA[
      L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(475(a,1),25(a,2,1))].">
      <j1 rule="para" parents="475 25"/>
    </justification>
  </clause>

  <clause id="722">
    <literal><![CDATA[
      L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(475(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="475 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="723">
    <literal><![CDATA[
      L(R(x,L(x,y,z) \ u,w),y,z) \ (u * w) = (L(x,y,z) \ u) * w
    ]]></literal>
    <justification jstring="[para(29(a,1),492(a,1,1))].">
      <j1 rule="para" parents="29 492"/>
    </justification>
  </clause>

  <clause id="724">
    <literal><![CDATA[
      x \ ((y * z) * (z \ x)) = R(T(y,x),z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,495,a(flip),b,252,a)].">
      <j1 rule="hyper" parents="133 495 252"/>
    </justification>
  </clause>

  <clause id="725">
    <literal><![CDATA[
      T((x * (y \ z)) / z,y) = R(y \ x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(508(a,1),262(a,1,1))].">
      <j1 rule="para" parents="508 262"/>
    </justification>
  </clause>

  <clause id="726">
    <literal><![CDATA[
      R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(509(a,1),27(a,2,1))].">
      <j1 rule="para" parents="509 27"/>
    </justification>
  </clause>

  <clause id="727">
    <literal><![CDATA[
      R(x / y,y,x) \ 1 = y * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,562,a(flip),b,514,a),flip(a)].">
      <j1 rule="hyper" parents="316 562 514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="728">
    <literal><![CDATA[
      R(x / y,y,x) = 1 / (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(209,a,562,a(flip),b,514,a),flip(a)].">
      <j1 rule="hyper" parents="209 562 514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="729">
    <literal><![CDATA[
      R(x,y,x * y) \ 1 = y * ((x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),727(a,1,1,1))].">
      <j1 rule="para" parents="11 727"/>
    </justification>
  </clause>

  <clause id="730">
    <literal><![CDATA[
      R(x,R(y / z,z,y),R(y / z,z,y) \ 1) = (x * R(y / z,z,y)) * (z * (y \ 1))
    ]]></literal>
    <justification jstring="[para(727(a,1),275(a,1,2)),flip(a)].">
      <j1 rule="para" parents="727 275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="731">
    <literal><![CDATA[
      (x \ (1 / x)) \ 1 = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,504,a(flip),b,568,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 504 568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="732">
    <literal><![CDATA[
      x * ((y \ (1 / y)) * ((1 / y) \ y)) = x
    ]]></literal>
    <justification jstring="[para(731(a,1),73(a,1,2,2))].">
      <j1 rule="para" parents="731 73"/>
    </justification>
  </clause>

  <clause id="733">
    <literal><![CDATA[
      ((x * y) / (z * y)) * z = z * R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,621,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 621 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="734">
    <literal><![CDATA[
      R(x,y,z) = T(((y * x) * z) / (y * z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),621(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9 621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="735">
    <literal><![CDATA[
      ((x \ y) / y) * x = x * R(x \ 1,x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),623(a,1,1,2))].">
      <j1 rule="para" parents="10 623"/>
    </justification>
  </clause>

  <clause id="736">
    <literal><![CDATA[
      T(((1 / x) * y) * x,1 / x) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(185(a,1),734(a,2,1)),flip(a)].">
      <j1 rule="para" parents="185 734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="737">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = T(R(z,x,y),x * y)
    ]]></literal>
    <justification jstring="[para(734(a,2),260(a,1,1)),flip(a)].">
      <j1 rule="para" parents="734 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="738">
    <literal><![CDATA[
      R(T(T(x,y),z),u,w) = T(T(R(x,u,w),z),y)
    ]]></literal>
    <justification jstring="[hyper(316,a,27,a,b,121,a)].">
      <j1 rule="hyper" parents="316 27 121"/>
    </justification>
  </clause>

  <clause id="739">
    <literal><![CDATA[
      x * (y / ((1 / z) * (1 / z))) = (x * y) * ((1 / z) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,683,a(flip),b,446,a)].">
      <j1 rule="hyper" parents="63 683 446"/>
    </justification>
  </clause>

  <clause id="740">
    <literal><![CDATA[
      x / (y \ (1 / y)) = x * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[para(287(a,1),446(a,1,2))].">
      <j1 rule="para" parents="287 446"/>
    </justification>
  </clause>

  <clause id="741">
    <literal><![CDATA[
      x / ((1 / y) \ y) = x * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(138,a,12,a(flip),b,740,a),flip(a)].">
      <j1 rule="hyper" parents="138 12 740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="743">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) \ 1) = y \ (x * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(133,a,564,a(flip),b,434,a),flip(a)].">
      <j1 rule="hyper" parents="133 564 434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="744">
    <literal><![CDATA[
      (x \ 1) / (y * (x \ 1)) = x / (y * x)
    ]]></literal>
    <justification jstring="[para(229(a,1),592(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="229 592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="745">
    <literal><![CDATA[
      (x \ 1) * (x * (y * (x \ 1))) = L(y,x \ 1,x) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(474(a,1),599(a,1,2))].">
      <j1 rule="para" parents="474 599"/>
    </justification>
  </clause>

  <clause id="746">
    <literal><![CDATA[
      (x * ((y * x) \ y)) / x = L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(136,a,359,a(flip),b,602,a)].">
      <j1 rule="hyper" parents="136 359 602"/>
    </justification>
  </clause>

  <clause id="749">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * (x \ y) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(356(a,1),602(a,2,2))].">
      <j1 rule="para" parents="356 602"/>
    </justification>
  </clause>

  <clause id="750">
    <literal><![CDATA[
      L(R(1 / x,x,x \ y),z,u) * y = y * L(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[para(370(a,2),602(a,1,1,1))].">
      <j1 rule="para" parents="370 602"/>
    </justification>
  </clause>

  <clause id="751">
    <literal><![CDATA[
      L((x * y) / x,z,u) = (x * L(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(149,a,603,a),flip(a)].">
      <j1 rule="hyper" parents="149 603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="752">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(136,a,100,a(flip),b,603,a),flip(a)].">
      <j1 rule="hyper" parents="136 100 603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="753">
    <literal><![CDATA[
      R(R(x / y,z,u),y,y \ 1) / (y \ 1) = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,392,a,b,609,a)].">
      <j1 rule="hyper" parents="63 392 609"/>
    </justification>
  </clause>

  <clause id="754">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) \ R(y / x,z,u) = L(x \ 1,x,R(y / x,z,u))
    ]]></literal>
    <justification jstring="[para(609(a,1),232(a,2,1)),flip(a)].">
      <j1 rule="para" parents="609 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="755">
    <literal><![CDATA[
      (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = R(R(y,x,K(x,y)),z,u) * (x * K(x,y))
    ]]></literal>
    <justification jstring="[para(308(a,1),609(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="308 609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="756">
    <literal><![CDATA[
      R((x * y) / x,z,u) = (x * R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(149,a,610,a),flip(a)].">
      <j1 rule="hyper" parents="149 610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="757">
    <literal><![CDATA[
      L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z
    ]]></literal>
    <justification jstring="[para(298(a,1),619(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="298 619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="758">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) / (x \ 1) = L(y / (x \ 1),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(474(a,1),619(a,1,1,2))].">
      <j1 rule="para" parents="474 619"/>
    </justification>
  </clause>

  <clause id="759">
    <literal><![CDATA[
      ((x * y) * z) / ((y * (z \ 1)) * (z * z)) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,20,a,b,639,a),flip(a)].">
      <j1 rule="hyper" parents="316 20 639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="760">
    <literal><![CDATA[
      x * T(K(y,z) * u,K(y,z) * x) = u * (K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(139,a,641,a(flip),b,477,a(flip))].">
      <j1 rule="hyper" parents="139 641 477"/>
    </justification>
  </clause>

  <clause id="761">
    <literal><![CDATA[
      K(x,y) * (((1 / z) * u) * w) = ((K(x,y) / z) * u) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,655,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 655 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="762">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[para(116(a,1),663(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="116 663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="764">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) \ (K(x \ 1,x) * y)) = y
    ]]></literal>
    <justification jstring="[hyper(139,a,666,a,b,xx)].">
      <j1 rule="hyper" parents="139 666"/>
    </justification>
  </clause>

  <clause id="765">
    <literal><![CDATA[
      (1 / x) \ (K(x,x \ 1) * y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(669(a,1),666(a,1,2)),flip(a)].">
      <j1 rule="para" parents="669 666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="766">
    <literal><![CDATA[
      T(T(R(x / y,z,u),w),y) = R(T(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(116(a,1),738(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="116 738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="767">
    <literal><![CDATA[
      (x * y) * ((z * L(u,y,x)) / z) = x * (y * ((z * u) / z))
    ]]></literal>
    <justification jstring="[hyper(139,a,751,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="139 751 18"/>
    </justification>
  </clause>

  <clause id="768">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x
    ]]></literal>
    <justification jstring="[para(363(a,1),751(a,2,1,2))].">
      <j1 rule="para" parents="363 751"/>
    </justification>
  </clause>

  <clause id="769">
    <literal><![CDATA[
      L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x
    ]]></literal>
    <justification jstring="[para(475(a,1),751(a,2,1,2))].">
      <j1 rule="para" parents="475 751"/>
    </justification>
  </clause>

  <clause id="771">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(669(a,1),764(a,1,2,2))].">
      <j1 rule="para" parents="669 764"/>
    </justification>
  </clause>

  <clause id="772">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,9,a(flip),b,765,a),flip(a)].">
      <j1 rule="hyper" parents="139 9 765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="774">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) * y) * z) = ((1 / x) * y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,772,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 772 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="775">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,365,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="139 365 18"/>
    </justification>
  </clause>

  <clause id="776">
    <literal><![CDATA[
      L(L(x \ 1,y * x,z),x,y) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,102,a(flip),b,366,a),flip(a)].">
      <j1 rule="hyper" parents="316 102 366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="777">
    <literal><![CDATA[
      (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,366,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="139 366 18"/>
    </justification>
  </clause>

  <clause id="779">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = T(x / (z * y),u) * (z * y)
    ]]></literal>
    <justification jstring="[para(303(a,1),401(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="303 401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="780">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(102(a,1),408(a,1,2,1))].">
      <j1 rule="para" parents="102 408"/>
    </justification>
  </clause>

  <clause id="781">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u))
    ]]></literal>
    <justification jstring="[para(298(a,1),408(a,1,2,1))].">
      <j1 rule="para" parents="298 408"/>
    </justification>
  </clause>

  <clause id="782">
    <literal><![CDATA[
      (x * y) * L(L(z,T(x,y),y),u,w) = y * (T(x,y) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),450(a,1,2))].">
      <j1 rule="para" parents="30 450"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      (x * y) * T((y * T(x,y)) \ y,z) = y * (T(x,y) * T(T(x,y) \ 1,z))
    ]]></literal>
    <justification jstring="[para(364(a,2),450(a,1,2))].">
      <j1 rule="para" parents="364 450"/>
    </justification>
  </clause>

  <clause id="784">
    <literal><![CDATA[
      (x * y) * R((y * T(x,y)) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(365(a,2),450(a,1,2))].">
      <j1 rule="para" parents="365 450"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      (x * y) * L((y * T(x,y)) \ y,z,u) = y * (T(x,y) * L(T(x,y) \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(366(a,1),450(a,1,2))].">
      <j1 rule="para" parents="366 450"/>
    </justification>
  </clause>

  <clause id="786">
    <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(485(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="485 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="787">
    <literal><![CDATA[
      R(x,T(y,x),T(z,y * x)) \ (z * (y * x)) = T(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,237,a(flip),b,491,a)].">
      <j1 rule="hyper" parents="63 237 491"/>
    </justification>
  </clause>

  <clause id="788">
    <literal><![CDATA[
      T(R(x / y,y,T(z,y)),z * y) = (z * y) \ (x * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(390,a,157,a(flip),b,494,a)].">
      <j1 rule="hyper" parents="390 157 494"/>
    </justification>
  </clause>

  <clause id="789">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(377,a,510,a),flip(a)].">
      <j1 rule="hyper" parents="377 510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="790">
    <literal><![CDATA[
      R(T((x * y) / x,x * y),x,y) = y
    ]]></literal>
    <justification jstring="[hyper(331,a,510,a),flip(a)].">
      <j1 rule="hyper" parents="331 510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="792">
    <literal><![CDATA[
      (x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(139,a,541,a,b,103,a),flip(a)].">
      <j1 rule="hyper" parents="139 541 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="793">
    <literal><![CDATA[
      (1 / x) * ((x \ y) * x) = T((1 / x) * y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,533,a(flip),b,549,a)].">
      <j1 rule="hyper" parents="63 533 549"/>
    </justification>
  </clause>

  <clause id="794">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) * x) = T(1 / x,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),793(a,2,1))].">
      <j1 rule="para" parents="8 793"/>
    </justification>
  </clause>

  <clause id="795">
    <literal><![CDATA[
      T((1 / x) * y,x) != (1 / x) * z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * x = z
    ]]></literal>
    <justification jstring="[para(793(a,1),43(a,1))].">
      <j1 rule="para" parents="793 43"/>
    </justification>
  </clause>

  <clause id="796">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,116,a(flip),b,794,a),flip(a)].">
      <j1 rule="hyper" parents="316 116 794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="797">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = (1 / x) \ 1
    ]]></literal>
    <justification jstring="[para(83(a,1),796(a,1,2,1))].">
      <j1 rule="para" parents="83 796"/>
    </justification>
  </clause>

  <clause id="798">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(272(a,2),796(a,1,2))].">
      <j1 rule="para" parents="272 796"/>
    </justification>
  </clause>

  <clause id="800">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,K(y \ 1,y)) = (x * K(y \ 1,y)) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(209,a,798,a(flip),b,493,a),flip(a)].">
      <j1 rule="hyper" parents="209 798 493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="801">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = x \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,798,a(flip),b,198,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 798 198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="803">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,83,a(flip),b,797,a),flip(a)].">
      <j1 rule="hyper" parents="316 83 797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,1 / x) = x
    ]]></literal>
    <justification jstring="[para(274(a,2),803(a,1,2))].">
      <j1 rule="para" parents="274 803"/>
    </justification>
  </clause>

  <clause id="806">
    <literal><![CDATA[
      (1 / (1 / x)) \ x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(144,a,805,a)].">
      <j1 rule="hyper" parents="144 805"/>
    </justification>
  </clause>

  <clause id="807">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,552,a(flip),b,271,a),flip(a)].">
      <j1 rule="hyper" parents="133 552 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      x \ T(x * y,x \ 1) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,552,a(flip),b,527,a(flip))].">
      <j1 rule="hyper" parents="133 552 527"/>
    </justification>
  </clause>

  <clause id="809">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = T(x / y,z) * y
    ]]></literal>
    <justification jstring="[hyper(136,a,553,a(flip),b,275,a)].">
      <j1 rule="hyper" parents="136 553 275"/>
    </justification>
  </clause>

  <clause id="810">
    <literal><![CDATA[
      ((x * y) / x) \ (y * (x * y)) = y * x
    ]]></literal>
    <justification jstring="[hyper(133,a,100,a(flip),b,559,a)].">
      <j1 rule="hyper" parents="133 100 559"/>
    </justification>
  </clause>

  <clause id="811">
    <literal><![CDATA[
      L(((x * y) * x) / (x * y),y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(35,a,603,a,b,559,a)].">
      <j1 rule="hyper" parents="35 603 559"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      R(T(x,y * T(z,x * y)),y,T(z,x * y)) = (y * T(z,x * y)) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,237,a(flip),b,560,a),flip(a)].">
      <j1 rule="hyper" parents="63 237 560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="813">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = L(x / y,z,u) * y
    ]]></literal>
    <justification jstring="[para(563(a,1),571(a,1,1,1))].">
      <j1 rule="para" parents="563 571"/>
    </justification>
  </clause>

  <clause id="814">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * (y * T(y \ 1,x * y))
    ]]></literal>
    <justification jstring="[hyper(316,a,360,a(flip),b,598,a)].">
      <j1 rule="hyper" parents="316 360 598"/>
    </justification>
  </clause>

  <clause id="815">
    <literal><![CDATA[
      L(T(x,y),y,z) * (z * y) = z * (T(x,z * y) * y)
    ]]></literal>
    <justification jstring="[para(250(a,1),598(a,1,2)),flip(a)].">
      <j1 rule="para" parents="250 598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      T(L(x,y,(y * x) / y),y) = T(y \ (y * x),y * x)
    ]]></literal>
    <justification jstring="[para(616(a,1),260(a,1,1))].">
      <j1 rule="para" parents="616 260"/>
    </justification>
  </clause>

  <clause id="818">
    <literal><![CDATA[
      R(L(x,y,(y * x) / y),y,x) = x
    ]]></literal>
    <justification jstring="[para(616(a,1),790(a,1,1))].">
      <j1 rule="para" parents="616 790"/>
    </justification>
  </clause>

  <clause id="819">
    <literal><![CDATA[
      L(R(x,y,x),y,(y * x) / y) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,29,a(flip),b,818,a)].">
      <j1 rule="hyper" parents="63 29 818"/>
    </justification>
  </clause>

  <clause id="820">
    <literal><![CDATA[
      (x * x) \ (x * y) = L(x \ y,x,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,582,a,b,674,a)].">
      <j1 rule="hyper" parents="35 582 674"/>
    </justification>
  </clause>

  <clause id="821">
    <literal><![CDATA[
      L(x,x \ y,z) * (x \ y) = (x \ y) * ((z * (x \ y)) \ (z * y))
    ]]></literal>
    <justification jstring="[para(10(a,1),710(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="822">
    <literal><![CDATA[
      (x \ y) * T(z * z,y) = x \ ((z * z) * y)
    ]]></literal>
    <justification jstring="[para(452(a,1),714(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="452 714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="823">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(356(a,1),714(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="356 714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="824">
    <literal><![CDATA[
      x / T(y * y,x) = (y * y) \ x
    ]]></literal>
    <justification jstring="[hyper(136,a,9,a(flip),b,822,a)].">
      <j1 rule="hyper" parents="136 9 822"/>
    </justification>
  </clause>

  <clause id="825">
    <literal><![CDATA[
      ((x * x) \ y) \ y = T(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,9,a(flip),b,822,a)].">
      <j1 rule="hyper" parents="133 9 822"/>
    </justification>
  </clause>

  <clause id="826">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[para(12(a,1),724(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="827">
    <literal><![CDATA[
      R(T(1 / x,y),x,x \ y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(81(a,1),724(a,1,2)),flip(a)].">
      <j1 rule="para" parents="81 724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="828">
    <literal><![CDATA[
      T((x * (y \ z)) / z,y) * z = ((y \ x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(138,a,725,a,b,108,a)].">
      <j1 rule="hyper" parents="138 725 108"/>
    </justification>
  </clause>

  <clause id="829">
    <literal><![CDATA[
      L(((x * y) * x) / (x * y),y,x) * y = y * x
    ]]></literal>
    <justification jstring="[hyper(138,a,811,a,b,xx)].">
      <j1 rule="hyper" parents="138 811"/>
    </justification>
  </clause>

  <clause id="830">
    <literal><![CDATA[
      R(T(x / y,x),y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,9,a(flip),b,826,a),flip(a)].">
      <j1 rule="hyper" parents="316 9 826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="831">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(138,a,826,a(flip),b,108,a)].">
      <j1 rule="hyper" parents="138 826 108"/>
    </justification>
  </clause>

  <clause id="832">
    <literal><![CDATA[
      (x * y) \ (x * ((((x * y) * x) / (x * y)) * y)) = x
    ]]></literal>
    <justification jstring="[hyper(34,a,710,a,b,829,a(flip))].">
      <j1 rule="hyper" parents="34 710 829"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      (x * x) \ (y * (z * (u * (x * x)))) = T(y * (z * u),x * x)
    ]]></literal>
    <justification jstring="[para(32(a,1),128(a,1,2,2))].">
      <j1 rule="para" parents="32 128"/>
    </justification>
  </clause>

  <clause id="835">
    <literal><![CDATA[
      x * (y \ L(L(z,u,w),v5,v6)) = x * (y \ L(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,167,a,b,9,a)].">
      <j1 rule="hyper" parents="139 167 9"/>
    </justification>
  </clause>

  <clause id="836">
    <literal><![CDATA[
      x * (L(L(y,z,u),w,v5) \ v6) = x * (L(L(y,w,v5),z,u) \ v6)
    ]]></literal>
    <justification jstring="[para(398(a,1),161(a,1,2,2))].">
      <j1 rule="para" parents="398 161"/>
    </justification>
  </clause>

  <clause id="837">
    <literal><![CDATA[
      x \ (y * (z * (u * (w * w)))) = (x \ (y * (z * u))) * (w * w)
    ]]></literal>
    <justification jstring="[para(32(a,1),585(a,1,2,2))].">
      <j1 rule="para" parents="32 585"/>
    </justification>
  </clause>

  <clause id="838">
    <literal><![CDATA[
      (x \ (y * (z \ 1))) * (u * u) = x \ (y * (z \ (u * u)))
    ]]></literal>
    <justification jstring="[para(389(a,1),585(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="389 585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="839">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * x = x * L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,159,a,b,605,a),flip(a)].">
      <j1 rule="hyper" parents="316 159 605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="840">
    <literal><![CDATA[
      T(x,K(y,z)) * K(K(y,z),x) = x
    ]]></literal>
    <justification jstring="[hyper(34,a,94,a(flip),b,642,a),flip(a)].">
      <j1 rule="hyper" parents="34 94 642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="841">
    <literal><![CDATA[
      (K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(136,a,656,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="136 656 109"/>
    </justification>
  </clause>

  <clause id="842">
    <literal><![CDATA[
      ((x * y) * z) / ((y * (z * (u * u))) / (u * u)) = R(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20,a,b,677,a),flip(a)].">
      <j1 rule="hyper" parents="63 20 677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="843">
    <literal><![CDATA[
      (x * (y * z)) / (u * (z * z)) = (x * (y * (z \ 1))) / u
    ]]></literal>
    <justification jstring="[para(562(a,1),686(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="562 686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="844">
    <literal><![CDATA[
      x * (y \ (z * ((z \ y) \ 1))) = x / ((z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(139,a,743,a(flip),b,443,a)].">
      <j1 rule="hyper" parents="139 743 443"/>
    </justification>
  </clause>

  <clause id="845">
    <literal><![CDATA[
      R(T(x \ y,x * z),x,z) = T((x * z) \ (y * z),x)
    ]]></literal>
    <justification jstring="[para(512(a,1),766(a,1,1)),flip(a)].">
      <j1 rule="para" parents="512 766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="846">
    <literal><![CDATA[
      T(x * (y * (x \ 1)),z) = x * (T(y,z) * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(139,a,414,a(flip),b,807,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 414 807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="847">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),807(a,2,2,1))].">
      <j1 rule="para" parents="8 807"/>
    </justification>
  </clause>

  <clause id="848">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),807(a,2,2,1))].">
      <j1 rule="para" parents="10 807"/>
    </justification>
  </clause>

  <clause id="850">
    <literal><![CDATA[
      T(x,y) \ (x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,847,a(flip),b,416,a(flip))].">
      <j1 rule="hyper" parents="133 847 416"/>
    </justification>
  </clause>

  <clause id="851">
    <literal><![CDATA[
      ((x \ 1) \ (x \ y)) * (x \ 1) = x \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),808(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="852">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,415,a(flip),b,809,a),flip(a)].">
      <j1 rule="hyper" parents="316 415 809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      (x \ y) \ K(y \ x,y) = T((x \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,95,a(flip),b,823,a)].">
      <j1 rule="hyper" parents="133 95 823"/>
    </justification>
  </clause>

  <clause id="854">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((x * y) \ x) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),853(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      x * ((((x * y) * x) / (x * y)) * y) = (x * y) * x
    ]]></literal>
    <justification jstring="[hyper(152,a,832,a),flip(a)].">
      <j1 rule="hyper" parents="152 832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="856">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),852(a,1,1,1))].">
      <j1 rule="para" parents="7 852"/>
    </justification>
  </clause>

  <clause id="857">
    <literal><![CDATA[
      K(x,y) = ((y * x) \ y) * T(((y * x) \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,854,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="139 854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(38,a,853,a,b,854,a(flip))].">
      <j1 rule="hyper" parents="38 853 854"/>
    </justification>
  </clause>

  <clause id="859">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) = ((y * x) \ y) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(232(a,2),854(a,1,1,1))].">
      <j1 rule="para" parents="232 854"/>
    </justification>
  </clause>

  <clause id="860">
    <literal><![CDATA[
      K(x \ (x * y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(70(a,1),858(a,1,1)),flip(a)].">
      <j1 rule="para" parents="70 858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="861">
    <literal><![CDATA[
      K((x / y) \ x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),860(a,1,1,2))].">
      <j1 rule="para" parents="12 860"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      (((x * y) * x) / (x * y)) * y = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(254,a,855,a),flip(a)].">
      <j1 rule="hyper" parents="254 855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="863">
    <literal><![CDATA[
      ((x * y) * x) / (x * y) = T(x * y,x) / y
    ]]></literal>
    <justification jstring="[hyper(149,a,862,a),flip(a)].">
      <j1 rule="hyper" parents="149 862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="864">
    <literal><![CDATA[
      T(T(x * y,x) / y,x * y) = x
    ]]></literal>
    <justification jstring="[para(863(a,1),240(a,1,1))].">
      <j1 rule="para" parents="863 240"/>
    </justification>
  </clause>

  <clause id="865">
    <literal><![CDATA[
      T(T(x,x / y) / y,(x / y) * y) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),864(a,1,1,1,1))].">
      <j1 rule="para" parents="12 864"/>
    </justification>
  </clause>

  <clause id="866">
    <literal><![CDATA[
      T(T(x,x / y) / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),865(a,1,2))].">
      <j1 rule="para" parents="12 865"/>
    </justification>
  </clause>

  <clause id="867">
    <literal><![CDATA[
      T(x,x / y) / y = (x * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(285,a,866,a),flip(a)].">
      <j1 rule="hyper" parents="285 866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="868">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y = T(x,x / y)
    ]]></literal>
    <justification jstring="[hyper(151,a,867,a)].">
      <j1 rule="hyper" parents="151 867"/>
    </justification>
  </clause>

  <clause id="869">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,762,a(flip),b,868,a)].">
      <j1 rule="hyper" parents="63 762 868"/>
    </justification>
  </clause>

  <clause id="870">
    <literal><![CDATA[
      (x * y) * L((x \ y) / y,y,x) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[para(757(a,2),869(a,1,2))].">
      <j1 rule="para" parents="757 869"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      L(x \ (y \ (z \ ((z * y) * x))),x,z * y) = a(z,y,y \ (z \ ((z * y) * x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,102,a,b,297,a)].">
      <j1 rule="hyper" parents="63 102 297"/>
    </justification>
  </clause>

  <clause id="872">
    <literal><![CDATA[
      R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y
    ]]></literal>
    <justification jstring="[para(110(a,1),397(a,1,1,1))].">
      <j1 rule="para" parents="110 397"/>
    </justification>
  </clause>

  <clause id="873">
    <literal><![CDATA[
      L(R(x,y,K(y,L(x,z,u))),z,u) \ (y * L(x,z,u)) = y * K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,94,a(flip),b,400,a)].">
      <j1 rule="hyper" parents="133 94 400"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      L(x / (y * x),z,u) * (y * x) = (L(1 / y,z,u) * y) * x
    ]]></literal>
    <justification jstring="[para(234(a,1),400(a,1,1,1))].">
      <j1 rule="para" parents="234 400"/>
    </justification>
  </clause>

  <clause id="875">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = L(x / (z * y),u,w) * (z * y)
    ]]></literal>
    <justification jstring="[para(303(a,1),400(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="303 400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="877">
    <literal><![CDATA[
      (x * y) * L(L(L(z,y,x),u,w),v5,v6) = x * (y * L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(30(a,1),403(a,1,2,1))].">
      <j1 rule="para" parents="30 403"/>
    </justification>
  </clause>

  <clause id="878">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (x * z),u,w) = x * (y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(102(a,1),403(a,1,2,1))].">
      <j1 rule="para" parents="102 403"/>
    </justification>
  </clause>

  <clause id="879">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(298(a,1),403(a,1,2,1))].">
      <j1 rule="para" parents="298 403"/>
    </justification>
  </clause>

  <clause id="880">
    <literal><![CDATA[
      (x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(544(a,1),403(a,1,2,1))].">
      <j1 rule="para" parents="544 403"/>
    </justification>
  </clause>

  <clause id="882">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(102(a,1),404(a,1,2,1))].">
      <j1 rule="para" parents="102 404"/>
    </justification>
  </clause>

  <clause id="883">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(298(a,1),404(a,1,2,1))].">
      <j1 rule="para" parents="298 404"/>
    </justification>
  </clause>

  <clause id="884">
    <literal><![CDATA[
      (x * y) * R(T(x,x * y),z,u) = x * (y * R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(544(a,1),404(a,1,2,1))].">
      <j1 rule="para" parents="544 404"/>
    </justification>
  </clause>

  <clause id="885">
    <literal><![CDATA[
      ((x / y) * z) * R(((x / y) * z) \ x,u,w) = (x / y) * (z * R(z \ y,u,w))
    ]]></literal>
    <justification jstring="[para(481(a,1),404(a,1,2,1))].">
      <j1 rule="para" parents="481 404"/>
    </justification>
  </clause>

  <clause id="886">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(34,a,667,a,b,464,a(flip))].">
      <j1 rule="hyper" parents="34 667 464"/>
    </justification>
  </clause>

  <clause id="887">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,886,a),flip(a)].">
      <j1 rule="hyper" parents="320 886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="888">
    <literal><![CDATA[
      (1 / x) \ L(L(x,y,z),x,x \ 1) = L(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,257,a,b,886,a),flip(a)].">
      <j1 rule="hyper" parents="316 257 886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="889">
    <literal><![CDATA[
      L(x,y,y \ 1) / (y * x) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(210,a,886,a)].">
      <j1 rule="hyper" parents="210 886"/>
    </justification>
  </clause>

  <clause id="890">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(152,a,886,a)].">
      <j1 rule="hyper" parents="152 886"/>
    </justification>
  </clause>

  <clause id="891">
    <literal><![CDATA[
      L(L(T(x,y),z,u),y,y \ 1) = (1 / y) * (L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,251,a(flip),b,886,a),flip(a)].">
      <j1 rule="hyper" parents="139 251 886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="892">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,114,a(flip),b,886,a),flip(a)].">
      <j1 rule="hyper" parents="139 114 886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="893">
    <literal><![CDATA[
      L(R(x \ y,z,u),x,x \ 1) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(887(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="887 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="894">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,x \ 1) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(887(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="887 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="895">
    <literal><![CDATA[
      x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x
    ]]></literal>
    <justification jstring="[para(887(a,1),599(a,1,2))].">
      <j1 rule="para" parents="887 599"/>
    </justification>
  </clause>

  <clause id="897">
    <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(100(a,1),484(a,2,1,1))].">
      <j1 rule="para" parents="100 484"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(474(a,1),524(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="474 524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="899">
    <literal><![CDATA[
      (x \ 1) * L(1 / x,y,z) = x \ L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(635(a,1),524(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="635 524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="901">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(474(a,1),525(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="474 525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="902">
    <literal><![CDATA[
      (x \ 1) * R(1 / x,y,z) = x \ R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(635(a,1),525(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="635 525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="904">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(355(a,1),532(a,1,2,1))].">
      <j1 rule="para" parents="355 532"/>
    </justification>
  </clause>

  <clause id="905">
    <literal><![CDATA[
      (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(473(a,1),532(a,1,2,1))].">
      <j1 rule="para" parents="473 532"/>
    </justification>
  </clause>

  <clause id="906">
    <literal><![CDATA[
      K(x \ 1,x) * L(1 / x,y,z) = (x \ 1) * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,904,a(flip),b,666,a),flip(a)].">
      <j1 rule="hyper" parents="139 904 666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      R(x / (1 / y),z,u) * (1 / y) = R(x * y,z,u) / y
    ]]></literal>
    <justification jstring="[para(506(a,1),534(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="506 534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="908">
    <literal><![CDATA[
      (x * y) * L(L((x * y) \ z,u,w),v5,v6) = x * (y * L(L(y \ (x \ z),u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(536(a,1),403(a,1,2,1))].">
      <j1 rule="para" parents="536 403"/>
    </justification>
  </clause>

  <clause id="909">
    <literal><![CDATA[
      (1 / x) \ R((1 / x) * y,z,u) = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,550,a(flip),b,273,a)].">
      <j1 rule="hyper" parents="133 550 273"/>
    </justification>
  </clause>

  <clause id="910">
    <literal><![CDATA[
      L((1 / x) * T(x,y),x,y) = L(K(x,y),x,1 / x)
    ]]></literal>
    <justification jstring="[para(715(a,2),551(a,1,1)),flip(a)].">
      <j1 rule="para" parents="715 551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="912">
    <literal><![CDATA[
      ((x \ y) * (x \ y)) * T(y \ x,(x \ y) * (x \ y)) = L(x \ y,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,114,a,b,594,a)].">
      <j1 rule="hyper" parents="63 114 594"/>
    </justification>
  </clause>

  <clause id="913">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(139,a,720,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="139 720 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="914">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y
    ]]></literal>
    <justification jstring="[hyper(138,a,726,a(flip),b,111,a),flip(a)].">
      <j1 rule="hyper" parents="138 726 111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="915">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = (x * y) \ ((z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,259,a,b,737,a),flip(a)].">
      <j1 rule="hyper" parents="316 259 737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="916">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,27,a,b,737,a),flip(a)].">
      <j1 rule="hyper" parents="316 27 737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="917">
    <literal><![CDATA[
      L(T(x,y),y,(y * x) / y) = T(y \ (y * x),y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a,b,816,a)].">
      <j1 rule="hyper" parents="63 25 816"/>
    </justification>
  </clause>

  <clause id="918">
    <literal><![CDATA[
      K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,859,a,b,358,a),flip(a)].">
      <j1 rule="hyper" parents="139 859 358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="919">
    <literal><![CDATA[
      x \ T(y,y / (x * y)) = y * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(133,a,870,a(flip),b,100,a(flip))].">
      <j1 rule="hyper" parents="133 870 100"/>
    </justification>
  </clause>

  <clause id="920">
    <literal><![CDATA[
      R(T(x,y * x),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),916(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="921">
    <literal><![CDATA[
      T(x,y) = (y * x) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,560,a,b,920,a),flip(a)].">
      <j1 rule="hyper" parents="63 560 920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="922">
    <literal><![CDATA[
      (x * y) * T(y,x) = (y * x) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,920,a(flip),b,560,a)].">
      <j1 rule="hyper" parents="139 920 560"/>
    </justification>
  </clause>

  <clause id="924">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),920(a,1,1,2))].">
      <j1 rule="para" parents="12 920"/>
    </justification>
  </clause>

  <clause id="925">
    <literal><![CDATA[
      T(x,1 / x) / x = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(136,a,921,a,b,178,a(flip))].">
      <j1 rule="hyper" parents="136 921 178"/>
    </justification>
  </clause>

  <clause id="926">
    <literal><![CDATA[
      ((x \ 1) * x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(71(a,1),921(a,2,2)),flip(a)].">
      <j1 rule="para" parents="71 921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="927">
    <literal><![CDATA[
      R((x * y) / x,x,T(y,x)) = ((y * x) * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(922(a,1),511(a,2,1))].">
      <j1 rule="para" parents="922 511"/>
    </justification>
  </clause>

  <clause id="928">
    <literal><![CDATA[
      T(x,1 / x) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(316,a,274,a,b,925,a),flip(a)].">
      <j1 rule="hyper" parents="316 274 925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="929">
    <literal><![CDATA[
      K(x \ 1,x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(272(a,2),926(a,1,1))].">
      <j1 rule="para" parents="272 926"/>
    </justification>
  </clause>

  <clause id="931">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,115,a(flip),b,929,a)].">
      <j1 rule="hyper" parents="139 115 929"/>
    </justification>
  </clause>

  <clause id="932">
    <literal><![CDATA[
      K(x,x \ 1) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,530,a(flip),b,929,a)].">
      <j1 rule="hyper" parents="63 530 929"/>
    </justification>
  </clause>

  <clause id="933">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(136,a,929,a(flip),b,530,a(flip))].">
      <j1 rule="hyper" parents="136 929 530"/>
    </justification>
  </clause>

  <clause id="934">
    <literal><![CDATA[
      K(x,x \ 1) * x = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(671,a,931,a)].">
      <j1 rule="hyper" parents="671 931"/>
    </justification>
  </clause>

  <clause id="935">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(138,a,932,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 932 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="936">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(138,a,934,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 934 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="937">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ K(x,x \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[para(934(a,1),357(a,1,1))].">
      <j1 rule="para" parents="934 357"/>
    </justification>
  </clause>

  <clause id="939">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(38,a,339,a,b,937,a)].">
      <j1 rule="hyper" parents="38 339 937"/>
    </justification>
  </clause>

  <clause id="940">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,801,a(flip),b,939,a)].">
      <j1 rule="hyper" parents="63 801 939"/>
    </justification>
  </clause>

  <clause id="941">
    <literal><![CDATA[
      x * K(x,x \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,940,a(flip),b,311,a)].">
      <j1 rule="hyper" parents="139 940 311"/>
    </justification>
  </clause>

  <clause id="942">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / T(y,y \ 1) = R(x / y,y,K(y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(209,a,941,a(flip),b,493,a)].">
      <j1 rule="hyper" parents="209 941 493"/>
    </justification>
  </clause>

  <clause id="943">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = T(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,238,a(flip),b,935,a)].">
      <j1 rule="hyper" parents="63 238 935"/>
    </justification>
  </clause>

  <clause id="944">
    <literal><![CDATA[
      K(x,x \ 1) * L(y,x \ 1,x) = T(x,x \ 1) * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(271(a,1),935(a,1,2))].">
      <j1 rule="para" parents="271 935"/>
    </justification>
  </clause>

  <clause id="945">
    <literal><![CDATA[
      L(T(x,y),y,(y * x) / y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),917(a,2,1))].">
      <j1 rule="para" parents="9 917"/>
    </justification>
  </clause>

  <clause id="946">
    <literal><![CDATA[
      R((x * y) / x,x,T(y,x)) = T(y * x,y) / x
    ]]></literal>
    <justification jstring="[hyper(316,a,863,a(flip),b,927,a),flip(a)].">
      <j1 rule="hyper" parents="316 863 927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="947">
    <literal><![CDATA[
      (x * y) * L(R(T(z,x * y),x,y),u,w) = (L(z,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(316,a,400,a(flip),b,601,a),flip(a)].">
      <j1 rule="hyper" parents="316 400 601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="949">
    <literal><![CDATA[
      (x * (y \ (1 / y))) / z = x / (z * ((1 / y) \ y))
    ]]></literal>
    <justification jstring="[para(446(a,1),684(a,1,2)),flip(a)].">
      <j1 rule="para" parents="446 684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="950">
    <literal><![CDATA[
      (x * (y * z)) * T(((x * y) * L(z,y,x)) \ (x * y),u) = (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u))
    ]]></literal>
    <justification jstring="[para(100(a,1),712(a,1,1))].">
      <j1 rule="para" parents="100 712"/>
    </justification>
  </clause>

  <clause id="951">
    <literal><![CDATA[
      (x * y) * ((1 / z) \ z) = x * (y * ((1 / z) \ z))
    ]]></literal>
    <justification jstring="[para(446(a,1),739(a,1,2)),flip(a)].">
      <j1 rule="para" parents="446 739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="952">
    <literal><![CDATA[
      (x * (y * z)) * ((1 / u) \ u) = x * (y * (z * ((1 / u) \ u)))
    ]]></literal>
    <justification jstring="[para(951(a,1),951(a,2,2))].">
      <j1 rule="para" parents="951 951"/>
    </justification>
  </clause>

  <clause id="953">
    <literal><![CDATA[
      x * T(K(y,z) * R(u / (K(y,z) * x),w,v5),K(y,z) * x) = (K(y,z) * x) * R((K(y,z) * x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,609,a(flip),b,760,a),flip(a)].">
      <j1 rule="hyper" parents="316 609 760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="954">
    <literal><![CDATA[
      R(K(x,y),((1 / z) * u) * w,v5) \ ((((K(x,y) / z) * u) * w) * v5) = (((1 / z) * u) * w) * v5
    ]]></literal>
    <justification jstring="[para(761(a,1),199(a,1,2,1))].">
      <j1 rule="para" parents="761 199"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      (x / y) \ (x * T(x \ (x / y),z)) = y * T(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,792,a)].">
      <j1 rule="hyper" parents="144 792"/>
    </justification>
  </clause>

  <clause id="956">
    <literal><![CDATA[
      K(x,1 / x) * T(K(x,1 / x) \ (K(x,1 / x) / (1 / x)),y) = x * ((1 / x) * T((1 / x) \ 1,y))
    ]]></literal>
    <justification jstring="[para(342(a,1),792(a,1,1)),flip(a)].">
      <j1 rule="para" parents="342 792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="957">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(337(a,1),792(a,1,2))].">
      <j1 rule="para" parents="337 792"/>
    </justification>
  </clause>

  <clause id="958">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,602,a(flip),b,813,a),flip(a)].">
      <j1 rule="hyper" parents="316 602 813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="959">
    <literal><![CDATA[
      L((x * y) * (x \ 1),z,u) = (x * L(y,z,u)) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(138,a,603,a(flip),b,813,a),flip(a)].">
      <j1 rule="hyper" parents="138 603 813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="960">
    <literal><![CDATA[
      K((x * y) \ x,x * y) = y * T(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(34,a,307,a,b,814,a(flip))].">
      <j1 rule="hyper" parents="34 307 814"/>
    </justification>
  </clause>

  <clause id="961">
    <literal><![CDATA[
      K((x * y) \ x,x * y) / y = T(1 / y,x * y)
    ]]></literal>
    <justification jstring="[hyper(136,a,960,a,b,415,a)].">
      <j1 rule="hyper" parents="136 960 415"/>
    </justification>
  </clause>

  <clause id="962">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ z) = z * T(z \ (y * (x \ z)),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,415,a(flip),b,828,a),flip(a)].">
      <j1 rule="hyper" parents="63 415 828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x)
    ]]></literal>
    <justification jstring="[para(415(a,1),831(a,2,1))].">
      <j1 rule="para" parents="415 831"/>
    </justification>
  </clause>

  <clause id="964">
    <literal><![CDATA[
      (x * (y * (z \ 1))) / (z \ 1) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(229(a,1),843(a,1,2)),flip(a)].">
      <j1 rule="para" parents="229 843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="965">
    <literal><![CDATA[
      (x \ 1) \ (x \ L(x * y,z,u)) = L((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,898,a)].">
      <j1 rule="hyper" parents="144 898"/>
    </justification>
  </clause>

  <clause id="966">
    <literal><![CDATA[
      x \ L(x * (y * (x \ 1)),z,u) = L(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,599,a(flip),b,898,a),flip(a)].">
      <j1 rule="hyper" parents="63 599 898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="967">
    <literal><![CDATA[
      L(x * (y * (x \ 1)),z,u) = x * (L(y,z,u) * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(139,a,599,a(flip),b,898,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 599 898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="968">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),898(a,2,2,1))].">
      <j1 rule="para" parents="8 898"/>
    </justification>
  </clause>

  <clause id="969">
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,604,a(flip),b,968,a)].">
      <j1 rule="hyper" parents="63 604 968"/>
    </justification>
  </clause>

  <clause id="971">
    <literal><![CDATA[
      L(x,y,z) \ (x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,968,a(flip),b,604,a(flip))].">
      <j1 rule="hyper" parents="133 968 604"/>
    </justification>
  </clause>

  <clause id="972">
    <literal><![CDATA[
      (x \ 1) * L(T(x,x \ 1),y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(115(a,2),968(a,1,2,1))].">
      <j1 rule="para" parents="115 968"/>
    </justification>
  </clause>

  <clause id="974">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (L(x,y,z) * ((x \ 1) * u)) = L(u,x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(969(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="969 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="975">
    <literal><![CDATA[
      (x \ (y \ z)) \ L(x \ (y \ z),x,y) = ((y * x) \ z) * ((x \ (y \ z)) \ 1)
    ]]></literal>
    <justification jstring="[para(298(a,1),969(a,1,1)),flip(a)].">
      <j1 rule="para" parents="298 969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="976">
    <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(969(a,1),623(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="969 623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="977">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),901(a,2,2,1))].">
      <j1 rule="para" parents="8 901"/>
    </justification>
  </clause>

  <clause id="978">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,611,a(flip),b,977,a)].">
      <j1 rule="hyper" parents="63 611 977"/>
    </justification>
  </clause>

  <clause id="979">
    <literal><![CDATA[
      R(x,y,z) \ (x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,977,a(flip),b,611,a(flip))].">
      <j1 rule="hyper" parents="133 977 611"/>
    </justification>
  </clause>

  <clause id="980">
    <literal><![CDATA[
      R(R(x,y,z) / x,x,x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,563,a,b,978,a)].">
      <j1 rule="hyper" parents="63 563 978"/>
    </justification>
  </clause>

  <clause id="981">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,R(x,y,z)) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,978,a(flip),b,201,a)].">
      <j1 rule="hyper" parents="138 978 201"/>
    </justification>
  </clause>

  <clause id="982">
    <literal><![CDATA[
      L((1 / x) * (y * x),z,u) = (1 / x) * (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(139,a,599,a(flip),b,905,a),flip(a)].">
      <j1 rule="hyper" parents="139 599 905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="983">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ y,z,u) = R(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,609,a(flip),b,907,a)].">
      <j1 rule="hyper" parents="63 609 907"/>
    </justification>
  </clause>

  <clause id="984">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) * (1 / x) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),907(a,2,1,1))].">
      <j1 rule="para" parents="7 907"/>
    </justification>
  </clause>

  <clause id="985">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,612,a(flip),b,984,a)].">
      <j1 rule="hyper" parents="63 612 984"/>
    </justification>
  </clause>

  <clause id="986">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,609,a(flip),b,984,a)].">
      <j1 rule="hyper" parents="63 609 984"/>
    </justification>
  </clause>

  <clause id="987">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),909(a,1,2,1))].">
      <j1 rule="para" parents="8 909"/>
    </justification>
  </clause>

  <clause id="988">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,x,y) = (y / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,623,a,b,987,a),flip(a)].">
      <j1 rule="hyper" parents="316 623 987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="989">
    <literal><![CDATA[
      (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,623,a,b,987,a)].">
      <j1 rule="hyper" parents="139 623 987"/>
    </justification>
  </clause>

  <clause id="990">
    <literal><![CDATA[
      K(x \ 1,x) * R(1 / x,y,z) = (x \ 1) * (x * R(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,987,a(flip),b,666,a),flip(a)].">
      <j1 rule="hyper" parents="139 987 666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="991">
    <literal><![CDATA[
      ((x \ y) / y) / (((x \ y) / (x * (x \ y))) * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(136,a,370,a(flip),b,989,a)].">
      <j1 rule="hyper" parents="136 370 989"/>
    </justification>
  </clause>

  <clause id="992">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) * (y * y) = (y * L(y \ x,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(138,a,958,a(flip),b,567,a),flip(a)].">
      <j1 rule="hyper" parents="138 958 567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="993">
    <literal><![CDATA[
      x * L(x \ (y / (x \ 1)),z,u) = L(y,z,u) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(12(a,1),958(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="994">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ 1) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(71(a,1),959(a,1,1)),flip(a)].">
      <j1 rule="para" parents="71 959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="995">
    <literal><![CDATA[
      (x * ((y * L(y \ 1,z,u)) * y)) / y = (x * L(y \ 1,z,u)) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(994(a,1),964(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="994 964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="996">
    <literal><![CDATA[
      ((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(7(a,1),962(a,2,2,1,2))].">
      <j1 rule="para" parents="7 962"/>
    </justification>
  </clause>

  <clause id="997">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(272(a,2),996(a,1,1))].">
      <j1 rule="para" parents="272 996"/>
    </justification>
  </clause>

  <clause id="998">
    <literal><![CDATA[
      (x \ (y \ x)) * x = (y * T(y \ 1,x)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(7(a,1),963(a,1,1,2))].">
      <j1 rule="para" parents="7 963"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      (T(x,y) * T(T(x,y) \ 1,x \ T(x,y))) * (T(x,y) \ (x \ T(x,y))) = ((x \ T(x,y)) \ (x \ 1)) * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(850(a,1),998(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="850 998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1000">
    <literal><![CDATA[
      L((x \ 1) \ (x \ y),z,u) = (x \ 1) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),965(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1001">
    <literal><![CDATA[
      L(x,y,z) * (x * (L(x,y,z) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,73,a(flip),b,967,a),flip(a)].">
      <j1 rule="hyper" parents="41 73 967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      x * (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(144,a,1001,a),flip(a)].">
      <j1 rule="hyper" parents="144 1001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1003">
    <literal><![CDATA[
      x \ (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1001(a,1),69(a,1,2,2))].">
      <j1 rule="para" parents="1001 69"/>
    </justification>
  </clause>

  <clause id="1004">
    <literal><![CDATA[
      L(x,y,z) * (L(x,u,w) \ 1) = L(x,u,w) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1001(a,1),966(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1001 966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1005">
    <literal><![CDATA[
      R(x / L(x,y,z),L(x,y,z),L(x,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,563,a,b,1002,a)].">
      <j1 rule="hyper" parents="63 563 1002"/>
    </justification>
  </clause>

  <clause id="1006">
    <literal><![CDATA[
      (L(x,y,z) \ 1) / (L(x,y,z) \ x) = R(1 / x,x,L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(209,a,1002,a(flip),b,369,a)].">
      <j1 rule="hyper" parents="209 1002 369"/>
    </justification>
  </clause>

  <clause id="1007">
    <literal><![CDATA[
      ((L(x,y,z) \ x) / x) \ ((L(x,y,z) \ 1) * (x * (L(x,y,z) \ 1))) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(1002(a,1),810(a,1,1,1))].">
      <j1 rule="para" parents="1002 810"/>
    </justification>
  </clause>

  <clause id="1008">
    <literal><![CDATA[
      (L(x,y,z) * T(L(x,y,z) \ 1,x)) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(1003(a,1),998(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1003 998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1009">
    <literal><![CDATA[
      (1 / x) * (L(x \ 1,y,z) * x) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(796(a,1),982(a,1,1)),flip(a)].">
      <j1 rule="para" parents="796 982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1010">
    <literal><![CDATA[
      (x * y) \ x = (1 / y) * (L(y \ 1,y,x) * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,232,a(flip),b,1009,a)].">
      <j1 rule="hyper" parents="316 232 1009"/>
    </justification>
  </clause>

  <clause id="1011">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) * (x \ y) = (1 / (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,356,a(flip),b,1009,a),flip(a)].">
      <j1 rule="hyper" parents="133 356 1009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      ((x \ y) / y) / (((x \ y) / y) * x) = 1 / x
    ]]></literal>
    <justification jstring="[para(10(a,1),991(a,1,2,1,2))].">
      <j1 rule="para" parents="10 991"/>
    </justification>
  </clause>

  <clause id="1013">
    <literal><![CDATA[
      (1 / x) \ ((x \ y) / y) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(204,a,1012,a)].">
      <j1 rule="hyper" parents="204 1012"/>
    </justification>
  </clause>

  <clause id="1014">
    <literal><![CDATA[
      K(x \ (x / y),x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,716,a,b,542,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 716 542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1015">
    <literal><![CDATA[
      x * ((x \ y) * L((x \ y) \ 1,z,u)) = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(356(a,1),693(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="356 693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1016">
    <literal><![CDATA[
      x * ((x \ y) * L((x \ y) \ z,u,w)) = y * L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(475(a,1),693(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="475 693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1017">
    <literal><![CDATA[
      (x / y) * (y * R(y \ 1,z,u)) = x * R(x \ (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(363(a,1),695(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="363 695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1018">
    <literal><![CDATA[
      L(R(x / (y / z),y / z,z),u,w) * y = ((y / z) * L((y / z) \ x,u,w)) * z
    ]]></literal>
    <justification jstring="[para(602(a,1),702(a,2,1))].">
      <j1 rule="para" parents="602 702"/>
    </justification>
  </clause>

  <clause id="1020">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(722(a,1),456(a,1,2,2))].">
      <j1 rule="para" parents="722 456"/>
    </justification>
  </clause>

  <clause id="1021">
    <literal><![CDATA[
      L(((x * y) * T(z,y)) / (x * y),y,x) = (x * (z * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(114(a,1),752(a,2,1,2))].">
      <j1 rule="para" parents="114 752"/>
    </justification>
  </clause>

  <clause id="1022">
    <literal><![CDATA[
      ((x * y) * z) / (y * ((z \ 1) * (z * z))) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(32(a,1),759(a,1,2))].">
      <j1 rule="para" parents="32 759"/>
    </justification>
  </clause>

  <clause id="1023">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[para(232(a,1),767(a,1,2,1,2))].">
      <j1 rule="para" parents="232 767"/>
    </justification>
  </clause>

  <clause id="1024">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(102(a,1),767(a,1,2,1,2))].">
      <j1 rule="para" parents="102 767"/>
    </justification>
  </clause>

  <clause id="1025">
    <literal><![CDATA[
      (x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z)
    ]]></literal>
    <justification jstring="[hyper(139,a,768,a(flip),b,103,a),flip(a)].">
      <j1 rule="hyper" parents="139 768 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1027">
    <literal><![CDATA[
      R(T(x / y,z * y),y,T(z,y)) = (z * y) \ (x * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,27,a,b,788,a)].">
      <j1 rule="hyper" parents="63 27 788"/>
    </justification>
  </clause>

  <clause id="1028">
    <literal><![CDATA[
      R(K(x,y) * z,u,w) = K(x,y) * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,661,a(flip),b,841,a),flip(a)].">
      <j1 rule="hyper" parents="63 661 841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      R(K(x,y) * z,u,w) * v5 = K(x,y) * (R(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(138,a,1028,a,b,410,a)].">
      <j1 rule="hyper" parents="138 1028 410"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      K(x \ 1,x) * R(1 / x,y,z) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(436(a,1),1028(a,1,1)),flip(a)].">
      <j1 rule="para" parents="436 1028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1031">
    <literal><![CDATA[
      T(R(K(x,y) * z,u,w),K(x,y)) = R(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(1028(a,2),471(a,1,1))].">
      <j1 rule="para" parents="1028 471"/>
    </justification>
  </clause>

  <clause id="1032">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(229(a,1),1022(a,1,2,2))].">
      <j1 rule="para" parents="229 1022"/>
    </justification>
  </clause>

  <clause id="1033">
    <literal><![CDATA[
      R(x,y,z \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,20,a,b,1032,a),flip(a)].">
      <j1 rule="hyper" parents="63 20 1032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1034">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1033,a(flip),b,1033,a),flip(a)].">
      <j1 rule="hyper" parents="316 1033 1033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1035">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,565,a,b,1033,a)].">
      <j1 rule="hyper" parents="63 565 1033"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      R(x / y,y,z) = (x * (z \ 1)) / (y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,110,a(flip),b,1033,a),flip(a)].">
      <j1 rule="hyper" parents="63 110 1033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1037">
    <literal><![CDATA[
      R(x,x \ 1,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(131,a,568,a(flip),b,1033,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 568 1033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1038">
    <literal><![CDATA[
      R(x,y,1 / z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),1033(a,1,3)),flip(a)].">
      <j1 rule="para" parents="83 1033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1039">
    <literal><![CDATA[
      R(x / y,y,1 / y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,563,a(flip),b,1038,a),flip(a)].">
      <j1 rule="hyper" parents="316 563 1038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      R(1 / x,x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(131,a,563,a(flip),b,1038,a),flip(a)].">
      <j1 rule="hyper" parents="131 563 1038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1041">
    <literal><![CDATA[
      (x * (y \ 1)) * T(y,y \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(115(a,2),1035(a,1,2))].">
      <j1 rule="para" parents="115 1035"/>
    </justification>
  </clause>

  <clause id="1042">
    <literal><![CDATA[
      R(x,y,y) * ((y \ 1) \ 1) = R(x * y,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(565(a,1),1035(a,1,1))].">
      <j1 rule="para" parents="565 1035"/>
    </justification>
  </clause>

  <clause id="1043">
    <literal><![CDATA[
      R(x,y,y) * T(y,y \ 1) = R(x * y,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(565(a,1),1041(a,1,1))].">
      <j1 rule="para" parents="565 1041"/>
    </justification>
  </clause>

  <clause id="1044">
    <literal><![CDATA[
      R(T((x * y) / x,y * x),x,T(y,x)) = (y * x) \ ((y * x) * y)
    ]]></literal>
    <justification jstring="[para(922(a,1),1027(a,2,2))].">
      <j1 rule="para" parents="922 1027"/>
    </justification>
  </clause>

  <clause id="1045">
    <literal><![CDATA[
      (x * K(y,z)) \ (K(y,z) * x) = K(K(y,z),K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,477,a(flip),b,650,a)].">
      <j1 rule="hyper" parents="63 477 650"/>
    </justification>
  </clause>

  <clause id="1046">
    <literal><![CDATA[
      K(K(x,y),K(x,y) * z) = K(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(329,a,1045,a),flip(a)].">
      <j1 rule="hyper" parents="329 1045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1047">
    <literal><![CDATA[
      (x * (y * z)) * R(((x * y) * L(z,y,x)) \ (x * y),u,w) = (x * y) * (L(z,y,x) * R(L(z,y,x) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(100(a,1),775(a,1,1))].">
      <j1 rule="para" parents="100 775"/>
    </justification>
  </clause>

  <clause id="1048">
    <literal><![CDATA[
      L(x \ 1,y,z) * (x * x) = x * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,607,a(flip),b,777,a)].">
      <j1 rule="hyper" parents="63 607 777"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = (z * y) * T((z * y) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,415,a(flip),b,779,a),flip(a)].">
      <j1 rule="hyper" parents="316 415 779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1051">
    <literal><![CDATA[
      (1 / x) \ T(((1 / x) * x) \ y,z) = x * T(x \ ((1 / x) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(133,a,81,a(flip),b,781,a(flip))].">
      <j1 rule="hyper" parents="133 81 781"/>
    </justification>
  </clause>

  <clause id="1052">
    <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(272(a,2),781(a,1,1))].">
      <j1 rule="para" parents="272 781"/>
    </justification>
  </clause>

  <clause id="1053">
    <literal><![CDATA[
      L(x,y,z) * ((x \ 1) * T((x \ 1) \ (L(x,y,z) \ u),w)) = (x \ L(x,y,z)) * T((L(x,y,z) * (x \ 1)) \ u,w)
    ]]></literal>
    <justification jstring="[para(969(a,1),781(a,1,1)),flip(a)].">
      <j1 rule="para" parents="969 781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1054">
    <literal><![CDATA[
      x * ((L(x,y,z) \ 1) * T((L(x,y,z) \ 1) \ (x \ u),w)) = (L(x,y,z) \ x) * T((x * (L(x,y,z) \ 1)) \ u,w)
    ]]></literal>
    <justification jstring="[para(1002(a,1),781(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1002 781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1055">
    <literal><![CDATA[
      T(x * (y * (z \ 1)),z * z) = (z * z) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(229(a,1),833(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="229 833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1056">
    <literal><![CDATA[
      (x * (y * (z * (u * u)))) / (w * (u * u)) = (x * (y * z)) / w
    ]]></literal>
    <justification jstring="[hyper(209,a,207,a(flip),b,837,a)].">
      <j1 rule="hyper" parents="209 207 837"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * (u * u)))) = L(z,y,x) * (u * u)
    ]]></literal>
    <justification jstring="[para(18(a,2),837(a,2,1))].">
      <j1 rule="para" parents="18 837"/>
    </justification>
  </clause>

  <clause id="1058">
    <literal><![CDATA[
      L(x * (y * y),z,u) = L(x,z,u) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,18,a,b,1057,a)].">
      <j1 rule="hyper" parents="63 18 1057"/>
    </justification>
  </clause>

  <clause id="1059">
    <literal><![CDATA[
      L(R(x,y,y) * (y * y),z,u) = (L(x,z,u) * y) * y
    ]]></literal>
    <justification jstring="[hyper(316,a,400,a(flip),b,1058,a),flip(a)].">
      <j1 rule="hyper" parents="316 400 1058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1060">
    <literal><![CDATA[
      x \ L(y * (z * z),u,w) = (x \ L(y,u,w)) * (z * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,1058,a,b,124,a)].">
      <j1 rule="hyper" parents="133 1058 124"/>
    </justification>
  </clause>

  <clause id="1061">
    <literal><![CDATA[
      L(x * ((1 / y) * (1 / y)),z,u) = L(x,z,u) * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[para(287(a,1),1058(a,2,2))].">
      <j1 rule="para" parents="287 1058"/>
    </justification>
  </clause>

  <clause id="1062">
    <literal><![CDATA[
      L((x * y) * y,z,u) = (L(x,z,u) * y) * y
    ]]></literal>
    <justification jstring="[para(109(a,1),1059(a,1,1))].">
      <j1 rule="para" parents="109 1059"/>
    </justification>
  </clause>

  <clause id="1063">
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,959,a(flip),b,1062,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 959 1062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1064">
    <literal><![CDATA[
      x * L(x \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,969,a(flip),b,1063,a),flip(a)].">
      <j1 rule="hyper" parents="63 969 1063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1065">
    <literal><![CDATA[
      x \ (x \ L(x,y,z)) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,969,a(flip),b,1063,a(flip))].">
      <j1 rule="hyper" parents="133 969 1063"/>
    </justification>
  </clause>

  <clause id="1066">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,904,a,b,1064,a)].">
      <j1 rule="hyper" parents="63 904 1064"/>
    </justification>
  </clause>

  <clause id="1067">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,968,a(flip),b,1064,a),flip(a)].">
      <j1 rule="hyper" parents="63 968 1064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1068">
    <literal><![CDATA[
      (x * y) \ L(x * y,y,x) = x * (y * ((x * y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,100,a(flip),b,1064,a),flip(a)].">
      <j1 rule="hyper" parents="63 100 1064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1070">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ 1) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1064(a,1),994(a,1,1))].">
      <j1 rule="para" parents="1064 994"/>
    </justification>
  </clause>

  <clause id="1071">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1064,a,b,1067,a),flip(a)].">
      <j1 rule="hyper" parents="316 1064 1067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1072">
    <literal><![CDATA[
      x \ L(x * L(x \ 1,y,z),u,w) = (x \ 1) * L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1067(a,1),898(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1067 898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      T(x,L(x \ 1,y,z)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(253,a,1071,a(flip),b,969,a)].">
      <j1 rule="hyper" parents="253 1071 969"/>
    </justification>
  </clause>

  <clause id="1074">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,x \ y,x) = ((x \ y) \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(356(a,1),1071(a,1,2)),flip(a)].">
      <j1 rule="para" parents="356 1071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1075">
    <literal><![CDATA[
      (x \ 1) * L(x * L(x \ 1,y,z),u,w) = x \ L(x * L(x \ 1,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1071(a,1),898(a,1,2,1))].">
      <j1 rule="para" parents="1071 898"/>
    </justification>
  </clause>

  <clause id="1076">
    <literal><![CDATA[
      T(x,(y * x) \ y) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(232(a,1),1073(a,1,2))].">
      <j1 rule="para" parents="232 1073"/>
    </justification>
  </clause>

  <clause id="1077">
    <literal><![CDATA[
      T(x,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(355(a,1),1073(a,1,2))].">
      <j1 rule="para" parents="355 1073"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      T(x \ y,y \ x) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(356(a,1),1073(a,1,2))].">
      <j1 rule="para" parents="356 1073"/>
    </justification>
  </clause>

  <clause id="1079">
    <literal><![CDATA[
      T(x,1 / x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,115,a,b,1077,a),flip(a)].">
      <j1 rule="hyper" parents="316 115 1077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1081">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(1079(a,1),928(a,1,1))].">
      <j1 rule="para" parents="1079 928"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      T(x,(y * x) \ y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,115,a,b,1076,a),flip(a)].">
      <j1 rule="hyper" parents="316 115 1076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      K(x,1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,933,a(flip),b,1081,a),flip(a)].">
      <j1 rule="hyper" parents="63 933 1081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1084">
    <literal><![CDATA[
      (1 / (1 / x)) \ x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,806,a,b,1083,a)].">
      <j1 rule="hyper" parents="63 806 1083"/>
    </justification>
  </clause>

  <clause id="1085">
    <literal><![CDATA[
      K(x,x \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,274,a(flip),b,1083,a),flip(a)].">
      <j1 rule="hyper" parents="63 274 1083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1086">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(138,a,1083,a(flip),b,438,a)].">
      <j1 rule="hyper" parents="138 1083 438"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      x \ K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(133,a,1083,a(flip),b,274,a(flip))].">
      <j1 rule="hyper" parents="133 1083 274"/>
    </justification>
  </clause>

  <clause id="1088">
    <literal><![CDATA[
      K(x,x \ 1) \ x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(1083(a,1),440(a,1,1))].">
      <j1 rule="para" parents="1083 440"/>
    </justification>
  </clause>

  <clause id="1089">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / ((1 / x) * y) = R(x,1 / x,y)
    ]]></literal>
    <justification jstring="[para(1085(a,2),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1085 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1090">
    <literal><![CDATA[
      L(x \ (1 / y),x,y) = (y * x) \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(1085(a,2),102(a,2,2))].">
      <j1 rule="para" parents="1085 102"/>
    </justification>
  </clause>

  <clause id="1091">
    <literal><![CDATA[
      K(x,x \ 1) * y != x * ((1 / x) * z)
    ]]></literal>
    <literal><![CDATA[
      L(z,1 / x,x) = y
    ]]></literal>
    <justification jstring="[para(1085(a,2),463(a,1,1))].">
      <j1 rule="para" parents="1085 463"/>
    </justification>
  </clause>

  <clause id="1092">
    <literal><![CDATA[
      T((x * y) \ (K(x,x \ 1) * y),x) = R(T(1 / x,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(1085(a,2),916(a,1,1,2,1))].">
      <j1 rule="para" parents="1085 916"/>
    </justification>
  </clause>

  <clause id="1093">
    <literal><![CDATA[
      K(x \ 1,x) * x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(670,a,1086,a)].">
      <j1 rule="hyper" parents="670 1086"/>
    </justification>
  </clause>

  <clause id="1094">
    <literal><![CDATA[
      x * ((1 / (1 / x)) \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(138,a,1086,a(flip),b,478,a)].">
      <j1 rule="hyper" parents="138 1086 478"/>
    </justification>
  </clause>

  <clause id="1095">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(138,a,1086,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 1086 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1096">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(138,a,1093,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 1093 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1097">
    <literal><![CDATA[
      (1 / (1 / x)) * (x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(138,a,1093,a(flip),b,378,a)].">
      <j1 rule="hyper" parents="138 1093 378"/>
    </justification>
  </clause>

  <clause id="1098">
    <literal><![CDATA[
      T(x \ (x / y),y) = ((x \ (x / y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(83(a,1),1078(a,1,2))].">
      <j1 rule="para" parents="83 1078"/>
    </justification>
  </clause>

  <clause id="1099">
    <literal><![CDATA[
      T(x / y,x \ y) = (y * (((y \ x) \ 1) \ 1)) / y
    ]]></literal>
    <justification jstring="[para(1078(a,1),420(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1078 420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1100">
    <literal><![CDATA[
      T(1 / (1 / x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(253,a,1097,a,b,272,a(flip))].">
      <j1 rule="hyper" parents="253 1097 272"/>
    </justification>
  </clause>

  <clause id="1101">
    <literal><![CDATA[
      T(T(1 / (1 / x),y),x \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1100(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1100 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1102">
    <literal><![CDATA[
      T(1 / (1 / x),(y * x) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,1082,a(flip),b,1101,a),flip(a)].">
      <j1 rule="hyper" parents="40 1082 1101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1103">
    <literal><![CDATA[
      (((x * y) \ x) * y) / ((x * y) \ x) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(285,a,1102,a)].">
      <j1 rule="hyper" parents="285 1102"/>
    </justification>
  </clause>

  <clause id="1104">
    <literal><![CDATA[
      (x * y) \ (K(x,x \ 1) * z) = ((1 / (1 / x)) * y) \ z
    ]]></literal>
    <justification jstring="[para(1095(a,1),477(a,1,1))].">
      <j1 rule="para" parents="1095 477"/>
    </justification>
  </clause>

  <clause id="1105">
    <literal><![CDATA[
      K(x,x \ 1) * K(L(y \ (1 / x),y,x),x * y) = ((x * y) \ K(x,x \ 1)) * (x * y)
    ]]></literal>
    <justification jstring="[para(1090(a,2),307(a,1,2,1))].">
      <j1 rule="para" parents="1090 307"/>
    </justification>
  </clause>

  <clause id="1106">
    <literal><![CDATA[
      K(x,x \ 1) * (y / ((1 / x) * y)) = R(x,1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,660,a(flip),b,1089,a)].">
      <j1 rule="hyper" parents="63 660 1089"/>
    </justification>
  </clause>

  <clause id="1107">
    <literal><![CDATA[
      (x \ L(y / (z * z),u,w)) * (z * z) = x \ L(y,u,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),1060(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 1060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1108">
    <literal><![CDATA[
      (x \ L(y \ 1,z,u)) * (y * y) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(229(a,1),1060(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="229 1060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1109">
    <literal><![CDATA[
      x \ L(L(y * (z * z),u,w),v5,v6) = (x \ L(L(y,u,w),v5,v6)) * (z * z)
    ]]></literal>
    <justification jstring="[para(1058(a,2),1060(a,1,2,1))].">
      <j1 rule="para" parents="1058 1060"/>
    </justification>
  </clause>

  <clause id="1110">
    <literal><![CDATA[
      L(x,y,z) / (x * x) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(209,a,182,a(flip),b,1108,a(flip))].">
      <j1 rule="hyper" parents="209 182 1108"/>
    </justification>
  </clause>

  <clause id="1112">
    <literal><![CDATA[
      L(x / (y * y),z,u) = L(x,z,u) / (y * y)
    ]]></literal>
    <justification jstring="[hyper(209,a,182,a(flip),b,1107,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="209 182 1107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1113">
    <literal><![CDATA[
      (x * x) * L((x * x) \ y,z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(37,a,619,a,b,1112,a(flip))].">
      <j1 rule="hyper" parents="37 619 1112"/>
    </justification>
  </clause>

  <clause id="1114">
    <literal><![CDATA[
      L((x * x) * y,x,x) = x * (x * y)
    ]]></literal>
    <justification jstring="[hyper(37,a,752,a(flip),b,1112,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="37 752 1112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1115">
    <literal><![CDATA[
      L((x * x) * y,z,u) = (x * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(37,a,751,a(flip),b,1112,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="37 751 1112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1116">
    <literal><![CDATA[
      x * (x * ((x * x) \ y)) = L(y,x,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),1114(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 1114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1117">
    <literal><![CDATA[
      L(L((x * x) * y,z,u),x,x) = L(x * (x * y),z,u)
    ]]></literal>
    <justification jstring="[para(1114(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1114 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1118">
    <literal><![CDATA[
      x * ((x * x) \ y) = x \ L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,1116,a),flip(a)].">
      <j1 rule="hyper" parents="144 1116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1120">
    <literal><![CDATA[
      L((x * x) \ y,z,u) = (x * x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,1113,a),flip(a)].">
      <j1 rule="hyper" parents="144 1113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1122">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (L(1 / x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,602,a(flip),b,874,a)].">
      <j1 rule="hyper" parents="63 602 874"/>
    </justification>
  </clause>

  <clause id="1123">
    <literal><![CDATA[
      x * (y * L(T(x,y),z,u)) = L(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,251,a(flip),b,880,a),flip(a)].">
      <j1 rule="hyper" parents="63 251 880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1124">
    <literal><![CDATA[
      L(x,y,z) * (x * u) = x * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,412,a(flip),b,1123,a),flip(a)].">
      <j1 rule="hyper" parents="63 412 1123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(133,a,412,a(flip),b,1123,a(flip))].">
      <j1 rule="hyper" parents="133 412 1123"/>
    </justification>
  </clause>

  <clause id="1126">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(543,a,1124,a)].">
      <j1 rule="hyper" parents="543 1124"/>
    </justification>
  </clause>

  <clause id="1127">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(323,a,1124,a),flip(a)].">
      <j1 rule="hyper" parents="323 1124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1128">
    <literal><![CDATA[
      L(x,y,z) * (x * (L(x,y,z) \ u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(316,a,160,a(flip),b,1124,a),flip(a)].">
      <j1 rule="hyper" parents="316 160 1124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1129">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,160,a(flip),b,1124,a)].">
      <j1 rule="hyper" parents="133 160 1124"/>
    </justification>
  </clause>

  <clause id="1130">
    <literal><![CDATA[
      x * (L(x,y,z) \ (x \ u)) = L(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(133,a,76,a(flip),b,1124,a),flip(a)].">
      <j1 rule="hyper" parents="133 76 1124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1131">
    <literal><![CDATA[
      L(x,y,z) * (x \ (L(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(133,a,76,a(flip),b,1124,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 76 1124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1132">
    <literal><![CDATA[
      x * (L(x,y,z) * (L(x,u,w) \ 1)) = L(x,y,z) * (L(x,u,w) \ x)
    ]]></literal>
    <justification jstring="[para(1002(a,1),1124(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1002 1124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1133">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (x * (L(x,y,z) * u)) = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1124(a,1),418(a,1,2))].">
      <j1 rule="para" parents="1124 418"/>
    </justification>
  </clause>

  <clause id="1134">
    <literal><![CDATA[
      x * (L(x,y,z) * L(x \ 1,u,w)) = L(x,y,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(1064(a,1),1124(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1064 1124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1135">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(u,x \ L(x,y,z),x)) = (x \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,456,a(flip),b,1126,a),flip(a)].">
      <j1 rule="hyper" parents="63 456 1126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * u) = L(x,y,z) * (x \ (u * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,388,a(flip),b,1126,a)].">
      <j1 rule="hyper" parents="63 388 1126"/>
    </justification>
  </clause>

  <clause id="1137">
    <literal><![CDATA[
      L(x,y,z) \ (x \ u) = x \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,168,a(flip),b,1126,a(flip))].">
      <j1 rule="hyper" parents="133 168 1126"/>
    </justification>
  </clause>

  <clause id="1139">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,u,w) * (x \ v5))) = L(x,y,z) \ (L(x,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(133,a,1127,a(flip),b,1128,a),flip(a)].">
      <j1 rule="hyper" parents="133 1127 1128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1140">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,u,w) \ 1)) = L(x,y,z) \ (L(x,u,w) \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,1002,a(flip),b,1128,a),flip(a)].">
      <j1 rule="hyper" parents="133 1002 1128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1141">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((x \ 1) * u)) = L(x,y,z) \ L(u,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,271,a(flip),b,1128,a),flip(a)].">
      <j1 rule="hyper" parents="133 271 1128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1142">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((x \ L(x,y,z)) * u)) = L(u,x \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(34,a,405,a,b,1128,a),flip(a)].">
      <j1 rule="hyper" parents="34 405 1128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1143">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ (L(x,u,w) * v5) = L(x,u,w) * (L(L(x,u,w),y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(34,a,398,a,b,1128,a)].">
      <j1 rule="hyper" parents="34 398 1128"/>
    </justification>
  </clause>

  <clause id="1144">
    <literal><![CDATA[
      (x * y) * L(z,x * (L(x,u,w) \ y),L(x,u,w)) = L(x,u,w) * ((x * (L(x,u,w) \ y)) * z)
    ]]></literal>
    <justification jstring="[hyper(138,a,1128,a(flip),b,202,a)].">
      <j1 rule="hyper" parents="138 1128 202"/>
    </justification>
  </clause>

  <clause id="1145">
    <literal><![CDATA[
      x * (L(x,1 / x,x) \ y) = (1 / (1 / x)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(557(a,1),1129(a,1,1)),flip(a)].">
      <j1 rule="para" parents="557 1129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1146">
    <literal><![CDATA[
      x * (y * (L(y,z,u) \ ((y \ L(y,z,u)) \ 1))) = x / ((y \ L(y,z,u)) * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(1129(a,1),844(a,1,2))].">
      <j1 rule="para" parents="1129 844"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      (1 / (1 / x)) \ (x * y) = x * ((1 / (1 / x)) \ y)
    ]]></literal>
    <justification jstring="[para(557(a,1),1145(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="557 1145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      (1 / (1 / x)) * (K(x,x \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(139,a,1094,a(flip),b,1149,a)].">
      <j1 rule="hyper" parents="139 1094 1149"/>
    </justification>
  </clause>

  <clause id="1151">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(133,a,10,a(flip),b,1150,a),flip(a)].">
      <j1 rule="hyper" parents="133 10 1150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1152">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1150(a,1),1095(a,1,2))].">
      <j1 rule="para" parents="1150 1095"/>
    </justification>
  </clause>

  <clause id="1153">
    <literal><![CDATA[
      x * (K(x,x \ 1) * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,935,a(flip),b,1152,a),flip(a)].">
      <j1 rule="hyper" parents="63 935 1152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1155">
    <literal><![CDATA[
      K(x,x \ 1) * (T(x,x \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(133,a,10,a(flip),b,1153,a),flip(a)].">
      <j1 rule="hyper" parents="133 10 1153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1156">
    <literal><![CDATA[
      T(x,x \ 1) * ((x \ 1) * y) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(772(a,1),1153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="772 1153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1157">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[para(115(a,1),1155(a,1,2,1))].">
      <j1 rule="para" parents="115 1155"/>
    </justification>
  </clause>

  <clause id="1158">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(670,a,1157,a)].">
      <j1 rule="hyper" parents="670 1157"/>
    </justification>
  </clause>

  <clause id="1159">
    <literal><![CDATA[
      T(x \ (y \ x),y) = x \ (((y \ 1) \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,1158,a(flip),b,997,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 1158 997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1160">
    <literal><![CDATA[
      x * (y * R(T(x,y),x,y)) = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,608,a(flip),b,884,a),flip(a)].">
      <j1 rule="hyper" parents="63 608 884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1161">
    <literal><![CDATA[
      x * (y * R(T(x,y),z,u)) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,252,a(flip),b,884,a),flip(a)].">
      <j1 rule="hyper" parents="63 252 884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1163">
    <literal><![CDATA[
      x * (R(x,x,y) * y) = (x * x) * y
    ]]></literal>
    <justification jstring="[para(252(a,1),1160(a,1,2))].">
      <j1 rule="para" parents="252 1160"/>
    </justification>
  </clause>

  <clause id="1164">
    <literal><![CDATA[
      x \ ((x * x) * y) = R(x,x,y) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,1163,a)].">
      <j1 rule="hyper" parents="144 1163"/>
    </justification>
  </clause>

  <clause id="1165">
    <literal><![CDATA[
      R(x,x,(x * x) \ y) * ((x * x) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(133,a,10,a(flip),b,1163,a),flip(a)].">
      <j1 rule="hyper" parents="133 10 1163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1166">
    <literal><![CDATA[
      R(x,y,z) * (x * u) = x * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(252(a,1),1161(a,1,2)),flip(a)].">
      <j1 rule="para" parents="252 1161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1167">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(543,a,1166,a)].">
      <j1 rule="hyper" parents="543 1166"/>
    </justification>
  </clause>

  <clause id="1169">
    <literal><![CDATA[
      R(x,y,z) \ (x * u) = x * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,160,a(flip),b,1166,a)].">
      <j1 rule="hyper" parents="133 160 1166"/>
    </justification>
  </clause>

  <clause id="1170">
    <literal><![CDATA[
      x * (R(x,y,z) \ (x \ u)) = R(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(133,a,76,a(flip),b,1166,a),flip(a)].">
      <j1 rule="hyper" parents="133 76 1166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1171">
    <literal><![CDATA[
      x * (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,73,a(flip),b,1166,a),flip(a)].">
      <j1 rule="hyper" parents="133 73 1166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1172">
    <literal><![CDATA[
      x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,238,a(flip),b,1166,a),flip(a)].">
      <j1 rule="hyper" parents="63 238 1166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1173">
    <literal><![CDATA[
      (R(x,y,z) * u) \ (x * (R(x,y,z) * u)) = L(T(x,u),u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1166(a,1),247(a,1,2))].">
      <j1 rule="para" parents="1166 247"/>
    </justification>
  </clause>

  <clause id="1174">
    <literal><![CDATA[
      R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(109(a,1),1167(a,1,2)),flip(a)].">
      <j1 rule="para" parents="109 1167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      R(x,y,z) = (x \ ((x * y) * z)) / (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(149,a,1174,a),flip(a)].">
      <j1 rule="hyper" parents="149 1174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1177">
    <literal><![CDATA[
      R(x,y,x) * T(y,x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(253,a,109,a(flip),b,1172,a),flip(a)].">
      <j1 rule="hyper" parents="253 109 1172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1180">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),913(a,2,2,1,2))].">
      <j1 rule="para" parents="8 913"/>
    </justification>
  </clause>

  <clause id="1181">
    <literal><![CDATA[
      x * T(x \ (y * x),z) = y * (T(y,z) * (y \ x))
    ]]></literal>
    <justification jstring="[para(416(a,1),913(a,1,2)),flip(a)].">
      <j1 rule="para" parents="416 913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1182">
    <literal><![CDATA[
      x * (T(x,y) * (x \ z)) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,414,a(flip),b,1181,a),flip(a)].">
      <j1 rule="hyper" parents="63 414 1181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1183">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) = x \ z
    ]]></literal>
    <justification jstring="[hyper(133,a,10,a(flip),b,1182,a),flip(a)].">
      <j1 rule="hyper" parents="133 10 1182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1184">
    <literal><![CDATA[
      T(x,y) * (x * z) = x * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1182(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1185">
    <literal><![CDATA[
      x * (T(x,y) * T(z,x)) = T(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(22(a,2),1182(a,1,2,2))].">
      <j1 rule="para" parents="22 1182"/>
    </justification>
  </clause>

  <clause id="1186">
    <literal><![CDATA[
      (x / y) * (T(x / y,z) * y) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(83(a,1),1182(a,1,2,2))].">
      <j1 rule="para" parents="83 1182"/>
    </justification>
  </clause>

  <clause id="1187">
    <literal><![CDATA[
      x \ (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,67,a(flip),b,1183,a),flip(a)].">
      <j1 rule="hyper" parents="133 67 1183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1188">
    <literal><![CDATA[
      x * (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(152,a,1187,a)].">
      <j1 rule="hyper" parents="152 1187"/>
    </justification>
  </clause>

  <clause id="1189">
    <literal><![CDATA[
      T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1187(a,1),793(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1187 793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1190">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,x \ 1) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(1187(a,1),887(a,1,1))].">
      <j1 rule="para" parents="1187 887"/>
    </justification>
  </clause>

  <clause id="1191">
    <literal><![CDATA[
      (T(x,y) * T(T(x,y) \ 1,x)) * (T(x,y) \ x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(1187(a,1),998(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1187 998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1192">
    <literal><![CDATA[
      L(x,T(x,y) \ 1,T(x,y)) * (T(x,y) \ 1) = (T(x,y) \ 1) * (T(x,y) * (T(x,y) \ x))
    ]]></literal>
    <justification jstring="[para(1188(a,1),745(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1188 745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1194">
    <literal><![CDATA[
      (x * y) / (x * (T(x,z) \ y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(136,a,160,a(flip),b,1184,a)].">
      <j1 rule="hyper" parents="136 160 1184"/>
    </justification>
  </clause>

  <clause id="1196">
    <literal><![CDATA[
      (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(116(a,1),1184(a,1,1)),flip(a)].">
      <j1 rule="para" parents="116 1184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,280,a,b,1194,a),flip(a)].">
      <j1 rule="hyper" parents="36 280 1194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1198">
    <literal><![CDATA[
      (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(415(a,1),1186(a,1,2))].">
      <j1 rule="para" parents="415 1186"/>
    </justification>
  </clause>

  <clause id="1199">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z)
    ]]></literal>
    <justification jstring="[para(1014(a,2),1180(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1014 1180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1200">
    <literal><![CDATA[
      K(x \ (x / (y \ z)),x) = y \ (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(133,a,1199,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="133 1199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1201">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(z \ (z / (x \ (x / y))),z)
    ]]></literal>
    <justification jstring="[para(83(a,1),1199(a,1,2,1))].">
      <j1 rule="para" parents="83 1199"/>
    </justification>
  </clause>

  <clause id="1202">
    <literal><![CDATA[
      K((x * (y \ z)) \ x,x * (y \ z)) = y \ (z * T(z \ y,x * (y \ z)))
    ]]></literal>
    <justification jstring="[para(11(a,1),1200(a,1,1,2))].">
      <j1 rule="para" parents="11 1200"/>
    </justification>
  </clause>

  <clause id="1203">
    <literal><![CDATA[
      (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(116(a,1),1196(a,1,2,1))].">
      <j1 rule="para" parents="116 1196"/>
    </justification>
  </clause>

  <clause id="1204">
    <literal><![CDATA[
      (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(240(a,1),1196(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="240 1196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1205">
    <literal><![CDATA[
      (x \ y) * ((y / x) * ((x \ y) \ z)) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(323,a,1203,a),flip(a)].">
      <j1 rule="hyper" parents="323 1203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1207">
    <literal><![CDATA[
      (1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(764(a,1),1205(a,1,2)),flip(a)].">
      <j1 rule="para" parents="764 1205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1208">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(771(a,1),1205(a,1,2))].">
      <j1 rule="para" parents="771 1205"/>
    </justification>
  </clause>

  <clause id="1209">
    <literal><![CDATA[
      (1 / x) \ ((x \ 1) * y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,1207,a)].">
      <j1 rule="hyper" parents="144 1207"/>
    </justification>
  </clause>

  <clause id="1210">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * R((1 / x) \ y,z,u)) = R(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(316,a,983,a(flip),b,1208,a),flip(a)].">
      <j1 rule="hyper" parents="316 983 1208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1211">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(133,a,10,a(flip),b,1208,a),flip(a)].">
      <j1 rule="hyper" parents="133 10 1208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1212">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ y) / y) * x) = (x \ 1) \ ((x \ y) / y)
    ]]></literal>
    <justification jstring="[para(1013(a,1),1211(a,1,2))].">
      <j1 rule="para" parents="1013 1211"/>
    </justification>
  </clause>

  <clause id="1214">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ z,u)) * y = T((z * y) / x,u) * x
    ]]></literal>
    <justification jstring="[para(415(a,1),914(a,1,1))].">
      <j1 rule="para" parents="415 914"/>
    </justification>
  </clause>

  <clause id="1215">
    <literal><![CDATA[
      L((x * (y \ 1)) * (y * y),z,u) = (y * L(y \ x,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1058,a,b,992,a)].">
      <j1 rule="hyper" parents="63 1058 992"/>
    </justification>
  </clause>

  <clause id="1216">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(144,a,1015,a),flip(a)].">
      <j1 rule="hyper" parents="144 1015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1217">
    <literal><![CDATA[
      (x \ y) \ (x \ (y * L(y \ x,z,u))) = L((x \ y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(1015(a,1),69(a,1,2,2))].">
      <j1 rule="para" parents="1015 69"/>
    </justification>
  </clause>

  <clause id="1218">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = z * (y * T(y \ (z \ x),u))
    ]]></literal>
    <justification jstring="[hyper(316,a,781,a(flip),b,1050,a),flip(a)].">
      <j1 rule="hyper" parents="316 781 1050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1219">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (T(1 / x,z) * x) * y
    ]]></literal>
    <justification jstring="[para(77(a,1),1050(a,1,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="77 1050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1220">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(415(a,1),1219(a,2,1))].">
      <j1 rule="para" parents="415 1219"/>
    </justification>
  </clause>

  <clause id="1221">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,781,a(flip),b,1220,a)].">
      <j1 rule="hyper" parents="63 781 1220"/>
    </justification>
  </clause>

  <clause id="1222">
    <literal><![CDATA[
      T(x,x * T(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(253,a,712,a(flip),b,1220,a(flip))].">
      <j1 rule="hyper" parents="253 712 1220"/>
    </justification>
  </clause>

  <clause id="1223">
    <literal><![CDATA[
      T(x \ 1,x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(847(a,1),1222(a,1,2))].">
      <j1 rule="para" parents="847 1222"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      x * (y \ T(y * (x \ (y \ 1)),z)) = (x * T(x \ 1,z)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(807(a,1),1221(a,1,2))].">
      <j1 rule="para" parents="807 1221"/>
    </justification>
  </clause>

  <clause id="1225">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = (x * T(x \ 1,x)) * y
    ]]></literal>
    <justification jstring="[para(997(a,2),1221(a,1,2))].">
      <j1 rule="para" parents="997 1221"/>
    </justification>
  </clause>

  <clause id="1226">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(337(a,1),1225(a,2,1))].">
      <j1 rule="para" parents="337 1225"/>
    </justification>
  </clause>

  <clause id="1227">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = x * (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1226(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1228">
    <literal><![CDATA[
      L(x,y,z) * (x \ (1 / x)) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(233(a,1),1061(a,1,1)),flip(a)].">
      <j1 rule="para" parents="233 1061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1229">
    <literal><![CDATA[
      L(x,y,z) * (1 / x) = x * L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,1228,a(flip),b,1126,a),flip(a)].">
      <j1 rule="hyper" parents="139 1228 1126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1230">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(602(a,1),1122(a,2,1))].">
      <j1 rule="para" parents="602 1122"/>
    </justification>
  </clause>

  <clause id="1231">
    <literal><![CDATA[
      L(x,L(y,z,u),y) = L(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18,a,b,1133,a)].">
      <j1 rule="hyper" parents="63 18 1133"/>
    </justification>
  </clause>

  <clause id="1233">
    <literal><![CDATA[
      ((x * y) / x) * (y * z) = y * (((x * y) / x) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1204(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1234">
    <literal><![CDATA[
      x * (((y * x) / y) * (x \ z)) = ((y * x) / y) * z
    ]]></literal>
    <justification jstring="[hyper(323,a,1233,a),flip(a)].">
      <j1 rule="hyper" parents="323 1233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1236">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,73,a(flip),b,1233,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 73 1233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1237">
    <literal><![CDATA[
      ((x * y) / x) \ (y \ ((x * y) / x)) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(144,a,1236,a)].">
      <j1 rule="hyper" parents="144 1236"/>
    </justification>
  </clause>

  <clause id="1238">
    <literal><![CDATA[
      (x \ (x * y)) \ 1 = ((z * y) / z) \ (y \ ((z * y) / z))
    ]]></literal>
    <justification jstring="[hyper(316,a,166,a,b,1237,a)].">
      <j1 rule="hyper" parents="316 166 1237"/>
    </justification>
  </clause>

  <clause id="1239">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(253,a,12,a(flip),b,1234,a)].">
      <j1 rule="hyper" parents="253 12 1234"/>
    </justification>
  </clause>

  <clause id="1241">
    <literal><![CDATA[
      T((x * y) / x,y \ x) = (y \ x) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(390,a,1239,a,b,xx)].">
      <j1 rule="hyper" parents="390 1239"/>
    </justification>
  </clause>

  <clause id="1242">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ y) = T(y,y \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),1239(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 1239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1243">
    <literal><![CDATA[
      (1 / x) * (x * x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(282(a,1),1242(a,1,2))].">
      <j1 rule="para" parents="282 1242"/>
    </justification>
  </clause>

  <clause id="1244">
    <literal><![CDATA[
      L(x,x,x \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,890,a(flip),b,1243,a)].">
      <j1 rule="hyper" parents="63 890 1243"/>
    </justification>
  </clause>

  <clause id="1245">
    <literal><![CDATA[
      L(R(x,y,z),x,x \ 1) = R(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1244(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1244 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1246">
    <literal><![CDATA[
      L(L(x,y,z),x,x \ 1) = L(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1244(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1244 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      (1 / x) \ R(T(x,x \ 1),y,z) = x * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,1245,a(flip),b,890,a)].">
      <j1 rule="hyper" parents="133 1245 890"/>
    </justification>
  </clause>

  <clause id="1248">
    <literal><![CDATA[
      (1 / x) \ L(T(x,x \ 1),y,z) = L(x,y,z) * x
    ]]></literal>
    <justification jstring="[para(1246(a,1),888(a,1,2))].">
      <j1 rule="para" parents="1246 888"/>
    </justification>
  </clause>

  <clause id="1249">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,415,a(flip),b,1214,a),flip(a)].">
      <j1 rule="hyper" parents="316 415 1214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1251">
    <literal><![CDATA[
      L(x * ((y \ 1) * (y * y)),z,u) = (y * L(y \ x,z,u)) * y
    ]]></literal>
    <justification jstring="[para(32(a,1),1215(a,1,1))].">
      <j1 rule="para" parents="32 1215"/>
    </justification>
  </clause>

  <clause id="1252">
    <literal><![CDATA[
      (x \ y) \ L(x \ y,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1064,a(flip),b,1216,a)].">
      <j1 rule="hyper" parents="63 1064 1216"/>
    </justification>
  </clause>

  <clause id="1253">
    <literal><![CDATA[
      (x \ y) * (x \ (y * L(y \ x,z,u))) = L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,1216,a(flip),b,1064,a(flip))].">
      <j1 rule="hyper" parents="139 1216 1064"/>
    </justification>
  </clause>

  <clause id="1254">
    <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),1216(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 1216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1255">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x * (R(x,y,z) \ L(x \ R(x,y,z),u,w))) = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,1169,a(flip),b,1252,a)].">
      <j1 rule="hyper" parents="139 1169 1252"/>
    </justification>
  </clause>

  <clause id="1256">
    <literal><![CDATA[
      (x \ y) * ((x \ y) * (y \ x)) = L(x \ y,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,456,a(flip),b,1252,a)].">
      <j1 rule="hyper" parents="139 456 1252"/>
    </justification>
  </clause>

  <clause id="1257">
    <literal><![CDATA[
      L(x \ 1,x,y) \ L((y * x) \ y,z,u) = (y * x) \ (y * L(y \ (y * x),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,358,a,b,1252,a)].">
      <j1 rule="hyper" parents="63 358 1252"/>
    </justification>
  </clause>

  <clause id="1258">
    <literal><![CDATA[
      (x \ y) \ ((z * x) \ (z * y)) = x \ (y * L(y \ x,x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,476,a(flip),b,1252,a)].">
      <j1 rule="hyper" parents="63 476 1252"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      x \ ((y \ z) * L((y \ z) \ x,x,y)) = (x \ (y \ z)) \ ((y * x) \ z)
    ]]></literal>
    <justification jstring="[para(298(a,1),1252(a,1,2)),flip(a)].">
      <j1 rule="para" parents="298 1252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1260">
    <literal><![CDATA[
      ((x \ y) * (x \ y)) * L(y \ x,x \ y,x \ y) = L(x \ y,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,100,a,b,1256,a)].">
      <j1 rule="hyper" parents="63 100 1256"/>
    </justification>
  </clause>

  <clause id="1261">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[para(116(a,1),1218(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="116 1218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1262">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u))
    ]]></literal>
    <justification jstring="[para(415(a,1),1218(a,1,1))].">
      <j1 rule="para" parents="415 1218"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = x * (z \ T(z * (x \ y),x))
    ]]></literal>
    <justification jstring="[para(807(a,1),1261(a,1,2)),flip(a)].">
      <j1 rule="para" parents="807 1261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * x = x * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,777,a(flip),b,1230,a),flip(a)].">
      <j1 rule="hyper" parents="63 777 1230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1265">
    <literal><![CDATA[
      T(x,x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(253,a,777,a(flip),b,1230,a(flip))].">
      <j1 rule="hyper" parents="253 777 1230"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      T(x,x * ((y * x) \ y)) = x
    ]]></literal>
    <justification jstring="[para(232(a,1),1265(a,1,2,2))].">
      <j1 rule="para" parents="232 1265"/>
    </justification>
  </clause>

  <clause id="1267">
    <literal><![CDATA[
      T(x \ y,(x \ y) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[para(356(a,1),1265(a,1,2,2))].">
      <j1 rule="para" parents="356 1265"/>
    </justification>
  </clause>

  <clause id="1268">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(604(a,1),1265(a,1,2))].">
      <j1 rule="para" parents="604 1265"/>
    </justification>
  </clause>

  <clause id="1269">
    <literal><![CDATA[
      T(x,x \ L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[para(1064(a,1),1265(a,1,2))].">
      <j1 rule="para" parents="1064 1265"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      T(x \ L(x,y,z),x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,1269,a)].">
      <j1 rule="hyper" parents="54 1269"/>
    </justification>
  </clause>

  <clause id="1272">
    <literal><![CDATA[
      L(x,y,z) / x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(209,a,1269,a(flip),b,115,a(flip))].">
      <j1 rule="hyper" parents="209 1269 115"/>
    </justification>
  </clause>

  <clause id="1273">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,1269,a(flip),b,115,a(flip))].">
      <j1 rule="hyper" parents="139 1269 115"/>
    </justification>
  </clause>

  <clause id="1274">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(x,u,w)) = (x \ L(x,u,w)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1269(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1269 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1275">
    <literal><![CDATA[
      (((x * y) \ x) * y) / ((x * y) \ x) = L(y,(x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(1266(a,1),546(a,1,1,2))].">
      <j1 rule="para" parents="1266 546"/>
    </justification>
  </clause>

  <clause id="1276">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) * (x \ y) = L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,1252,a(flip),b,1272,a)].">
      <j1 rule="hyper" parents="138 1252 1272"/>
    </justification>
  </clause>

  <clause id="1277">
    <literal><![CDATA[
      ((x * (y \ L(y,z,u))) * y) / L(y,z,u) = R(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(209,a,1273,a(flip),b,199,a)].">
      <j1 rule="hyper" parents="209 1273 199"/>
    </justification>
  </clause>

  <clause id="1278">
    <literal><![CDATA[
      L(x,y,z) * L(u,x,x \ L(x,y,z)) = (x \ L(x,y,z)) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(138,a,1273,a(flip),b,202,a)].">
      <j1 rule="hyper" parents="138 1273 202"/>
    </justification>
  </clause>

  <clause id="1279">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ L(x,y,z)) * (x * u)) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1273(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1273 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1280">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) * (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(1267(a,1),548(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1267 548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1281">
    <literal><![CDATA[
      R(x \ 1,L(x,y,z),x \ 1) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1268(a,1),920(a,1,1))].">
      <j1 rule="para" parents="1268 920"/>
    </justification>
  </clause>

  <clause id="1283">
    <literal><![CDATA[
      (x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))) * (L(x,y,z) \ x) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(1129(a,1),1276(a,1,1))].">
      <j1 rule="para" parents="1129 1276"/>
    </justification>
  </clause>

  <clause id="1286">
    <literal><![CDATA[
      L(x,(y * x) \ y,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1103,a(flip),b,1275,a),flip(a)].">
      <j1 rule="hyper" parents="63 1103 1275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1288">
    <literal><![CDATA[
      L(x,x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1286(a,1,2,1))].">
      <j1 rule="para" parents="7 1286"/>
    </justification>
  </clause>

  <clause id="1289">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(10(a,1),1286(a,1,2,1))].">
      <j1 rule="para" parents="10 1286"/>
    </justification>
  </clause>

  <clause id="1290">
    <literal><![CDATA[
      x * K(x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,528,a,b,1288,a)].">
      <j1 rule="hyper" parents="63 528 1288"/>
    </justification>
  </clause>

  <clause id="1291">
    <literal><![CDATA[
      T(L(x,T(x,y) \ 1,T(x,y)),y) = 1 / (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a(flip),b,1288,a)].">
      <j1 rule="hyper" parents="63 25 1288"/>
    </justification>
  </clause>

  <clause id="1292">
    <literal><![CDATA[
      x \ (1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,1288,a(flip),b,528,a)].">
      <j1 rule="hyper" parents="133 1288 528"/>
    </justification>
  </clause>

  <clause id="1293">
    <literal><![CDATA[
      a(x,x \ 1,x) = (1 / (1 / x)) \ x
    ]]></literal>
    <justification jstring="[para(1288(a,1),703(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1288 703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1295">
    <literal><![CDATA[
      x \ L(1 / (1 / x),y,z) = (x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1288(a,1),524(a,1,2,1))].">
      <j1 rule="para" parents="1288 524"/>
    </justification>
  </clause>

  <clause id="1296">
    <literal><![CDATA[
      a(x,x \ 1,x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,1084,a(flip),b,1293,a),flip(a)].">
      <j1 rule="hyper" parents="316 1084 1293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1297">
    <literal><![CDATA[
      L((x * y) \ x,y,(x * y) \ x) = 1 / (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(9(a,1),1289(a,1,2))].">
      <j1 rule="para" parents="9 1289"/>
    </justification>
  </clause>

  <clause id="1298">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,749,a,b,1280,a),flip(a)].">
      <j1 rule="hyper" parents="35 749 1280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1299">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,1289,a(flip),b,1298,a),flip(a)].">
      <j1 rule="hyper" parents="63 1289 1298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1300">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),1249(a,2,2,1,2))].">
      <j1 rule="para" parents="7 1249"/>
    </justification>
  </clause>

  <clause id="1301">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ x,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1249(a,2,2,1))].">
      <j1 rule="para" parents="9 1249"/>
    </justification>
  </clause>

  <clause id="1302">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(136,a,7,a(flip),b,1301,a),flip(a)].">
      <j1 rule="hyper" parents="136 7 1301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1303">
    <literal><![CDATA[
      ((x / y) * T(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),1301(a,1,1,2,1))].">
      <j1 rule="para" parents="83 1301"/>
    </justification>
  </clause>

  <clause id="1306">
    <literal><![CDATA[
      (x * T(y,z)) / y = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(149,a,1303,a)].">
      <j1 rule="hyper" parents="149 1303"/>
    </justification>
  </clause>

  <clause id="1308">
    <literal><![CDATA[
      (x / y) * T(y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(136,a,114,a(flip),b,1303,a),flip(a)].">
      <j1 rule="hyper" parents="136 114 1303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1310">
    <literal><![CDATA[
      (1 / x) * T(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(136,a,7,a(flip),b,1303,a),flip(a)].">
      <j1 rule="hyper" parents="136 7 1303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1311">
    <literal><![CDATA[
      (x * T(y,z)) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),1303(a,1,1,1))].">
      <j1 rule="para" parents="11 1303"/>
    </justification>
  </clause>

  <clause id="1313">
    <literal><![CDATA[
      (T(x,y) / y) \ x = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(133,a,241,a(flip),b,1308,a)].">
      <j1 rule="hyper" parents="133 241 1308"/>
    </justification>
  </clause>

  <clause id="1314">
    <literal><![CDATA[
      K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(133,a,1308,a(flip),b,1201,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 1308 1201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1315">
    <literal><![CDATA[
      (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = (y * x) * T(L(x \ 1,x,y),y)
    ]]></literal>
    <justification jstring="[para(361(a,1),1308(a,1,1)),flip(a)].">
      <j1 rule="para" parents="361 1308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1316">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(390,a,xx,b,1310,a),flip(a)].">
      <j1 rule="hyper" parents="390 1310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1317">
    <literal><![CDATA[
      L(K(x,y),x,1 / x) = L(T(x,y) / x,x,y)
    ]]></literal>
    <justification jstring="[para(1310(a,1),910(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1310 910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1319">
    <literal><![CDATA[
      (x * y) / T(y,z) = (x / T(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(629,a,1311,a)].">
      <j1 rule="hyper" parents="629 1311"/>
    </justification>
  </clause>

  <clause id="1320">
    <literal><![CDATA[
      (1 / T(x,y)) * x = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(374,a,1311,a),flip(a)].">
      <j1 rule="hyper" parents="374 1311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(116(a,1),1311(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="116 1311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1322">
    <literal><![CDATA[
      (1 / T(x,y)) \ (x / T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,1320,a)].">
      <j1 rule="hyper" parents="144 1320"/>
    </justification>
  </clause>

  <clause id="1324">
    <literal><![CDATA[
      K(x \ (x / (1 / y)),x) = T(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,1014,a,b,1302,a)].">
      <j1 rule="hyper" parents="63 1014 1302"/>
    </justification>
  </clause>

  <clause id="1325">
    <literal><![CDATA[
      T(x,y) = K(y \ (y / (1 / x)),y) * x
    ]]></literal>
    <justification jstring="[hyper(138,a,1014,a,b,1302,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="138 1014 1302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1326">
    <literal><![CDATA[
      T(1 / x,T(x,y) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1302(a,1),1222(a,1,2))].">
      <j1 rule="para" parents="1302 1222"/>
    </justification>
  </clause>

  <clause id="1327">
    <literal><![CDATA[
      L(x,y,T(z,u) / z) = x
    ]]></literal>
    <justification jstring="[para(1324(a,1),155(a,1,3))].">
      <j1 rule="para" parents="1324 155"/>
    </justification>
  </clause>

  <clause id="1328">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,363,a(flip),b,1327,a)].">
      <j1 rule="hyper" parents="63 363 1327"/>
    </justification>
  </clause>

  <clause id="1329">
    <literal><![CDATA[
      T(x,y) / x = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(38,a,850,a,b,1328,a),flip(a)].">
      <j1 rule="hyper" parents="38 850 1328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      (x \ T(x,y)) * x = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(151,a,1329,a)].">
      <j1 rule="hyper" parents="151 1329"/>
    </justification>
  </clause>

  <clause id="1331">
    <literal><![CDATA[
      x * (T(x,y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,1329,a,b,xx)].">
      <j1 rule="hyper" parents="139 1329"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      (x \ 1) * (x * T(x \ 1,y)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,856,a(flip),b,1329,a(flip))].">
      <j1 rule="hyper" parents="139 856 1329"/>
    </justification>
  </clause>

  <clause id="1333">
    <literal><![CDATA[
      K(x,y) = L(T(x,y) / x,x,y)
    ]]></literal>
    <justification jstring="[para(1329(a,2),715(a,2,1))].">
      <j1 rule="para" parents="1329 715"/>
    </justification>
  </clause>

  <clause id="1335">
    <literal><![CDATA[
      T(1 / x,T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1328,a(flip),b,1316,a),flip(a)].">
      <j1 rule="hyper" parents="63 1328 1316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1338">
    <literal><![CDATA[
      T(x \ 1,T(x,y)) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1335(a,1),260(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1335 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1339">
    <literal><![CDATA[
      L(K(x,y),x,1 / x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1333,a,b,1317,a),flip(a)].">
      <j1 rule="hyper" parents="316 1333 1317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1340">
    <literal><![CDATA[
      K(x,y) / (x * K(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(136,a,1339,a(flip),b,273,a)].">
      <j1 rule="hyper" parents="136 1339 273"/>
    </justification>
  </clause>

  <clause id="1341">
    <literal><![CDATA[
      (x \ 1) * K(x \ 1,y) = x \ K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,195,a,b,1340,a),flip(a)].">
      <j1 rule="hyper" parents="36 195 1340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1342">
    <literal><![CDATA[
      R(x,x \ 1,K(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(39,a,382,a,b,1341,a(flip))].">
      <j1 rule="hyper" parents="39 382 1341"/>
    </justification>
  </clause>

  <clause id="1343">
    <literal><![CDATA[
      (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y
    ]]></literal>
    <justification jstring="[hyper(149,a,1300,a),flip(a)].">
      <j1 rule="hyper" parents="149 1300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1344">
    <literal><![CDATA[
      (x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(116(a,1),1321(a,1,2))].">
      <j1 rule="para" parents="116 1321"/>
    </justification>
  </clause>

  <clause id="1345">
    <literal><![CDATA[
      (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z
    ]]></literal>
    <justification jstring="[para(240(a,1),1321(a,1,2)),flip(a)].">
      <j1 rule="para" parents="240 1321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1347">
    <literal><![CDATA[
      (x * (y / z)) / (z \ y) = (x / (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(136,a,157,a(flip),b,1344,a)].">
      <j1 rule="hyper" parents="136 157 1344"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * x = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(229(a,1),1251(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="229 1251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      L(x * y,z,u) / y = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(149,a,1348,a)].">
      <j1 rule="hyper" parents="149 1348"/>
    </justification>
  </clause>

  <clause id="1350">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,958,a(flip),b,1349,a),flip(a)].">
      <j1 rule="hyper" parents="63 958 1349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1351">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ x,z,u) = L(y,z,u) / (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1349(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 1349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1352">
    <literal><![CDATA[
      x * L(x \ (y / x),z,u) = L(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),1349(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1354">
    <literal><![CDATA[
      L((x \ 1) \ (y / x),z,u) = (x \ 1) \ (L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,1352,a(flip),b,1350,a),flip(a)].">
      <j1 rule="hyper" parents="133 1352 1350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1355">
    <literal><![CDATA[
      x \ L(x * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,898,a(flip),b,1350,a)].">
      <j1 rule="hyper" parents="63 898 1350"/>
    </justification>
  </clause>

  <clause id="1356">
    <literal><![CDATA[
      x * (x * L(x \ y,z,u)) = L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,1350,a(flip),b,898,a(flip))].">
      <j1 rule="hyper" parents="139 1350 898"/>
    </justification>
  </clause>

  <clause id="1357">
    <literal><![CDATA[
      x * L(x \ y,x \ 1,x) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(474(a,1),1350(a,1,2)),flip(a)].">
      <j1 rule="para" parents="474 1350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1358">
    <literal><![CDATA[
      L(x * (y / x),z,u) = x * (L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(139,a,1352,a(flip),b,1355,a),flip(a)].">
      <j1 rule="hyper" parents="139 1352 1355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1359">
    <literal><![CDATA[
      L(x * (y * x),z,u) = x * (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(139,a,599,a(flip),b,1355,a),flip(a)].">
      <j1 rule="hyper" parents="139 599 1355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1360">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) * x = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,1355,a,b,1349,a)].">
      <j1 rule="hyper" parents="138 1355 1349"/>
    </justification>
  </clause>

  <clause id="1361">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * u) = x * L(x \ (u * u),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1060,a(flip),b,1355,a)].">
      <j1 rule="hyper" parents="63 1060 1355"/>
    </justification>
  </clause>

  <clause id="1362">
    <literal><![CDATA[
      x \ ((x \ 1) * (x * y)) = L(x \ y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,387,a(flip),b,1355,a(flip))].">
      <j1 rule="hyper" parents="133 387 1355"/>
    </justification>
  </clause>

  <clause id="1363">
    <literal><![CDATA[
      x * L(x \ (x \ y),z,u) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1355(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1364">
    <literal><![CDATA[
      L(x \ (y * L(y \ z,u,w)),x,y) = (y * x) \ L(y * z,u,w)
    ]]></literal>
    <justification jstring="[para(1355(a,1),298(a,1,1,2))].">
      <j1 rule="para" parents="1355 298"/>
    </justification>
  </clause>

  <clause id="1365">
    <literal><![CDATA[
      (x / (y \ 1)) * L((x / (y \ 1)) \ y,z,u) = (x / (y \ 1)) \ L(x * (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(576(a,1),1355(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="576 1355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1366">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ (x \ 1),u,w) = L(x,y,z) \ L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(969(a,1),1355(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="969 1355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1367">
    <literal><![CDATA[
      L(x * (x * y),z,u) = x * (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),1356(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1368">
    <literal><![CDATA[
      x * (x * L(x \ (x \ y),z,u)) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1356(a,2,1))].">
      <j1 rule="para" parents="10 1356"/>
    </justification>
  </clause>

  <clause id="1369">
    <literal><![CDATA[
      L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),1360(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1370">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = L(y * x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(387(a,1),1360(a,1,1))].">
      <j1 rule="para" parents="387 1360"/>
    </justification>
  </clause>

  <clause id="1371">
    <literal><![CDATA[
      L(L(x,y,z) \ (L(x,y,z) \ x),y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,67,a(flip),b,1363,a),flip(a)].">
      <j1 rule="hyper" parents="133 67 1363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1372">
    <literal><![CDATA[
      x * L(L(x \ 1,y,z),u,w) = x \ L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1065(a,1),1363(a,1,2,1))].">
      <j1 rule="para" parents="1065 1363"/>
    </justification>
  </clause>

  <clause id="1373">
    <literal><![CDATA[
      x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(253,a,1348,a,b,1368,a),flip(a)].">
      <j1 rule="hyper" parents="253 1348 1368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1375">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,182,a(flip),b,1369,a),flip(a)].">
      <j1 rule="hyper" parents="41 182 1369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1376">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(474(a,1),1369(a,2,1,2))].">
      <j1 rule="para" parents="474 1369"/>
    </justification>
  </clause>

  <clause id="1377">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x,y,z) = 1 * x
    ]]></literal>
    <justification jstring="[hyper(316,a,7,a,b,1375,a),flip(a)].">
      <j1 rule="hyper" parents="316 7 1375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      x / L(x,y,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(149,a,1375,a)].">
      <j1 rule="hyper" parents="149 1375"/>
    </justification>
  </clause>

  <clause id="1379">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,1375,a)].">
      <j1 rule="hyper" parents="144 1375"/>
    </justification>
  </clause>

  <clause id="1381">
    <literal><![CDATA[
      (x * y) / (L(x * (y \ 1),z,u) * (y * y)) = L(x * (y \ 1),z,u) \ (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,639,a,b,1378,a)].">
      <j1 rule="hyper" parents="63 639 1378"/>
    </justification>
  </clause>

  <clause id="1382">
    <literal><![CDATA[
      R(L(x,y,z) \ x,L(x,y,z),L(x,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(1378(a,1),1005(a,1,1))].">
      <j1 rule="para" parents="1378 1005"/>
    </justification>
  </clause>

  <clause id="1384">
    <literal><![CDATA[
      a(x,x \ 1,y) \ y = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(703(a,1),1379(a,1,1))].">
      <j1 rule="para" parents="703 1379"/>
    </justification>
  </clause>

  <clause id="1385">
    <literal><![CDATA[
      T((x \ 1) * (x * y),x) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(253,a,1370,a,b,271,a)].">
      <j1 rule="hyper" parents="253 1370 271"/>
    </justification>
  </clause>

  <clause id="1386">
    <literal><![CDATA[
      (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),1385(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1387">
    <literal><![CDATA[
      (x \ 1) \ T((x \ 1) * y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,1386,a)].">
      <j1 rule="hyper" parents="144 1386"/>
    </justification>
  </clause>

  <clause id="1388">
    <literal><![CDATA[
      (x \ y) \ L((x \ y) * x,z,u) = L(y,z,u) / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1355,a,b,1351,a)].">
      <j1 rule="hyper" parents="63 1355 1351"/>
    </justification>
  </clause>

  <clause id="1389">
    <literal><![CDATA[
      x \ (y * L(y \ (z * z),u,w)) = (x \ (y \ L(y,u,w))) * (z * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,1361,a(flip),b,124,a)].">
      <j1 rule="hyper" parents="133 1361 124"/>
    </justification>
  </clause>

  <clause id="1390">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,1376,a(flip),b,271,a),flip(a)].">
      <j1 rule="hyper" parents="133 1376 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1391">
    <literal><![CDATA[
      x \ (y * (x * T(x \ (y \ z),u))) = T(y * T(y \ (z / x),u),x)
    ]]></literal>
    <justification jstring="[hyper(390,a,xx,b,1262,a),flip(a)].">
      <j1 rule="hyper" parents="390 1262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1392">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) / y = x * T(x \ (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(149,a,1262,a)].">
      <j1 rule="hyper" parents="149 1262"/>
    </justification>
  </clause>

  <clause id="1393">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(11(a,1),1262(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 1262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1394">
    <literal><![CDATA[
      (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y
    ]]></literal>
    <justification jstring="[para(807(a,1),1262(a,1,1)),flip(a)].">
      <j1 rule="para" parents="807 1262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1395">
    <literal><![CDATA[
      x * ((x \ L(x,y,z)) * L(x,u,w)) = L(x,u,w) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,1274,a(flip),b,1126,a)].">
      <j1 rule="hyper" parents="139 1274 1126"/>
    </justification>
  </clause>

  <clause id="1396">
    <literal><![CDATA[
      (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1345(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1397">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(629,a,1396,a)].">
      <j1 rule="hyper" parents="629 1396"/>
    </justification>
  </clause>

  <clause id="1398">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * y = y / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(374,a,1396,a),flip(a)].">
      <j1 rule="hyper" parents="374 1396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1399">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(136,a,81,a(flip),b,1396,a),flip(a)].">
      <j1 rule="hyper" parents="136 81 1396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1401">
    <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),1373(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1402">
    <literal><![CDATA[
      x * ((y \ (x \ (z * y))) * y) = (x * T(x \ z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,238,a(flip),b,1393,a)].">
      <j1 rule="hyper" parents="63 238 1393"/>
    </justification>
  </clause>

  <clause id="1403">
    <literal><![CDATA[
      ((x * y) * T((x * y) \ x,z)) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(67(a,1),1393(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="67 1393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1404">
    <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(102(a,2),1393(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="102 1393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1405">
    <literal><![CDATA[
      ((x * (y \ z)) * T((x * (y \ z)) \ x,z)) * z = (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z)
    ]]></literal>
    <justification jstring="[para(336(a,2),1402(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="336 1402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1407">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) \ (x * (z * y)) = a(z,y,T(x,z * y))
    ]]></literal>
    <justification jstring="[para(598(a,1),245(a,1,1))].">
      <j1 rule="para" parents="598 245"/>
    </justification>
  </clause>

  <clause id="1409">
    <literal><![CDATA[
      (L(x,T(y,z),z) * (y * z)) \ (x * (z * T(y,z))) = a(z,T(y,z),T(x,z * T(y,z)))
    ]]></literal>
    <justification jstring="[para(114(a,1),1407(a,1,1,2))].">
      <j1 rule="para" parents="114 1407"/>
    </justification>
  </clause>

  <clause id="1411">
    <literal><![CDATA[
      (L(1 / x,y,z) * x) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,700,a(flip),b,750,a)].">
      <j1 rule="hyper" parents="63 700 750"/>
    </justification>
  </clause>

  <clause id="1412">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(602(a,1),1411(a,1,1))].">
      <j1 rule="para" parents="602 1411"/>
    </justification>
  </clause>

  <clause id="1413">
    <literal><![CDATA[
      (x * L(x \ (y \ x),z,u)) / (y \ x) = y * L(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(149,a,1412,a)].">
      <j1 rule="hyper" parents="149 1412"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      (x * L(x \ 1,y,x)) * (x \ y) = y * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(298(a,1),1412(a,2,2))].">
      <j1 rule="para" parents="298 1412"/>
    </justification>
  </clause>

  <clause id="1415">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(1064(a,1),1412(a,1,1))].">
      <j1 rule="para" parents="1064 1412"/>
    </justification>
  </clause>

  <clause id="1416">
    <literal><![CDATA[
      (x \ L(x,y,x)) * (x \ y) = y * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(1064(a,1),1414(a,1,1))].">
      <j1 rule="para" parents="1064 1414"/>
    </justification>
  </clause>

  <clause id="1418">
    <literal><![CDATA[
      (x * y) * (L(z,u,w) * L(L(z,u,w) \ (z \ L(z,u,w)),u,w)) = x * (y * ((z \ L(z,u,w)) * (z \ L(z,u,w))))
    ]]></literal>
    <justification jstring="[hyper(139,a,1415,a(flip),b,123,a)].">
      <j1 rule="hyper" parents="139 1415 123"/>
    </justification>
  </clause>

  <clause id="1421">
    <literal><![CDATA[
      (((x * y) * z) * L(((x * y) * z) \ (y * z),u,w)) / (R(x,y,z) \ ((x * y) * z)) = R(x,y,z) * L(R(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(199(a,1),1413(a,1,1,2,1,2))].">
      <j1 rule="para" parents="199 1413"/>
    </justification>
  </clause>

  <clause id="1422">
    <literal><![CDATA[
      R(x * (y \ 1),z,u) / (y \ 1) = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(554(a,1),753(a,1,1))].">
      <j1 rule="para" parents="554 753"/>
    </justification>
  </clause>

  <clause id="1423">
    <literal><![CDATA[
      R(x \ R(x,y,z),u,w) / (x \ 1) = x * R(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(978(a,1),1422(a,1,1,1))].">
      <j1 rule="para" parents="978 1422"/>
    </justification>
  </clause>

  <clause id="1424">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (y * z),u,w) = y * (T(x,y) * L(T(x,y) \ z,u,w))
    ]]></literal>
    <justification jstring="[para(485(a,1),782(a,1,2,1))].">
      <j1 rule="para" parents="485 782"/>
    </justification>
  </clause>

  <clause id="1425">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (y * z),u,w) = y * (T(x,y) * R(T(x,y) \ z,u,w))
    ]]></literal>
    <justification jstring="[para(786(a,1),450(a,1,2))].">
      <j1 rule="para" parents="786 450"/>
    </justification>
  </clause>

  <clause id="1426">
    <literal><![CDATA[
      K(x,x \ 1) * L(y,x \ 1,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1156,a(flip),b,944,a),flip(a)].">
      <j1 rule="hyper" parents="316 1156 944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1427">
    <literal><![CDATA[
      L(x,1 / y,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1091,a,1426,a)].">
      <j1 rule="hyper" parents="1091 1426"/>
    </justification>
  </clause>

  <clause id="1428">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,y \ 1) = L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(80(a,1),1427(a,1,2)),flip(a)].">
      <j1 rule="para" parents="80 1427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1429">
    <literal><![CDATA[
      L(((x \ 1) \ 1) \ y,x,x \ 1) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,474,a(flip),b,1428,a),flip(a)].">
      <j1 rule="hyper" parents="63 474 1428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1430">
    <literal><![CDATA[
      x \ ((L(y,z,x) * x) * z) = z * R(T(y,x * z),x,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,947,a(flip),b,100,a(flip))].">
      <j1 rule="hyper" parents="133 947 100"/>
    </justification>
  </clause>

  <clause id="1431">
    <literal><![CDATA[
      (L((x * y) / x,z,u) * x) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(790(a,1),947(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="790 947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1432">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[para(789(a,1),947(a,1,2,1))].">
      <j1 rule="para" parents="789 947"/>
    </justification>
  </clause>

  <clause id="1433">
    <literal><![CDATA[
      (x * L(y,z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(603(a,1),1431(a,1,1))].">
      <j1 rule="para" parents="603 1431"/>
    </justification>
  </clause>

  <clause id="1434">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) * L(y,z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(630,a,1433,a),flip(a)].">
      <j1 rule="hyper" parents="630 1433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1435">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = (x / L(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(629,a,1433,a)].">
      <j1 rule="hyper" parents="629 1433"/>
    </justification>
  </clause>

  <clause id="1436">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) * y = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,157,a(flip),b,1433,a),flip(a)].">
      <j1 rule="hyper" parents="316 157 1433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1437">
    <literal><![CDATA[
      (x * L(y,y,x)) * y = x * (y * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,100,a(flip),b,1433,a),flip(a)].">
      <j1 rule="hyper" parents="316 100 1433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1438">
    <literal><![CDATA[
      (x * L(y,z,u)) / y = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(136,a,157,a(flip),b,1433,a)].">
      <j1 rule="hyper" parents="136 157 1433"/>
    </justification>
  </clause>

  <clause id="1439">
    <literal><![CDATA[
      (x * (y * y)) / y = x * L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(136,a,100,a(flip),b,1433,a)].">
      <j1 rule="hyper" parents="136 100 1433"/>
    </justification>
  </clause>

  <clause id="1440">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(136,a,81,a(flip),b,1433,a),flip(a)].">
      <j1 rule="hyper" parents="136 81 1433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1442">
    <literal><![CDATA[
      (x / L(x \ y,z,u)) * (x \ y) = y / L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(136,a,304,a(flip),b,1433,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 304 1433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1443">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,157,a(flip),b,1433,a(flip))].">
      <j1 rule="hyper" parents="133 157 1433"/>
    </justification>
  </clause>

  <clause id="1444">
    <literal><![CDATA[
      ((x * y) * L(y,z,u)) / (y * L(y,z,u)) = R(x,L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(1433(a,1),419(a,1,1))].">
      <j1 rule="para" parents="1433 419"/>
    </justification>
  </clause>

  <clause id="1445">
    <literal><![CDATA[
      x * L(y,y,x) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,576,a,b,1437,a),flip(a)].">
      <j1 rule="hyper" parents="35 576 1437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      L(x,x,y) = y \ (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(144,a,1445,a),flip(a)].">
      <j1 rule="hyper" parents="144 1445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1448">
    <literal><![CDATA[
      L(x,x,R(y,x,x)) = R(y,x,x) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(133,a,569,a(flip),b,1445,a),flip(a)].">
      <j1 rule="hyper" parents="133 569 1445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1449">
    <literal><![CDATA[
      L(L(x,x,y) \ z,L(x,x,y),y) = (y / (x \ 1)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(1445(a,1),102(a,2,1))].">
      <j1 rule="para" parents="1445 102"/>
    </justification>
  </clause>

  <clause id="1450">
    <literal><![CDATA[
      (x / (y \ 1)) * L(L(z,L(y,y,x),x),u,w) = x * (L(y,y,x) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1445(a,1),403(a,1,1))].">
      <j1 rule="para" parents="1445 403"/>
    </justification>
  </clause>

  <clause id="1451">
    <literal><![CDATA[
      (x \ y) \ (x \ (x / ((x \ y) \ 1))) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,1447,a(flip),b,1256,a)].">
      <j1 rule="hyper" parents="133 1447 1256"/>
    </justification>
  </clause>

  <clause id="1452">
    <literal><![CDATA[
      L(1 / x,1 / x,y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(83(a,1),1447(a,2,2,2))].">
      <j1 rule="para" parents="83 1447"/>
    </justification>
  </clause>

  <clause id="1453">
    <literal><![CDATA[
      x \ (x / T(y,y \ 1)) = L(y \ 1,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(115(a,2),1447(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="115 1447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1454">
    <literal><![CDATA[
      (x / (y \ 1)) * K(x \ (x / (y \ 1)),x) = L(y,y,x) * x
    ]]></literal>
    <justification jstring="[para(1447(a,2),307(a,2,1))].">
      <j1 rule="para" parents="1447 307"/>
    </justification>
  </clause>

  <clause id="1456">
    <literal><![CDATA[
      x * (y \ L(L(z,u,w),z,v5)) = x * (y \ L(v5 \ (v5 / (z \ 1)),u,w))
    ]]></literal>
    <justification jstring="[para(1447(a,1),835(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1447 835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1457">
    <literal><![CDATA[
      L(1 / ((x / (y \ 1)) \ x),(x / (y \ 1)) \ x,x / (y \ 1)) = 1 / (1 / L(y,y,x))
    ]]></literal>
    <justification jstring="[para(1447(a,2),1299(a,2,2,2))].">
      <j1 rule="para" parents="1447 1299"/>
    </justification>
  </clause>

  <clause id="1458">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1272,a(flip),b,1440,a),flip(a)].">
      <j1 rule="hyper" parents="316 1272 1440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1459">
    <literal><![CDATA[
      T(1 / x,L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(253,a,1458,a,b,969,a)].">
      <j1 rule="hyper" parents="253 1458 969"/>
    </justification>
  </clause>

  <clause id="1461">
    <literal><![CDATA[
      (K(x,y) / z) * L(z,u,w) = K(x,y) * (z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1458(a,1),655(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1458 655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1462">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(35,a,1377,a,b,1434,a),flip(a)].">
      <j1 rule="hyper" parents="35 1377 1434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1463">
    <literal><![CDATA[
      (L(x,y,z) \ x) / x = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(149,a,1462,a)].">
      <j1 rule="hyper" parents="149 1462"/>
    </justification>
  </clause>

  <clause id="1464">
    <literal><![CDATA[
      (x / L(y,z,u)) / y = (x / y) / L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(136,a,162,a(flip),b,1435,a(flip))].">
      <j1 rule="hyper" parents="136 162 1435"/>
    </justification>
  </clause>

  <clause id="1465">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(136,a,100,a(flip),b,1436,a),flip(a)].">
      <j1 rule="hyper" parents="136 100 1436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1466">
    <literal><![CDATA[
      L(x,y,z) = ((z * y) * x) \ ((z * (y * x)) * x)
    ]]></literal>
    <justification jstring="[para(202(a,1),1443(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="202 1443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1468">
    <literal><![CDATA[
      (x * (y * (z \ (x * y)))) / (z \ (x * y)) = z * L(z \ (x * y),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,198,a(flip),b,1465,a),flip(a)].">
      <j1 rule="hyper" parents="63 198 1465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1469">
    <literal><![CDATA[
      ((x * L(y,z,u)) / y) * L(y,L(y,z,u),x) = (x * (y * L(y,z,u))) / y
    ]]></literal>
    <justification jstring="[para(257(a,1),1465(a,2,1,2))].">
      <j1 rule="para" parents="257 1465"/>
    </justification>
  </clause>

  <clause id="1471">
    <literal><![CDATA[
      R(x,L(y,z,u),y) = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20,a,b,1444,a),flip(a)].">
      <j1 rule="hyper" parents="63 20 1444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1472">
    <literal><![CDATA[
      (1 / (x \ y)) \ (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(356(a,1),1011(a,1,1)),flip(a)].">
      <j1 rule="para" parents="356 1011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1473">
    <literal><![CDATA[
      (1 / (x \ y)) * ((y \ x) * (x \ y)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(152,a,1472,a)].">
      <j1 rule="hyper" parents="152 1472"/>
    </justification>
  </clause>

  <clause id="1474">
    <literal><![CDATA[
      T(1 / (x \ y),(y \ x) * (x \ y)) = ((y \ x) * (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(390,a,xx,b,1473,a)].">
      <j1 rule="hyper" parents="390 1473"/>
    </justification>
  </clause>

  <clause id="1475">
    <literal><![CDATA[
      (x \ y) / L(y \ x,x \ y,1 / (y \ x)) = (1 / (y \ x)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(136,a,1473,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="136 1473 100"/>
    </justification>
  </clause>

  <clause id="1476">
    <literal><![CDATA[
      L(T(((x * y) * z) / (x * y),y),y,x) = (x * (z * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(422(a,1),1021(a,1,1))].">
      <j1 rule="para" parents="422 1021"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      R(L(x,y,x),y,T(x,y)) = (x * y) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[para(547(a,1),1044(a,1,1))].">
      <j1 rule="para" parents="547 1044"/>
    </justification>
  </clause>

  <clause id="1478">
    <literal><![CDATA[
      L(R(x,y,T(x,y)),y,x) = (x * y) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,29,a(flip),b,1477,a)].">
      <j1 rule="hyper" parents="63 29 1477"/>
    </justification>
  </clause>

  <clause id="1479">
    <literal><![CDATA[
      L(R(x,y,T(x,y)),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,9,a(flip),b,1478,a),flip(a)].">
      <j1 rule="hyper" parents="316 9 1478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1481">
    <literal><![CDATA[
      L((x * R(y,z,T(y,z))) / x,z,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(1479(a,1),751(a,2,1,2))].">
      <j1 rule="para" parents="1479 751"/>
    </justification>
  </clause>

  <clause id="1482">
    <literal><![CDATA[
      L(R((x * y) / x,z,T(y,z)),z,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(756(a,2),1481(a,1,1))].">
      <j1 rule="para" parents="756 1481"/>
    </justification>
  </clause>

  <clause id="1483">
    <literal><![CDATA[
      ((x \ y) \ 1) \ (y \ x) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(356(a,1),1074(a,1,2)),flip(a)].">
      <j1 rule="para" parents="356 1074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1484">
    <literal><![CDATA[
      T((x * y) \ (K(x,x \ 1) * y),x) = (x * y) \ (1 * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,789,a(flip),b,1092,a),flip(a)].">
      <j1 rule="hyper" parents="316 789 1092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1485">
    <literal><![CDATA[
      T((x * y) \ (K(x,x \ 1) * y),x) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(328,a,1484,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="328 1484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1486">
    <literal><![CDATA[
      T(((1 / (1 / x)) * y) \ y,x) = (x * y) \ y
    ]]></literal>
    <justification jstring="[para(1104(a,1),1485(a,1,1))].">
      <j1 rule="para" parents="1104 1485"/>
    </justification>
  </clause>

  <clause id="1487">
    <literal><![CDATA[
      T(((1 / x) * y) \ y,x \ 1) = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(80(a,1),1486(a,1,1,1,1,2))].">
      <j1 rule="para" parents="80 1486"/>
    </justification>
  </clause>

  <clause id="1488">
    <literal><![CDATA[
      (x * (L(x,y,z) * u)) \ ((x * L(x,y,z)) * u) = a(L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(1124(a,1),417(a,1,1))].">
      <j1 rule="para" parents="1124 417"/>
    </justification>
  </clause>

  <clause id="1490">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,609,a(flip),b,872,a)].">
      <j1 rule="hyper" parents="63 609 872"/>
    </justification>
  </clause>

  <clause id="1491">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = (z * y) * L((z * y) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,602,a(flip),b,875,a),flip(a)].">
      <j1 rule="hyper" parents="316 602 875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1493">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1230,a(flip),b,879,a),flip(a)].">
      <j1 rule="hyper" parents="63 1230 879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1494">
    <literal><![CDATA[
      x * (y * L(y \ (x \ 1),z,u)) = (x * y) \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1064,a(flip),b,879,a),flip(a)].">
      <j1 rule="hyper" parents="63 1064 879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1495">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x \ L(x,z,u)) * y
    ]]></literal>
    <justification jstring="[para(1064(a,1),1493(a,2,1))].">
      <j1 rule="para" parents="1064 1493"/>
    </justification>
  </clause>

  <clause id="1496">
    <literal><![CDATA[
      x * ((x \ L(x,y,z)) * (x \ u)) = (x \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(1415(a,2),1495(a,1,2))].">
      <j1 rule="para" parents="1415 1495"/>
    </justification>
  </clause>

  <clause id="1497">
    <literal><![CDATA[
      x * ((x \ L(x,y,z)) * (x \ ((x \ L(x,y,z)) \ u))) = u
    ]]></literal>
    <justification jstring="[hyper(316,a,10,a(flip),b,1496,a),flip(a)].">
      <j1 rule="hyper" parents="316 10 1496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1498">
    <literal><![CDATA[
      (x \ y) * ((y \ L(y,z,u)) * (y \ L(y,z,u))) = x \ ((y \ L(y,z,u)) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,1496,a(flip),b,124,a),flip(a)].">
      <j1 rule="hyper" parents="133 1496 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1499">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * u) = x * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1496(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1500">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ (L(x,y,z) * (x \ u)) = a(x,x \ L(x,y,z),x \ u)
    ]]></literal>
    <justification jstring="[para(1496(a,1),91(a,1,1))].">
      <j1 rule="para" parents="1496 91"/>
    </justification>
  </clause>

  <clause id="1501">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ u) = x \ ((x \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(1497(a,1),69(a,1,2,2))].">
      <j1 rule="para" parents="1497 69"/>
    </justification>
  </clause>

  <clause id="1503">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (L(x,u,w) * L(x,y,z)) = x * L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,1395,a(flip),b,1499,a)].">
      <j1 rule="hyper" parents="133 1395 1499"/>
    </justification>
  </clause>

  <clause id="1504">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x * u) = x * ((x \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,160,a(flip),b,1499,a)].">
      <j1 rule="hyper" parents="133 160 1499"/>
    </justification>
  </clause>

  <clause id="1505">
    <literal><![CDATA[
      x * ((x * L(x \ 1,y,z)) * u) = (x \ L(x,y,z)) * (x * u)
    ]]></literal>
    <justification jstring="[para(1064(a,2),1499(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1064 1499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1506">
    <literal><![CDATA[
      ((1 / x) * y) \ L((1 / x) * y,z,u) = (1 / x) * (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(83(a,1),1494(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="83 1494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1507">
    <literal><![CDATA[
      x * ((y / (z * z)) * L((y / (z * z)) \ (x \ 1),u,w)) = ((x * y) / (z * z)) \ L(x * (y / (z * z)),u,w)
    ]]></literal>
    <justification jstring="[para(683(a,2),1494(a,2,1))].">
      <j1 rule="para" parents="683 1494"/>
    </justification>
  </clause>

  <clause id="1509">
    <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(1067(a,1),1505(a,2,1))].">
      <j1 rule="para" parents="1067 1505"/>
    </justification>
  </clause>

  <clause id="1510">
    <literal><![CDATA[
      (x \ 1) * (x * R(x \ 1,y,z)) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1030,a(flip),b,990,a),flip(a)].">
      <j1 rule="hyper" parents="63 1030 990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1511">
    <literal><![CDATA[
      (x \ 1) \ R(x \ 1,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,1030,a(flip),b,990,a(flip))].">
      <j1 rule="hyper" parents="133 1030 990"/>
    </justification>
  </clause>

  <clause id="1512">
    <literal><![CDATA[
      T((R(x \ 1,y,z) * ((x \ 1) \ u)) / u,x \ 1) = R(x * R(x \ 1,y,z),x \ 1,(x \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1511(a,1),725(a,2,1))].">
      <j1 rule="para" parents="1511 725"/>
    </justification>
  </clause>

  <clause id="1513">
    <literal><![CDATA[
      (x \ (y \ 1)) * L((x \ (y \ 1)) \ z,u,w) = x \ (y * L(y \ (x * z),u,w))
    ]]></literal>
    <justification jstring="[hyper(133,a,1350,a(flip),b,1016,a),flip(a)].">
      <j1 rule="hyper" parents="133 1350 1016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1514">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ (x \ z),u,w) = x \ (y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),1020(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1515">
    <literal><![CDATA[
      ((x * y) \ (x * (y * z))) * L(((x * y) \ (x * (y * z))) \ z,u,w) = (x * y) \ ((x * (y * z)) * L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(14(a,2),1020(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14 1020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1516">
    <literal><![CDATA[
      x \ (y * L(y \ (x * (x \ (y * L(y \ x,z,u)))),w,v5)) = (x \ y) * L(L((x \ y) \ 1,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(1217(a,1),1020(a,2,2,1))].">
      <j1 rule="para" parents="1217 1020"/>
    </justification>
  </clause>

  <clause id="1517">
    <literal><![CDATA[
      (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z)
    ]]></literal>
    <justification jstring="[hyper(144,a,1025,a)].">
      <j1 rule="hyper" parents="144 1025"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      x * T(x \ ((1 / x) \ y),z) = (1 / x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(178(a,1),1051(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="178 1051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1520">
    <literal><![CDATA[
      ((1 / x) * ((1 / x) \ T(y,z))) / x = (1 / x) * T((1 / x) \ (y / x),z)
    ]]></literal>
    <justification jstring="[para(1519(a,1),1392(a,1,1,2))].">
      <j1 rule="para" parents="1519 1392"/>
    </justification>
  </clause>

  <clause id="1521">
    <literal><![CDATA[
      L(x,y,z) * (L(x,u,w) \ x) = x * (L(x,u,w) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1004(a,1),1132(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1004 1132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1522">
    <literal><![CDATA[
      x / (L(x,y,z) * L(x,y,z)) = L(x,y,z) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,434,a(flip),b,1140,a)].">
      <j1 rule="hyper" parents="63 434 1140"/>
    </justification>
  </clause>

  <clause id="1523">
    <literal><![CDATA[
      L(T(x,y),y,R(x,z,u)) = T(x,R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(325,a,1173,a),flip(a)].">
      <j1 rule="hyper" parents="325 1173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1524">
    <literal><![CDATA[
      R(x,y,z) \ (T(x,R(x,y,z) * (R(x,y,z) \ u)) * u) = (R(x,y,z) \ u) * T(T(x,R(x,y,z) \ u),u)
    ]]></literal>
    <justification jstring="[para(1523(a,1),714(a,1,2,1))].">
      <j1 rule="para" parents="1523 714"/>
    </justification>
  </clause>

  <clause id="1525">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * ((y \ 1) \ 1) = x * ((y \ (x \ ((y \ 1) \ 1))) * y)
    ]]></literal>
    <justification jstring="[para(1387(a,1),1224(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1387 1224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1526">
    <literal><![CDATA[
      L(x,y,z) \ (x * ((x \ L(x,y,z)) * u)) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,1499,a(flip),b,1278,a)].">
      <j1 rule="hyper" parents="133 1499 1278"/>
    </justification>
  </clause>

  <clause id="1528">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(602(a,1),1432(a,2,1))].">
      <j1 rule="para" parents="602 1432"/>
    </justification>
  </clause>

  <clause id="1529">
    <literal><![CDATA[
      a(L(x,y,z),x,u) = a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14,a,b,1488,a),flip(a)].">
      <j1 rule="hyper" parents="63 14 1488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1530">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(609(a,1),1490(a,2,1))].">
      <j1 rule="para" parents="609 1490"/>
    </justification>
  </clause>

  <clause id="1531">
    <literal><![CDATA[
      (x * y) * R((x * y) \ ((x * z) * y),u,w) = (x * R(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(610(a,1),1490(a,2,1))].">
      <j1 rule="para" parents="610 1490"/>
    </justification>
  </clause>

  <clause id="1533">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = (x * z) * L((x * z) \ y,u,w)
    ]]></literal>
    <justification jstring="[para(602(a,1),1491(a,1,1))].">
      <j1 rule="para" parents="602 1491"/>
    </justification>
  </clause>

  <clause id="1534">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L((L(x,y,z) \ x) \ (L(x,y,z) \ u),w,v5) = x * (L(x,y,z) \ L(x \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,1129,a(flip),b,1514,a),flip(a)].">
      <j1 rule="hyper" parents="316 1129 1514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1535">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * ((u * ((x * (y * z)) \ ((x * (y * z)) / L(z,y,x)))) / u)) = L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)
    ]]></literal>
    <justification jstring="[para(202(a,1),1517(a,1,1))].">
      <j1 rule="para" parents="202 1517"/>
    </justification>
  </clause>

  <clause id="1536">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((x \ L(x,y,z)) * u)) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1129,a(flip),b,1526,a)].">
      <j1 rule="hyper" parents="63 1129 1526"/>
    </justification>
  </clause>

  <clause id="1537">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),y) = L(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,101,a(flip),b,1526,a)].">
      <j1 rule="hyper" parents="63 101 1526"/>
    </justification>
  </clause>

  <clause id="1539">
    <literal><![CDATA[
      (x * y) \ ((x * L(x \ z,u,w)) * y) = L((x * y) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(144,a,1528,a)].">
      <j1 rule="hyper" parents="144 1528"/>
    </justification>
  </clause>

  <clause id="1540">
    <literal><![CDATA[
      (x \ (y * z)) * L((x \ (y * z)) \ z,u,w) = x \ ((y * L(y \ x,u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,1528,a(flip),b,1016,a),flip(a)].">
      <j1 rule="hyper" parents="133 1528 1016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1541">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,883,a(flip),b,1530,a)].">
      <j1 rule="hyper" parents="63 883 1530"/>
    </justification>
  </clause>

  <clause id="1542">
    <literal><![CDATA[
      x * R(x \ (x \ (y * x)),z,u) = T(x * R(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(253,a,1530,a(flip),b,883,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="253 1530 883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1543">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),1530(a,1,2,1,2))].">
      <j1 rule="para" parents="7 1530"/>
    </justification>
  </clause>

  <clause id="1544">
    <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),1542(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1547">
    <literal><![CDATA[
      T(x,x * R(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(253,a,775,a(flip),b,1543,a(flip))].">
      <j1 rule="hyper" parents="253 775 1543"/>
    </justification>
  </clause>

  <clause id="1549">
    <literal><![CDATA[
      T(x,(y / (x * y)) * x) = x
    ]]></literal>
    <justification jstring="[para(623(a,2),1547(a,1,2))].">
      <j1 rule="para" parents="623 1547"/>
    </justification>
  </clause>

  <clause id="1550">
    <literal><![CDATA[
      (x * R(y,z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1531(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1551">
    <literal><![CDATA[
      (x * y) / R(y,z,u) = (x / R(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(629,a,1550,a)].">
      <j1 rule="hyper" parents="629 1550"/>
    </justification>
  </clause>

  <clause id="1552">
    <literal><![CDATA[
      T((x / y) * R(y,z,u),y) = y \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(390,a,157,a(flip),b,1550,a)].">
      <j1 rule="hyper" parents="390 157 1550"/>
    </justification>
  </clause>

  <clause id="1554">
    <literal><![CDATA[
      ((x / y) / R(y,z,u)) * y = x / R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(136,a,88,a(flip),b,1550,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 88 1550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1557">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ u,x,x \ L(x,y,z)) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1536(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 1536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1558">
    <literal><![CDATA[
      L(x * y,x,x \ L(x,z,u)) = x * L(y,x,x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[para(1279(a,1),1536(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1279 1536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1559">
    <literal><![CDATA[
      L(x * y,y,y \ L(y,z,u)) = L(x,y,y \ L(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(34,a,1359,a(flip),b,1558,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 1359 1558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1560">
    <literal><![CDATA[
      x * (T(y,z) * R(T(y,z) \ (x \ (y * z)),u,w)) = (x * R(x \ z,u,w)) * T(y,z)
    ]]></literal>
    <justification jstring="[para(114(a,1),1541(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="114 1541"/>
    </justification>
  </clause>

  <clause id="1561">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,14,a,b,488,a)].">
      <j1 rule="hyper" parents="316 14 488"/>
    </justification>
  </clause>

  <clause id="1562">
    <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),1561(a,2,2))].">
      <j1 rule="para" parents="18 1561"/>
    </justification>
  </clause>

  <clause id="1563">
    <literal><![CDATA[
      L(R(L(x,y,z) \ x,u,w),L(x,y,z),z * y) = R(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(1561(a,2),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1561 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1564">
    <literal><![CDATA[
      (K(x,y) * (z * u)) \ (K(x,y) * (z * (u * w))) = L(w,u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(406(a,1),651(a,1,2))].">
      <j1 rule="para" parents="406 651"/>
    </justification>
  </clause>

  <clause id="1565">
    <literal><![CDATA[
      (x * (y * T(z,u))) / (x * y) = T((x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(408(a,1),662(a,1,1))].">
      <j1 rule="para" parents="408 662"/>
    </justification>
  </clause>

  <clause id="1566">
    <literal><![CDATA[
      T((x * (y * z)) / (x * y),y) = (x * (z * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(114(a,1),1565(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="114 1565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1567">
    <literal><![CDATA[
      (x * (y * T(T(z,y),u))) / (x * y) = T((x * (z * y)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(114(a,1),1565(a,2,1,1,2))].">
      <j1 rule="para" parents="114 1565"/>
    </justification>
  </clause>

  <clause id="1568">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) / ((x \ L(x,y,z)) * x) = T(((x \ L(x,y,z)) * (x * u)) / L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(1273(a,1),1566(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1273 1566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1569">
    <literal><![CDATA[
      (x * (T(y,z) * u)) / (x * u) = T((x * (y * u)) / (x * u),z)
    ]]></literal>
    <justification jstring="[para(250(a,1),1567(a,1,1,2))].">
      <j1 rule="para" parents="250 1567"/>
    </justification>
  </clause>

  <clause id="1570">
    <literal><![CDATA[
      ((x * y) * z) / (y * ((z * (u * u)) / (u * u))) = R(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[para(683(a,1),842(a,1,2))].">
      <j1 rule="para" parents="683 842"/>
    </justification>
  </clause>

  <clause id="1571">
    <literal><![CDATA[
      (x * y) * L(L(T(x,x * y),z,u),w,v5) = x * (y * L(L(T(x,y),z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(544(a,1),877(a,1,2,1,1))].">
      <j1 rule="para" parents="544 877"/>
    </justification>
  </clause>

  <clause id="1573">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) = (w * y) \ (w * (y * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,477,a(flip),b,1564,a),flip(a)].">
      <j1 rule="hyper" parents="63 477 1564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1575">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,18,a,b,1573,a),flip(a)].">
      <j1 rule="hyper" parents="316 18 1573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1576">
    <literal><![CDATA[
      L(x,y,K(z,u) * K(w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,155,a(flip),b,1575,a),flip(a)].">
      <j1 rule="hyper" parents="316 155 1575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1577">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(436(a,1),1575(a,1,3)),flip(a)].">
      <j1 rule="para" parents="436 1575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1578">
    <literal><![CDATA[
      L(x,y,(K(z,u) * w) * v5) = L(x,y,w * v5)
    ]]></literal>
    <justification jstring="[para(406(a,2),1575(a,1,3))].">
      <j1 rule="para" parents="406 1575"/>
    </justification>
  </clause>

  <clause id="1579">
    <literal><![CDATA[
      L(x,y,K(z,u) * L(L(w,v5,v6),v7,v8)) = L(x,y,L(L(w,v7,v8),v5,v6))
    ]]></literal>
    <justification jstring="[para(159(a,1),1575(a,1,3))].">
      <j1 rule="para" parents="159 1575"/>
    </justification>
  </clause>

  <clause id="1580">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(931(a,1),1575(a,1,3)),flip(a)].">
      <j1 rule="para" parents="931 1575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1581">
    <literal><![CDATA[
      L(x,y,T(z,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1325(a,2),1575(a,1,3))].">
      <j1 rule="para" parents="1325 1575"/>
    </justification>
  </clause>

  <clause id="1582">
    <literal><![CDATA[
      L(x,y,T(z,u)) = w * (w \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,10,a,b,1581,a),flip(a)].">
      <j1 rule="hyper" parents="316 10 1581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1584">
    <literal><![CDATA[
      L(x,y,z \ (u * z)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(22(a,1),1581(a,1,3))].">
      <j1 rule="para" parents="22 1581"/>
    </justification>
  </clause>

  <clause id="1585">
    <literal><![CDATA[
      L(x,y,L(T(z,u),w,v5)) = L(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(25(a,2),1581(a,1,3))].">
      <j1 rule="para" parents="25 1581"/>
    </justification>
  </clause>

  <clause id="1586">
    <literal><![CDATA[
      L(x,y,z / u) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(116(a,1),1581(a,1,3)),flip(a)].">
      <j1 rule="para" parents="116 1581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1587">
    <literal><![CDATA[
      L(x,y,(z * u) / z) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(240(a,1),1581(a,1,3)),flip(a)].">
      <j1 rule="para" parents="240 1581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1588">
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(115(a,1),1581(a,1,3))].">
      <j1 rule="para" parents="115 1581"/>
    </justification>
  </clause>

  <clause id="1589">
    <literal><![CDATA[
      L(x,y,z / (z / u)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(258(a,1),1581(a,1,3)),flip(a)].">
      <j1 rule="para" parents="258 1581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1590">
    <literal><![CDATA[
      L(x,y,(z * z) \ z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(283(a,1),1581(a,1,3))].">
      <j1 rule="para" parents="283 1581"/>
    </justification>
  </clause>

  <clause id="1591">
    <literal><![CDATA[
      L(x,y,L(z / u,w,v5)) = L(x,y,L(u \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(261(a,1),1581(a,1,3)),flip(a)].">
      <j1 rule="para" parents="261 1581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1592">
    <literal><![CDATA[
      L(x,y,(z \ (z \ 1)) \ u) = L(x,y,u * (z * z))
    ]]></literal>
    <justification jstring="[para(447(a,1),1581(a,1,3))].">
      <j1 rule="para" parents="447 1581"/>
    </justification>
  </clause>

  <clause id="1593">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x \ 1) = (x \ (x \ 1)) \ ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,581,a(flip),b,1577,a),flip(a)].">
      <j1 rule="hyper" parents="63 581 1577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1594">
    <literal><![CDATA[
      L(T(x,1 / y) \ z,T(x,1 / y),y \ 1) = (x * (1 / y)) \ ((1 / y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,485,a(flip),b,1577,a),flip(a)].">
      <j1 rule="hyper" parents="63 485 1577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1595">
    <literal><![CDATA[
      (x \ y) / L(y \ x,x \ y,(y \ x) \ 1) = (1 / (y \ x)) * (x \ y)
    ]]></literal>
    <justification jstring="[para(1577(a,1),1475(a,1,2))].">
      <j1 rule="para" parents="1577 1475"/>
    </justification>
  </clause>

  <clause id="1596">
    <literal><![CDATA[
      L(x,y,z / (u / (w * w))) = L(x,y,u \ (z * (w * w)))
    ]]></literal>
    <justification jstring="[para(595(a,1),1584(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="595 1584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1597">
    <literal><![CDATA[
      L(x,y,T(z / u,w)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1581,a,b,1586,a)].">
      <j1 rule="hyper" parents="63 1581 1586"/>
    </justification>
  </clause>

  <clause id="1598">
    <literal><![CDATA[
      x \ ((x / y) * (y * z)) = L(z,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,103,a,b,1586,a)].">
      <j1 rule="hyper" parents="63 103 1586"/>
    </justification>
  </clause>

  <clause id="1599">
    <literal><![CDATA[
      L(x \ ((y / z) * L((y / z) \ u,w,v5)),x,z \ y) = ((y / z) * x) \ L((y / z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,1364,a(flip),b,1586,a),flip(a)].">
      <j1 rule="hyper" parents="63 1364 1586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1601">
    <literal><![CDATA[
      L(x \ y,x,y \ z) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,481,a(flip),b,1586,a),flip(a)].">
      <j1 rule="hyper" parents="63 481 1586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1602">
    <literal><![CDATA[
      L(x \ y,x,x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,480,a(flip),b,1586,a),flip(a)].">
      <j1 rule="hyper" parents="63 480 1586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1603">
    <literal><![CDATA[
      L(x \ 1,x,x \ y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,363,a(flip),b,1586,a),flip(a)].">
      <j1 rule="hyper" parents="63 363 1586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1604">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = ((z / (y * x)) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,105,a(flip),b,1586,a),flip(a)].">
      <j1 rule="hyper" parents="63 105 1586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1605">
    <literal><![CDATA[
      x / L(y,z,(z * y) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(209,a,1586,a(flip),b,105,a(flip))].">
      <j1 rule="hyper" parents="209 1586 105"/>
    </justification>
  </clause>

  <clause id="1606">
    <literal><![CDATA[
      x * L(y,z,z \ x) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,1586,a(flip),b,103,a)].">
      <j1 rule="hyper" parents="139 1586 103"/>
    </justification>
  </clause>

  <clause id="1607">
    <literal><![CDATA[
      x * L(y \ 1,y,y \ x) = x / y
    ]]></literal>
    <justification jstring="[hyper(139,a,1586,a(flip),b,363,a(flip))].">
      <j1 rule="hyper" parents="139 1586 363"/>
    </justification>
  </clause>

  <clause id="1608">
    <literal><![CDATA[
      ((x / y) * z) * L(L(u,z,y \ x),w,v5) = (x / y) * (z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(1586(a,1),403(a,1,2,1))].">
      <j1 rule="para" parents="1586 403"/>
    </justification>
  </clause>

  <clause id="1609">
    <literal><![CDATA[
      T((x * y) / x,x * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,616,a,b,1587,a)].">
      <j1 rule="hyper" parents="63 616 1587"/>
    </justification>
  </clause>

  <clause id="1610">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,945,a(flip),b,1587,a),flip(a)].">
      <j1 rule="hyper" parents="63 945 1587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1611">
    <literal><![CDATA[
      L(R(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,819,a(flip),b,1587,a),flip(a)].">
      <j1 rule="hyper" parents="63 819 1587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1612">
    <literal><![CDATA[
      (x * y) \ (((x * y) / x) * z) = L(x \ z,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,480,a(flip),b,1587,a)].">
      <j1 rule="hyper" parents="63 480 1587"/>
    </justification>
  </clause>

  <clause id="1613">
    <literal><![CDATA[
      R(L(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[para(1587(a,1),818(a,1,1))].">
      <j1 rule="para" parents="1587 818"/>
    </justification>
  </clause>

  <clause id="1615">
    <literal><![CDATA[
      R(x,y,T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,1479,a,b,1611,a)].">
      <j1 rule="hyper" parents="41 1479 1611"/>
    </justification>
  </clause>

  <clause id="1616">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,453,a,b,1611,a)].">
      <j1 rule="hyper" parents="41 453 1611"/>
    </justification>
  </clause>

  <clause id="1617">
    <literal><![CDATA[
      L(T(R(x,y,x),z),y,x) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1611(a,1),25(a,2,1))].">
      <j1 rule="para" parents="1611 25"/>
    </justification>
  </clause>

  <clause id="1618">
    <literal><![CDATA[
      L(L(R(x,y,x),z,u),y,x) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(1611(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1611 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1620">
    <literal><![CDATA[
      x * (y * L(L(R(x,y,x),z,u),w,v5)) = (x * y) * L(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(1611(a,1),877(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1611 877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1621">
    <literal><![CDATA[
      ((x * (y * x)) / x) / y = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(42,a,496,a,b,1613,a)].">
      <j1 rule="hyper" parents="42 496 1613"/>
    </justification>
  </clause>

  <clause id="1622">
    <literal><![CDATA[
      R(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      L(z,y,z) = x
    ]]></literal>
    <justification jstring="[para(1613(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="1613 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1623">
    <literal><![CDATA[
      (x * (y * x)) / x = L(x,y,x) * y
    ]]></literal>
    <justification jstring="[para(1613(a,1),301(a,1,1,1))].">
      <j1 rule="para" parents="1613 301"/>
    </justification>
  </clause>

  <clause id="1625">
    <literal><![CDATA[
      T(R(x,y,x),x * y) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1615(a,1),615(a,1,1))].">
      <j1 rule="para" parents="1615 615"/>
    </justification>
  </clause>

  <clause id="1627">
    <literal><![CDATA[
      T(x,y * x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,544,a(flip),b,1610,a),flip(a)].">
      <j1 rule="hyper" parents="63 544 1610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1628">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a(flip),b,1610,a)].">
      <j1 rule="hyper" parents="63 25 1610"/>
    </justification>
  </clause>

  <clause id="1629">
    <literal><![CDATA[
      x * T(y,x * y) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(1610(a,1),251(a,1,2))].">
      <j1 rule="para" parents="1610 251"/>
    </justification>
  </clause>

  <clause id="1630">
    <literal><![CDATA[
      T(x,x * (y / (x * y))) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,1549,a(flip),b,1627,a),flip(a)].">
      <j1 rule="hyper" parents="63 1549 1627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1631">
    <literal><![CDATA[
      T(x,(x \ y) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1627(a,2,2))].">
      <j1 rule="para" parents="10 1627"/>
    </justification>
  </clause>

  <clause id="1632">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1627(a,1),920(a,1,1))].">
      <j1 rule="para" parents="1627 920"/>
    </justification>
  </clause>

  <clause id="1633">
    <literal><![CDATA[
      L(x,y / (x * y),x) * (y / (x * y)) = (y / (x * y)) * x
    ]]></literal>
    <justification jstring="[para(1630(a,1),548(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1630 548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1634">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(1631(a,1),920(a,1,1))].">
      <j1 rule="para" parents="1631 920"/>
    </justification>
  </clause>

  <clause id="1635">
    <literal><![CDATA[
      x \ T(L(y,z,u) * x,L(y,z,u)) = L(R(y,x,L(y,z,u)),z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,29,a(flip),b,1616,a),flip(a)].">
      <j1 rule="hyper" parents="316 29 1616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1636">
    <literal><![CDATA[
      x * R(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(152,a,1616,a)].">
      <j1 rule="hyper" parents="152 1616"/>
    </justification>
  </clause>

  <clause id="1637">
    <literal><![CDATA[
      R(x,x \ y,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),1616(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1638">
    <literal><![CDATA[
      T(x,R(y,x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(253,a,1636,a,b,1177,a)].">
      <j1 rule="hyper" parents="253 1636 1177"/>
    </justification>
  </clause>

  <clause id="1639">
    <literal><![CDATA[
      L(R(T(x,y),z,x),z,x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(27(a,2),1617(a,1,1))].">
      <j1 rule="para" parents="27 1617"/>
    </justification>
  </clause>

  <clause id="1640">
    <literal><![CDATA[
      x * L(y \ 1,y,y \ z) = x * (z \ (z / y))
    ]]></literal>
    <justification jstring="[hyper(139,a,1603,a,b,9,a)].">
      <j1 rule="hyper" parents="139 1603 9"/>
    </justification>
  </clause>

  <clause id="1641">
    <literal><![CDATA[
      ((x \ y) * x) \ (x \ y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,232,a(flip),b,1603,a)].">
      <j1 rule="hyper" parents="63 232 1603"/>
    </justification>
  </clause>

  <clause id="1642">
    <literal><![CDATA[
      L(x,1 / x,(1 / x) \ y) = y \ (y / (1 / x))
    ]]></literal>
    <justification jstring="[para(83(a,1),1603(a,1,1))].">
      <j1 rule="para" parents="83 1603"/>
    </justification>
  </clause>

  <clause id="1643">
    <literal><![CDATA[
      L(L(x \ 1,x,x \ y) \ z,y \ (y / x),y) = (y / x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(1603(a,2),475(a,1,1,1))].">
      <j1 rule="para" parents="1603 475"/>
    </justification>
  </clause>

  <clause id="1644">
    <literal><![CDATA[
      (x * (y \ (y / x))) * (x \ 1) = L(x \ 1,x,x \ y)
    ]]></literal>
    <justification jstring="[para(1603(a,1),994(a,1,1,2))].">
      <j1 rule="para" parents="1603 994"/>
    </justification>
  </clause>

  <clause id="1645">
    <literal><![CDATA[
      ((x \ 1) \ (y \ (y / x))) * (x \ 1) = L(x \ 1,x,x \ y)
    ]]></literal>
    <justification jstring="[para(1603(a,1),1273(a,1,1,2))].">
      <j1 rule="para" parents="1603 1273"/>
    </justification>
  </clause>

  <clause id="1647">
    <literal><![CDATA[
      ((x * (y * x)) / x) * L(z,y,L(x,y,x)) = L(x,y,x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(138,a,1623,a,b,202,a)].">
      <j1 rule="hyper" parents="138 1623 202"/>
    </justification>
  </clause>

  <clause id="1648">
    <literal><![CDATA[
      ((x \ 1) * (y * x)) / x = L(x \ 1,y,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,964,a(flip),b,1623,a)].">
      <j1 rule="hyper" parents="63 964 1623"/>
    </justification>
  </clause>

  <clause id="1649">
    <literal><![CDATA[
      T(L(x,y,x) * y,x) = y * x
    ]]></literal>
    <justification jstring="[para(1623(a,1),240(a,1,1))].">
      <j1 rule="para" parents="1623 240"/>
    </justification>
  </clause>

  <clause id="1650">
    <literal><![CDATA[
      x * T((y \ x) \ 1,R(y,y \ x,y \ x)) = L((y \ x) \ 1,x,(y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(568(a,2),1629(a,1,2,2))].">
      <j1 rule="para" parents="568 1629"/>
    </justification>
  </clause>

  <clause id="1651">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(316,a,115,a(flip),b,1634,a),flip(a)].">
      <j1 rule="hyper" parents="316 115 1634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1652">
    <literal><![CDATA[
      L(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(1582(a,2),219(a,1)),flip(b)].">
      <j1 rule="para" parents="1582 219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      L(x,y,(z \ u) * (z * z)) = L(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(613(a,1),1597(a,1,3))].">
      <j1 rule="para" parents="613 1597"/>
    </justification>
  </clause>

  <clause id="1654">
    <literal><![CDATA[
      x \ ((x * y) * L(x,z,u)) = y * L(R(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(1618(a,1),296(a,1,2,2))].">
      <j1 rule="para" parents="1618 296"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      L(x \ y,x,y \ (x \ y)) \ (x \ y) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(39,a,1379,a,b,1601,a(flip))].">
      <j1 rule="hyper" parents="39 1379 1601"/>
    </justification>
  </clause>

  <clause id="1657">
    <literal><![CDATA[
      x * L(y \ z,y,y \ u) = x * (u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[hyper(139,a,1602,a,b,9,a)].">
      <j1 rule="hyper" parents="139 1602 9"/>
    </justification>
  </clause>

  <clause id="1661">
    <literal><![CDATA[
      ((x / y) * (y * x)) / x = L(x,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(136,a,1606,a(flip),b,257,a)].">
      <j1 rule="hyper" parents="136 1606 257"/>
    </justification>
  </clause>

  <clause id="1662">
    <literal><![CDATA[
      L(x,y,T(z,u) * w) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(1325(a,2),1578(a,1,3,1))].">
      <j1 rule="para" parents="1325 1578"/>
    </justification>
  </clause>

  <clause id="1663">
    <literal><![CDATA[
      L(x,y,L(T(z,u),w,v5) * v6) = L(x,y,L(z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(25(a,2),1662(a,1,3,1))].">
      <j1 rule="para" parents="25 1662"/>
    </justification>
  </clause>

  <clause id="1664">
    <literal><![CDATA[
      L(x,y,(z / u) * w) = L(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(116(a,1),1662(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="116 1662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1665">
    <literal><![CDATA[
      L(x,y,z * (u * (z \ 1))) = L(x,y,L(u,z \ 1,z))
    ]]></literal>
    <justification jstring="[para(527(a,1),1585(a,1,3))].">
      <j1 rule="para" parents="527 1585"/>
    </justification>
  </clause>

  <clause id="1666">
    <literal><![CDATA[
      L(x,y,T((z / u) * w,v5)) = L(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1581,a,b,1664,a)].">
      <j1 rule="hyper" parents="63 1581 1664"/>
    </justification>
  </clause>

  <clause id="1667">
    <literal><![CDATA[
      L(x,y,(z \ u) * z) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),1664(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12 1664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1668">
    <literal><![CDATA[
      L(x,y,z * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1667(a,1,3,1))].">
      <j1 rule="para" parents="9 1667"/>
    </justification>
  </clause>

  <clause id="1669">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * (w * u)) = L(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[para(18(a,2),1667(a,1,3,1))].">
      <j1 rule="para" parents="18 1667"/>
    </justification>
  </clause>

  <clause id="1671">
    <literal><![CDATA[
      L(x,y,L(z * u,w,v5)) = L(x,y,L(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(1360(a,1),1667(a,1,3))].">
      <j1 rule="para" parents="1360 1667"/>
    </justification>
  </clause>

  <clause id="1672">
    <literal><![CDATA[
      L(x,y,T(z * u,w)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1581,a,b,1668,a)].">
      <j1 rule="hyper" parents="316 1581 1668"/>
    </justification>
  </clause>

  <clause id="1673">
    <literal><![CDATA[
      L(L(x,y,z * u),w,K(v5,v6)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,155,a,b,1668,a)].">
      <j1 rule="hyper" parents="316 155 1668"/>
    </justification>
  </clause>

  <clause id="1674">
    <literal><![CDATA[
      L(x,y,z * T(u,w)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1662,a(flip),b,1668,a),flip(a)].">
      <j1 rule="hyper" parents="316 1662 1668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      L(x,y,z * (K(u,w) * v5)) = L(x,y,v5 * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1578,a(flip),b,1668,a),flip(a)].">
      <j1 rule="hyper" parents="316 1578 1668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1676">
    <literal><![CDATA[
      L(x,y,z * K(u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1575,a(flip),b,1668,a),flip(a)].">
      <j1 rule="hyper" parents="316 1575 1668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1677">
    <literal><![CDATA[
      L(x \ ((y * z) \ u),x,z * y) = ((y * z) * x) \ u
    ]]></literal>
    <justification jstring="[hyper(316,a,298,a(flip),b,1668,a),flip(a)].">
      <j1 rule="hyper" parents="316 298 1668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1678">
    <literal><![CDATA[
      L(x,y,(z * z) \ (u * z)) = L(x,y,(z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(577(a,1),1672(a,1,3))].">
      <j1 rule="para" parents="577 1672"/>
    </justification>
  </clause>

  <clause id="1679">
    <literal><![CDATA[
      L(x,y,z * T(u,w)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(316,a,1668,a,b,1674,a),flip(a)].">
      <j1 rule="hyper" parents="316 1668 1674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1680">
    <literal><![CDATA[
      L(x,y,z \ ((u * u) * w)) = L(x,y,(u * u) * (z \ w))
    ]]></literal>
    <justification jstring="[para(822(a,1),1674(a,1,3))].">
      <j1 rule="para" parents="822 1674"/>
    </justification>
  </clause>

  <clause id="1681">
    <literal><![CDATA[
      L(x,y,z * L(T(u,w),v5,v6)) = L(x,y,z * L(u,v5,v6))
    ]]></literal>
    <justification jstring="[para(25(a,2),1679(a,1,3,2))].">
      <j1 rule="para" parents="25 1679"/>
    </justification>
  </clause>

  <clause id="1682">
    <literal><![CDATA[
      L(x,y,z * (u / w)) = L(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[para(116(a,1),1679(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="116 1679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1683">
    <literal><![CDATA[
      L(x,y,z * ((u \ w) \ w)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(115(a,1),1679(a,1,3,2))].">
      <j1 rule="para" parents="115 1679"/>
    </justification>
  </clause>

  <clause id="1684">
    <literal><![CDATA[
      L(x,y,z * (K(u,w) * v5)) = L(x,y,z * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,1668,a,b,1675,a),flip(a)].">
      <j1 rule="hyper" parents="316 1668 1675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1685">
    <literal><![CDATA[
      L(x,y,z * ((u * u) \ (w * v5))) = L(x,y,z * (w * (v5 / (u * u))))
    ]]></literal>
    <justification jstring="[para(683(a,1),1682(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="683 1682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1686">
    <literal><![CDATA[
      x * (x * (y \ (y / x))) = L(x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,1640,a(flip),b,1064,a(flip))].">
      <j1 rule="hyper" parents="139 1640 1064"/>
    </justification>
  </clause>

  <clause id="1687">
    <literal><![CDATA[
      L(L(x,y \ (y / z),z),z * (y \ (y / z)),z) = L(z,z,z \ y) \ (z * (z * ((y \ (y / z)) * x)))
    ]]></literal>
    <justification jstring="[para(1686(a,1),460(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1686 460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1688">
    <literal><![CDATA[
      L(x,y,L((z * z) \ (u * w),v5,v6)) = L(x,y,L(u * (w / (z * z)),v5,v6))
    ]]></literal>
    <justification jstring="[para(683(a,1),1591(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="683 1591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1689">
    <literal><![CDATA[
      L(x,y,L((z * z) \ T(u * z,z),w,v5)) = L(x,y,L(z \ R(u,z,z),w,v5))
    ]]></literal>
    <justification jstring="[para(681(a,1),1591(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="681 1591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1690">
    <literal><![CDATA[
      x * L(y \ z,y,y \ L(y,u,w)) = x * (L(y,u,w) \ ((y \ L(y,u,w)) * z))
    ]]></literal>
    <justification jstring="[para(1272(a,1),1657(a,2,2,2,1))].">
      <j1 rule="para" parents="1272 1657"/>
    </justification>
  </clause>

  <clause id="1691">
    <literal><![CDATA[
      L(x,y,(z / (u * u)) \ w) = L(x,y,z \ (w * (u * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,1586,a(flip),b,1596,a)].">
      <j1 rule="hyper" parents="63 1586 1596"/>
    </justification>
  </clause>

  <clause id="1692">
    <literal><![CDATA[
      L(x,y,z * L((u * u) \ u,w,v5)) = L(x,y,z * L(u \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(283(a,1),1681(a,1,3,2,1))].">
      <j1 rule="para" parents="283 1681"/>
    </justification>
  </clause>

  <clause id="1693">
    <literal><![CDATA[
      L(x,y,(z * u) \ (w * (u * u))) = L(x,y,(z * (u \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(562(a,1),1691(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="562 1691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1694">
    <literal><![CDATA[
      ((x / (y * x)) * y) / R(1 / y,y,x) = L(y,x / (y * x),y)
    ]]></literal>
    <justification jstring="[para(1633(a,1),409(a,1,1))].">
      <j1 rule="para" parents="1633 409"/>
    </justification>
  </clause>

  <clause id="1695">
    <literal><![CDATA[
      (x \ 1) \ (y \ (y / x)) = x * (y \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(35,a,1644,a,b,1645,a),flip(a)].">
      <j1 rule="hyper" parents="35 1644 1645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1696">
    <literal><![CDATA[
      L(x,y,L(z,z,u)) = L(x,y,(u * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(18(a,2),1693(a,1,3))].">
      <j1 rule="para" parents="18 1693"/>
    </justification>
  </clause>

  <clause id="1698">
    <literal><![CDATA[
      L(x,y,L(z / (u \ 1),u \ 1,u \ 1)) = L(x,y,(u \ (u \ 1)) \ ((1 / u) * z))
    ]]></literal>
    <justification jstring="[para(1593(a,1),1591(a,2,3))].">
      <j1 rule="para" parents="1593 1591"/>
    </justification>
  </clause>

  <clause id="1699">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w),v5,v6)) = L(x,y,L(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,1575,a(flip),b,1579,a)].">
      <j1 rule="hyper" parents="63 1575 1579"/>
    </justification>
  </clause>

  <clause id="1700">
    <literal><![CDATA[
      R(x,y,z * (u * u)) = ((x * y) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(11(a,1),1570(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 1570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1701">
    <literal><![CDATA[
      R(x,y,z * (u * u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,20,a,b,1700,a),flip(a)].">
      <j1 rule="hyper" parents="316 20 1700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1702">
    <literal><![CDATA[
      R(x,y,z / (u * u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),1701(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12 1701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1703">
    <literal><![CDATA[
      R(x,y,z * (u * (w * w))) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(32(a,1),1701(a,1,3))].">
      <j1 rule="para" parents="32 1701"/>
    </justification>
  </clause>

  <clause id="1704">
    <literal><![CDATA[
      R(x,y,z * (u \ (1 / u))) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(287(a,1),1701(a,1,3,2))].">
      <j1 rule="para" parents="287 1701"/>
    </justification>
  </clause>

  <clause id="1705">
    <literal><![CDATA[
      R(x,y,z \ (u * u)) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(389(a,1),1701(a,1,3))].">
      <j1 rule="para" parents="389 1701"/>
    </justification>
  </clause>

  <clause id="1707">
    <literal><![CDATA[
      R(x,y,z \ (u * (w * w))) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(388(a,2),1701(a,1,3))].">
      <j1 rule="para" parents="388 1701"/>
    </justification>
  </clause>

  <clause id="1708">
    <literal><![CDATA[
      R(x,y,z \ (u / (w * w))) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(586(a,1),1701(a,1,3)),flip(a)].">
      <j1 rule="para" parents="586 1701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1709">
    <literal><![CDATA[
      R(x,y,z * (1 / u)) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(411(a,1),1701(a,1,3))].">
      <j1 rule="para" parents="411 1701"/>
    </justification>
  </clause>

  <clause id="1710">
    <literal><![CDATA[
      R(x,y,L(z * (u * u),w,v5)) = R(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(1058(a,2),1701(a,1,3))].">
      <j1 rule="para" parents="1058 1701"/>
    </justification>
  </clause>

  <clause id="1711">
    <literal><![CDATA[
      R(x,y,z * (u \ 1)) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(562(a,1),1702(a,1,3))].">
      <j1 rule="para" parents="562 1702"/>
    </justification>
  </clause>

  <clause id="1712">
    <literal><![CDATA[
      R(x,y,z * (u / (w * w))) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(683(a,1),1702(a,1,3))].">
      <j1 rule="para" parents="683 1702"/>
    </justification>
  </clause>

  <clause id="1713">
    <literal><![CDATA[
      R(x,y,L(z \ 1,u,w)) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1110(a,1),1702(a,1,3))].">
      <j1 rule="para" parents="1110 1702"/>
    </justification>
  </clause>

  <clause id="1714">
    <literal><![CDATA[
      R(x,y,L(1 / z,u,w)) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1228(a,1),1704(a,1,3))].">
      <j1 rule="para" parents="1228 1704"/>
    </justification>
  </clause>

  <clause id="1715">
    <literal><![CDATA[
      R(x,y,z \ (u * u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1033,a(flip),b,1705,a),flip(a)].">
      <j1 rule="hyper" parents="316 1033 1705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1716">
    <literal><![CDATA[
      R(x,y,z * (u * (z * u))) = R(x,y,a(z,u,z * u))
    ]]></literal>
    <justification jstring="[para(14(a,2),1715(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14 1715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1717">
    <literal><![CDATA[
      R(x,y,L(z \ u,z,u)) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(102(a,2),1715(a,1,3))].">
      <j1 rule="para" parents="102 1715"/>
    </justification>
  </clause>

  <clause id="1718">
    <literal><![CDATA[
      R(x,y,z \ L(z,u,w)) = R(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1503(a,1),1715(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1503 1715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1720">
    <literal><![CDATA[
      R(x,y,(z \ 1) * z) = x
    ]]></literal>
    <justification jstring="[hyper(503,a,1711,a),flip(a)].">
      <j1 rule="hyper" parents="503 1711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1721">
    <literal><![CDATA[
      R(x,y,L(z,u,w) \ z) = R(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1002(a,1),1711(a,1,3))].">
      <j1 rule="para" parents="1002 1711"/>
    </justification>
  </clause>

  <clause id="1722">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(272(a,2),1720(a,1,3))].">
      <j1 rule="para" parents="272 1720"/>
    </justification>
  </clause>

  <clause id="1723">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(1722(a,1),51(a,2))].">
      <j1 rule="para" parents="1722 51"/>
    </justification>
  </clause>

  <clause id="1724">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(939(a,1),1722(a,1,3))].">
      <j1 rule="para" parents="939 1722"/>
    </justification>
  </clause>

  <clause id="1725">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(1724(a,1),51(a,2))].">
      <j1 rule="para" parents="1724 51"/>
    </justification>
  </clause>

  <clause id="1727">
    <literal><![CDATA[
      R(x,y,z * ((u * w) * w)) = R(x,y,z * R(u,w,w))
    ]]></literal>
    <justification jstring="[para(109(a,1),1703(a,1,3,2))].">
      <j1 rule="para" parents="109 1703"/>
    </justification>
  </clause>

  <clause id="1728">
    <literal><![CDATA[
      R(x,y,z \ (u * (w \ 1))) = R(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(562(a,1),1708(a,1,3,2))].">
      <j1 rule="para" parents="562 1708"/>
    </justification>
  </clause>

  <clause id="1729">
    <literal><![CDATA[
      R(x,y,z * (u * (w \ 1))) = R(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(562(a,1),1712(a,1,3,2))].">
      <j1 rule="para" parents="562 1712"/>
    </justification>
  </clause>

  <clause id="1731">
    <literal><![CDATA[
      R(x,y,z * (L(u,w,v5) \ u)) = R(x,y,z * (u * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(1002(a,1),1729(a,1,3,2))].">
      <j1 rule="para" parents="1002 1729"/>
    </justification>
  </clause>

  <clause id="1732">
    <literal><![CDATA[
      (x * R(x \ 1,x,x \ y)) \ R(1 / x,x,x \ y) = L(x \ 1,x,(x \ y) / y)
    ]]></literal>
    <justification jstring="[para(370(a,1),754(a,2,3))].">
      <j1 rule="para" parents="370 754"/>
    </justification>
  </clause>

  <clause id="1733">
    <literal><![CDATA[
      x * (T(y,x) * T(T(y,x) \ 1,z)) = (y * x) * T((y * x) \ x,z)
    ]]></literal>
    <justification jstring="[para(114(a,1),783(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="114 783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1734">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(253,a,1220,a(flip),b,1733,a),flip(a)].">
      <j1 rule="hyper" parents="253 1220 1733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1735">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1014,a,b,1734,a),flip(a)].">
      <j1 rule="hyper" parents="63 1014 1734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1736">
    <literal><![CDATA[
      T(x * T(x \ 1,x),y) * (T(x,y) \ x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(1734(a,1),1191(a,1,1))].">
      <j1 rule="para" parents="1734 1191"/>
    </justification>
  </clause>

  <clause id="1737">
    <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(1338(a,1),1735(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1338 1735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1738">
    <literal><![CDATA[
      T(K(x \ 1,x),y) * (T(x,y) \ x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(337(a,1),1736(a,1,1,1))].">
      <j1 rule="para" parents="337 1736"/>
    </justification>
  </clause>

  <clause id="1739">
    <literal><![CDATA[
      (x \ 1) * L(x \ L(x,y,z),u,w) = x \ L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1064(a,1),1072(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1064 1072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1740">
    <literal><![CDATA[
      (x \ 1) \ (x \ L(x \ L(x,y,z),u,w)) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(144,a,1739,a)].">
      <j1 rule="hyper" parents="144 1739"/>
    </justification>
  </clause>

  <clause id="1741">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x \ y),(x \ y) * (y \ x)) = y \ (x * (x \ y))
    ]]></literal>
    <justification jstring="[para(1267(a,1),1202(a,2,2,2))].">
      <j1 rule="para" parents="1267 1202"/>
    </justification>
  </clause>

  <clause id="1742">
    <literal><![CDATA[
      (x \ 1) * R(K(x,x \ 1) * ((1 / x) \ y),z,u) = R(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(1028(a,2),1210(a,1,2))].">
      <j1 rule="para" parents="1028 1210"/>
    </justification>
  </clause>

  <clause id="1743">
    <literal><![CDATA[
      ((1 / (x * y)) * x) \ L((1 / (x * y)) * x,z,u) = (1 / (x * y)) * (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),1506(a,2,2,2,1))].">
      <j1 rule="para" parents="9 1506"/>
    </justification>
  </clause>

  <clause id="1746">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(347,a,1520,a),flip(a)].">
      <j1 rule="hyper" parents="347 1520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1748">
    <literal><![CDATA[
      (1 / T(x,y)) * T(x,z) = T(x,z) / T(x,y)
    ]]></literal>
    <justification jstring="[para(1322(a,1),1746(a,1,2,1))].">
      <j1 rule="para" parents="1322 1746"/>
    </justification>
  </clause>

  <clause id="1749">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / T(x,z)) = T(1 / T(x,z),T(x,y))
    ]]></literal>
    <justification jstring="[hyper(390,a,xx,b,1748,a),flip(a)].">
      <j1 rule="hyper" parents="390 1748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1750">
    <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(1749(a,1),1737(a,1,1))].">
      <j1 rule="para" parents="1749 1737"/>
    </justification>
  </clause>

  <clause id="1751">
    <literal><![CDATA[
      K(T(1 / T(x,y),T(x,z)),T(x,z)) = T(K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(337(a,1),1750(a,2,1))].">
      <j1 rule="para" parents="337 1750"/>
    </justification>
  </clause>

  <clause id="1752">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x \ y),(x \ y) * (y \ x)) = 1
    ]]></literal>
    <justification jstring="[hyper(316,a,268,a(flip),b,1741,a),flip(a)].">
      <j1 rule="hyper" parents="316 268 1741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1754">
    <literal><![CDATA[
      T(1 / (x \ y),(y \ x) * (x \ y)) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[para(1752(a,1),961(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1752 961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1474,a(flip),b,1754,a)].">
      <j1 rule="hyper" parents="63 1474 1754"/>
    </justification>
  </clause>

  <clause id="1756">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),1755(a,1,1,2))].">
      <j1 rule="para" parents="9 1755"/>
    </justification>
  </clause>

  <clause id="1757">
    <literal><![CDATA[
      (T(x,y) * ((x * y) \ y)) \ (y \ (x * y)) = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(22(a,2),1755(a,1,1,1))].">
      <j1 rule="para" parents="22 1755"/>
    </justification>
  </clause>

  <clause id="1758">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y
    ]]></literal>
    <justification jstring="[para(9(a,1),1756(a,2,2))].">
      <j1 rule="para" parents="9 1756"/>
    </justification>
  </clause>

  <clause id="1759">
    <literal><![CDATA[
      L(x \ 1,x,(y * x) \ y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(379,a,1758,a)].">
      <j1 rule="hyper" parents="379 1758"/>
    </justification>
  </clause>

  <clause id="1760">
    <literal><![CDATA[
      L(x \ 1,x,y \ (y / x)) = 1 / x
    ]]></literal>
    <justification jstring="[para(12(a,1),1759(a,1,3,1))].">
      <j1 rule="para" parents="12 1759"/>
    </justification>
  </clause>

  <clause id="1761">
    <literal><![CDATA[
      L((x * y) \ x,y,(z * y) \ z) = L(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(1759(a,1),366(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1759 366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1762">
    <literal><![CDATA[
      ((x \ (x / y)) * y) \ (x \ (x / y)) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(63,a,232,a(flip),b,1760,a)].">
      <j1 rule="hyper" parents="63 232 1760"/>
    </justification>
  </clause>

  <clause id="1763">
    <literal><![CDATA[
      L(1 / x,x,y) = 1 / (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1297,a(flip),b,1761,a),flip(a)].">
      <j1 rule="hyper" parents="63 1297 1761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1764">
    <literal><![CDATA[
      L(1 / x,x,y) \ 1 = 1 / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(137,a,1763,a,b,163,a)].">
      <j1 rule="hyper" parents="137 1763 163"/>
    </justification>
  </clause>

  <clause id="1766">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = R(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(1211(a,1),1742(a,1,2,1))].">
      <j1 rule="para" parents="1211 1742"/>
    </justification>
  </clause>

  <clause id="1767">
    <literal><![CDATA[
      (x \ R(x * y,z,u)) * x = R(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,901,a(flip),b,1766,a(flip))].">
      <j1 rule="hyper" parents="138 901 1766"/>
    </justification>
  </clause>

  <clause id="1768">
    <literal><![CDATA[
      R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),1767(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1769">
    <literal><![CDATA[
      (R(x,y,z) \ x) * R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,182,a(flip),b,1768,a),flip(a)].">
      <j1 rule="hyper" parents="42 182 1768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1770">
    <literal><![CDATA[
      (x \ R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(182(a,1),1768(a,1,1)),flip(a)].">
      <j1 rule="para" parents="182 1768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1771">
    <literal><![CDATA[
      R(x * K(y \ x,y),z,u) = (y \ R(x,z,u)) * y
    ]]></literal>
    <justification jstring="[para(307(a,2),1768(a,1,1))].">
      <j1 rule="para" parents="307 1768"/>
    </justification>
  </clause>

  <clause id="1772">
    <literal><![CDATA[
      x / R(x,y,z) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(149,a,1769,a)].">
      <j1 rule="hyper" parents="149 1769"/>
    </justification>
  </clause>

  <clause id="1774">
    <literal><![CDATA[
      R(x,y,z) / x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(149,a,1770,a)].">
      <j1 rule="hyper" parents="149 1770"/>
    </justification>
  </clause>

  <clause id="1775">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,1770,a)].">
      <j1 rule="hyper" parents="144 1770"/>
    </justification>
  </clause>

  <clause id="1777">
    <literal><![CDATA[
      L(x,y,z) / L(R(x,u,w),y,z) = R(L(x,y,z),u,w) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(29(a,1),1772(a,1,2))].">
      <j1 rule="para" parents="29 1772"/>
    </justification>
  </clause>

  <clause id="1778">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,985,a,b,1774,a)].">
      <j1 rule="hyper" parents="63 985 1774"/>
    </justification>
  </clause>

  <clause id="1780">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) \ R(1 / x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[para(987(a,1),1775(a,1,1))].">
      <j1 rule="para" parents="987 1775"/>
    </justification>
  </clause>

  <clause id="1781">
    <literal><![CDATA[
      T(1 / x,R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(253,a,1778,a,b,978,a)].">
      <j1 rule="hyper" parents="253 1778 978"/>
    </justification>
  </clause>

  <clause id="1782">
    <literal><![CDATA[
      ((x / (y * x)) * y) / R(1 / y,y,x) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(136,a,988,a(flip),b,1778,a)].">
      <j1 rule="hyper" parents="136 988 1778"/>
    </justification>
  </clause>

  <clause id="1783">
    <literal><![CDATA[
      T(1 / (1 / x),R(1 / x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,83,a(flip),b,1781,a),flip(a)].">
      <j1 rule="hyper" parents="316 83 1781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1784">
    <literal><![CDATA[
      T(1 / (1 / x),y / (x * y)) = x
    ]]></literal>
    <justification jstring="[para(234(a,1),1783(a,1,2))].">
      <j1 rule="para" parents="234 1783"/>
    </justification>
  </clause>

  <clause id="1785">
    <literal><![CDATA[
      T(x,y / (x * y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1784(a,1),1101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1784 1101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1786">
    <literal><![CDATA[
      T(x,y / (x * y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,115,a(flip),b,1785,a),flip(a)].">
      <j1 rule="hyper" parents="316 115 1785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1787">
    <literal><![CDATA[
      T(x,(x \ y) / y) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),1786(a,1,2,2))].">
      <j1 rule="para" parents="10 1786"/>
    </justification>
  </clause>

  <clause id="1788">
    <literal><![CDATA[
      T(x / y,y / x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(12(a,1),1786(a,1,2,2))].">
      <j1 rule="para" parents="12 1786"/>
    </justification>
  </clause>

  <clause id="1789">
    <literal><![CDATA[
      T(x / (y * x),y) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(11(a,1),1788(a,1,2))].">
      <j1 rule="para" parents="11 1788"/>
    </justification>
  </clause>

  <clause id="1790">
    <literal><![CDATA[
      T(((x / y) \ 1) \ 1,y) = T(y \ x,y / x)
    ]]></literal>
    <justification jstring="[para(1788(a,1),260(a,1,1))].">
      <j1 rule="para" parents="1788 260"/>
    </justification>
  </clause>

  <clause id="1791">
    <literal><![CDATA[
      R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,620,a(flip),b,1789,a)].">
      <j1 rule="hyper" parents="63 620 1789"/>
    </justification>
  </clause>

  <clause id="1792">
    <literal><![CDATA[
      L(x,y / (x * y),x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1694,a(flip),b,1782,a)].">
      <j1 rule="hyper" parents="63 1694 1782"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      L(T(x,y),z / (x * z),x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1792(a,1),25(a,2,1))].">
      <j1 rule="para" parents="1792 25"/>
    </justification>
  </clause>

  <clause id="1795">
    <literal><![CDATA[
      L(x,y,z) / L(R(x,u,w),y,z) = L(R(x,u,w),y,z) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(29(a,1),1777(a,2,1))].">
      <j1 rule="para" parents="29 1777"/>
    </justification>
  </clause>

  <clause id="1796">
    <literal><![CDATA[
      (K(x,y) * (z * (u * w))) \ (K(x,y) * ((z * u) * w)) = a(K(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(656(a,1),649(a,1,2))].">
      <j1 rule="para" parents="656 649"/>
    </justification>
  </clause>

  <clause id="1797">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ 1) * L(x,y,z)) = (x \ 1) * K(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1342(a,1),873(a,1,1,1))].">
      <j1 rule="para" parents="1342 873"/>
    </justification>
  </clause>

  <clause id="1798">
    <literal><![CDATA[
      (x \ 1) * K(x \ 1,L(x,y,z)) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,1797,a),flip(a)].">
      <j1 rule="hyper" parents="325 1797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1799">
    <literal><![CDATA[
      x * T(x \ 1,L(x,y,z)) = K(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,1332,a,b,1798,a)].">
      <j1 rule="hyper" parents="34 1332 1798"/>
    </justification>
  </clause>

  <clause id="1800">
    <literal><![CDATA[
      ((x * y) \ z) * ((y \ (x \ z)) \ 1) = (y \ (x \ z)) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(298(a,1),975(a,1,2)),flip(a)].">
      <j1 rule="para" parents="298 975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1801">
    <literal><![CDATA[
      (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,408,a(flip),b,1315,a),flip(a)].">
      <j1 rule="hyper" parents="316 408 1315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1802">
    <literal><![CDATA[
      (x \ (x * y)) \ 1 = (y * (z * T(z \ 1,y))) \ (y \ ((L(z \ 1,z,y) * y) / L(z \ 1,z,y)))
    ]]></literal>
    <justification jstring="[para(1801(a,1),1238(a,2,1))].">
      <j1 rule="para" parents="1801 1238"/>
    </justification>
  </clause>

  <clause id="1803">
    <literal><![CDATA[
      (x / (y \ 1)) * L(L(L(y,y,x) \ 1,L(y,y,x),x),z,u) = x * (L(y,y,x) \ L(L(y,y,x),z,u))
    ]]></literal>
    <justification jstring="[para(1064(a,1),1450(a,2,2))].">
      <j1 rule="para" parents="1064 1450"/>
    </justification>
  </clause>

  <clause id="1804">
    <literal><![CDATA[
      a(K(x,y) * z,u,w) = (z * (u * w)) \ ((z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,477,a(flip),b,1796,a),flip(a)].">
      <j1 rule="hyper" parents="63 477 1796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1806">
    <literal><![CDATA[
      a(K(x,y) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,14,a,b,1804,a),flip(a)].">
      <j1 rule="hyper" parents="316 14 1804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1807">
    <literal><![CDATA[
      a(1 * x,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(180(a,1),1806(a,1,1,1))].">
      <j1 rule="para" parents="180 1806"/>
    </justification>
  </clause>

  <clause id="1808">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(436(a,1),1806(a,1,1)),flip(a)].">
      <j1 rule="para" parents="436 1806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1809">
    <literal><![CDATA[
      a((x \ 1) \ 1,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(931(a,1),1806(a,1,1)),flip(a)].">
      <j1 rule="para" parents="931 1806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1810">
    <literal><![CDATA[
      a(T(x,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(1325(a,2),1806(a,1,1))].">
      <j1 rule="para" parents="1325 1806"/>
    </justification>
  </clause>

  <clause id="1811">
    <literal><![CDATA[
      a(x \ (y * x),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(22(a,1),1810(a,1,1))].">
      <j1 rule="para" parents="22 1810"/>
    </justification>
  </clause>

  <clause id="1812">
    <literal><![CDATA[
      a(L(T(x,y),z,u),w,v5) = a(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(25(a,2),1810(a,1,1))].">
      <j1 rule="para" parents="25 1810"/>
    </justification>
  </clause>

  <clause id="1813">
    <literal><![CDATA[
      a(x / y,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(116(a,1),1810(a,1,1)),flip(a)].">
      <j1 rule="para" parents="116 1810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1815">
    <literal><![CDATA[
      a(L(x / y,z,u),w,v5) = a(L(y \ x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(261(a,1),1810(a,1,1)),flip(a)].">
      <j1 rule="para" parents="261 1810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1816">
    <literal><![CDATA[
      a((x * y) * (x \ 1),z,u) = a(R(y,x,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(627(a,1),1810(a,1,1)),flip(a)].">
      <j1 rule="para" parents="627 1810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1817">
    <literal><![CDATA[
      a((x \ (x \ 1)) \ y,z,u) = a(y * (x * x),z,u)
    ]]></literal>
    <justification jstring="[para(447(a,1),1810(a,1,1))].">
      <j1 rule="para" parents="447 1810"/>
    </justification>
  </clause>

  <clause id="1818">
    <literal><![CDATA[
      a(x / (y * (z * z)),u,w) = a(y \ (x / (z * z)),u,w)
    ]]></literal>
    <justification jstring="[para(395(a,1),1811(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="395 1811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1819">
    <literal><![CDATA[
      a(x / (y / (z * z)),u,w) = a(y \ (x * (z * z)),u,w)
    ]]></literal>
    <justification jstring="[para(595(a,1),1811(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="595 1811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1820">
    <literal><![CDATA[
      (((x / y) / z) * (z * y)) \ x = a(z \ (x / y),z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,302,a,b,1813,a)].">
      <j1 rule="hyper" parents="63 302 1813"/>
    </justification>
  </clause>

  <clause id="1821">
    <literal><![CDATA[
      a((x * x) \ (y * z),u,w) = a(y * (z / (x * x)),u,w)
    ]]></literal>
    <justification jstring="[para(683(a,1),1813(a,1,1)),flip(a)].">
      <j1 rule="para" parents="683 1813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1822">
    <literal><![CDATA[
      a(L(x,x,y),z,u) = a((y / (x \ 1)) / y,z,u)
    ]]></literal>
    <justification jstring="[para(1447(a,2),1813(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1447 1813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1823">
    <literal><![CDATA[
      a(L(L(T(x,y),z,u),w,v5),v6,v7) = a(L(L(x,z,u),w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(25(a,2),1812(a,1,1,1))].">
      <j1 rule="para" parents="25 1812"/>
    </justification>
  </clause>

  <clause id="1824">
    <literal><![CDATA[
      a(L(x,x,y),z,u) = a(y \ (y / (x \ 1)),z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,1813,a(flip),b,1822,a),flip(a)].">
      <j1 rule="hyper" parents="316 1813 1822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1825">
    <literal><![CDATA[
      a((x * (y * y)) \ z,u,w) = a(x \ (z / (y * y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1813,a(flip),b,1818,a)].">
      <j1 rule="hyper" parents="63 1813 1818"/>
    </justification>
  </clause>

  <clause id="1826">
    <literal><![CDATA[
      a((x / (y * y)) \ z,u,w) = a(x \ (z * (y * y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1813,a(flip),b,1819,a)].">
      <j1 rule="hyper" parents="63 1813 1819"/>
    </justification>
  </clause>

  <clause id="1827">
    <literal><![CDATA[
      a((x / (y * y)) \ z,u,w) = a((x \ z) * (y * y),u,w)
    ]]></literal>
    <justification jstring="[para(388(a,1),1826(a,2,1))].">
      <j1 rule="para" parents="388 1826"/>
    </justification>
  </clause>

  <clause id="1828">
    <literal><![CDATA[
      a((x \ y) * (x * x),z,u) = a((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(281(a,1),1827(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="281 1827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1829">
    <literal><![CDATA[
      x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * x) * R((y * x) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(114(a,1),784(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="114 784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1830">
    <literal><![CDATA[
      x * (T(y,x) * R(T(y,x) \ 1,z,u)) = y * (x * R(x \ (y \ x),z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,883,a(flip),b,1829,a),flip(a)].">
      <j1 rule="hyper" parents="316 883 1829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1831">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(253,a,1543,a(flip),b,1829,a),flip(a)].">
      <j1 rule="hyper" parents="253 1543 1829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1832">
    <literal><![CDATA[
      T((x / y) * R((x / y) \ 1,z,u),y) = (y \ x) * R(T(x / y,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(116(a,1),1831(a,1,1)),flip(a)].">
      <j1 rule="para" parents="116 1831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1833">
    <literal><![CDATA[
      x * (T(y,x) * L(T(y,x) \ 1,z,u)) = (y * x) * L((y * x) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(114(a,1),785(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="114 785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1834">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(253,a,1230,a(flip),b,1833,a),flip(a)].">
      <j1 rule="hyper" parents="253 1230 1833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1835">
    <literal><![CDATA[
      T(x * L(x \ 1,y,z),u) / T(x,u) = L(1 / T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(136,a,1834,a(flip),b,602,a)].">
      <j1 rule="hyper" parents="136 1834 602"/>
    </justification>
  </clause>

  <clause id="1836">
    <literal><![CDATA[
      T(((x \ 1) \ 1) * ((x \ 1) * 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1429(a,1),1835(a,1,1,1,2))].">
      <j1 rule="para" parents="1429 1835"/>
    </justification>
  </clause>

  <clause id="1838">
    <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,1533,a,b,1424,a(flip))].">
      <j1 rule="hyper" parents="253 1533 1424"/>
    </justification>
  </clause>

  <clause id="1839">
    <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(241(a,1),1838(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="241 1838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1840">
    <literal><![CDATA[
      x * (T(y,x) * R(T(y,x) \ z,u,w)) = y * (x * R(x \ (y \ (x * z)),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,883,a(flip),b,1425,a),flip(a)].">
      <j1 rule="hyper" parents="63 883 1425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1842">
    <literal><![CDATA[
      (x \ (y \ 1)) * L((x \ (y \ 1)) \ z,u,w) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,1020,a(flip),b,1513,a),flip(a)].">
      <j1 rule="hyper" parents="316 1020 1513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1843">
    <literal><![CDATA[
      x * (y * L(L(T(x,y),z,u),w,v5)) = L(L(x,z,u),w,v5) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,600,a(flip),b,1571,a),flip(a)].">
      <j1 rule="hyper" parents="63 600 1571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1844">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (x * v5) = x * (L(L(x,y,z),u,w) * v5)
    ]]></literal>
    <justification jstring="[para(600(a,1),1843(a,1,2)),flip(a)].">
      <j1 rule="para" parents="600 1843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1845">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ (x * v5) = x * (L(L(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(133,a,160,a(flip),b,1844,a)].">
      <j1 rule="hyper" parents="133 160 1844"/>
    </justification>
  </clause>

  <clause id="1846">
    <literal><![CDATA[
      x * (L(L(x,y,z),u,w) \ (x \ v5)) = L(L(x,y,z),u,w) \ v5
    ]]></literal>
    <justification jstring="[hyper(133,a,76,a(flip),b,1844,a),flip(a)].">
      <j1 rule="hyper" parents="133 76 1844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1847">
    <literal><![CDATA[
      x * (L(L(x,y,z),u,w) \ 1) = L(L(x,y,z),u,w) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,73,a(flip),b,1844,a),flip(a)].">
      <j1 rule="hyper" parents="133 73 1844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1848">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (x \ 1) = x \ L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,73,a(flip),b,1844,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 73 1844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1849">
    <literal><![CDATA[
      x \ (L(L(x,y,z),u,w) \ x) = L(L(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(144,a,1847,a)].">
      <j1 rule="hyper" parents="144 1847"/>
    </justification>
  </clause>

  <clause id="1850">
    <literal><![CDATA[
      R(x,y,z \ (L(L(u,w,v5),v6,v7) \ u)) = R(x,y,z \ (u * L(L(u,w,v5),v6,v7)))
    ]]></literal>
    <justification jstring="[para(1847(a,1),1728(a,1,3,2))].">
      <j1 rule="para" parents="1847 1728"/>
    </justification>
  </clause>

  <clause id="1851">
    <literal><![CDATA[
      x * L(x \ y,x,x \ L(x,z,u)) = L(y,x \ L(x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,1142,a(flip),b,1690,a),flip(a)].">
      <j1 rule="hyper" parents="316 1142 1690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1852">
    <literal><![CDATA[
      (x \ L(x,y,y \ L(y,z,u))) * (x \ y) = L(x \ y,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1415,a,b,1851,a)].">
      <j1 rule="hyper" parents="63 1415 1851"/>
    </justification>
  </clause>

  <clause id="1853">
    <literal><![CDATA[
      (x \ L(x,y,y \ L(y,z,u))) * (x \ y) = L(x \ y,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,1537,a(flip),b,1852,a),flip(a)].">
      <j1 rule="hyper" parents="316 1537 1852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1854">
    <literal><![CDATA[
      T((x / y) * R((x / y) \ 1,z,u),y) = (y \ x) * R((y \ x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(116(a,1),1832(a,2,2,1,1))].">
      <j1 rule="para" parents="116 1832"/>
    </justification>
  </clause>

  <clause id="1855">
    <literal><![CDATA[
      T(T((x / y) * R((x / y) \ 1,z,u),w),y) = T((y \ x) * R((y \ x) \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(1854(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1854 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1856">
    <literal><![CDATA[
      (x \ ((L(x,y,z) \ x) \ 1)) * L((x \ ((L(x,y,z) \ x) \ 1)) \ u,w,v5) = (L(x,y,z) \ 1) * L((x \ (L(x,y,z) \ x)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(1003(a,1),1842(a,2,1))].">
      <j1 rule="para" parents="1003 1842"/>
    </justification>
  </clause>

  <clause id="1857">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ z,u,w)) * y = L((z * y) / x,u,w) * x
    ]]></literal>
    <justification jstring="[para(509(a,1),1018(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="509 1018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1858">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ z,u,w)) * y = x * L(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,602,a(flip),b,1857,a),flip(a)].">
      <j1 rule="hyper" parents="316 602 1857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1859">
    <literal><![CDATA[
      (x * L(x \ (y * z),u,w)) / z = (x / z) * L((x / z) \ y,u,w)
    ]]></literal>
    <justification jstring="[hyper(136,a,602,a(flip),b,1857,a)].">
      <j1 rule="hyper" parents="136 602 1857"/>
    </justification>
  </clause>

  <clause id="1860">
    <literal><![CDATA[
      (x / y) * L((x / y) \ 1,z,u) = (x * L(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1859(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 1859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1861">
    <literal><![CDATA[
      L(x \ 1,x,y) \ L((y * x) \ y,z,u) = (y * x) \ (y * L(x,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),1257(a,2,2,2,1))].">
      <j1 rule="para" parents="9 1257"/>
    </justification>
  </clause>

  <clause id="1862">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * (y * T(y \ 1,u))) * z
    ]]></literal>
    <justification jstring="[para(712(a,1),1404(a,1,1)),flip(a)].">
      <j1 rule="para" parents="712 1404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1866">
    <literal><![CDATA[
      L(x \ 1,x,(x \ y) / y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(63,a,1780,a(flip),b,1732,a),flip(a)].">
      <j1 rule="hyper" parents="63 1780 1732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1868">
    <literal><![CDATA[
      L((x / y) \ 1,x / y,y / x) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(83(a,1),1866(a,1,3,1))].">
      <j1 rule="para" parents="83 1866"/>
    </justification>
  </clause>

  <clause id="1869">
    <literal><![CDATA[
      x * L(x \ (1 * y),x / y,y / x) = ((x / y) * (1 / (x / y))) * y
    ]]></literal>
    <justification jstring="[para(1868(a,1),1858(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1868 1858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1870">
    <literal><![CDATA[
      x * L(x \ (1 * y),x / y,y / x) = K(x / y,(x / y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(1085(a,2),1869(a,2,1))].">
      <j1 rule="para" parents="1085 1869"/>
    </justification>
  </clause>

  <clause id="1871">
    <literal><![CDATA[
      x * L(x \ y,x / y,y / x) = K(x / y,(x / y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),1870(a,1,2,1,2))].">
      <j1 rule="para" parents="7 1870"/>
    </justification>
  </clause>

  <clause id="1872">
    <literal><![CDATA[
      K(x / (y * x),(x / (y * x)) \ 1) * (y * x) = x * L(x \ (y * x),x / (y * x),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1871(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="11 1871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1873">
    <literal><![CDATA[
      (x * R(y / z,z,y)) * (z * (y \ 1)) = R(x,R(y / z,z,y),z * (y \ 1))
    ]]></literal>
    <justification jstring="[para(727(a,1),730(a,1,3)),flip(a)].">
      <j1 rule="para" parents="727 730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1874">
    <literal><![CDATA[
      (x * R(y / z,z,y)) * (z * (y \ 1)) = R(x,R(y / z,z,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1711,a(flip),b,1873,a),flip(a)].">
      <j1 rule="hyper" parents="316 1711 1873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1875">
    <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(272(a,2),1052(a,1,2,1,1))].">
      <j1 rule="para" parents="272 1052"/>
    </justification>
  </clause>

  <clause id="1876">
    <literal><![CDATA[
      (x / (y \ 1)) * L((x / (y \ 1)) \ y,z,u) = ((x / (y \ 1)) \ L(x,z,u)) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1060,a(flip),b,1365,a),flip(a)].">
      <j1 rule="hyper" parents="316 1060 1365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1877">
    <literal><![CDATA[
      (x * L(x,y,z)) \ L(x * L(x,y,z),u,w) = x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(1366(a,1),1494(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1366 1494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1878">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) \ (x * (y \ 1)) = (x * y) / ((y * L(y \ x,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(992(a,1),1381(a,1,2)),flip(a)].">
      <j1 rule="para" parents="992 1381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1879">
    <literal><![CDATA[
      (L(x,T(y,z),z) * (y * z)) \ (x * (y * z)) = a(z,T(y,z),T(x,z * T(y,z)))
    ]]></literal>
    <justification jstring="[para(114(a,1),1409(a,1,2,2))].">
      <j1 rule="para" parents="114 1409"/>
    </justification>
  </clause>

  <clause id="1880">
    <literal><![CDATA[
      (L(x,T(y,z),z) * (y * z)) \ (x * (y * z)) = a(z,T(y,z),T(x,y * z))
    ]]></literal>
    <justification jstring="[para(114(a,1),1879(a,2,3,2))].">
      <j1 rule="para" parents="114 1879"/>
    </justification>
  </clause>

  <clause id="1881">
    <literal><![CDATA[
      L(1 / (x \ 1),(y / (x \ 1)) \ y,y / (x \ 1)) = 1 / (1 / L(x,x,y))
    ]]></literal>
    <justification jstring="[para(83(a,1),1457(a,1,1,2))].">
      <j1 rule="para" parents="83 1457"/>
    </justification>
  </clause>

  <clause id="1882">
    <literal><![CDATA[
      L(x,(y / (x \ 1)) \ y,y / (x \ 1)) = 1 / (1 / L(x,x,y))
    ]]></literal>
    <justification jstring="[para(80(a,1),1881(a,1,1))].">
      <j1 rule="para" parents="80 1881"/>
    </justification>
  </clause>

  <clause id="1885">
    <literal><![CDATA[
      L(x,x \ 1,y / (x \ 1)) = 1 / (1 / L(x,x,y))
    ]]></literal>
    <justification jstring="[para(83(a,1),1882(a,1,2))].">
      <j1 rule="para" parents="83 1882"/>
    </justification>
  </clause>

  <clause id="1886">
    <literal><![CDATA[
      L(x,x \ 1,(x \ 1) \ y) = 1 / (1 / L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1586,a(flip),b,1885,a)].">
      <j1 rule="hyper" parents="63 1586 1885"/>
    </justification>
  </clause>

  <clause id="1888">
    <literal><![CDATA[
      (x \ y) * ((y \ L(y,z,u)) * (y \ L(y,z,u))) = x \ (L(y,z,u) * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(1274(a,2),1498(a,2,2))].">
      <j1 rule="para" parents="1274 1498"/>
    </justification>
  </clause>

  <clause id="1889">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(968(a,1),1509(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="968 1509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1891">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,1394,a(flip),b,1875,a),flip(a)].">
      <j1 rule="hyper" parents="316 1394 1875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1892">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[para(530(a,1),1891(a,1,2,1))].">
      <j1 rule="para" parents="530 1891"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (x \ L(x,y,z)) = (x \ L(x,y,z)) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,9,a(flip),b,1888,a)].">
      <j1 rule="hyper" parents="133 9 1888"/>
    </justification>
  </clause>

  <clause id="1894">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(39,a,282,a,b,1893,a)].">
      <j1 rule="hyper" parents="39 282 1893"/>
    </justification>
  </clause>

  <clause id="1895">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(210,a,1894,a)].">
      <j1 rule="hyper" parents="210 1894"/>
    </justification>
  </clause>

  <clause id="1896">
    <literal><![CDATA[
      x / ((y \ L(y,z,u)) * (y \ L(y,z,u))) = (x / (y \ L(y,z,u))) * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(1894(a,1),566(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1894 566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      R((x \ L(x,y,z)) / u,u,x \ L(x,y,z)) = 1 / (u * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(1894(a,1),728(a,2,2,2))].">
      <j1 rule="para" parents="1894 728"/>
    </justification>
  </clause>

  <clause id="1899">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(969(a,2),1894(a,1,1))].">
      <j1 rule="para" parents="969 1894"/>
    </justification>
  </clause>

  <clause id="1900">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) \ 1 = L(x \ y,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(1252(a,1),1894(a,1,1))].">
      <j1 rule="para" parents="1252 1894"/>
    </justification>
  </clause>

  <clause id="1901">
    <literal><![CDATA[
      L(x,x,y) \ x = (x \ (y \ (y / (x \ 1)))) \ 1
    ]]></literal>
    <justification jstring="[para(1447(a,1),1894(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1447 1894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1902">
    <literal><![CDATA[
      R(x,y,L(L(z,u,w) \ z,v5,v6)) = R(x,y,L(z \ L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(1894(a,1),1713(a,1,3,1))].">
      <j1 rule="para" parents="1894 1713"/>
    </justification>
  </clause>

  <clause id="1904">
    <literal><![CDATA[
      (1 \ (L(x,y,z) * (x \ 1))) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(66(a,2),1899(a,1,1))].">
      <j1 rule="para" parents="66 1899"/>
    </justification>
  </clause>

  <clause id="1905">
    <literal><![CDATA[
      L(x \ y,x \ y,x) \ (x \ y) = ((x \ y) * (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(1451(a,1),1901(a,2,1))].">
      <j1 rule="para" parents="1451 1901"/>
    </justification>
  </clause>

  <clause id="1906">
    <literal><![CDATA[
      L((x * y) \ x,z,u) \ ((x * y) \ x) = ((x * y) \ (x * L(y,z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),1900(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1907">
    <literal><![CDATA[
      L(x \ (y \ x),z,u) \ (x \ (y \ x)) = (x \ (L(y,z,u) * (y \ x))) \ 1
    ]]></literal>
    <justification jstring="[para(604(a,1),1900(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="604 1900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1908">
    <literal><![CDATA[
      (x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))) \ 1 = L(L(x,y,z) \ x,u,w) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(1129(a,1),1900(a,1,1))].">
      <j1 rule="para" parents="1129 1900"/>
    </justification>
  </clause>

  <clause id="1909">
    <literal><![CDATA[
      L((x \ y) \ x,z,u) \ ((x \ y) \ x) = ((x \ y) \ (x \ L(y,z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(1363(a,1),1900(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1363 1900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1914">
    <literal><![CDATA[
      L(x,T(x,y) \ 1,T(x,y)) * (T(x,y) \ 1) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,160,a(flip),b,1192,a),flip(a)].">
      <j1 rule="hyper" parents="316 160 1192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1916">
    <literal><![CDATA[
      K(x / (y * x),(x / (y * x)) \ 1) * (y * x) = x * L(T(y,x),x / (y * x),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),1872(a,2,2,1))].">
      <j1 rule="para" parents="22 1872"/>
    </justification>
  </clause>

  <clause id="1917">
    <literal><![CDATA[
      K(x / (y * x),(x / (y * x)) \ 1) * (y * x) = x * T(1 / (1 / y),x)
    ]]></literal>
    <justification jstring="[para(1794(a,1),1916(a,2,2))].">
      <j1 rule="para" parents="1794 1916"/>
    </justification>
  </clause>

  <clause id="1918">
    <literal><![CDATA[
      K(x / (y * x),(x / (y * x)) \ 1) * (y * x) = (1 / (1 / y)) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,114,a(flip),b,1917,a),flip(a)].">
      <j1 rule="hyper" parents="316 114 1917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1920">
    <literal><![CDATA[
      K(x / (y * x),(x / (y * x)) \ 1) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1096,a,b,1918,a),flip(a)].">
      <j1 rule="hyper" parents="35 1096 1918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1922">
    <literal><![CDATA[
      (1 / L(x,y,z)) \ ((L(x,y,z) \ 1) * (x * (L(x,y,z) \ 1))) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(1463(a,1),1007(a,1,1))].">
      <j1 rule="para" parents="1463 1007"/>
    </justification>
  </clause>

  <clause id="1923">
    <literal><![CDATA[
      (1 / L(x,y,z)) \ ((L(x,y,z) \ 1) * (L(x,y,z) \ x)) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(1002(a,1),1922(a,1,2,2))].">
      <j1 rule="para" parents="1002 1922"/>
    </justification>
  </clause>

  <clause id="1924">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,y,z)) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,1209,a(flip),b,1923,a)].">
      <j1 rule="hyper" parents="63 1209 1923"/>
    </justification>
  </clause>

  <clause id="1925">
    <literal><![CDATA[
      x / ((y \ L(y,z,u)) * (y \ L(y,z,u))) = x * (y * (L(y,z,u) \ (L(y,z,u) \ y)))
    ]]></literal>
    <justification jstring="[para(1894(a,1),1146(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1894 1146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1926">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x * (R(x,y,z) \ L(x \ R(x,y,z),u,w))) = 1 * L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,7,a,b,1255,a),flip(a)].">
      <j1 rule="hyper" parents="316 7 1255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1927">
    <literal><![CDATA[
      (x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))) * (L(x,y,z) \ x) = L(x / L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1378(a,2),1283(a,2,1))].">
      <j1 rule="para" parents="1378 1283"/>
    </justification>
  </clause>

  <clause id="1928">
    <literal><![CDATA[
      (x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))) \ 1 = L(x * L(x,y,z),u,w) \ (x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1877(a,1),1894(a,1,1))].">
      <j1 rule="para" parents="1877 1894"/>
    </justification>
  </clause>

  <clause id="1930">
    <literal><![CDATA[
      (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = (R(y,z,u) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,397,a(flip),b,755,a),flip(a)].">
      <j1 rule="hyper" parents="316 397 755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1931">
    <literal><![CDATA[
      x * (K(x,y) * R(K(x,y) \ y,z,u)) = (R(y,z,u) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,882,a(flip),b,1930,a)].">
      <j1 rule="hyper" parents="63 882 1930"/>
    </justification>
  </clause>

  <clause id="1932">
    <literal><![CDATA[
      x * R(K(x,y) * (K(x,y) \ y),z,u) = (R(y,z,u) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(1028(a,2),1931(a,1,2))].">
      <j1 rule="para" parents="1028 1931"/>
    </justification>
  </clause>

  <clause id="1934">
    <literal><![CDATA[
      (R(x,y,z) * u) * K(u,x) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1932(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1935">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(309,a,1934,a)].">
      <j1 rule="hyper" parents="309 1934"/>
    </justification>
  </clause>

  <clause id="1937">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,R(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,647,a,b,1935,a)].">
      <j1 rule="hyper" parents="316 647 1935"/>
    </justification>
  </clause>

  <clause id="1938">
    <literal><![CDATA[
      K(x,R(y,z,u)) * w = K(x,y) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,1935,a,b,11,a)].">
      <j1 rule="hyper" parents="138 1935 11"/>
    </justification>
  </clause>

  <clause id="1939">
    <literal><![CDATA[
      K(x,L(R(y,z,u),w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(29(a,1),1935(a,1,2))].">
      <j1 rule="para" parents="29 1935"/>
    </justification>
  </clause>

  <clause id="1940">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(234(a,1),1935(a,1,2))].">
      <j1 rule="para" parents="234 1935"/>
    </justification>
  </clause>

  <clause id="1941">
    <literal><![CDATA[
      K(x,y * (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(507(a,1),1935(a,1,2))].">
      <j1 rule="para" parents="507 1935"/>
    </justification>
  </clause>

  <clause id="1942">
    <literal><![CDATA[
      K(x,T(y,y * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(617(a,1),1935(a,1,2)),flip(a)].">
      <j1 rule="para" parents="617 1935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1943">
    <literal><![CDATA[
      K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(509(a,1),1935(a,1,2))].">
      <j1 rule="para" parents="509 1935"/>
    </justification>
  </clause>

  <clause id="1944">
    <literal><![CDATA[
      K(x,T((y * z) / (u * z),w)) = K(x,T(y / u,w))
    ]]></literal>
    <justification jstring="[para(510(a,2),1935(a,1,2))].">
      <j1 rule="para" parents="510 1935"/>
    </justification>
  </clause>

  <clause id="1945">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(618(a,1),1935(a,1,2))].">
      <j1 rule="para" parents="618 1935"/>
    </justification>
  </clause>

  <clause id="1946">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(830(a,1),1935(a,1,2)),flip(a)].">
      <j1 rule="para" parents="830 1935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1947">
    <literal><![CDATA[
      K(x,T((y * z) / u,w)) = K(x,T(y / (u / z),w))
    ]]></literal>
    <justification jstring="[para(726(a,1),1935(a,1,2))].">
      <j1 rule="para" parents="726 1935"/>
    </justification>
  </clause>

  <clause id="1948">
    <literal><![CDATA[
      K(x,T(y,z * y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(920(a,1),1935(a,1,2)),flip(a)].">
      <j1 rule="para" parents="920 1935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1949">
    <literal><![CDATA[
      K(x,T(y,z / y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(924(a,1),1935(a,1,2))].">
      <j1 rule="para" parents="924 1935"/>
    </justification>
  </clause>

  <clause id="1950">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1037(a,1),1935(a,1,2))].">
      <j1 rule="para" parents="1037 1935"/>
    </justification>
  </clause>

  <clause id="1951">
    <literal><![CDATA[
      K(x,1 / y) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(1040(a,1),1935(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1040 1935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1952">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(1651(a,1),1935(a,1,2))].">
      <j1 rule="para" parents="1651 1935"/>
    </justification>
  </clause>

  <clause id="1953">
    <literal><![CDATA[
      R(x,y,K(z \ 1,R(z,u,w))) = x
    ]]></literal>
    <justification jstring="[para(1935(a,2),1722(a,1,3))].">
      <j1 rule="para" parents="1935 1722"/>
    </justification>
  </clause>

  <clause id="1954">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(1937(a,1),1638(a,1,2))].">
      <j1 rule="para" parents="1937 1638"/>
    </justification>
  </clause>

  <clause id="1955">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,1951,a(flip),b,1940,a),flip(a)].">
      <j1 rule="hyper" parents="316 1951 1940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1956">
    <literal><![CDATA[
      K(x,(y \ z) / z) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),1955(a,1,2,2))].">
      <j1 rule="para" parents="10 1955"/>
    </justification>
  </clause>

  <clause id="1957">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),1955(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 1955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1958">
    <literal><![CDATA[
      K(x,L(T(y,y \ z),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(618(a,1),1939(a,1,2,1))].">
      <j1 rule="para" parents="618 1939"/>
    </justification>
  </clause>

  <clause id="1959">
    <literal><![CDATA[
      K(x,L(1 / y,z,u)) = K(x,L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(1040(a,1),1939(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1040 1939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1960">
    <literal><![CDATA[
      K(x,T(y / z,y * u)) = K(x,(z * u) \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1946,a(flip),b,1944,a),flip(a)].">
      <j1 rule="hyper" parents="63 1946 1944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1961">
    <literal><![CDATA[
      K(x,T(y / (z / u),y * u)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1946,a(flip),b,1947,a),flip(a)].">
      <j1 rule="hyper" parents="63 1946 1947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1962">
    <literal><![CDATA[
      K(x,T((R(y,z,u) * z) / (y * z),(R(y,z,u) * z) * u)) = K(x,a(R(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[para(499(a,1),1960(a,2,2))].">
      <j1 rule="para" parents="499 1960"/>
    </justification>
  </clause>

  <clause id="1963">
    <literal><![CDATA[
      K(x,T(R(y,z,u) / y,(R(y,z,u) * z) * u)) = K(x,a(R(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1944,a(flip),b,1962,a)].">
      <j1 rule="hyper" parents="63 1944 1962"/>
    </justification>
  </clause>

  <clause id="1965">
    <literal><![CDATA[
      K(x,T(y \ R(y,z,u),(R(y,z,u) * z) * u)) = K(x,a(R(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[para(1774(a,1),1963(a,1,2,1))].">
      <j1 rule="para" parents="1774 1963"/>
    </justification>
  </clause>

  <clause id="1966">
    <literal><![CDATA[
      K(x,y) \ ((((K(x,y) / z) * u) * w) * v5) = (((1 / z) * u) * w) * v5
    ]]></literal>
    <justification jstring="[para(647(a,1),954(a,1,1))].">
      <j1 rule="para" parents="647 954"/>
    </justification>
  </clause>

  <clause id="1968">
    <literal><![CDATA[
      (x \ (x * y)) \ 1 = (y * (z * T(z \ 1,y))) \ (y \ (y * (z * T(z \ 1,y))))
    ]]></literal>
    <justification jstring="[para(1801(a,1),1802(a,2,2,2))].">
      <j1 rule="para" parents="1801 1802"/>
    </justification>
  </clause>

  <clause id="1969">
    <literal><![CDATA[
      (x \ (x * y)) \ 1 = (y * (z * T(z \ 1,y))) \ (z * T(z \ 1,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),1968(a,2,2))].">
      <j1 rule="para" parents="9 1968"/>
    </justification>
  </clause>

  <clause id="1970">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) \ (y * T(y \ 1,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,166,a(flip),b,1969,a),flip(a)].">
      <j1 rule="hyper" parents="63 166 1969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1972">
    <literal><![CDATA[
      (x * K(y,x)) \ (L(y \ 1,y,x) * T(L(y \ 1,y,x) \ 1,x)) = x \ 1
    ]]></literal>
    <justification jstring="[para(918(a,2),1970(a,1,1,2))].">
      <j1 rule="para" parents="918 1970"/>
    </justification>
  </clause>

  <clause id="1973">
    <literal><![CDATA[
      (x * K(y,x)) \ K(y,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(918(a,2),1972(a,1,2))].">
      <j1 rule="para" parents="918 1972"/>
    </justification>
  </clause>

  <clause id="1974">
    <literal><![CDATA[
      K(x,y) * y = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,357,a,b,1973,a)].">
      <j1 rule="hyper" parents="39 357 1973"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      T(x,K(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(254,a,1974,a)].">
      <j1 rule="hyper" parents="254 1974"/>
    </justification>
  </clause>

  <clause id="1977">
    <literal><![CDATA[
      (K(x,y) \ y) * K(x,y) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,640,a,b,1974,a)].">
      <j1 rule="hyper" parents="34 640 1974"/>
    </justification>
  </clause>

  <clause id="1978">
    <literal><![CDATA[
      (x * K(y,x)) * z = K(y,x) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(138,a,1974,a(flip),b,410,a)].">
      <j1 rule="hyper" parents="138 1974 410"/>
    </justification>
  </clause>

  <clause id="1979">
    <literal><![CDATA[
      ((x * K(y,z)) * z) \ ((x * (z * K(y,z))) * z) = L(z,K(y,z),x)
    ]]></literal>
    <justification jstring="[para(1974(a,1),1466(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1974 1466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1983">
    <literal><![CDATA[
      T(x,y * T(y \ 1,x)) = x
    ]]></literal>
    <justification jstring="[para(1014(a,1),1975(a,1,2))].">
      <j1 rule="para" parents="1014 1975"/>
    </justification>
  </clause>

  <clause id="1984">
    <literal><![CDATA[
      T(x,x \ ((y * x) / y)) = x
    ]]></literal>
    <justification jstring="[para(1314(a,1),1975(a,1,2))].">
      <j1 rule="para" parents="1314 1975"/>
    </justification>
  </clause>

  <clause id="1986">
    <literal><![CDATA[
      K(K(x,y),z) \ z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,840,a,b,1977,a),flip(a)].">
      <j1 rule="hyper" parents="35 840 1977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1988">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * ((T(y,x * T(x \ 1,y)) \ z) \ z) = T(y,y \ z) * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(1983(a,1),407(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1983 407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1989">
    <literal><![CDATA[
      T(x,y \ T(y,x)) = x
    ]]></literal>
    <justification jstring="[para(847(a,1),1983(a,1,2))].">
      <j1 rule="para" parents="847 1983"/>
    </justification>
  </clause>

  <clause id="1990">
    <literal><![CDATA[
      (x \ T(x,y)) * y = y * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,1989,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 1989 22"/>
    </justification>
  </clause>

  <clause id="1991">
    <literal><![CDATA[
      ((x * y) / x) / y = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(209,a,1984,a(flip),b,115,a(flip))].">
      <j1 rule="hyper" parents="209 1984 115"/>
    </justification>
  </clause>

  <clause id="1992">
    <literal><![CDATA[
      (x \ ((y * x) / y)) * x = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(139,a,1984,a(flip),b,115,a(flip))].">
      <j1 rule="hyper" parents="139 1984 115"/>
    </justification>
  </clause>

  <clause id="1993">
    <literal><![CDATA[
      T(T(x,y),T(x,y) \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(241(a,1),1984(a,1,2,2))].">
      <j1 rule="para" parents="241 1984"/>
    </justification>
  </clause>

  <clause id="1994">
    <literal><![CDATA[
      K(K(x,y),K(x,y) * z) \ (K(x,y) * z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,471,a(flip),b,1986,a),flip(a)].">
      <j1 rule="hyper" parents="316 471 1986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1995">
    <literal><![CDATA[
      (T(x,y) \ x) * T(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,1993,a(flip),b,115,a(flip))].">
      <j1 rule="hyper" parents="139 1993 115"/>
    </justification>
  </clause>

  <clause id="1996">
    <literal><![CDATA[
      ((T(x,y) \ x) / x) * T(x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,1995,a(flip),b,1303,a),flip(a)].">
      <j1 rule="hyper" parents="134 1995 1303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1997">
    <literal><![CDATA[
      ((T(x,y) \ x) / x) \ 1 = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,1996,a)].">
      <j1 rule="hyper" parents="144 1996"/>
    </justification>
  </clause>

  <clause id="1998">
    <literal><![CDATA[
      R(x,x \ T(x,y),y) \ (T(x,y) * y) = y * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,492,a,b,1990,a)].">
      <j1 rule="hyper" parents="63 492 1990"/>
    </justification>
  </clause>

  <clause id="1999">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1399,a,b,1991,a)].">
      <j1 rule="hyper" parents="63 1399 1991"/>
    </justification>
  </clause>

  <clause id="2000">
    <literal><![CDATA[
      (1 / x) \ (x \ ((y * x) / y)) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(133,a,1991,a(flip),b,1399,a)].">
      <j1 rule="hyper" parents="133 1991 1399"/>
    </justification>
  </clause>

  <clause id="2001">
    <literal><![CDATA[
      (x * y) / x != z * y
    ]]></literal>
    <literal><![CDATA[
      y \ ((x * y) / x) = z
    ]]></literal>
    <justification jstring="[para(1992(a,1),44(a,1))].">
      <j1 rule="para" parents="1992 44"/>
    </justification>
  </clause>

  <clause id="2002">
    <literal><![CDATA[
      T(1 / x,(y * x) / y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(253,a,1999,a,b,1236,a)].">
      <j1 rule="hyper" parents="253 1999 1236"/>
    </justification>
  </clause>

  <clause id="2004">
    <literal><![CDATA[
      (x \ 1) \ ((y * (x \ 1)) / y) = x * ((y * (x \ 1)) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,198,a(flip),b,1999,a),flip(a)].">
      <j1 rule="hyper" parents="63 198 1999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2005">
    <literal><![CDATA[
      T(1 / T(x,y),x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(241(a,1),2002(a,1,2))].">
      <j1 rule="para" parents="241 2002"/>
    </justification>
  </clause>

  <clause id="2006">
    <literal><![CDATA[
      (1 / x) \ (x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x))) = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,1801,a(flip),b,2000,a),flip(a)].">
      <j1 rule="hyper" parents="316 1801 2000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2008">
    <literal><![CDATA[
      K(K(x,y),z) \ (K(x,y) * z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[para(1046(a,1),1994(a,1,1))].">
      <j1 rule="para" parents="1046 1994"/>
    </justification>
  </clause>

  <clause id="2009">
    <literal><![CDATA[
      K(K(x,y),y * x) * (x * y) = K(x,y) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(139,a,94,a(flip),b,2008,a)].">
      <j1 rule="hyper" parents="139 94 2008"/>
    </justification>
  </clause>

  <clause id="2010">
    <literal><![CDATA[
      T(K(K(x,y),y * x) * x,y) = y \ (K(x,y) * (y * x))
    ]]></literal>
    <justification jstring="[hyper(390,a,2009,a(flip),b,406,a)].">
      <j1 rule="hyper" parents="390 2009 406"/>
    </justification>
  </clause>

  <clause id="2011">
    <literal><![CDATA[
      T((K(K(x,y),y * x) * x) * R((K(K(x,y),y * x) * x) \ 1,z,u),y) = (y \ (K(x,y) * (y * x))) * R(T(K(K(x,y),y * x) * x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(2010(a,1),1831(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2010 1831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2012">
    <literal><![CDATA[
      T(T(((K(x,y) * (y * x)) / y) * R(((K(x,y) * (y * x)) / y) \ 1,z,u),w),y) = T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(2010(a,2),1855(a,2,1,1))].">
      <j1 rule="para" parents="2010 1855"/>
    </justification>
  </clause>

  <clause id="2013">
    <literal><![CDATA[
      (1 / x) \ (x \ (x * (y * T(y \ 1,x)))) = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[para(1801(a,1),2006(a,1,2,2))].">
      <j1 rule="para" parents="1801 2006"/>
    </justification>
  </clause>

  <clause id="2014">
    <literal><![CDATA[
      (1 / x) \ (y * T(y \ 1,x)) = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),2013(a,1,2))].">
      <j1 rule="para" parents="9 2013"/>
    </justification>
  </clause>

  <clause id="2016">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x * (R(x,y,z) \ L(x \ R(x,y,z),u,w))) = 1 * L(1 \ (R(x,y,z) \ x),u,w)
    ]]></literal>
    <justification jstring="[para(66(a,2),1926(a,2,2,1))].">
      <j1 rule="para" parents="66 1926"/>
    </justification>
  </clause>

  <clause id="2017">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ (L(x,y,z) \ x) = L(x * L(x,y,z),u,w) \ (x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1908,a(flip),b,1928,a)].">
      <j1 rule="hyper" parents="63 1908 1928"/>
    </justification>
  </clause>

  <clause id="2018">
    <literal><![CDATA[
      (L(x * L(x,y,z),u,w) \ (x * L(x,y,z))) * L(L(x,y,z) \ x,u,w) = 1 * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(2017(a,1),1377(a,1,1))].">
      <j1 rule="para" parents="2017 1377"/>
    </justification>
  </clause>

  <clause id="2019">
    <literal><![CDATA[
      T(x,x \ y) * (z * T(z \ 1,x)) = (z * T(z \ 1,x)) * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(1983(a,1),1988(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1983 1988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2020">
    <literal><![CDATA[
      L(L(x,y \ (y / z),z),z * (y \ (y / z)),z) = z * (L(z,z,z \ y) \ (z * ((y \ (y / z)) * x)))
    ]]></literal>
    <justification jstring="[hyper(316,a,1129,a(flip),b,1687,a),flip(a)].">
      <j1 rule="hyper" parents="316 1129 1687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2021">
    <literal><![CDATA[
      (x / (y \ 1)) * L((x / (y \ 1)) \ (x * 1),z,u) = x * (L(y,y,x) \ L(L(y,y,x),z,u))
    ]]></literal>
    <justification jstring="[para(1449(a,1),1803(a,1,2,1))].">
      <j1 rule="para" parents="1449 1803"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      (x / (y \ 1)) * L((x / (y \ 1)) \ x,z,u) = x * (L(y,y,x) \ L(L(y,y,x),z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),2021(a,1,2,1,2))].">
      <j1 rule="para" parents="8 2021"/>
    </justification>
  </clause>

  <clause id="2023">
    <literal><![CDATA[
      x * (L(y,y,x) \ L(L(y,y,x),z,u)) = (x / (y \ 1)) * L(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(83(a,1),2022(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 2022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2025">
    <literal><![CDATA[
      T(((x \ 1) \ 1) * (x \ 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(8(a,1),1836(a,1,1,1,2))].">
      <j1 rule="para" parents="8 1836"/>
    </justification>
  </clause>

  <clause id="2026">
    <literal><![CDATA[
      T(K((x \ 1) \ 1,x \ 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(272(a,2),2025(a,1,1,1))].">
      <j1 rule="para" parents="272 2025"/>
    </justification>
  </clause>

  <clause id="2027">
    <literal><![CDATA[
      T(K(x,x \ 1),y) / T((x \ 1) \ 1,y) = L(1 / T((x \ 1) \ 1,y),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(939(a,1),2026(a,1,1,1))].">
      <j1 rule="para" parents="939 2026"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      L(L(x,y \ (y / z),z),z * (y \ (y / z)),z) = z * (z * (L(z,z,z \ y) \ ((y \ (y / z)) * x)))
    ]]></literal>
    <justification jstring="[para(1129(a,1),2020(a,2,2))].">
      <j1 rule="para" parents="1129 2020"/>
    </justification>
  </clause>

  <clause id="2029">
    <literal><![CDATA[
      K(x,1 / x) * T(K(x,1 / x) \ (K(x,1 / x) / (1 / x)),y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1302(a,1),956(a,2,2))].">
      <j1 rule="para" parents="1302 956"/>
    </justification>
  </clause>

  <clause id="2030">
    <literal><![CDATA[
      K(x,1 / x) * T(1 / (1 / x),y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(437(a,1),2029(a,1,2,1))].">
      <j1 rule="para" parents="437 2029"/>
    </justification>
  </clause>

  <clause id="2032">
    <literal><![CDATA[
      K(x,x \ 1) * T(1 / (1 / x),y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1083(a,1),2030(a,1,1))].">
      <j1 rule="para" parents="1083 2030"/>
    </justification>
  </clause>

  <clause id="2033">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ x,y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1088(a,2),2032(a,1,2,1))].">
      <j1 rule="para" parents="1088 2032"/>
    </justification>
  </clause>

  <clause id="2034">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * (K(x,x \ 1) \ 1) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(138,a,2033,a(flip),b,852,a)].">
      <j1 rule="hyper" parents="138 2033 852"/>
    </justification>
  </clause>

  <clause id="2035">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[para(435(a,1),2034(a,1,2))].">
      <j1 rule="para" parents="435 2034"/>
    </justification>
  </clause>

  <clause id="2036">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(435(a,1),2035(a,2,1,2))].">
      <j1 rule="para" parents="435 2035"/>
    </justification>
  </clause>

  <clause id="2037">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1290(a,1),2036(a,2,1))].">
      <j1 rule="para" parents="1290 2036"/>
    </justification>
  </clause>

  <clause id="2038">
    <literal><![CDATA[
      T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1331(a,1),2037(a,1,1))].">
      <j1 rule="para" parents="1331 2037"/>
    </justification>
  </clause>

  <clause id="2039">
    <literal><![CDATA[
      (x \ y) * L(L((x \ y) \ 1,z,u),w,v5) = x \ (y * L(L(y \ x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(74(a,1),1516(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="74 1516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2040">
    <literal><![CDATA[
      (x \ y) \ L(L(x \ y,z,u),w,v5) = x \ (y * L(L(y \ x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,1372,a(flip),b,2039,a)].">
      <j1 rule="hyper" parents="63 1372 2039"/>
    </justification>
  </clause>

  <clause id="2042">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * L(L((x * (y * z)) \ (x * y),u,w),v5,v6)) = L(z,y,x) \ L(L((x * y) \ (x * (y * z)),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(18(a,2),2040(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 2040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2043">
    <literal><![CDATA[
      (x * (y * z)) * T((x * (y * z)) \ (x * y),u) = (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u))
    ]]></literal>
    <justification jstring="[para(100(a,1),950(a,1,2,1,1))].">
      <j1 rule="para" parents="100 950"/>
    </justification>
  </clause>

  <clause id="2044">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)) = x * ((y * z) * T((y * z) \ y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,780,a(flip),b,2043,a),flip(a)].">
      <j1 rule="hyper" parents="63 780 2043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2045">
    <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(712(a,1),2044(a,2,2))].">
      <j1 rule="para" parents="712 2044"/>
    </justification>
  </clause>

  <clause id="2046">
    <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(463,a,2045,a),flip(a)].">
      <j1 rule="hyper" parents="463 2045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2047">
    <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="[hyper(63,a,337,a(flip),b,2046,a),flip(a)].">
      <j1 rule="hyper" parents="63 337 2046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2048">
    <literal><![CDATA[
      L(x * T(x \ 1,x),y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(2046(a,1),1008(a,1,1))].">
      <j1 rule="para" parents="2046 1008"/>
    </justification>
  </clause>

  <clause id="2049">
    <literal><![CDATA[
      L(K(x \ 1,L(x,y,z)),y,z) = K(L(x,y,z) \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1799(a,1),2047(a,1,1))].">
      <j1 rule="para" parents="1799 2047"/>
    </justification>
  </clause>

  <clause id="2050">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(337(a,1),2048(a,1,1,1))].">
      <j1 rule="para" parents="337 2048"/>
    </justification>
  </clause>

  <clause id="2051">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,y,z)) = L(K(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,1924,a,b,2050,a)].">
      <j1 rule="hyper" parents="35 1924 2050"/>
    </justification>
  </clause>

  <clause id="2052">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,2049,a,b,2051,a(flip))].">
      <j1 rule="hyper" parents="41 2049 2051"/>
    </justification>
  </clause>

  <clause id="2053">
    <literal><![CDATA[
      R(x,y,L(K(z \ 1,z),u,w)) = x
    ]]></literal>
    <justification jstring="[para(2051(a,1),1722(a,1,3))].">
      <j1 rule="para" parents="2051 1722"/>
    </justification>
  </clause>

  <clause id="2054">
    <literal><![CDATA[
      x * L(K(y \ 1,y),x,z) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(137,a,2053,a(flip),b,462,a),flip(a)].">
      <j1 rule="hyper" parents="137 2053 462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2055">
    <literal><![CDATA[
      x * K(y \ 1,L(y,z,u)) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,2052,a,b,9,a)].">
      <j1 rule="hyper" parents="139 2052 9"/>
    </justification>
  </clause>

  <clause id="2057">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(354,a,2054,a),flip(a)].">
      <j1 rule="hyper" parents="354 2054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2061">
    <literal><![CDATA[
      (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * ((y \ z) * T((y \ z) \ 1,z))) * z
    ]]></literal>
    <justification jstring="[para(712(a,1),1405(a,1,1)),flip(a)].">
      <j1 rule="para" parents="712 1405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2062">
    <literal><![CDATA[
      (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * (y \ ((z \ y) * z))) * z
    ]]></literal>
    <justification jstring="[para(823(a,1),2061(a,2,1,2))].">
      <j1 rule="para" parents="823 2061"/>
    </justification>
  </clause>

  <clause id="2063">
    <literal><![CDATA[
      (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * K(z \ y,z)) * z
    ]]></literal>
    <justification jstring="[para(95(a,1),2062(a,2,1,2))].">
      <j1 rule="para" parents="95 2062"/>
    </justification>
  </clause>

  <clause id="2064">
    <literal><![CDATA[
      (x * (y \ z)) * L((z \ T(y,y \ z)) * z,y \ z,x) = (x * K(z \ y,z)) * z
    ]]></literal>
    <justification jstring="[para(1369(a,2),2063(a,1,2))].">
      <j1 rule="para" parents="1369 2063"/>
    </justification>
  </clause>

  <clause id="2065">
    <literal><![CDATA[
      x * ((y \ z) * ((z \ T(y,y \ z)) * z)) = (x * K(z \ y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,100,a(flip),b,2064,a)].">
      <j1 rule="hyper" parents="63 100 2064"/>
    </justification>
  </clause>

  <clause id="2066">
    <literal><![CDATA[
      (x \ y) * ((y \ T(x,x \ y)) * y) = K(y \ x,y) * y
    ]]></literal>
    <justification jstring="[hyper(654,a,2065,a),flip(a)].">
      <j1 rule="hyper" parents="654 2065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      (x \ y) * ((y \ T(x,x \ y)) * y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1974,a(flip),b,2066,a),flip(a)].">
      <j1 rule="hyper" parents="316 1974 2066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2068">
    <literal><![CDATA[
      (x * K(y \ z,y)) * y = x * (y * K(y \ z,y))
    ]]></literal>
    <justification jstring="[para(2067(a,1),2065(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2067 2065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2069">
    <literal><![CDATA[
      x * (y * K(y \ (y * z),y)) = (x * K(z,y)) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),2068(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2070">
    <literal><![CDATA[
      (x * K(y,z)) * z = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),2069(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2071">
    <literal><![CDATA[
      (x * y) / (y * K(z,y)) = x / K(z,y)
    ]]></literal>
    <justification jstring="[hyper(629,a,2070,a)].">
      <j1 rule="hyper" parents="629 2070"/>
    </justification>
  </clause>

  <clause id="2073">
    <literal><![CDATA[
      (x * (y * K(z,y))) \ ((x * (y * K(z,y))) * y) = L(y,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(2070(a,1),1979(a,1,1))].">
      <j1 rule="para" parents="2070 1979"/>
    </justification>
  </clause>

  <clause id="2074">
    <literal><![CDATA[
      L(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(322,a,2073,a),flip(a)].">
      <j1 rule="hyper" parents="322 2073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2076">
    <literal><![CDATA[
      L(T(x,y),K(z,x),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2074(a,1),25(a,2,1))].">
      <j1 rule="para" parents="2074 25"/>
    </justification>
  </clause>

  <clause id="2077">
    <literal><![CDATA[
      (R(x,y,z) \ u) * T(T(x,R(x,y,z) \ u),u) = R(x,y,z) \ (T(x,u) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1524(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      R(x,y,z) \ (T(x,u) * u) = T(x,u) * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,250,a(flip),b,2077,a),flip(a)].">
      <j1 rule="hyper" parents="63 250 2077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2079">
    <literal><![CDATA[
      T(x,y) * (R(x,x \ T(x,y),y) \ y) = y * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1998,a(flip),b,2078,a),flip(a)].">
      <j1 rule="hyper" parents="63 1998 2078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2080">
    <literal><![CDATA[
      x * T(R(K(y,z) * (u / (K(y,z) * x)),w,v5),K(y,z) * x) = (K(y,z) * x) * R((K(y,z) * x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(1028(a,2),953(a,1,2,1))].">
      <j1 rule="para" parents="1028 953"/>
    </justification>
  </clause>

  <clause id="2083">
    <literal><![CDATA[
      x * R(T(K(y,z) * (u / (K(y,z) * x)),K(y,z) * x),w,v5) = (K(y,z) * x) * R((K(y,z) * x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(27(a,2),2080(a,1,2))].">
      <j1 rule="para" parents="27 2080"/>
    </justification>
  </clause>

  <clause id="2084">
    <literal><![CDATA[
      (K(x,y) * z) * R((K(x,y) * z) \ u,w,v5) = z * R((K(x,y) * z) \ (K(x,y) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(678(a,1),2083(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="678 2083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2085">
    <literal><![CDATA[
      (K(x,y) * z) * R((K(x,y) * z) \ u,w,v5) = z * R(z \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(477(a,1),2084(a,2,2,1))].">
      <j1 rule="para" parents="477 2084"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      (x * (y * z)) * R((x * (y * z)) \ (x * y),u,w) = (x * y) * (L(z,y,x) * R(L(z,y,x) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(100(a,1),1047(a,1,2,1,1))].">
      <j1 rule="para" parents="100 1047"/>
    </justification>
  </clause>

  <clause id="2088">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * R(L(z,y,x) \ 1,u,w)) = x * ((y * z) * R((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,882,a(flip),b,2087,a),flip(a)].">
      <j1 rule="hyper" parents="63 882 2087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2089">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * R(L(z,y,x) \ 1,u,w)) = x * (y * (z * R(z \ 1,u,w)))
    ]]></literal>
    <justification jstring="[para(775(a,1),2088(a,2,2))].">
      <j1 rule="para" parents="775 2088"/>
    </justification>
  </clause>

  <clause id="2090">
    <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(463,a,2089,a),flip(a)].">
      <j1 rule="hyper" parents="463 2089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2091">
    <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,976,a(flip),b,2090,a),flip(a)].">
      <j1 rule="hyper" parents="63 976 2090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2092">
    <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(1281(a,1),2091(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1281 2091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2093">
    <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(316,a,2047,a(flip),b,2092,a),flip(a)].">
      <j1 rule="hyper" parents="316 2047 2092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2094">
    <literal><![CDATA[
      (x \ 1) / (x \ L(x,y,z)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,272,a(flip),b,2093,a),flip(a)].">
      <j1 rule="hyper" parents="35 272 2093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2095">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(204,a,2094,a)].">
      <j1 rule="hyper" parents="204 2094"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * (x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(151,a,2094,a)].">
      <j1 rule="hyper" parents="151 2094"/>
    </justification>
  </clause>

  <clause id="2097">
    <literal><![CDATA[
      x / ((1 / x) \ L(1 / x,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(83(a,1),2094(a,1,1))].">
      <j1 rule="para" parents="83 2094"/>
    </justification>
  </clause>

  <clause id="2098">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ u,x \ L(x,y,z),L(x,y,z) \ 1) = (x \ 1) \ ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(2096(a,1),102(a,2,1))].">
      <j1 rule="para" parents="2096 102"/>
    </justification>
  </clause>

  <clause id="2099">
    <literal><![CDATA[
      x / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(904(a,1),2097(a,1,2))].">
      <j1 rule="para" parents="904 2097"/>
    </justification>
  </clause>

  <clause id="2100">
    <literal><![CDATA[
      T(x * T(x \ 1,x \ T(x,y)),y) * (T(x,y) \ (x \ T(x,y))) = ((x \ T(x,y)) \ (x \ 1)) * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(1734(a,1),999(a,1,1))].">
      <j1 rule="para" parents="1734 999"/>
    </justification>
  </clause>

  <clause id="2101">
    <literal><![CDATA[
      T(x * (x \ 1),y) * (T(x,y) \ (x \ T(x,y))) = ((x \ T(x,y)) \ (x \ 1)) * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(1223(a,1),2100(a,1,1,1,2))].">
      <j1 rule="para" parents="1223 2100"/>
    </justification>
  </clause>

  <clause id="2102">
    <literal><![CDATA[
      T(1,x) * (T(y,x) \ (y \ T(y,x))) = ((y \ T(y,x)) \ (y \ 1)) * (y \ T(y,x))
    ]]></literal>
    <justification jstring="[para(10(a,1),2101(a,1,1,1))].">
      <j1 rule="para" parents="10 2101"/>
    </justification>
  </clause>

  <clause id="2105">
    <literal><![CDATA[
      ((x \ T(x,y)) \ (x \ 1)) * (x \ T(x,y)) = 1 * (T(x,y) \ (x \ T(x,y)))
    ]]></literal>
    <justification jstring="[para(213(a,1),2102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="213 2102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2107">
    <literal><![CDATA[
      ((x \ T(x,y)) \ (x \ 1)) * (x \ T(x,y)) = 1 * (x \ 1)
    ]]></literal>
    <justification jstring="[para(850(a,1),2105(a,2,2))].">
      <j1 rule="para" parents="850 2105"/>
    </justification>
  </clause>

  <clause id="2108">
    <literal><![CDATA[
      ((x \ T(x,y)) \ (x \ 1)) * (x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,7,a(flip),b,2107,a),flip(a)].">
      <j1 rule="hyper" parents="316 7 2107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2110">
    <literal><![CDATA[
      L(x,y,z) * ((x \ 1) * T((x \ 1) \ (L(x,y,z) \ u),w)) = (x \ L(x,y,z)) * T((x \ L(x,y,z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(969(a,1),1053(a,2,2,1,1))].">
      <j1 rule="para" parents="969 1053"/>
    </justification>
  </clause>

  <clause id="2111">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T((x \ L(x,y,z)) \ u,w) = L(x,y,z) * (x \ T(x * (L(x,y,z) \ u),w))
    ]]></literal>
    <justification jstring="[para(807(a,1),2110(a,1,2)),flip(a)].">
      <j1 rule="para" parents="807 2110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2112">
    <literal><![CDATA[
      x * ((L(x,y,z) \ 1) * T((L(x,y,z) \ 1) \ (x \ u),w)) = (L(x,y,z) \ x) * T((L(x,y,z) \ x) \ u,w)
    ]]></literal>
    <justification jstring="[para(1002(a,1),1054(a,2,2,1,1))].">
      <j1 rule="para" parents="1002 1054"/>
    </justification>
  </clause>

  <clause id="2113">
    <literal><![CDATA[
      (L(x,y,z) \ x) * T((L(x,y,z) \ x) \ u,w) = x * (L(x,y,z) \ T(L(x,y,z) * (x \ u),w))
    ]]></literal>
    <justification jstring="[para(807(a,1),2112(a,1,2)),flip(a)].">
      <j1 rule="para" parents="807 2112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2114">
    <literal><![CDATA[
      x * (y * ((z \ L(z,u,w)) * (z \ L(z,u,w)))) = (x * y) * (L(z,u,w) * L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(971(a,1),1418(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="971 1418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2130">
    <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),1254(a,2,2,1,1))].">
      <j1 rule="para" parents="18 1254"/>
    </justification>
  </clause>

  <clause id="2131">
    <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(878(a,1),2130(a,1,2))].">
      <j1 rule="para" parents="878 2130"/>
    </justification>
  </clause>

  <clause id="2132">
    <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(777(a,1),2131(a,1,2,2))].">
      <j1 rule="para" parents="777 2131"/>
    </justification>
  </clause>

  <clause id="2133">
    <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(63,a,18,a,b,2132,a),flip(a)].">
      <j1 rule="hyper" parents="63 18 2132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2135">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),u,w) = L(x * L(x \ 1,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1064,a(flip),b,2133,a)].">
      <j1 rule="hyper" parents="63 1064 2133"/>
    </justification>
  </clause>

  <clause id="2136">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),u,w) = L(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(1064(a,1),2135(a,2,1))].">
      <j1 rule="para" parents="1064 2135"/>
    </justification>
  </clause>

  <clause id="2137">
    <literal><![CDATA[
      L(x,y,z) * L(x \ L(x,u,w),y,z) = L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(152,a,2136,a)].">
      <j1 rule="hyper" parents="152 2136"/>
    </justification>
  </clause>

  <clause id="2138">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,u,w),y,z) = L(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,167,a,b,2136,a)].">
      <j1 rule="hyper" parents="63 167 2136"/>
    </justification>
  </clause>

  <clause id="2139">
    <literal><![CDATA[
      L(x,y,z) * L(x \ L(x,u,w),y,z) = L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,2136,a(flip),b,167,a)].">
      <j1 rule="hyper" parents="139 2136 167"/>
    </justification>
  </clause>

  <clause id="2140">
    <literal><![CDATA[
      L(x,y,z) \ L(x \ L(x,u,w),y,z) = L(L(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,2136,a(flip),b,1064,a)].">
      <j1 rule="hyper" parents="133 2136 1064"/>
    </justification>
  </clause>

  <clause id="2141">
    <literal><![CDATA[
      L(L(x,y,z) \ L(L(x,y,z),u,w),v5,v6) = L(L(x \ L(x,u,w),v5,v6),y,z)
    ]]></literal>
    <justification jstring="[para(2136(a,2),30(a,1,1))].">
      <j1 rule="para" parents="2136 30"/>
    </justification>
  </clause>

  <clause id="2142">
    <literal><![CDATA[
      x * L(y \ L(y,y,z),u,w) = x * (L(y,u,w) \ L(z \ (z / (y \ 1)),u,w))
    ]]></literal>
    <justification jstring="[para(2136(a,1),1456(a,1,2))].">
      <j1 rule="para" parents="2136 1456"/>
    </justification>
  </clause>

  <clause id="2143">
    <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(2136(a,1),1894(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2136 1894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2145">
    <literal><![CDATA[
      L(((x * x) * y) \ L((x * x) * y,z,u),x,x) = (x * (x * y)) \ L(L((x * x) * y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(1114(a,1),2138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1114 2138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2147">
    <literal><![CDATA[
      L(x,y,z) \ (L(x \ L(x,u,w),y,z) \ 1) = L(L(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,2143,a(flip),b,1002,a)].">
      <j1 rule="hyper" parents="133 2143 1002"/>
    </justification>
  </clause>

  <clause id="2148">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(x,u,w) = L(x \ L(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(30(a,1),2143(a,1,1))].">
      <j1 rule="para" parents="30 2143"/>
    </justification>
  </clause>

  <clause id="2149">
    <literal><![CDATA[
      x * (L(L(y,z,u),w,v5) \ L(y,w,v5)) = x * (L(y \ L(y,z,u),w,v5) \ 1)
    ]]></literal>
    <justification jstring="[para(2143(a,1),836(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2143 836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2151">
    <literal><![CDATA[
      L(((x * x) * y) \ L((x * x) * y,z,u),x,x) = (x * (x * y)) \ L(x * (x * y),z,u)
    ]]></literal>
    <justification jstring="[para(1117(a,1),2145(a,2,2))].">
      <j1 rule="para" parents="1117 2145"/>
    </justification>
  </clause>

  <clause id="2152">
    <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(199(a,1),1421(a,1,2))].">
      <j1 rule="para" parents="199 1421"/>
    </justification>
  </clause>

  <clause id="2154">
    <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(1528(a,1),2152(a,1,1))].">
      <j1 rule="para" parents="1528 2152"/>
    </justification>
  </clause>

  <clause id="2155">
    <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(1230(a,1),2154(a,1,1,1))].">
      <j1 rule="para" parents="1230 2154"/>
    </justification>
  </clause>

  <clause id="2156">
    <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(63,a,20,a,b,2155,a),flip(a)].">
      <j1 rule="hyper" parents="63 20 2155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2157">
    <literal><![CDATA[
      R(x,y,z) * L(R(x,y,z) \ 1,u,w) = R(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(1064(a,1),2156(a,2,1))].">
      <j1 rule="para" parents="1064 2156"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      R(x,y,z) \ L(R(x,y,z),u,w) = R(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1064,a(flip),b,2157,a)].">
      <j1 rule="hyper" parents="63 1064 2157"/>
    </justification>
  </clause>

  <clause id="2159">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * ((u * ((x * (y * z)) \ (x * y))) / u)) = L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)
    ]]></literal>
    <justification jstring="[para(202(a,1),1535(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="202 1535"/>
    </justification>
  </clause>

  <clause id="2161">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * ((u * ((y * z) \ y)) / u))) = L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)
    ]]></literal>
    <justification jstring="[para(1024(a,1),2159(a,1,2))].">
      <j1 rule="para" parents="1024 2159"/>
    </justification>
  </clause>

  <clause id="2162">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * ((u * (z \ 1)) / u)))) = L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)
    ]]></literal>
    <justification jstring="[para(1023(a,1),2161(a,1,2,2))].">
      <j1 rule="para" parents="1023 2161"/>
    </justification>
  </clause>

  <clause id="2163">
    <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(63,a,18,a,b,2162,a),flip(a)].">
      <j1 rule="hyper" parents="63 18 2162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2164">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * L(L((x * (y * z)) \ (x * y),u,w),v5,v6)) = L(z,y,x) \ L(L(L(z,y,x),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(18(a,2),2042(a,2,2,1,1))].">
      <j1 rule="para" parents="18 2042"/>
    </justification>
  </clause>

  <clause id="2165">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L(L((y * z) \ (x \ (x * y)),u,w),v5,v6))) = L(z,y,x) \ L(L(L(z,y,x),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(908(a,1),2164(a,1,2))].">
      <j1 rule="para" parents="908 2164"/>
    </justification>
  </clause>

  <clause id="2166">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L(L((y * z) \ y,u,w),v5,v6))) = L(z,y,x) \ L(L(L(z,y,x),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(9(a,1),2165(a,1,2,2,2,1,1,2))].">
      <j1 rule="para" parents="9 2165"/>
    </justification>
  </clause>

  <clause id="2167">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * L(L(z \ (y \ y),u,w),v5,v6)))) = L(z,y,x) \ L(L(L(z,y,x),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(908(a,1),2166(a,1,2,2))].">
      <j1 rule="para" parents="908 2166"/>
    </justification>
  </clause>

  <clause id="2168">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * L(L(z \ 1,u,w),v5,v6)))) = L(z,y,x) \ L(L(L(z,y,x),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(67(a,1),2167(a,1,2,2,2,2,1,1,2))].">
      <j1 rule="para" parents="67 2167"/>
    </justification>
  </clause>

  <clause id="2170">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z \ L(L(z,u,w),v5,v6)))) = L(z,y,x) \ L(L(L(z,y,x),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(1372(a,1),2168(a,1,2,2,2))].">
      <j1 rule="para" parents="1372 2168"/>
    </justification>
  </clause>

  <clause id="2171">
    <literal><![CDATA[
      L(x,y,z) \ L(L(L(x,y,z),u,w),v5,v6) = L(x \ L(L(x,u,w),v5,v6),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,18,a,b,2170,a),flip(a)].">
      <j1 rule="hyper" parents="63 18 2170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2172">
    <literal><![CDATA[
      T((K(K(x,y),y * x) * x) * R((K(K(x,y),y * x) * x) \ 1,z,u),y) = (y \ (K(x,y) * (y * x))) * R((y \ (K(x,y) * (y * x))) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(2010(a,1),2011(a,2,2,1,1))].">
      <j1 rule="para" parents="2010 2011"/>
    </justification>
  </clause>

  <clause id="2173">
    <literal><![CDATA[
      (x \ (K(y,x) * (x * y))) * R((x \ (K(y,x) * (x * y))) \ 1,z,u) = T(y * R(y \ 1,z,u),x)
    ]]></literal>
    <justification jstring="[para(2085(a,1),2172(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2085 2172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2175">
    <literal><![CDATA[
      T(T((K(x,y) * ((y * x) / y)) * R(((K(x,y) * (y * x)) / y) \ 1,z,u),w),y) = T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(660(a,1),2012(a,1,1,1,1))].">
      <j1 rule="para" parents="660 2012"/>
    </justification>
  </clause>

  <clause id="2176">
    <literal><![CDATA[
      T(T((K(x,y) * ((y * x) / y)) * R((K(x,y) * ((y * x) / y)) \ 1,z,u),w),y) = T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(660(a,1),2175(a,1,1,1,2,1,1))].">
      <j1 rule="para" parents="660 2175"/>
    </justification>
  </clause>

  <clause id="2177">
    <literal><![CDATA[
      T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T(T(((y * x) / y) * R(((y * x) / y) \ 1,z,u),w),y)
    ]]></literal>
    <justification jstring="[para(2085(a,1),2176(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2085 2176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2178">
    <literal><![CDATA[
      T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T((y \ (y * x)) * R((y \ (y * x)) \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,1855,a(flip),b,2177,a),flip(a)].">
      <j1 rule="hyper" parents="316 1855 2177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2180">
    <literal><![CDATA[
      T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T(x * R((y \ (y * x)) \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(9(a,1),2178(a,2,1,1))].">
      <j1 rule="para" parents="9 2178"/>
    </justification>
  </clause>

  <clause id="2181">
    <literal><![CDATA[
      T(T(K(K(x,y),y * x) * x,y) * R((y \ (K(x,y) * (y * x))) \ 1,z,u),w) = T(x * R(x \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(9(a,1),2180(a,2,1,2,1,1))].">
      <j1 rule="para" parents="9 2180"/>
    </justification>
  </clause>

  <clause id="2183">
    <literal><![CDATA[
      T((x \ (K(y,x) * (x * y))) * R((x \ (K(y,x) * (x * y))) \ 1,z,u),w) = T(y * R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(2010(a,1),2181(a,1,1,1))].">
      <j1 rule="para" parents="2010 2181"/>
    </justification>
  </clause>

  <clause id="2184">
    <literal><![CDATA[
      T(T(x * R(x \ 1,y,z),u),w) = T(x * R(x \ 1,y,z),w)
    ]]></literal>
    <justification jstring="[para(2173(a,1),2183(a,1,1))].">
      <j1 rule="para" parents="2173 2183"/>
    </justification>
  </clause>

  <clause id="2185">
    <literal><![CDATA[
      T(x * R(x \ 1,y,z),u) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(154,a,2184,a)].">
      <j1 rule="hyper" parents="154 2184"/>
    </justification>
  </clause>

  <clause id="2187">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,z,u) = x * R(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1831,a,b,2185,a)].">
      <j1 rule="hyper" parents="63 1831 2185"/>
    </justification>
  </clause>

  <clause id="2188">
    <literal><![CDATA[
      T(x,y * R(y \ 1,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,2185,a)].">
      <j1 rule="hyper" parents="54 2185"/>
    </justification>
  </clause>

  <clause id="2190">
    <literal><![CDATA[
      T(x,(y / (z * y)) * z) = x
    ]]></literal>
    <justification jstring="[para(623(a,2),2188(a,1,2))].">
      <j1 rule="para" parents="623 2188"/>
    </justification>
  </clause>

  <clause id="2191">
    <literal><![CDATA[
      T(x,y \ R(y,z,u)) = x
    ]]></literal>
    <justification jstring="[para(977(a,1),2188(a,1,2))].">
      <j1 rule="para" parents="977 2188"/>
    </justification>
  </clause>

  <clause id="2192">
    <literal><![CDATA[
      T(x,R(y,z,u) / y) = x
    ]]></literal>
    <justification jstring="[para(986(a,1),2188(a,1,2))].">
      <j1 rule="para" parents="986 2188"/>
    </justification>
  </clause>

  <clause id="2193">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ u) * (x \ R(x,y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(795,a,2191,a)].">
      <j1 rule="hyper" parents="795 2191"/>
    </justification>
  </clause>

  <clause id="2194">
    <literal><![CDATA[
      x / (y \ R(y,z,u)) = (y \ R(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(377,a,2191,a),flip(a)].">
      <j1 rule="hyper" parents="377 2191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2195">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,2191,a)].">
      <j1 rule="hyper" parents="55 2191"/>
    </justification>
  </clause>

  <clause id="2196">
    <literal><![CDATA[
      T(x \ R(x,y,z),u) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,2191,a)].">
      <j1 rule="hyper" parents="54 2191"/>
    </justification>
  </clause>

  <clause id="2197">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) / x = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(209,a,2191,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="209 2191 22"/>
    </justification>
  </clause>

  <clause id="2198">
    <literal><![CDATA[
      (x \ R(x,y,z)) * u = u * (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,2191,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 2191 22"/>
    </justification>
  </clause>

  <clause id="2200">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(707(a,2),2191(a,1,2))].">
      <j1 rule="para" parents="707 2191"/>
    </justification>
  </clause>

  <clause id="2201">
    <literal><![CDATA[
      T(x,y \ (z * ((y \ z) \ 1))) = x
    ]]></literal>
    <justification jstring="[para(568(a,1),2191(a,1,2,2))].">
      <j1 rule="para" parents="568 2191"/>
    </justification>
  </clause>

  <clause id="2202">
    <literal><![CDATA[
      (1 / (x \ R(x,y,z))) * (u * (x \ R(x,y,z))) = L(u,x \ R(x,y,z),(x \ R(x,y,z)) \ 1)
    ]]></literal>
    <justification jstring="[para(2191(a,1),892(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2191 892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2203">
    <literal><![CDATA[
      T(x,y * (1 / y)) = x
    ]]></literal>
    <justification jstring="[para(391(a,1),2192(a,1,2))].">
      <j1 rule="para" parents="391 2192"/>
    </justification>
  </clause>

  <clause id="2204">
    <literal><![CDATA[
      T(x,(y \ 1) * y) = x
    ]]></literal>
    <justification jstring="[para(392(a,1),2192(a,1,2))].">
      <j1 rule="para" parents="392 2192"/>
    </justification>
  </clause>

  <clause id="2205">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1085(a,2),2203(a,1,2))].">
      <j1 rule="para" parents="1085 2203"/>
    </justification>
  </clause>

  <clause id="2206">
    <literal><![CDATA[
      T(x,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(272(a,2),2204(a,1,2))].">
      <j1 rule="para" parents="272 2204"/>
    </justification>
  </clause>

  <clause id="2208">
    <literal><![CDATA[
      K(x,x \ 1) * y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,471,a(flip),b,2205,a),flip(a)].">
      <j1 rule="hyper" parents="63 471 2205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2209">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(54,a,2205,a)].">
      <j1 rule="hyper" parents="54 2205"/>
    </justification>
  </clause>

  <clause id="2210">
    <literal><![CDATA[
      T(x,K(y \ 1,R(y,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,1954,a,b,2206,a)].">
      <j1 rule="hyper" parents="63 1954 2206"/>
    </justification>
  </clause>

  <clause id="2211">
    <literal><![CDATA[
      K(x \ 1,x) * y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,471,a(flip),b,2206,a),flip(a)].">
      <j1 rule="hyper" parents="63 471 2206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2212">
    <literal><![CDATA[
      T(K(x \ 1,x),y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(54,a,2206,a)].">
      <j1 rule="hyper" parents="54 2206"/>
    </justification>
  </clause>

  <clause id="2214">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(2206(a,1),642(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2206 642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2215">
    <literal><![CDATA[
      T(x,(y / z) * (z / y)) = x
    ]]></literal>
    <justification jstring="[para(12(a,1),2190(a,1,2,1,2))].">
      <j1 rule="para" parents="12 2190"/>
    </justification>
  </clause>

  <clause id="2216">
    <literal><![CDATA[
      T(x,y * (z / (y * z))) = x
    ]]></literal>
    <justification jstring="[para(11(a,1),2215(a,1,2,1))].">
      <j1 rule="para" parents="11 2215"/>
    </justification>
  </clause>

  <clause id="2217">
    <literal><![CDATA[
      x / (y * (z / (y * z))) = (y * (z / (y * z))) \ x
    ]]></literal>
    <justification jstring="[hyper(377,a,2216,a),flip(a)].">
      <j1 rule="hyper" parents="377 2216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2218">
    <literal><![CDATA[
      T(x * (y / (x * y)),z) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(54,a,2216,a)].">
      <j1 rule="hyper" parents="54 2216"/>
    </justification>
  </clause>

  <clause id="2219">
    <literal><![CDATA[
      (x * (y / (x * y))) * z = z * (x * (y / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(139,a,2216,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 2216 22"/>
    </justification>
  </clause>

  <clause id="2220">
    <literal><![CDATA[
      T(K(x \ 1,R(x,y,z)),u) = K(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(54,a,2210,a)].">
      <j1 rule="hyper" parents="54 2210"/>
    </justification>
  </clause>

  <clause id="2221">
    <literal><![CDATA[
      (x * ((y \ x) \ 1)) / y = y \ (x * ((y \ x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(209,a,2201,a(flip),b,115,a(flip))].">
      <j1 rule="hyper" parents="209 2201 115"/>
    </justification>
  </clause>

  <clause id="2222">
    <literal><![CDATA[
      L(1 / T((x \ 1) \ 1,y),x,x \ 1) = K(x,x \ 1) / T((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2209(a,1),2027(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2209 2027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2223">
    <literal><![CDATA[
      K(T(1 / T(x,y),T(x,z)),T(x,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1751,a,b,2212,a)].">
      <j1 rule="hyper" parents="63 1751 2212"/>
    </justification>
  </clause>

  <clause id="2224">
    <literal><![CDATA[
      T((x \ 1) * x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(272(a,1),2212(a,1,1))].">
      <j1 rule="para" parents="272 2212"/>
    </justification>
  </clause>

  <clause id="2225">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) * (z * y) = z * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2212(a,1),598(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2212 598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2226">
    <literal><![CDATA[
      K(x \ 1,x) * (T(x,y) \ x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(2212(a,1),1738(a,1,1))].">
      <j1 rule="para" parents="2212 1738"/>
    </justification>
  </clause>

  <clause id="2228">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) * (w * u) = w * (u * (x \ R(x,y,z)))
    ]]></literal>
    <justification jstring="[para(2196(a,1),598(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2196 598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2229">
    <literal><![CDATA[
      (L(x \ R(x,y,z),u,w) \ v5) \ v5 = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(2196(a,1),310(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2196 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2230">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) * L(x \ R(x,y,z),u,w) = (x \ R(x,y,z)) \ L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(2196(a,1),972(a,1,2,1))].">
      <j1 rule="para" parents="2196 972"/>
    </justification>
  </clause>

  <clause id="2231">
    <literal><![CDATA[
      (1 / x) * (L(y \ R(y,z,u),w,v5) * x) = L(L(y \ R(y,z,u),w,v5),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2196(a,1),891(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2196 891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2232">
    <literal><![CDATA[
      K(x,a(R(y,z,u),z,u)) = K(x,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(2196(a,1),1965(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2196 1965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2233">
    <literal><![CDATA[
      K(x \ 1,x) * (y * K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(670,a,2208,a)].">
      <j1 rule="hyper" parents="670 2208"/>
    </justification>
  </clause>

  <clause id="2234">
    <literal><![CDATA[
      K(x \ 1,x) \ y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,530,a,b,2208,a)].">
      <j1 rule="hyper" parents="63 530 2208"/>
    </justification>
  </clause>

  <clause id="2235">
    <literal><![CDATA[
      ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,1211,a(flip),b,2208,a),flip(a)].">
      <j1 rule="hyper" parents="63 1211 2208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2236">
    <literal><![CDATA[
      (x \ y) * K(x,x \ 1) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,1151,a(flip),b,2208,a),flip(a)].">
      <j1 rule="hyper" parents="63 1151 2208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2237">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,936,a(flip),b,2208,a),flip(a)].">
      <j1 rule="hyper" parents="63 936 2208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2238">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,935,a(flip),b,2208,a),flip(a)].">
      <j1 rule="hyper" parents="63 935 2208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2239">
    <literal><![CDATA[
      (((x \ 1) * y) * z) * K(x,x \ 1) = ((1 / x) * y) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,774,a(flip),b,2208,a),flip(a)].">
      <j1 rule="hyper" parents="63 774 2208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2240">
    <literal><![CDATA[
      (1 / x) * K(y,y \ 1) = K(y,y \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,424,a(flip),b,2208,a),flip(a)].">
      <j1 rule="hyper" parents="63 424 2208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2241">
    <literal><![CDATA[
      ((x * y) * K(z,z \ 1)) \ ((K(z,z \ 1) * x) * y) = a(K(z,z \ 1),x,y)
    ]]></literal>
    <justification jstring="[para(2208(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2208 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2243">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = y \ (z * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(2208(a,1),679(a,2,2))].">
      <j1 rule="para" parents="2208 679"/>
    </justification>
  </clause>

  <clause id="2244">
    <literal><![CDATA[
      K(x,x \ 1) * (y * K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[hyper(671,a,2211,a)].">
      <j1 rule="hyper" parents="671 2211"/>
    </justification>
  </clause>

  <clause id="2245">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = (y / z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,660,a,b,2211,a)].">
      <j1 rule="hyper" parents="63 660 2211"/>
    </justification>
  </clause>

  <clause id="2246">
    <literal><![CDATA[
      L(1 / x,y,z) * K(x \ 1,x) = (x \ 1) * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,906,a(flip),b,2211,a),flip(a)].">
      <j1 rule="hyper" parents="63 906 2211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2247">
    <literal><![CDATA[
      L(x,y,y \ 1) * K(y \ 1,y) = (y \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,464,a(flip),b,2211,a),flip(a)].">
      <j1 rule="hyper" parents="63 464 2211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2248">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ y = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,669,a(flip),b,2211,a(flip))].">
      <j1 rule="hyper" parents="133 669 2211"/>
    </justification>
  </clause>

  <clause id="2249">
    <literal><![CDATA[
      (x * K(y \ 1,y)) / z = K(y \ 1,y) * (x / z)
    ]]></literal>
    <justification jstring="[para(2211(a,1),660(a,1,1))].">
      <j1 rule="para" parents="2211 660"/>
    </justification>
  </clause>

  <clause id="2250">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ ((z * y) * K(x \ 1,x)) = L(T(z,y),y,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2211(a,1),247(a,1,2))].">
      <j1 rule="para" parents="2211 247"/>
    </justification>
  </clause>

  <clause id="2251">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ ((z * y) * K(x \ 1,x)) = R(T(z,y * K(x \ 1,x)),y,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2211(a,2),560(a,1,1))].">
      <j1 rule="para" parents="2211 560"/>
    </justification>
  </clause>

  <clause id="2253">
    <literal><![CDATA[
      (x * (y \ 1)) \ (K(y \ 1,y) * x) = L(y,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(2211(a,2),341(a,1,2))].">
      <j1 rule="para" parents="2211 341"/>
    </justification>
  </clause>

  <clause id="2254">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(354,a,2233,a),flip(a)].">
      <j1 rule="hyper" parents="354 2233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2256">
    <literal><![CDATA[
      ((1 / x) * y) * K(x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,774,a(flip),b,2244,a)].">
      <j1 rule="hyper" parents="63 774 2244"/>
    </justification>
  </clause>

  <clause id="2257">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(34,a,1211,a,b,2244,a),flip(a)].">
      <j1 rule="hyper" parents="34 1211 2244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2258">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ 1 = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2244(a,1),357(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2244 357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2259">
    <literal><![CDATA[
      x * (y * K(x \ 1,x)) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(2244(a,1),1150(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2244 1150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2260">
    <literal><![CDATA[
      R((K(x \ 1,x) * y) / x,x,K(x,x \ 1)) = y / T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2254(a,1),942(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2254 942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2261">
    <literal><![CDATA[
      x / (L(y,z,u) \ L(R(y,w,v5),z,u)) = (L(y,z,u) \ R(L(y,z,u),w,v5)) \ x
    ]]></literal>
    <justification jstring="[para(29(a,1),2194(a,1,2,2))].">
      <j1 rule="para" parents="29 2194"/>
    </justification>
  </clause>

  <clause id="2262">
    <literal><![CDATA[
      (x * y) \ ((x * (z \ R(z,u,w))) * y) = R(T(z \ R(z,u,w),x * y),x,y)
    ]]></literal>
    <justification jstring="[para(2197(a,1),789(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2197 789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2263">
    <literal><![CDATA[
      (x * (y * (z \ R(z,u,w)))) / (x * y) = L(z \ R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(2197(a,1),752(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2197 752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2264">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * u) \ w = (u * (x \ R(x,y,z))) \ w
    ]]></literal>
    <justification jstring="[hyper(61,a,2198,a)].">
      <j1 rule="hyper" parents="61 2198"/>
    </justification>
  </clause>

  <clause id="2265">
    <literal><![CDATA[
      K(x * (y / (x * y)),z) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,2218,a)].">
      <j1 rule="hyper" parents="55 2218"/>
    </justification>
  </clause>

  <clause id="2266">
    <literal><![CDATA[
      ((1 / x) \ (y * T(y \ 1,x))) * K(x,x \ 1) = T(x,x \ 1) * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[para(2014(a,2),2238(a,1,1))].">
      <j1 rule="para" parents="2014 2238"/>
    </justification>
  </clause>

  <clause id="2267">
    <literal><![CDATA[
      K(x,a(R(y,z,u),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(316,a,2195,a(flip),b,2232,a),flip(a)].">
      <j1 rule="hyper" parents="316 2195 2232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2270">
    <literal><![CDATA[
      K(x,a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[para(496(a,1),2267(a,1,2,1))].">
      <j1 rule="para" parents="496 2267"/>
    </justification>
  </clause>

  <clause id="2273">
    <literal><![CDATA[
      T(x,a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,2270,a)].">
      <j1 rule="hyper" parents="56 2270"/>
    </justification>
  </clause>

  <clause id="2274">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(x,y,z) = u
    ]]></literal>
    <justification jstring="[hyper(795,a,2273,a)].">
      <j1 rule="hyper" parents="795 2273"/>
    </justification>
  </clause>

  <clause id="2275">
    <literal><![CDATA[
      a(x,y,z) \ (u * a(x,y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(383,a,2273,a)].">
      <j1 rule="hyper" parents="383 2273"/>
    </justification>
  </clause>

  <clause id="2276">
    <literal><![CDATA[
      x / a(y,z,u) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(377,a,2273,a),flip(a)].">
      <j1 rule="hyper" parents="377 2273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2277">
    <literal><![CDATA[
      (a(x,y,z) * u) / a(x,y,z) = u
    ]]></literal>
    <justification jstring="[hyper(331,a,2273,a),flip(a)].">
      <j1 rule="hyper" parents="331 2273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2278">
    <literal><![CDATA[
      T(x,a(y,z,u)) = w \ (w * x)
    ]]></literal>
    <justification jstring="[hyper(316,a,9,a,b,2273,a),flip(a)].">
      <j1 rule="hyper" parents="316 9 2273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2279">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),a(w,v5,v6)) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,155,a(flip),b,2273,a),flip(a)].">
      <j1 rule="hyper" parents="316 155 2273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2280">
    <literal><![CDATA[
      ((a(x,y,z) * u) * w) / (a(x,y,z) * w) = R(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,734,a,b,2273,a),flip(a)].">
      <j1 rule="hyper" parents="63 734 2273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2281">
    <literal><![CDATA[
      L(T(x,a(y,z,u)),w,v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a,b,2273,a)].">
      <j1 rule="hyper" parents="63 25 2273"/>
    </justification>
  </clause>

  <clause id="2282">
    <literal><![CDATA[
      R(a(x,y,z) \ u,a(x,y,z),a(x,y,z)) = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,622,a(flip),b,2273,a)].">
      <j1 rule="hyper" parents="63 622 2273"/>
    </justification>
  </clause>

  <clause id="2284">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,a(x,y,z),u) = u / (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,620,a(flip),b,2273,a)].">
      <j1 rule="hyper" parents="63 620 2273"/>
    </justification>
  </clause>

  <clause id="2286">
    <literal><![CDATA[
      T(a(x,y,z),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,2273,a)].">
      <j1 rule="hyper" parents="54 2273"/>
    </justification>
  </clause>

  <clause id="2287">
    <literal><![CDATA[
      (x * a(y,z,u)) / x = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(209,a,2273,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="209 2273 22"/>
    </justification>
  </clause>

  <clause id="2288">
    <literal><![CDATA[
      a(x,y,z) * (u / (a(x,y,z) \ 1)) = u * (a(x,y,z) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,2273,a(flip),b,580,a(flip))].">
      <j1 rule="hyper" parents="139 2273 580"/>
    </justification>
  </clause>

  <clause id="2289">
    <literal><![CDATA[
      a(x,y,z) * (u / a(x,y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(139,a,2273,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="139 2273 116"/>
    </justification>
  </clause>

  <clause id="2290">
    <literal><![CDATA[
      a(x,y,z) * u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,2273,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 2273 22"/>
    </justification>
  </clause>

  <clause id="2292">
    <literal><![CDATA[
      (a(x,y,z) * u) * w = (u * a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(38,a,915,a(flip),b,2273,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 915 2273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2293">
    <literal><![CDATA[
      x * (a(y,z,u) * w) = x * (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(37,a,1566,a(flip),b,2273,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="37 1566 2273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2294">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(2273(a,1),49(a,2))].">
      <j1 rule="para" parents="2273 49"/>
    </justification>
  </clause>

  <clause id="2295">
    <literal><![CDATA[
      x \ (a(y,z,u) * x) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(2273(a,1),242(a,1,2,2))].">
      <j1 rule="para" parents="2273 242"/>
    </justification>
  </clause>

  <clause id="2296">
    <literal><![CDATA[
      x \ (a(y,z,u) * w) = x \ (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(2273(a,1),237(a,1,2,2))].">
      <j1 rule="para" parents="2273 237"/>
    </justification>
  </clause>

  <clause id="2297">
    <literal><![CDATA[
      a(x,y,z) * (u * (u \ w)) = w * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2273(a,1),243(a,1,2,2,2))].">
      <j1 rule="para" parents="2273 243"/>
    </justification>
  </clause>

  <clause id="2298">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,v5) = a(u,w,v5) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2273(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2273 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2299">
    <literal><![CDATA[
      L(x \ y,x,a(z,u,w)) = (a(z,u,w) * x) \ (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(2273(a,1),413(a,1,1,2))].">
      <j1 rule="para" parents="2273 413"/>
    </justification>
  </clause>

  <clause id="2300">
    <literal><![CDATA[
      x \ ((y * y) * a(z,u,w)) = (x \ a(z,u,w)) * (y * y)
    ]]></literal>
    <justification jstring="[para(2273(a,1),822(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2273 822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2301">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ u = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(384,a,2286,a)].">
      <j1 rule="hyper" parents="384 2286"/>
    </justification>
  </clause>

  <clause id="2302">
    <literal><![CDATA[
      T(a(x,y,z),u) = T(a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,2286,a,b,2286,a)].">
      <j1 rule="hyper" parents="316 2286 2286"/>
    </justification>
  </clause>

  <clause id="2303">
    <literal><![CDATA[
      K(a(x,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,2286,a)].">
      <j1 rule="hyper" parents="55 2286"/>
    </justification>
  </clause>

  <clause id="2304">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * v5 = v5 * L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(2286(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2286 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2305">
    <literal><![CDATA[
      R(a(x,y,z),u,w) * v5 = v5 * R(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(2286(a,1),252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2286 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2306">
    <literal><![CDATA[
      x * (a(y,z,u) * (x \ 1)) = L(a(y,z,u),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2286(a,1),527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2286 527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2307">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (w * u) = w * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(2286(a,1),598(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2286 598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2308">
    <literal><![CDATA[
      L(a(x,y,z),u \ w,u) * w = u * ((u \ w) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(2286(a,1),713(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2286 713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2309">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) \ v5 = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(2286(a,1),310(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2286 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2310">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z) \ u,w) = (w * (a(x,y,z) \ u)) \ (w * u)
    ]]></literal>
    <justification jstring="[para(2286(a,1),336(a,1,1))].">
      <j1 rule="para" parents="2286 336"/>
    </justification>
  </clause>

  <clause id="2312">
    <literal><![CDATA[
      K(a(x,y,z),u) * w = w
    ]]></literal>
    <justification jstring="[hyper(138,a,2303,a,b,77,a)].">
      <j1 rule="hyper" parents="138 2303 77"/>
    </justification>
  </clause>

  <clause id="2314">
    <literal><![CDATA[
      L(a(x,y,z) * u,w,v5) = L(u * a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,1360,a(flip),b,2274,a),flip(a)].">
      <j1 rule="hyper" parents="63 1360 2274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2315">
    <literal><![CDATA[
      a(x,y,z) \ ((x * y) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(35,a,89,a,b,2274,a),flip(a)].">
      <j1 rule="hyper" parents="35 89 2274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2317">
    <literal><![CDATA[
      (x * (x \ y)) * a(z,u,w) = a(z,u,w) * y
    ]]></literal>
    <justification jstring="[para(173(a,1),2274(a,1,1))].">
      <j1 rule="para" parents="173 2274"/>
    </justification>
  </clause>

  <clause id="2319">
    <literal><![CDATA[
      (a(x,y,z) * u) * L(w,u,a(x,y,z)) = (u * w) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(296(a,1),2274(a,1,1)),flip(a)].">
      <j1 rule="para" parents="296 2274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2320">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (a(x,y,z) \ 1) = u / (a(x,y,z) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(2274(a,1),562(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2274 562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2321">
    <literal><![CDATA[
      (x * ((x \ (a(y,z,u) \ w)) * a(y,z,u))) \ w = a(x,x \ (a(y,z,u) \ w),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(2274(a,1),91(a,1,2))].">
      <j1 rule="para" parents="2274 91"/>
    </justification>
  </clause>

  <clause id="2322">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) * a(y,z,u) = a(y,z,u) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(1447(a,2),2274(a,1,1))].">
      <j1 rule="para" parents="1447 2274"/>
    </justification>
  </clause>

  <clause id="2324">
    <literal><![CDATA[
      (a(x,y,z) * u) \ w = (u * a(x,y,z)) \ w
    ]]></literal>
    <justification jstring="[para(2275(a,1),165(a,1,1,2))].">
      <j1 rule="para" parents="2275 165"/>
    </justification>
  </clause>

  <clause id="2326">
    <literal><![CDATA[
      T(x / a(y,z,u),a(w,v5,v6)) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,2273,a,b,2276,a)].">
      <j1 rule="hyper" parents="63 2273 2276"/>
    </justification>
  </clause>

  <clause id="2327">
    <literal><![CDATA[
      a(x,x \ y,z) \ (y * z) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,687,a(flip),b,2276,a),flip(a)].">
      <j1 rule="hyper" parents="63 687 2276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2328">
    <literal><![CDATA[
      (x * y) / (z * ((z \ x) * y)) = a(z,z \ x,y)
    ]]></literal>
    <justification jstring="[hyper(209,a,687,a(flip),b,2276,a(flip))].">
      <j1 rule="hyper" parents="209 687 2276"/>
    </justification>
  </clause>

  <clause id="2329">
    <literal><![CDATA[
      a(x,y,z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(209,a,200,a(flip),b,2276,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="209 200 2276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2330">
    <literal><![CDATA[
      a(x,y,z) * (x * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,200,a(flip),b,2276,a(flip))].">
      <j1 rule="hyper" parents="139 200 2276"/>
    </justification>
  </clause>

  <clause id="2332">
    <literal><![CDATA[
      x / T(a(y,z,u),w) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(2286(a,2),2276(a,1,2))].">
      <j1 rule="para" parents="2286 2276"/>
    </justification>
  </clause>

  <clause id="2333">
    <literal><![CDATA[
      (a(x,y,z) * u) / (a(x,y,z) * a(x,y,z)) = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(2277(a,1),566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2277 566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2334">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),w) = (a(x,y,z) * w) \ (w * u)
    ]]></literal>
    <justification jstring="[para(2277(a,1),1612(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2277 1612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2335">
    <literal><![CDATA[
      ((x * a(y,z,u)) * w) / (x * w) = R(a(y,z,u),x,w)
    ]]></literal>
    <justification jstring="[para(2287(a,1),110(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2287 110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2336">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / (x * z) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(690(a,1),2287(a,1,1))].">
      <j1 rule="para" parents="690 2287"/>
    </justification>
  </clause>

  <clause id="2337">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (x * (z * y)) = a(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[para(692(a,1),2287(a,1,1))].">
      <j1 rule="para" parents="692 2287"/>
    </justification>
  </clause>

  <clause id="2338">
    <literal><![CDATA[
      L(x \ y,x,a(z,u,w)) = (x * a(z,u,w)) \ (a(z,u,w) * y)
    ]]></literal>
    <justification jstring="[para(2287(a,1),1612(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2287 1612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2339">
    <literal><![CDATA[
      x / (a(y,z,u) * w) = x / (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(209,a,2290,a,b,83,a)].">
      <j1 rule="hyper" parents="209 2290 83"/>
    </justification>
  </clause>

  <clause id="2340">
    <literal><![CDATA[
      a(x,y,z) * (a(u,w,v5) * v6) = (v6 * a(u,w,v5)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,2290,a,b,2275,a)].">
      <j1 rule="hyper" parents="139 2290 2275"/>
    </justification>
  </clause>

  <clause id="2341">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) / (w * a(x,y,z)) = R(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(136,a,2290,a,b,109,a)].">
      <j1 rule="hyper" parents="136 2290 109"/>
    </justification>
  </clause>

  <clause id="2342">
    <literal><![CDATA[
      L(x,y,z) \ (a(u,w,v5) * x) = x * (L(x,y,z) \ a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(133,a,2290,a,b,1128,a)].">
      <j1 rule="hyper" parents="133 2290 1128"/>
    </justification>
  </clause>

  <clause id="2343">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ (a(z,u,w) * (x * y)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(133,a,2290,a,b,89,a)].">
      <j1 rule="hyper" parents="133 2290 89"/>
    </justification>
  </clause>

  <clause id="2345">
    <literal><![CDATA[
      x / ((a(y,z,u) * w) \ x) = w * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,80,a,b,2290,a)].">
      <j1 rule="hyper" parents="63 80 2290"/>
    </justification>
  </clause>

  <clause id="2346">
    <literal><![CDATA[
      (x * T(y,a(z,u,w) * x)) * a(z,u,w) = L(y,x,a(z,u,w)) * (a(z,u,w) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,598,a(flip),b,2290,a),flip(a)].">
      <j1 rule="hyper" parents="63 598 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2347">
    <literal><![CDATA[
      (a(x,y,z) * u) * T(w,a(x,y,z) * u) = w * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,2290,a(flip),b,242,a),flip(a)].">
      <j1 rule="hyper" parents="139 2290 242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2348">
    <literal><![CDATA[
      R(a(x,y,z),u,w) * (u * w) = (u * a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,2290,a(flip),b,301,a),flip(a)].">
      <j1 rule="hyper" parents="138 2290 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2349">
    <literal><![CDATA[
      (a(x,y,z) * u) \ ((u * w) * a(x,y,z)) = L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,2290,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="133 2290 100"/>
    </justification>
  </clause>

  <clause id="2350">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ ((x * a(z,u,w)) * y) = a(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(2290(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2290 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2351">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) \ ((u * a(x,y,z)) * w) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(2290(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2290 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2352">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) \ ((a(y,z,u) * x) * w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(2290(a,2),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2290 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2353">
    <literal><![CDATA[
      (x * a(y,z,u)) \ (a(y,z,u) * (x * w)) = L(w,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(2290(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2290 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2354">
    <literal><![CDATA[
      L(x \ (a(y,z,u) \ w),x,a(y,z,u)) = (x * a(y,z,u)) \ w
    ]]></literal>
    <justification jstring="[para(2290(a,1),298(a,2,1))].">
      <j1 rule="para" parents="2290 298"/>
    </justification>
  </clause>

  <clause id="2355">
    <literal><![CDATA[
      (x * a(y,z,u)) \ (a(y,z,u) * (w * x)) = L(T(w,x),x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(2290(a,1),247(a,1,1))].">
      <j1 rule="para" parents="2290 247"/>
    </justification>
  </clause>

  <clause id="2357">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ (x * (a(z,u,w) * (y * v5))) = L(L(v5,y,a(z,u,w)),a(z,u,w) * y,x)
    ]]></literal>
    <justification jstring="[para(2290(a,1),460(a,1,1,2))].">
      <j1 rule="para" parents="2290 460"/>
    </justification>
  </clause>

  <clause id="2358">
    <literal><![CDATA[
      x * T(a(y,z,u),w) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(2286(a,2),2290(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2286 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2359">
    <literal><![CDATA[
      x * ((a(y,z,u) \ w) \ w) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,2301,a,b,2295,a)].">
      <j1 rule="hyper" parents="139 2301 2295"/>
    </justification>
  </clause>

  <clause id="2360">
    <literal><![CDATA[
      a(x \ (y / z),x,z) \ y = ((y / z) / x) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(39,a,1820,a,b,2301,a),flip(a)].">
      <j1 rule="hyper" parents="39 1820 2301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2361">
    <literal><![CDATA[
      a(x / y,y,z) \ (x * z) = (x / y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(39,a,93,a,b,2301,a),flip(a)].">
      <j1 rule="hyper" parents="39 93 2301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2362">
    <literal><![CDATA[
      R((a(x,y,z) \ 1) \ u,a(x,y,z) \ 1,a(x,y,z) \ 1) = T(u * a(x,y,z),a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(2301(a,1),622(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2301 622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2363">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,1628,a,b,2302,a)].">
      <j1 rule="hyper" parents="40 1628 2302"/>
    </justification>
  </clause>

  <clause id="2364">
    <literal><![CDATA[
      R(a(x,y,z),u,a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,1625,a,b,2302,a)].">
      <j1 rule="hyper" parents="40 1625 2302"/>
    </justification>
  </clause>

  <clause id="2366">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ 1)) = R(u,a(x,y,z) \ 1,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1041,a(flip),b,2358,a),flip(a)].">
      <j1 rule="hyper" parents="63 1041 2358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2369">
    <literal><![CDATA[
      ((x * y) * z) / ((x * (y * (z \ 1))) * (z * z)) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,639,a,b,2329,a)].">
      <j1 rule="hyper" parents="316 639 2329"/>
    </justification>
  </clause>

  <clause id="2370">
    <literal><![CDATA[
      a(x,y,z) = R(R(x,y,z) / x,x,y * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,516,a,b,2329,a),flip(a)].">
      <j1 rule="hyper" parents="316 516 2329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2371">
    <literal><![CDATA[
      x / (((x / y) / z) * (z * y)) = a((x / y) / z,z,y)
    ]]></literal>
    <justification jstring="[para(88(a,1),2329(a,2,1)),flip(a)].">
      <j1 rule="para" parents="88 2329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2372">
    <literal><![CDATA[
      ((x * L(y,z,u)) * y) / (x * (y * L(y,z,u))) = a(x,L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(257(a,1),2329(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="257 2329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2373">
    <literal><![CDATA[
      (((x * y) * z) * (u \ (1 / u))) / (x * (y * (z * (u \ (1 / u))))) = a(x,y,z * (u \ (1 / u)))
    ]]></literal>
    <justification jstring="[para(505(a,2),2329(a,2,1)),flip(a)].">
      <j1 rule="para" parents="505 2329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2374">
    <literal><![CDATA[
      (L(x,y,z) * u) / ((x \ L(x,y,z)) * (x * u)) = a(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(1273(a,1),2329(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1273 2329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2375">
    <literal><![CDATA[
      ((x * y) * z) / L(y * z,x,a(x,y,z)) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(136,a,2330,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="136 2330 100"/>
    </justification>
  </clause>

  <clause id="2376">
    <literal><![CDATA[
      R(x,y,y) / x = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,497,a(flip),b,2370,a)].">
      <j1 rule="hyper" parents="316 497 2370"/>
    </justification>
  </clause>

  <clause id="2377">
    <literal><![CDATA[
      a(x,y,y) * x = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,2370,a,b,497,a(flip))].">
      <j1 rule="hyper" parents="138 2370 497"/>
    </justification>
  </clause>

  <clause id="2378">
    <literal><![CDATA[
      a(x,y,z) = R(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[para(1774(a,1),2370(a,2,1))].">
      <j1 rule="para" parents="1774 2370"/>
    </justification>
  </clause>

  <clause id="2379">
    <literal><![CDATA[
      (1 / x) * R(x,y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,985,a,b,2376,a)].">
      <j1 rule="hyper" parents="63 985 2376"/>
    </justification>
  </clause>

  <clause id="2380">
    <literal><![CDATA[
      x \ R(x,y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1774,a(flip),b,2376,a)].">
      <j1 rule="hyper" parents="63 1774 2376"/>
    </justification>
  </clause>

  <clause id="2381">
    <literal><![CDATA[
      x * a(x,y,y) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,2287,a,b,2376,a)].">
      <j1 rule="hyper" parents="37 2287 2376"/>
    </justification>
  </clause>

  <clause id="2382">
    <literal><![CDATA[
      L(x \ y,x,a(x,z,z)) = R(x,z,z) \ (a(x,z,z) * y)
    ]]></literal>
    <justification jstring="[para(2377(a,1),102(a,2,1))].">
      <j1 rule="para" parents="2377 102"/>
    </justification>
  </clause>

  <clause id="2383">
    <literal><![CDATA[
      a(x,y,y \ 1) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,707,a,b,2380,a)].">
      <j1 rule="hyper" parents="63 707 2380"/>
    </justification>
  </clause>

  <clause id="2384">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,u),y,z) = a(L(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[para(29(a,1),2380(a,1,2))].">
      <j1 rule="para" parents="29 2380"/>
    </justification>
  </clause>

  <clause id="2385">
    <literal><![CDATA[
      a(x,y * (z \ 1),y * (z \ 1)) = x \ R(x,y * (z \ 1),y * z)
    ]]></literal>
    <justification jstring="[para(1711(a,1),2380(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1711 2380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2386">
    <literal><![CDATA[
      x \ R(x,y \ L(y,z,u),y * L(y,z,u)) = a(x,y \ L(y,z,u),y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1718(a,1),2380(a,1,2))].">
      <j1 rule="para" parents="1718 2380"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1720,a(flip),b,2378,a)].">
      <j1 rule="hyper" parents="316 1720 2378"/>
    </justification>
  </clause>

  <clause id="2388">
    <literal><![CDATA[
      R((1 / x) * R(x,y,z),x,y * z) = L(a(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2378(a,2),893(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2378 893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2389">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) / (x \ 1) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2378(a,2),1423(a,2,2))].">
      <j1 rule="para" parents="2378 1423"/>
    </justification>
  </clause>

  <clause id="2390">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u \ 1,u),y,z) = a(L(x,y,z),u \ 1,u)
    ]]></literal>
    <justification jstring="[para(29(a,1),2387(a,1,2))].">
      <j1 rule="para" parents="29 2387"/>
    </justification>
  </clause>

  <clause id="2391">
    <literal><![CDATA[
      L(x,y,(z * a(u,w,v5)) * v6) = L(x,y,v6 * (a(u,w,v5) * z))
    ]]></literal>
    <justification jstring="[para(2292(a,1),1668(a,1,3))].">
      <j1 rule="para" parents="2292 1668"/>
    </justification>
  </clause>

  <clause id="2392">
    <literal><![CDATA[
      T((x * (a(y,z,u) * w)) / x,x * (w * a(y,z,u))) = L(w * a(y,z,u),x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(2293(a,2),1609(a,1,1,1))].">
      <j1 rule="para" parents="2293 1609"/>
    </justification>
  </clause>

  <clause id="2393">
    <literal><![CDATA[
      x \ (y \ (a(z,u,w) * v5)) = x \ (y \ (v5 * a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(133,a,2296,a,b,10,a)].">
      <j1 rule="hyper" parents="133 2296 10"/>
    </justification>
  </clause>

  <clause id="2394">
    <literal><![CDATA[
      x * ((a(y,z,u) * w) \ v5) = x * ((w * a(y,z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(139,a,2324,a,b,9,a)].">
      <j1 rule="hyper" parents="139 2324 9"/>
    </justification>
  </clause>

  <clause id="2395">
    <literal><![CDATA[
      ((a(x,y,z) * u) \ w) * v5 = ((u * a(x,y,z)) \ w) * v5
    ]]></literal>
    <justification jstring="[hyper(138,a,2324,a,b,11,a)].">
      <j1 rule="hyper" parents="138 2324 11"/>
    </justification>
  </clause>

  <clause id="2396">
    <literal><![CDATA[
      ((a(x,y,z) * u) \ w) \ v5 = ((u * a(x,y,z)) \ w) \ v5
    ]]></literal>
    <justification jstring="[hyper(61,a,2324,a)].">
      <j1 rule="hyper" parents="61 2324"/>
    </justification>
  </clause>

  <clause id="2397">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * v5) = K(u,w) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(133,a,479,a(flip),b,2359,a(flip))].">
      <j1 rule="hyper" parents="133 479 2359"/>
    </justification>
  </clause>

  <clause id="2398">
    <literal><![CDATA[
      x / (y * ((y \ (x / z)) * z)) = a(y,y \ (x / z),z)
    ]]></literal>
    <justification jstring="[para(2327(a,1),318(a,1,2))].">
      <j1 rule="para" parents="2327 318"/>
    </justification>
  </clause>

  <clause id="2399">
    <literal><![CDATA[
      (x * y) * ((y \ x) / (x * x)) = a(x,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,683,a(flip),b,2336,a)].">
      <j1 rule="hyper" parents="63 683 2336"/>
    </justification>
  </clause>

  <clause id="2400">
    <literal><![CDATA[
      a(x \ y,x,z) \ (y * z) = (y / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(1813(a,1),2361(a,1,1))].">
      <j1 rule="para" parents="1813 2361"/>
    </justification>
  </clause>

  <clause id="2401">
    <literal><![CDATA[
      (x * y) * (y \ (x \ 1)) = a(x,y,y \ x)
    ]]></literal>
    <justification jstring="[para(588(a,1),2399(a,1,2))].">
      <j1 rule="para" parents="588 2399"/>
    </justification>
  </clause>

  <clause id="2402">
    <literal><![CDATA[
      a(x \ 1,x,y) \ y = (1 / x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(328,a,2400,a)].">
      <j1 rule="hyper" parents="328 2400"/>
    </justification>
  </clause>

  <clause id="2404">
    <literal><![CDATA[
      a(x \ (y \ L(y,z,u)),x,y) \ L(y,z,u) = ((y \ L(y,z,u)) / x) * (x * y)
    ]]></literal>
    <justification jstring="[para(1273(a,1),2400(a,1,2))].">
      <j1 rule="para" parents="1273 2400"/>
    </justification>
  </clause>

  <clause id="2405">
    <literal><![CDATA[
      R(x,y,(z / u) * (u * z)) = R(x,y,a(u \ z,u,z))
    ]]></literal>
    <justification jstring="[para(2400(a,1),1715(a,1,3))].">
      <j1 rule="para" parents="2400 1715"/>
    </justification>
  </clause>

  <clause id="2406">
    <literal><![CDATA[
      a(x \ 1,x,y) \ y = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,890,a(flip),b,2402,a),flip(a)].">
      <j1 rule="hyper" parents="316 890 2402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2408">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,1379,a,b,2406,a)].">
      <j1 rule="hyper" parents="39 1379 2406"/>
    </justification>
  </clause>

  <clause id="2409">
    <literal><![CDATA[
      L(x \ L(x,y,y \ 1),z,u) \ 1 = a(y \ 1,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2143,a(flip),b,2408,a)].">
      <j1 rule="hyper" parents="63 2143 2408"/>
    </justification>
  </clause>

  <clause id="2410">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) * (u * w) = (u * K(x \ 1,x)) * w
    ]]></literal>
    <justification jstring="[hyper(316,a,1938,a,b,2214,a)].">
      <j1 rule="hyper" parents="316 1938 2214"/>
    </justification>
  </clause>

  <clause id="2412">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(116(a,1),2223(a,1,1))].">
      <j1 rule="para" parents="116 2223"/>
    </justification>
  </clause>

  <clause id="2413">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K(x,x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,435,a,b,2412,a),flip(a)].">
      <j1 rule="hyper" parents="316 435 2412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2414">
    <literal><![CDATA[
      T(x,y) * K(x \ 1,x) = 1 / (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,2412,a(flip),b,1292,a)].">
      <j1 rule="hyper" parents="139 2412 1292"/>
    </justification>
  </clause>

  <clause id="2415">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(39,a,435,a,b,2413,a(flip))].">
      <j1 rule="hyper" parents="39 435 2413"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      K(x,x \ 1) * (T(x,y) \ z) = (1 / (1 / T(x,y))) \ z
    ]]></literal>
    <justification jstring="[para(2415(a,1),1151(a,1,1))].">
      <j1 rule="para" parents="2415 1151"/>
    </justification>
  </clause>

  <clause id="2417">
    <literal><![CDATA[
      1 / (1 / T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2038,a(flip),b,2414,a),flip(a)].">
      <j1 rule="hyper" parents="63 2038 2414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2418">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(204,a,2417,a)].">
      <j1 rule="hyper" parents="204 2417"/>
    </justification>
  </clause>

  <clause id="2419">
    <literal><![CDATA[
      L(x,T(x,y) \ 1,T(x,y)) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(40,a,1291,a,b,2417,a(flip))].">
      <j1 rule="hyper" parents="40 1291 2417"/>
    </justification>
  </clause>

  <clause id="2420">
    <literal><![CDATA[
      1 / T((x \ 1) \ 1,y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(205(a,1),2418(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="205 2418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2421">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(204,a,2420,a),flip(a)].">
      <j1 rule="hyper" parents="204 2420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      K(x,y) / T((z \ 1) \ 1,u) = K(x,y) * (T(z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,2420,a(flip),b,437,a),flip(a)].">
      <j1 rule="hyper" parents="139 2420 437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2423">
    <literal><![CDATA[
      T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(116(a,1),2421(a,2,1,1))].">
      <j1 rule="para" parents="116 2421"/>
    </justification>
  </clause>

  <clause id="2424">
    <literal><![CDATA[
      (1 / (1 / x)) * (T(x,y) \ 1) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(2419(a,1),1914(a,1,1))].">
      <j1 rule="para" parents="2419 1914"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      (x * (((x \ y) \ 1) \ 1)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(285,a,2423,a)].">
      <j1 rule="hyper" parents="285 2423"/>
    </justification>
  </clause>

  <clause id="2427">
    <literal><![CDATA[
      T(x \ y,x / y) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1790,a(flip),b,2423,a)].">
      <j1 rule="hyper" parents="63 1790 2423"/>
    </justification>
  </clause>

  <clause id="2428">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x * y) \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(11(a,1),2427(a,1,2))].">
      <j1 rule="para" parents="11 2427"/>
    </justification>
  </clause>

  <clause id="2429">
    <literal><![CDATA[
      T(x \ (y \ x),y) = ((x \ (y \ x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(80(a,1),2427(a,1,2))].">
      <j1 rule="para" parents="80 2427"/>
    </justification>
  </clause>

  <clause id="2430">
    <literal><![CDATA[
      x * (((x \ (y \ x)) \ 1) \ 1) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,2429,a(flip),b,1159,a(flip))].">
      <j1 rule="hyper" parents="139 2429 1159"/>
    </justification>
  </clause>

  <clause id="2431">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,2226,a(flip),b,1209,a)].">
      <j1 rule="hyper" parents="139 2226 1209"/>
    </justification>
  </clause>

  <clause id="2433">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,K(y \ 1,y)) = K(y \ 1,y) * (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,800,a,b,2249,a)].">
      <j1 rule="hyper" parents="63 800 2249"/>
    </justification>
  </clause>

  <clause id="2434">
    <literal><![CDATA[
      x / L(a(y,z,u),w,v5) = L(a(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(346,a,2304,a)].">
      <j1 rule="hyper" parents="346 2304"/>
    </justification>
  </clause>

  <clause id="2435">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ w) * w = (w / u) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,1606,a(flip),b,2304,a),flip(a)].">
      <j1 rule="hyper" parents="316 1606 2304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      T(x,L(a(y,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(255,a,2304,a)].">
      <j1 rule="hyper" parents="255 2304"/>
    </justification>
  </clause>

  <clause id="2437">
    <literal><![CDATA[
      ((x / y) * (y * a(z,u,w))) / x = L(a(z,u,w),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(136,a,1606,a(flip),b,2304,a)].">
      <j1 rule="hyper" parents="136 1606 2304"/>
    </justification>
  </clause>

  <clause id="2438">
    <literal><![CDATA[
      K(x,L(a(y,z,u),w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(132,a,2304,a,b,94,a),flip(a)].">
      <j1 rule="hyper" parents="132 2304 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2439">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * v5) \ ((v6 * v5) * L(a(x,y,z),u,w)) = L(T(v6,v5),v5,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(2304(a,1),247(a,1,2))].">
      <j1 rule="para" parents="2304 247"/>
    </justification>
  </clause>

  <clause id="2440">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * v5) \ (v5 * (v6 * L(a(x,y,z),u,w))) = L(T(v6,L(a(x,y,z),u,w)),L(a(x,y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(2304(a,2),247(a,1,1))].">
      <j1 rule="para" parents="2304 247"/>
    </justification>
  </clause>

  <clause id="2441">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * v5) \ ((v6 * v5) * L(a(x,y,z),u,w)) = R(T(v6,v5 * L(a(x,y,z),u,w)),v5,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(2304(a,2),560(a,1,1))].">
      <j1 rule="para" parents="2304 560"/>
    </justification>
  </clause>

  <clause id="2442">
    <literal><![CDATA[
      T(1 / (1 / x),T(x,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(253,a,2424,a,b,xx)].">
      <j1 rule="hyper" parents="253 2424"/>
    </justification>
  </clause>

  <clause id="2445">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2442(a,1),1101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2442 1101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2446">
    <literal><![CDATA[
      T(x / y,x \ y) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1099,a,b,2426,a)].">
      <j1 rule="hyper" parents="63 1099 2426"/>
    </justification>
  </clause>

  <clause id="2448">
    <literal><![CDATA[
      (x * ((y / z) \ 1)) * T(y / z,y \ z) = R(x,(y / z) \ 1,y / z)
    ]]></literal>
    <justification jstring="[para(2446(a,2),1035(a,1,2))].">
      <j1 rule="para" parents="2446 1035"/>
    </justification>
  </clause>

  <clause id="2449">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) \ x = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(83(a,1),2430(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="83 2430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2452">
    <literal><![CDATA[
      L(x,y,y \ 1) \ K(y,y \ 1) = ((y \ 1) * (y * x)) \ 1
    ]]></literal>
    <justification jstring="[para(2247(a,1),2258(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2247 2258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2453">
    <literal><![CDATA[
      ((x * y) * (x \ 1)) \ ((1 / (1 / x)) * y) = L(x,x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(1096(a,1),2253(a,1,2))].">
      <j1 rule="para" parents="1096 2253"/>
    </justification>
  </clause>

  <clause id="2454">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) / (x * w) = L(a(y,z,u),w,x)
    ]]></literal>
    <justification jstring="[hyper(136,a,2293,a,b,2307,a)].">
      <j1 rule="hyper" parents="136 2293 2307"/>
    </justification>
  </clause>

  <clause id="2455">
    <literal><![CDATA[
      a(x \ (a(y,z,u) \ w),x,a(y,z,u)) \ w = ((w / a(y,z,u)) / x) * (x * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(2276(a,1),2360(a,1,1,1,2))].">
      <j1 rule="para" parents="2276 2360"/>
    </justification>
  </clause>

  <clause id="2456">
    <literal><![CDATA[
      a((x / (y \ 1)) / y,y,y \ 1) = x / ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(73(a,1),2371(a,1,2)),flip(a)].">
      <j1 rule="para" parents="73 2371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2458">
    <literal><![CDATA[
      x * ((a(y,z,u) * x) / (x * x)) = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,683,a(flip),b,2454,a)].">
      <j1 rule="hyper" parents="63 683 2454"/>
    </justification>
  </clause>

  <clause id="2459">
    <literal><![CDATA[
      x * (a(y,z,u) * (x \ 1)) = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(562(a,1),2458(a,1,2))].">
      <j1 rule="para" parents="562 2458"/>
    </justification>
  </clause>

  <clause id="2460">
    <literal><![CDATA[
      x \ L(a(y,z,u),x,x) = a(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,2459,a)].">
      <j1 rule="hyper" parents="144 2459"/>
    </justification>
  </clause>

  <clause id="2461">
    <literal><![CDATA[
      L(a(x,y,z),u \ 1,u) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2306,a(flip),b,2459,a)].">
      <j1 rule="hyper" parents="63 2306 2459"/>
    </justification>
  </clause>

  <clause id="2462">
    <literal><![CDATA[
      x \ L(a(y,z,u),x,x) = (x \ 1) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,2459,a(flip),b,2293,a(flip))].">
      <j1 rule="hyper" parents="133 2459 2293"/>
    </justification>
  </clause>

  <clause id="2464">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = y * (x * R(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(2187(a,1),1830(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2187 1830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2466">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ 1) = a(z,u,w) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(327,a,2397,a),flip(a)].">
      <j1 rule="hyper" parents="327 2397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2467">
    <literal><![CDATA[
      (a(x,y,z) \ K(u,w)) * (v5 * v5) = K(u,w) * (a(x,y,z) \ (v5 * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,388,a(flip),b,2397,a)].">
      <j1 rule="hyper" parents="63 388 2397"/>
    </justification>
  </clause>

  <clause id="2468">
    <literal><![CDATA[
      K(x,y) * ((a(z,u,w) \ 1) * v5) = (a(z,u,w) \ K(x,y)) * v5
    ]]></literal>
    <justification jstring="[hyper(138,a,2466,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 2466 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2469">
    <literal><![CDATA[
      K(x,x \ 1) * (T(x,y) \ z) = T(1 / (1 / x),y) \ z
    ]]></literal>
    <justification jstring="[para(2417(a,1),2416(a,2,1))].">
      <j1 rule="para" parents="2417 2416"/>
    </justification>
  </clause>

  <clause id="2470">
    <literal><![CDATA[
      T((1 / x) * (T(x,y) \ x),x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1189,a,b,2431,a)].">
      <j1 rule="hyper" parents="63 1189 2431"/>
    </justification>
  </clause>

  <clause id="2471">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) * (z * y) = z * (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(2211(a,2),2225(a,2,2))].">
      <j1 rule="para" parents="2211 2225"/>
    </justification>
  </clause>

  <clause id="2472">
    <literal><![CDATA[
      ((x * y) * L(y \ 1,z,u)) / L(y \ L(y,z,u),x,a(x,y,L(y \ 1,z,u))) = a(x,y,L(y \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[para(1064(a,1),2375(a,1,2,1))].">
      <j1 rule="para" parents="1064 2375"/>
    </justification>
  </clause>

  <clause id="2473">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / L((1 / x) * y,x,a(x,1 / x,y)) = a(x,1 / x,y) * x
    ]]></literal>
    <justification jstring="[para(1085(a,2),2375(a,1,1,1))].">
      <j1 rule="para" parents="1085 2375"/>
    </justification>
  </clause>

  <clause id="2474">
    <literal><![CDATA[
      a(x,y,z) / (x \ 1) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2378(a,2),2389(a,1,1))].">
      <j1 rule="para" parents="2378 2389"/>
    </justification>
  </clause>

  <clause id="2475">
    <literal><![CDATA[
      R(x,T(y,x),T(K(z \ 1,R(z,u,w)),y * x)) \ ((y * K(z \ 1,z)) * x) = T(y,x) * T(K(z \ 1,R(z,u,w)),y * x)
    ]]></literal>
    <justification jstring="[para(2410(a,1),787(a,1,2))].">
      <j1 rule="para" parents="2410 787"/>
    </justification>
  </clause>

  <clause id="2476">
    <literal><![CDATA[
      T(x,y / ((y / (z \ 1)) / z)) = x
    ]]></literal>
    <justification jstring="[para(2456(a,1),2200(a,1,2))].">
      <j1 rule="para" parents="2456 2200"/>
    </justification>
  </clause>

  <clause id="2477">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[para(2057(a,1),2471(a,1,1))].">
      <j1 rule="para" parents="2057 2471"/>
    </justification>
  </clause>

  <clause id="2479">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (K(z \ 1,z) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2211,a(flip),b,2477,a)].">
      <j1 rule="hyper" parents="63 2211 2477"/>
    </justification>
  </clause>

  <clause id="2480">
    <literal><![CDATA[
      K(x \ 1,x) * (y * (1 / x)) = y * (x \ 1)
    ]]></literal>
    <justification jstring="[para(436(a,1),2477(a,2,2))].">
      <j1 rule="para" parents="436 2477"/>
    </justification>
  </clause>

  <clause id="2483">
    <literal><![CDATA[
      K(x \ 1,x) * (y * (1 / x)) = R(y / x,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(316,a,1039,a,b,2480,a),flip(a)].">
      <j1 rule="hyper" parents="316 1039 2480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2484">
    <literal><![CDATA[
      (x * (1 / y)) \ (z * K(y,y \ 1)) = (x * (y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(2480(a,1),2243(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2480 2243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2485">
    <literal><![CDATA[
      (x * y) * K(z \ 1,L(z,u,w)) = x * (K(z \ 1,z) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2055,a,b,2479,a)].">
      <j1 rule="hyper" parents="63 2055 2479"/>
    </justification>
  </clause>

  <clause id="2488">
    <literal><![CDATA[
      L(L((1 / x) \ 1,y * (1 / x),K(x \ 1,x)),1 / x,y) = R(y / x,x,1 / x) \ (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(2483(a,1),776(a,2,1))].">
      <j1 rule="para" parents="2483 776"/>
    </justification>
  </clause>

  <clause id="2489">
    <literal><![CDATA[
      ((x * (y \ 1)) * z) * K(y,y \ 1) = (x * (1 / y)) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,9,a(flip),b,2484,a),flip(a)].">
      <j1 rule="hyper" parents="139 9 2484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2490">
    <literal><![CDATA[
      (x * y) * K(z,L(1 / z,u,w)) = x * (K((1 / z) \ 1,1 / z) * y)
    ]]></literal>
    <justification jstring="[para(83(a,1),2485(a,1,2,1))].">
      <j1 rule="para" parents="83 2485"/>
    </justification>
  </clause>

  <clause id="2492">
    <literal><![CDATA[
      L(x \ y,x,a(z,u,w)) = (x * a(z,u,w)) \ (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,2324,a(flip),b,2299,a),flip(a)].">
      <j1 rule="hyper" parents="316 2324 2299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      L(x \ (y / (a(z,u,w) \ 1)),x,a(z,u,w)) = (a(z,u,w) * x) \ (y * (a(z,u,w) * a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(576(a,1),2299(a,2,2))].">
      <j1 rule="para" parents="576 2299"/>
    </justification>
  </clause>

  <clause id="2494">
    <literal><![CDATA[
      (x * a(y,z,u)) \ ((x * w) * a(y,z,u)) = L(w,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,2319,a(flip),b,2292,a(flip))].">
      <j1 rule="hyper" parents="133 2319 2292"/>
    </justification>
  </clause>

  <clause id="2496">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (w * a(x,y,z))) = L(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(2275(a,1),2334(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2275 2334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2497">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) / (a(x,y,z) * w) = R(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2339,a,b,2341,a)].">
      <j1 rule="hyper" parents="63 2339 2341"/>
    </justification>
  </clause>

  <clause id="2498">
    <literal><![CDATA[
      a(x,y,z) * ((u * a(x,y,z)) / (a(x,y,z) * a(x,y,z))) = R(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,683,a(flip),b,2341,a)].">
      <j1 rule="hyper" parents="63 683 2341"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = L(a(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1778(a,1),2388(a,1,1))].">
      <j1 rule="para" parents="1778 2388"/>
    </justification>
  </clause>

  <clause id="2500">
    <literal><![CDATA[
      L(a(x,y,z),x,x \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2378,a,b,2499,a),flip(a)].">
      <j1 rule="hyper" parents="63 2378 2499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2501">
    <literal><![CDATA[
      (1 / x) \ a(x,y,z) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,2500,a(flip),b,890,a)].">
      <j1 rule="hyper" parents="133 2500 890"/>
    </justification>
  </clause>

  <clause id="2502">
    <literal><![CDATA[
      (x \ 1) * a(x \ 1,y,z) = x \ a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(80(a,1),2501(a,1,1)),flip(a)].">
      <j1 rule="para" parents="80 2501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2510">
    <literal><![CDATA[
      R(T(x,x * a(y,z,u)),x,a(y,z,u)) = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,560,a(flip),b,2494,a)].">
      <j1 rule="hyper" parents="63 560 2494"/>
    </justification>
  </clause>

  <clause id="2511">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ (x * ((y * v5) * a(z,u,w))) = L(L(v5,y,a(z,u,w)),y * a(z,u,w),x)
    ]]></literal>
    <justification jstring="[para(2494(a,1),102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2494 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2512">
    <literal><![CDATA[
      x \ ((a(y,z,u) \ x) * (w * a(y,z,u))) = L(w,a(y,z,u),a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(332,a,2496,a)].">
      <j1 rule="hyper" parents="332 2496"/>
    </justification>
  </clause>

  <clause id="2513">
    <literal><![CDATA[
      (a(x,y,z) * u) \ L(a(x,y,z),u \ 1,u) = L(u \ 1,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(271(a,1),2496(a,1,2))].">
      <j1 rule="para" parents="271 2496"/>
    </justification>
  </clause>

  <clause id="2514">
    <literal><![CDATA[
      (a(x,y,z) * u) / ((a(x,y,z) * (w * w)) / (w * w)) = R(u,w * w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,677,a(flip),b,2497,a)].">
      <j1 rule="hyper" parents="63 677 2497"/>
    </justification>
  </clause>

  <clause id="2515">
    <literal><![CDATA[
      (a(x,y,z) * ((u * w) * v5)) / (a(x,y,z) * (w * v5)) = R(R(u,w,v5),w * v5,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(109(a,1),2497(a,1,1,2))].">
      <j1 rule="para" parents="109 2497"/>
    </justification>
  </clause>

  <clause id="2516">
    <literal><![CDATA[
      R((x / y) * K(y \ 1,y),y,K(y,y \ 1)) = x / T(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2245(a,1),2260(a,1,1))].">
      <j1 rule="para" parents="2245 2260"/>
    </justification>
  </clause>

  <clause id="2517">
    <literal><![CDATA[
      (x * ((y \ R(y,z,u)) * w)) / (x * w) = L(y \ R(y,z,u),w,x)
    ]]></literal>
    <justification jstring="[para(2198(a,2),2263(a,1,1,2))].">
      <j1 rule="para" parents="2198 2263"/>
    </justification>
  </clause>

  <clause id="2518">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(253,a,2347,a(flip),b,2292,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="253 2347 2292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2519">
    <literal><![CDATA[
      ((x * y) * z) / (x * ((y * (z \ 1)) * (z * z))) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(32(a,1),2369(a,1,2))].">
      <j1 rule="para" parents="32 2369"/>
    </justification>
  </clause>

  <clause id="2520">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x / T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1725,a,2516,a)].">
      <j1 rule="hyper" parents="1725 2516"/>
    </justification>
  </clause>

  <clause id="2522">
    <literal><![CDATA[
      x * T(x \ (x / y),y) = x / T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,957,a(flip),b,2520,a)].">
      <j1 rule="hyper" parents="63 957 2520"/>
    </justification>
  </clause>

  <clause id="2523">
    <literal><![CDATA[
      x \ (x / T(y,y \ 1)) = T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(133,a,2520,a(flip),b,957,a(flip))].">
      <j1 rule="hyper" parents="133 2520 957"/>
    </justification>
  </clause>

  <clause id="2524">
    <literal><![CDATA[
      T(x \ (x / y),y) = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(115(a,1),2523(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="115 2523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2525">
    <literal><![CDATA[
      T(x \ (x / (1 / y)),1 / y) = x \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(614(a,1),2523(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="614 2523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2526">
    <literal><![CDATA[
      1 / (x \ (x / ((y \ 1) \ 1))) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(209,a,2524,a(flip),b,1098,a(flip))].">
      <j1 rule="hyper" parents="209 2524 1098"/>
    </justification>
  </clause>

  <clause id="2527">
    <literal><![CDATA[
      (x \ (x / (1 / (1 / y)))) \ 1 = 1 / (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(208(a,1),2526(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="208 2526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2528">
    <literal><![CDATA[
      1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(210,a,2527,a)].">
      <j1 rule="hyper" parents="210 2527"/>
    </justification>
  </clause>

  <clause id="2529">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(139,a,2528,a,b,xx)].">
      <j1 rule="hyper" parents="139 2528"/>
    </justification>
  </clause>

  <clause id="2530">
    <literal><![CDATA[
      x / (1 / (1 / (y \ x))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[para(80(a,1),2529(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="80 2529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2531">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) \ x = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(204,a,2530,a)].">
      <j1 rule="hyper" parents="204 2530"/>
    </justification>
  </clause>

  <clause id="2532">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * ((z \ 1) * (z * z)))) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(32(a,1),2519(a,1,2,2))].">
      <j1 rule="para" parents="32 2519"/>
    </justification>
  </clause>

  <clause id="2533">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * z)) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(229(a,1),2532(a,1,2,2,2))].">
      <j1 rule="para" parents="229 2532"/>
    </justification>
  </clause>

  <clause id="2534">
    <literal><![CDATA[
      a(x,y,z \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2329,a,b,2533,a),flip(a)].">
      <j1 rule="hyper" parents="63 2329 2533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2535">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),2534(a,1,3)),flip(a)].">
      <j1 rule="para" parents="83 2534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2536">
    <literal><![CDATA[
      a(x,y,z) \ ((x * y) * (z \ 1)) = x * (y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(2534(a,1),2315(a,1,1))].">
      <j1 rule="para" parents="2534 2315"/>
    </justification>
  </clause>

  <clause id="2537">
    <literal><![CDATA[
      x * (y * ((x * y) \ 1)) = a(x,y,x * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,168,a(flip),b,2536,a),flip(a)].">
      <j1 rule="hyper" parents="63 168 2536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2538">
    <literal><![CDATA[
      (x * y) \ L(x * y,y,x) = a(x,y,x * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1068,a,b,2537,a)].">
      <j1 rule="hyper" parents="63 1068 2537"/>
    </justification>
  </clause>

  <clause id="2539">
    <literal><![CDATA[
      L((a(x,y,x * y) \ 1) \ z,x * y,(x * y) \ L(x * y,y,x)) = (x * y) * (L(x * y,y,x) \ z)
    ]]></literal>
    <justification jstring="[para(2538(a,1),1557(a,1,1,1))].">
      <j1 rule="para" parents="2538 1557"/>
    </justification>
  </clause>

  <clause id="2541">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z) \ u,w) \ (w * u) = w * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(39,a,2309,a,b,2310,a(flip))].">
      <j1 rule="hyper" parents="39 2309 2310"/>
    </justification>
  </clause>

  <clause id="2542">
    <literal><![CDATA[
      a(x,y,z) * (u / (a(x,y,z) * a(x,y,z))) = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,683,a(flip),b,2333,a)].">
      <j1 rule="hyper" parents="63 683 2333"/>
    </justification>
  </clause>

  <clause id="2543">
    <literal><![CDATA[
      (x * y) \ (a(z,u,w) * (x * (a(z,u,w) \ y))) = a(x,a(z,u,w) \ y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(2274(a,1),2343(a,1,1,2))].">
      <j1 rule="para" parents="2274 2343"/>
    </justification>
  </clause>

  <clause id="2544">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) \ (a(y,z,u) * (x * w)) = a(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(2290(a,2),2343(a,1,1,2))].">
      <j1 rule="para" parents="2290 2343"/>
    </justification>
  </clause>

  <clause id="2545">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ ((a(z,u,w) * x) * y) = a(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(2290(a,2),2350(a,1,2,1))].">
      <j1 rule="para" parents="2290 2350"/>
    </justification>
  </clause>

  <clause id="2546">
    <literal><![CDATA[
      ((x * y) * L(y,z,u)) / (x * (y * L(y,z,u))) = a(x,L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(1433(a,1),2372(a,1,1))].">
      <j1 rule="para" parents="1433 2372"/>
    </justification>
  </clause>

  <clause id="2547">
    <literal><![CDATA[
      (x \ a(y,z,u)) * (a(y,z,u) \ 1) = a(y,z,u) * (x \ (a(y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(588(a,1),2542(a,1,2)),flip(a)].">
      <j1 rule="para" parents="588 2542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2548">
    <literal><![CDATA[
      a(x,L(y,z,u),y) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2329,a,b,2546,a),flip(a)].">
      <j1 rule="hyper" parents="63 2329 2546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2549">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x \ 1)) = y / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1723,a,2433,a),flip(a)].">
      <j1 rule="hyper" parents="1723 2433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2551">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2211,a(flip),b,2549,a)].">
      <j1 rule="hyper" parents="63 2211 2549"/>
    </justification>
  </clause>

  <clause id="2552">
    <literal><![CDATA[
      (x * y) * K(z,L(z \ 1,u,w)) = x * (K((1 / z) \ 1,1 / z) * y)
    ]]></literal>
    <justification jstring="[para(1959(a,1),2490(a,1,2))].">
      <j1 rule="para" parents="1959 2490"/>
    </justification>
  </clause>

  <clause id="2553">
    <literal><![CDATA[
      (a(x,y,z) * u) \ L(a(x,y,z),u,u) = L(u \ 1,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(2461(a,1),2513(a,1,2))].">
      <j1 rule="para" parents="2461 2513"/>
    </justification>
  </clause>

  <clause id="2554">
    <literal><![CDATA[
      (x * y) * K(z,L(z \ 1,u,w)) = x * (K(z,1 / z) * y)
    ]]></literal>
    <justification jstring="[para(83(a,1),2552(a,2,2,1,1))].">
      <j1 rule="para" parents="83 2552"/>
    </justification>
  </clause>

  <clause id="2556">
    <literal><![CDATA[
      (x * y) * K(z,L(z \ 1,u,w)) = x * (K(z,z \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1083(a,1),2554(a,2,2,1))].">
      <j1 rule="para" parents="1083 2554"/>
    </justification>
  </clause>

  <clause id="2558">
    <literal><![CDATA[
      (x * y) * K(z,z \ 1) = x * (K(z,z \ 1) * y)
    ]]></literal>
    <justification jstring="[para(155(a,1),2556(a,1,2,2))].">
      <j1 rule="para" parents="155 2556"/>
    </justification>
  </clause>

  <clause id="2563">
    <literal><![CDATA[
      a(K(x,y),z,u) = ((w * v5) * K(v6,v6 \ 1)) \ (w * (K(v6,v6 \ 1) * v5))
    ]]></literal>
    <justification jstring="[hyper(133,a,2558,a(flip),b,129,a),flip(a)].">
      <j1 rule="hyper" parents="133 2558 129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2564">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(934(a,1),2558(a,2,2))].">
      <j1 rule="para" parents="934 2558"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      ((x * (y \ 1)) * y) * K(y,y \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1035,a(flip),b,2564,a),flip(a)].">
      <j1 rule="hyper" parents="316 1035 2564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2566">
    <literal><![CDATA[
      ((x \ 1) * y) * ((x \ 1) \ 1) = ((1 / x) * y) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,2239,a(flip),b,2564,a),flip(a)].">
      <j1 rule="hyper" parents="63 2239 2564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2567">
    <literal><![CDATA[
      ((1 / R(x / y,y,x)) * z) * R(x / y,y,x) = ((y * (x \ 1)) * z) * ((R(x / y,y,x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(727(a,1),2566(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="727 2566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2568">
    <literal><![CDATA[
      K(x \ 1,x) \ ((y * (x \ 1)) * x) = R(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2234,a,b,2565,a)].">
      <j1 rule="hyper" parents="63 2234 2565"/>
    </justification>
  </clause>

  <clause id="2569">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2489,a(flip),b,2565,a)].">
      <j1 rule="hyper" parents="63 2489 2565"/>
    </justification>
  </clause>

  <clause id="2570">
    <literal><![CDATA[
      R(x,y \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(136,a,2565,a(flip),b,2489,a(flip))].">
      <j1 rule="hyper" parents="136 2565 2489"/>
    </justification>
  </clause>

  <clause id="2571">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(630,a,2569,a),flip(a)].">
      <j1 rule="hyper" parents="630 2569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2572">
    <literal><![CDATA[
      R(x,1 / y,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,276,a(flip),b,2569,a)].">
      <j1 rule="hyper" parents="63 276 2569"/>
    </justification>
  </clause>

  <clause id="2573">
    <literal><![CDATA[
      R(x,y \ 1,y) * (y \ 1) = R(x * (1 / y),y,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,2569,a(flip),b,569,a)].">
      <j1 rule="hyper" parents="138 2569 569"/>
    </justification>
  </clause>

  <clause id="2575">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(2571(a,1),1768(a,2,1,2))].">
      <j1 rule="para" parents="2571 1768"/>
    </justification>
  </clause>

  <clause id="2576">
    <literal><![CDATA[
      K(x \ 1,x) \ (x * R(y,x,x)) = R(x * y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(628(a,1),2568(a,1,2))].">
      <j1 rule="para" parents="628 2568"/>
    </justification>
  </clause>

  <clause id="2578">
    <literal><![CDATA[
      (L(x,y,z) * u) / (x * ((x \ L(x,y,z)) * u)) = a(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(1499(a,1),2374(a,1,2))].">
      <j1 rule="para" parents="1499 2374"/>
    </justification>
  </clause>

  <clause id="2579">
    <literal><![CDATA[
      a(x \ L(x,y,z),x,u) = a(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2328,a(flip),b,2578,a),flip(a)].">
      <j1 rule="hyper" parents="63 2328 2578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2580">
    <literal><![CDATA[
      L(1 / T((x \ 1) \ 1,y),x,x \ 1) = K(x,x \ 1) * (T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,2422,a(flip),b,2222,a),flip(a)].">
      <j1 rule="hyper" parents="316 2422 2222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      L(1 / T((x \ 1) \ 1,y),x,x \ 1) = T(1 / (1 / x),y) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,2469,a(flip),b,2580,a),flip(a)].">
      <j1 rule="hyper" parents="316 2469 2580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2583">
    <literal><![CDATA[
      L(1 / T((x \ 1) \ 1,y),x,x \ 1) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2418,a(flip),b,2582,a),flip(a)].">
      <j1 rule="hyper" parents="316 2418 2582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2584">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,x \ 1) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(2420(a,1),2583(a,1,1))].">
      <j1 rule="para" parents="2420 2583"/>
    </justification>
  </clause>

  <clause id="2585">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1190,a(flip),b,2584,a)].">
      <j1 rule="hyper" parents="63 1190 2584"/>
    </justification>
  </clause>

  <clause id="2586">
    <literal><![CDATA[
      (x \ 1) * (T(x,y) \ x) = T(1 / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(2585(a,1),2470(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2585 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2587">
    <literal><![CDATA[
      (x \ 1) * (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,2005,a(flip),b,2586,a),flip(a)].">
      <j1 rule="hyper" parents="316 2005 2586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2588">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(38,a,2563,a(flip),b,2241,a),flip(a)].">
      <j1 rule="hyper" parents="38 2563 2241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2589">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(932(a,1),2588(a,2,2))].">
      <j1 rule="para" parents="932 2588"/>
    </justification>
  </clause>

  <clause id="2591">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,406,a(flip),b,2589,a)].">
      <j1 rule="hyper" parents="63 406 2589"/>
    </justification>
  </clause>

  <clause id="2592">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * T(x,x \ 1) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(1157(a,1),2589(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1157 2589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2593">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(253,a,2591,a(flip),b,943,a(flip))].">
      <j1 rule="hyper" parents="253 2591 943"/>
    </justification>
  </clause>

  <clause id="2594">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(115(a,1),2593(a,1,2))].">
      <j1 rule="para" parents="115 2593"/>
    </justification>
  </clause>

  <clause id="2595">
    <literal><![CDATA[
      T(x,1 / y) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(614(a,1),2593(a,1,2)),flip(a)].">
      <j1 rule="para" parents="614 2593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2596">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2593(a,1),399(a,1,2))].">
      <j1 rule="para" parents="2593 399"/>
    </justification>
  </clause>

  <clause id="2597">
    <literal><![CDATA[
      T(x,T((y \ 1) \ 1,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(2421(a,2),2594(a,1,2))].">
      <j1 rule="para" parents="2421 2594"/>
    </justification>
  </clause>

  <clause id="2598">
    <literal><![CDATA[
      T(x / (1 / y),y \ 1) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[hyper(377,a,2595,a),flip(a)].">
      <j1 rule="hyper" parents="377 2595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2599">
    <literal><![CDATA[
      T(((1 / x) * y) \ y,1 / x) = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(316,a,1487,a(flip),b,2595,a),flip(a)].">
      <j1 rule="hyper" parents="316 1487 2595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2600">
    <literal><![CDATA[
      T(((1 / x) * y) * x,x \ 1) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,736,a(flip),b,2595,a),flip(a)].">
      <j1 rule="hyper" parents="63 736 2595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2601">
    <literal><![CDATA[
      L(T(x,y \ 1) \ z,T(x,1 / y),y \ 1) = (x * (1 / y)) \ ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(2595(a,1),1594(a,1,1,1))].">
      <j1 rule="para" parents="2595 1594"/>
    </justification>
  </clause>

  <clause id="2602">
    <literal><![CDATA[
      T(x,T(1 / y,z)) = T(x,T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(83(a,1),2597(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="83 2597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2603">
    <literal><![CDATA[
      (x * y) * ((((z \ 1) \ 1) \ L(y \ ((z \ 1) \ 1),y,x)) * T(z,z \ 1)) = (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2596(a,1),1862(a,1,2))].">
      <j1 rule="para" parents="2596 1862"/>
    </justification>
  </clause>

  <clause id="2604">
    <literal><![CDATA[
      T(((1 / x) * y) * x,x \ 1) = R(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,2572,a(flip),b,2600,a),flip(a)].">
      <j1 rule="hyper" parents="316 2572 2600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2605">
    <literal><![CDATA[
      (x \ 1) * R(y,x \ 1,x) = R((1 / x) * y,x,x)
    ]]></literal>
    <justification jstring="[para(2604(a,1),572(a,1,2))].">
      <j1 rule="para" parents="2604 572"/>
    </justification>
  </clause>

  <clause id="2606">
    <literal><![CDATA[
      1 / (((x \ 1) * y) \ y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(209,a,2599,a(flip),b,2428,a(flip))].">
      <j1 rule="hyper" parents="209 2599 2428"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      (x * y) \ ((x * (z \ R(z,u,w))) * y) = R(z \ R(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[para(2196(a,1),2262(a,2,1))].">
      <j1 rule="para" parents="2196 2262"/>
    </justification>
  </clause>

  <clause id="2609">
    <literal><![CDATA[
      L(T(x,y \ 1) \ z,T(x,y \ 1),y \ 1) = (x * (1 / y)) \ ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(2595(a,1),2601(a,1,2))].">
      <j1 rule="para" parents="2595 2601"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      (x * (1 / y)) \ ((1 / y) * z) = (x * (y \ 1)) \ ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,485,a(flip),b,2609,a),flip(a)].">
      <j1 rule="hyper" parents="63 485 2609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2611">
    <literal><![CDATA[
      (x * (y \ 1)) \ ((y \ 1) * x) = K(1 / y,x)
    ]]></literal>
    <justification jstring="[hyper(329,a,2610,a),flip(a)].">
      <j1 rule="hyper" parents="329 2610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2612">
    <literal><![CDATA[
      K(1 / x,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(329,a,2611,a),flip(a)].">
      <j1 rule="hyper" parents="329 2611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2613">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(80(a,1),2612(a,1,1)),flip(a)].">
      <j1 rule="para" parents="80 2612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2614">
    <literal><![CDATA[
      x / (L(y,z,u) \ L(R(y,w,v5),z,u)) = (L(y,z,u) \ L(R(y,w,v5),z,u)) \ x
    ]]></literal>
    <justification jstring="[para(29(a,1),2261(a,2,1,2))].">
      <j1 rule="para" parents="29 2261"/>
    </justification>
  </clause>

  <clause id="2616">
    <literal><![CDATA[
      R(x,y * y,a(z,u,w)) = (a(z,u,w) * x) / a(z,u,w)
    ]]></literal>
    <justification jstring="[para(11(a,1),2514(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 2514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2617">
    <literal><![CDATA[
      R(x,y * y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,2277,a(flip),b,2616,a),flip(a)].">
      <j1 rule="hyper" parents="316 2277 2616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2620">
    <literal><![CDATA[
      (x * (y * y)) * a(z,u,w) = x * ((y * y) * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(138,a,2617,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="138 2617 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2621">
    <literal><![CDATA[
      ((L(x,y,z) \ L(R(x,u,w),y,z)) \ v5) \ v5 = L(x,y,z) \ L(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(204,a,2614,a)].">
      <j1 rule="hyper" parents="204 2614"/>
    </justification>
  </clause>

  <clause id="2625">
    <literal><![CDATA[
      T(x,x \ 1) * (y * T(y \ 1,x)) = (x \ 1) \ (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,2235,a(flip),b,2266,a),flip(a)].">
      <j1 rule="hyper" parents="63 2235 2266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2626">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * ((y \ 1) \ 1) = (y \ 1) \ (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,2019,a(flip),b,2625,a)].">
      <j1 rule="hyper" parents="63 2019 2625"/>
    </justification>
  </clause>

  <clause id="2627">
    <literal><![CDATA[
      x * ((y \ (x \ ((y \ 1) \ 1))) * y) = (y \ 1) \ (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1525,a(flip),b,2626,a)].">
      <j1 rule="hyper" parents="63 1525 2626"/>
    </justification>
  </clause>

  <clause id="2628">
    <literal><![CDATA[
      ((x * (y * T(y \ 1,z))) * ((z \ 1) \ 1)) / ((z \ 1) \ (y * T(y \ 1,z))) = R(x,y * T(y \ 1,z),(z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(209,a,2626,a(flip),b,199,a)].">
      <j1 rule="hyper" parents="209 2626 199"/>
    </justification>
  </clause>

  <clause id="2629">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ 1)) = R(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(562(a,1),2498(a,1,2))].">
      <j1 rule="para" parents="562 2498"/>
    </justification>
  </clause>

  <clause id="2630">
    <literal><![CDATA[
      a(x,y,z) \ R(u,a(x,y,z),a(x,y,z)) = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,2629,a)].">
      <j1 rule="hyper" parents="144 2629"/>
    </justification>
  </clause>

  <clause id="2631">
    <literal><![CDATA[
      R(x,a(y,z,u) \ 1,a(y,z,u)) = R(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2366,a(flip),b,2629,a)].">
      <j1 rule="hyper" parents="63 2366 2629"/>
    </justification>
  </clause>

  <clause id="2632">
    <literal><![CDATA[
      (x * a(y,z,u)) \ R(x,a(y,z,u),a(y,z,u)) = L(a(y,z,u) \ 1,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(2629(a,1),2353(a,1,2))].">
      <j1 rule="para" parents="2629 2353"/>
    </justification>
  </clause>

  <clause id="2633">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,a(x,y,z)) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,570,a(flip),b,2632,a),flip(a)].">
      <j1 rule="hyper" parents="63 570 2632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2635">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) * (u * (x \ R(x,y,z))) = L(u,x \ R(x,y,z),(x \ R(x,y,z)) \ 1)
    ]]></literal>
    <justification jstring="[para(2194(a,1),2202(a,1,1))].">
      <j1 rule="para" parents="2194 2202"/>
    </justification>
  </clause>

  <clause id="2636">
    <literal><![CDATA[
      R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) = L(T(x,y),y,K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2250,a(flip),b,2251,a),flip(a)].">
      <j1 rule="hyper" parents="63 2250 2251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2637">
    <literal><![CDATA[
      R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,155,a(flip),b,2636,a),flip(a)].">
      <j1 rule="hyper" parents="316 155 2636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2638">
    <literal><![CDATA[
      T(x,y * K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1723,a,2637,a)].">
      <j1 rule="hyper" parents="1723 2637"/>
    </justification>
  </clause>

  <clause id="2641">
    <literal><![CDATA[
      T(x,y * K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(939(a,1),2638(a,1,2,2))].">
      <j1 rule="para" parents="939 2638"/>
    </justification>
  </clause>

  <clause id="2642">
    <literal><![CDATA[
      T(x,K(y,y \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2208(a,2),2641(a,1,2))].">
      <j1 rule="para" parents="2208 2641"/>
    </justification>
  </clause>

  <clause id="2643">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2564(a,1),2641(a,1,2))].">
      <j1 rule="para" parents="2564 2641"/>
    </justification>
  </clause>

  <clause id="2644">
    <literal><![CDATA[
      ((x * y) * z) / ((x * (y * (z * (u \ (1 / u))))) * ((1 / u) \ u)) = a(x,y,z * (u \ (1 / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,949,a(flip),b,2373,a)].">
      <j1 rule="hyper" parents="63 949 2373"/>
    </justification>
  </clause>

  <clause id="2645">
    <literal><![CDATA[
      ((x * y) * z) / (x * ((y * (z * (u \ (1 / u)))) * ((1 / u) \ u))) = a(x,y,z * (u \ (1 / u)))
    ]]></literal>
    <justification jstring="[para(951(a,1),2644(a,1,2))].">
      <j1 rule="para" parents="951 2644"/>
    </justification>
  </clause>

  <clause id="2646">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * (z * ((u \ (1 / u)) * ((1 / u) \ u))))) = a(x,y,z * (u \ (1 / u)))
    ]]></literal>
    <justification jstring="[para(952(a,1),2645(a,1,2,2))].">
      <j1 rule="para" parents="952 2645"/>
    </justification>
  </clause>

  <clause id="2647">
    <literal><![CDATA[
      a(x,y,z * (u \ (1 / u))) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(732(a,1),2646(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="732 2646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2648">
    <literal><![CDATA[
      a(x,y,z * (u \ (1 / u))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2329,a,b,2647,a),flip(a)].">
      <j1 rule="hyper" parents="316 2329 2647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2649">
    <literal><![CDATA[
      a(x,y,z * (1 / u)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(699(a,1),2648(a,1,3))].">
      <j1 rule="para" parents="699 2648"/>
    </justification>
  </clause>

  <clause id="2650">
    <literal><![CDATA[
      a(x,y,L(1 / z,u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1228(a,1),2648(a,1,3))].">
      <j1 rule="para" parents="1228 2648"/>
    </justification>
  </clause>

  <clause id="2651">
    <literal><![CDATA[
      a(x,y,z * (u \ 1)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(80(a,1),2649(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="80 2649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2652">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ z) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1002(a,1),2651(a,1,3))].">
      <j1 rule="para" parents="1002 2651"/>
    </justification>
  </clause>

  <clause id="2653">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ L(z,v5,v6)) = a(x,y,L(z,v5,v6) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1004(a,1),2651(a,1,3))].">
      <j1 rule="para" parents="1004 2651"/>
    </justification>
  </clause>

  <clause id="2654">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,v5) \ 1)) = a(x,y,a(u,w,v5) * z)
    ]]></literal>
    <justification jstring="[para(2290(a,2),2651(a,2,3))].">
      <j1 rule="para" parents="2290 2651"/>
    </justification>
  </clause>

  <clause id="2655">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(80(a,1),2650(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="80 2650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2656">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ z,v5,v6)) = a(x,y,L(z \ L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(1895(a,1),2650(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1895 2650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2657">
    <literal><![CDATA[
      a(x,y,L(z \ u,z \ u,z)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(356(a,1),2655(a,1,3)),flip(a)].">
      <j1 rule="para" parents="356 2655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2659">
    <literal><![CDATA[
      a(x,y,z * L(z,u \ 1,u)) = a(x,y,a(u,u \ 1,z))
    ]]></literal>
    <justification jstring="[para(703(a,1),2652(a,1,3)),flip(a)].">
      <j1 rule="para" parents="703 2652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2660">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(z \ u,z,z \ 1)) = a(x,y,((1 / z) * u) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(887(a,1),2652(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="887 2652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2661">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) \ w) * L(L(z,z,u) \ w,L(z,z,u),u)) = a(x,y,((u / (z \ 1)) \ (u * w)) \ (L(z,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(1449(a,1),2652(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1449 2652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2662">
    <literal><![CDATA[
      a(x,y,((1 / z) * u) \ (z \ u)) = a(x,y,(z \ u) * ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(887(a,1),2660(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="887 2660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2664">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) * L(x \ R(x,y,z),u,w) = x \ (R(x,y,z) * L(R(x,y,z) \ x,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,1252,a(flip),b,2230,a),flip(a)].">
      <j1 rule="hyper" parents="316 1252 2230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2665">
    <literal><![CDATA[
      R((a(x,y,z) \ 1) \ u,a(x,y,z) \ 1,a(x,y,z)) = T(u * a(x,y,z),a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1033,a(flip),b,2362,a)].">
      <j1 rule="hyper" parents="63 1033 2362"/>
    </justification>
  </clause>

  <clause id="2666">
    <literal><![CDATA[
      R((a(x,y,z) \ 1) \ u,a(x,y,z),a(x,y,z)) = T(u * a(x,y,z),a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2631,a(flip),b,2665,a)].">
      <j1 rule="hyper" parents="63 2631 2665"/>
    </justification>
  </clause>

  <clause id="2667">
    <literal><![CDATA[
      ((1 / R(x / y,y,x)) * z) * R(x / y,y,x) = ((y * (x \ 1)) * z) * ((y * (x \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(727(a,1),2567(a,2,2,1))].">
      <j1 rule="para" parents="727 2567"/>
    </justification>
  </clause>

  <clause id="2669">
    <literal><![CDATA[
      L((a(x,y,x * y) \ 1) \ z,x * y,a(x,y,x * y) \ 1) = (x * y) * (L(x * y,y,x) \ z)
    ]]></literal>
    <justification jstring="[para(2538(a,1),2539(a,1,3))].">
      <j1 rule="para" parents="2538 2539"/>
    </justification>
  </clause>

  <clause id="2670">
    <literal><![CDATA[
      L(L(x,y * (1 / x),K(x \ 1,x)),1 / x,y) = R(y / x,x,1 / x) \ (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(83(a,1),2488(a,1,1,1))].">
      <j1 rule="para" parents="83 2488"/>
    </justification>
  </clause>

  <clause id="2671">
    <literal><![CDATA[
      L(L(x,y * (1 / x),K(x \ 1,x)),1 / x,y) = (y * (x \ 1)) \ (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(1039(a,1),2670(a,2,1))].">
      <j1 rule="para" parents="1039 2670"/>
    </justification>
  </clause>

  <clause id="2672">
    <literal><![CDATA[
      L(L(x,y * (1 / x),K(x \ 1,x)),1 / x,y) = L(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2253,a(flip),b,2671,a),flip(a)].">
      <j1 rule="hyper" parents="316 2253 2671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2673">
    <literal><![CDATA[
      L(x,1 / x,y) = L(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(155(a,1),2672(a,1,1))].">
      <j1 rule="para" parents="155 2672"/>
    </justification>
  </clause>

  <clause id="2674">
    <literal><![CDATA[
      L(x,x \ 1,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,235,a(flip),b,2673,a),flip(a)].">
      <j1 rule="hyper" parents="63 235 2673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2675">
    <literal><![CDATA[
      L(x \ 1,(x \ 1) \ 1,y) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(80(a,1),2673(a,1,2)),flip(a)].">
      <j1 rule="para" parents="80 2673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2676">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * v5) \ (v5 * (v6 * L(a(x,y,z),u,w))) = L(v6,L(a(x,y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(2436(a,1),2440(a,2,1))].">
      <j1 rule="para" parents="2436 2440"/>
    </justification>
  </clause>

  <clause id="2677">
    <literal><![CDATA[
      ((x * y) * L(y \ 1,z,u)) / L(y \ L(y,z,u),x,a(x,y,L(y,z,u))) = a(x,y,L(y \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[para(2655(a,1),2472(a,1,2,3))].">
      <j1 rule="para" parents="2655 2472"/>
    </justification>
  </clause>

  <clause id="2678">
    <literal><![CDATA[
      R(T(x,y * L(a(z,u,w),v5,v6)),y,L(a(z,u,w),v5,v6)) = L(T(x,y),y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,2439,a(flip),b,2441,a),flip(a)].">
      <j1 rule="hyper" parents="63 2439 2441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2679">
    <literal><![CDATA[
      R(T(x,L(a(y,z,u),w,v5) * v6),v6,L(a(y,z,u),w,v5)) = L(T(x,v6),v6,L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(2304(a,2),2678(a,1,1,2))].">
      <j1 rule="para" parents="2304 2678"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      (x * y) * ((z \ L(y \ ((z \ 1) \ 1),y,x)) * z) = (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2592(a,1),2603(a,1,2))].">
      <j1 rule="para" parents="2592 2603"/>
    </justification>
  </clause>

  <clause id="2681">
    <literal><![CDATA[
      (x * y) * L((z \ (y \ ((z \ 1) \ 1))) * z,y,x) = (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1369(a,2),2680(a,1,2))].">
      <j1 rule="para" parents="1369 2680"/>
    </justification>
  </clause>

  <clause id="2682">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1) = x * (y * ((z \ (y \ ((z \ 1) \ 1))) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,100,a(flip),b,2681,a),flip(a)].">
      <j1 rule="hyper" parents="63 100 2681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2683">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * ((z \ 1) \ 1) = x * ((z \ 1) \ (y * T(y \ 1,z)))
    ]]></literal>
    <justification jstring="[para(2627(a,1),2682(a,2,2))].">
      <j1 rule="para" parents="2627 2682"/>
    </justification>
  </clause>

  <clause id="2684">
    <literal><![CDATA[
      ((x * (y * T(y \ 1,z))) * ((z \ 1) \ 1)) / ((z \ 1) \ (y * T(y \ 1,z))) = R(x,y * T(y \ 1,z),z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1034,a(flip),b,2628,a),flip(a)].">
      <j1 rule="hyper" parents="316 1034 2628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2685">
    <literal><![CDATA[
      (x * ((y \ 1) \ (z * T(z \ 1,y)))) / ((y \ 1) \ (z * T(z \ 1,y))) = R(x,z * T(z \ 1,y),y)
    ]]></literal>
    <justification jstring="[para(2683(a,1),2684(a,1,1))].">
      <j1 rule="para" parents="2683 2684"/>
    </justification>
  </clause>

  <clause id="2686">
    <literal><![CDATA[
      R(x,y * T(y \ 1,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(267,a,2685,a),flip(a)].">
      <j1 rule="hyper" parents="267 2685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2688">
    <literal><![CDATA[
      R(x,y \ T(y,z),z) = x
    ]]></literal>
    <justification jstring="[para(847(a,1),2686(a,1,2))].">
      <j1 rule="para" parents="847 2686"/>
    </justification>
  </clause>

  <clause id="2689">
    <literal><![CDATA[
      R(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[para(857(a,2),2686(a,1,2))].">
      <j1 rule="para" parents="857 2686"/>
    </justification>
  </clause>

  <clause id="2690">
    <literal><![CDATA[
      (x * y) \ ((y * x) * x) = K(y,x) * x
    ]]></literal>
    <justification jstring="[para(2689(a,1),519(a,1,1))].">
      <j1 rule="para" parents="2689 519"/>
    </justification>
  </clause>

  <clause id="2691">
    <literal><![CDATA[
      T(x,y) * (x \ y) = y * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(2688(a,1),2079(a,1,2,1))].">
      <j1 rule="para" parents="2688 2079"/>
    </justification>
  </clause>

  <clause id="2692">
    <literal><![CDATA[
      R(x,T(y,x),K(z \ 1,R(z,u,w))) \ ((y * K(z \ 1,z)) * x) = T(y,x) * T(K(z \ 1,R(z,u,w)),y * x)
    ]]></literal>
    <justification jstring="[para(2220(a,1),2475(a,1,1,3))].">
      <j1 rule="para" parents="2220 2475"/>
    </justification>
  </clause>

  <clause id="2693">
    <literal><![CDATA[
      T(x,y) * T(K(z \ 1,R(z,u,w)),x * y) = y \ ((x * K(z \ 1,z)) * y)
    ]]></literal>
    <justification jstring="[para(1953(a,1),2692(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1953 2692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2695">
    <literal><![CDATA[
      T(x,y) * T(K(z \ 1,R(z,u,w)),x * y) = T(x * K(z \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(316,a,22,a,b,2693,a),flip(a)].">
      <j1 rule="hyper" parents="316 22 2693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2696">
    <literal><![CDATA[
      T(x,y) * K(z \ 1,R(z,u,w)) = T(x * K(z \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(2220(a,1),2695(a,1,2))].">
      <j1 rule="para" parents="2220 2695"/>
    </justification>
  </clause>

  <clause id="2697">
    <literal><![CDATA[
      T(x * K(y \ 1,y),z) = T(x,z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(497(a,1),2696(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="497 2696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2700">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,z) = T(y,z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2211(a,2),2697(a,1,1))].">
      <j1 rule="para" parents="2211 2697"/>
    </justification>
  </clause>

  <clause id="2701">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,z) = K(x \ 1,x) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2211,a,b,2700,a),flip(a)].">
      <j1 rule="hyper" parents="316 2211 2700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2702">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[para(669(a,1),2701(a,1,1)),flip(a)].">
      <j1 rule="para" parents="669 2701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2703">
    <literal><![CDATA[
      (x \ T(x * (y / x),z)) * x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1892,a(flip),b,2702,a)].">
      <j1 rule="hyper" parents="63 1892 2702"/>
    </justification>
  </clause>

  <clause id="2705">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x = T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),2703(a,1,1,2,1,2))].">
      <j1 rule="para" parents="11 2703"/>
    </justification>
  </clause>

  <clause id="2706">
    <literal><![CDATA[
      T((x \ y) * x,z) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(79(a,1),2703(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 2703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2707">
    <literal><![CDATA[
      T(x * y,z) / y = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(149,a,2705,a)].">
      <j1 rule="hyper" parents="149 2705"/>
    </justification>
  </clause>

  <clause id="2708">
    <literal><![CDATA[
      x * ((y \ T(z,x)) * y) = ((y \ z) * y) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,2706,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 2706 22"/>
    </justification>
  </clause>

  <clause id="2710">
    <literal><![CDATA[
      T((x \ (y / z)) * x,z) = (x \ (z \ y)) * x
    ]]></literal>
    <justification jstring="[para(116(a,1),2706(a,2,1,2))].">
      <j1 rule="para" parents="116 2706"/>
    </justification>
  </clause>

  <clause id="2713">
    <literal><![CDATA[
      R((x * y) / x,x,T(y,x)) = x \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,946,a,b,2707,a)].">
      <j1 rule="hyper" parents="63 946 2707"/>
    </justification>
  </clause>

  <clause id="2714">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[para(116(a,1),2708(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="116 2708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2715">
    <literal><![CDATA[
      ((x \ (y \ L(y,z,u))) * x) * y = y * ((x \ (y \ L(y,z,u))) * x)
    ]]></literal>
    <justification jstring="[para(1271(a,1),2708(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1271 2708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2716">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) / x = (y \ (z / x)) * y
    ]]></literal>
    <justification jstring="[hyper(285,a,2710,a)].">
      <j1 rule="hyper" parents="285 2710"/>
    </justification>
  </clause>

  <clause id="2717">
    <literal><![CDATA[
      L(x \ T(x * y,y),x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(2713(a,1),1482(a,1,1))].">
      <j1 rule="para" parents="2713 1482"/>
    </justification>
  </clause>

  <clause id="2718">
    <literal><![CDATA[
      (x * y) \ ((y * x) * x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,413,a(flip),b,2717,a)].">
      <j1 rule="hyper" parents="63 413 2717"/>
    </justification>
  </clause>

  <clause id="2719">
    <literal><![CDATA[
      (x * y) / x = K(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,2690,a(flip),b,2718,a),flip(a)].">
      <j1 rule="hyper" parents="63 2690 2718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2720">
    <literal><![CDATA[
      K(x,y) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(2001,a,2719,a),flip(a)].">
      <j1 rule="hyper" parents="2001 2719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2721">
    <literal><![CDATA[
      K(x,x \ y) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(347,a,2719,a),flip(a)].">
      <j1 rule="hyper" parents="347 2719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2722">
    <literal><![CDATA[
      (x * y) / x = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1974,a(flip),b,2719,a),flip(a)].">
      <j1 rule="hyper" parents="316 1974 2719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2723">
    <literal><![CDATA[
      (x * K(y,x)) * y = y * x
    ]]></literal>
    <justification jstring="[hyper(138,a,1974,a(flip),b,2719,a)].">
      <j1 rule="hyper" parents="138 1974 2719"/>
    </justification>
  </clause>

  <clause id="2724">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,2719,a,b,478,a)].">
      <j1 rule="hyper" parents="138 2719 478"/>
    </justification>
  </clause>

  <clause id="2726">
    <literal><![CDATA[
      K(x,y / x) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(37,a,660,a,b,2719,a)].">
      <j1 rule="hyper" parents="37 660 2719"/>
    </justification>
  </clause>

  <clause id="2727">
    <literal><![CDATA[
      K(x \ y,x) * y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(37,a,478,a,b,2719,a)].">
      <j1 rule="hyper" parents="37 478 2719"/>
    </justification>
  </clause>

  <clause id="2728">
    <literal><![CDATA[
      K(x,y) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[hyper(37,a,410,a,b,2719,a)].">
      <j1 rule="hyper" parents="37 410 2719"/>
    </justification>
  </clause>

  <clause id="2729">
    <literal><![CDATA[
      T(K(x,y) * y,x) = y
    ]]></literal>
    <justification jstring="[para(2719(a,1),240(a,1,1))].">
      <j1 rule="para" parents="2719 240"/>
    </justification>
  </clause>

  <clause id="2730">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * x) = y
    ]]></literal>
    <justification jstring="[hyper(38,a,641,a,b,2729,a(flip))].">
      <j1 rule="hyper" parents="38 641 2729"/>
    </justification>
  </clause>

  <clause id="2731">
    <literal><![CDATA[
      T(x * K(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(1974(a,1),2729(a,1,1))].">
      <j1 rule="para" parents="1974 2729"/>
    </justification>
  </clause>

  <clause id="2732">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(263,a,2731,a),flip(a)].">
      <j1 rule="hyper" parents="263 2731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2733">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,2731,a)].">
      <j1 rule="hyper" parents="49 2731"/>
    </justification>
  </clause>

  <clause id="2734">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2731(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2731 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2735">
    <literal><![CDATA[
      T(R(x * K(y,x),z,u),y) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(2731(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2731 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2736">
    <literal><![CDATA[
      (x * K(y,x)) \ (y * x) = y
    ]]></literal>
    <justification jstring="[para(2731(a,1),242(a,1,2,2))].">
      <j1 rule="para" parents="2731 242"/>
    </justification>
  </clause>

  <clause id="2737">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * y = y * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(2731(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2731 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2739">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,2004,a(flip),b,2720,a)].">
      <j1 rule="hyper" parents="316 2004 2720"/>
    </justification>
  </clause>

  <clause id="2740">
    <literal><![CDATA[
      ((x \ 1) * y) / (x \ 1) = y * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,2612,a,b,2720,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 2612 2720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2741">
    <literal><![CDATA[
      (x \ y) \ (y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),2720(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      x \ (y / (y / x)) = K(y / x,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),2720(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 2720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2743">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x * y) = L(y / (x \ 1),x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,758,a(flip),b,2722,a),flip(a)].">
      <j1 rule="hyper" parents="63 758 2722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2744">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(2722(a,1),294(a,1))].">
      <j1 rule="para" parents="2722 294"/>
    </justification>
  </clause>

  <clause id="2745">
    <literal><![CDATA[
      T(x * K(y,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(2722(a,1),326(a,1,1))].">
      <j1 rule="para" parents="2722 326"/>
    </justification>
  </clause>

  <clause id="2746">
    <literal><![CDATA[
      R(x * K(y,x),y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(2722(a,1),110(a,1,1))].">
      <j1 rule="para" parents="2722 110"/>
    </justification>
  </clause>

  <clause id="2747">
    <literal><![CDATA[
      T(x * K(y,x),x * y) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(2722(a,1),547(a,1,1))].">
      <j1 rule="para" parents="2722 547"/>
    </justification>
  </clause>

  <clause id="2748">
    <literal><![CDATA[
      R(x * K(y,x),y,y) = (y * x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(2722(a,1),563(a,1,1))].">
      <j1 rule="para" parents="2722 563"/>
    </justification>
  </clause>

  <clause id="2749">
    <literal><![CDATA[
      L(x * K(y * z,x),z,y) = (y * (z * x)) / (y * z)
    ]]></literal>
    <justification jstring="[para(2722(a,1),752(a,1,1))].">
      <j1 rule="para" parents="2722 752"/>
    </justification>
  </clause>

  <clause id="2750">
    <literal><![CDATA[
      L(T(x * K(y * z,x),z),z,y) = (y * (x * z)) / (y * z)
    ]]></literal>
    <justification jstring="[para(2722(a,1),1476(a,1,1,1))].">
      <j1 rule="para" parents="2722 1476"/>
    </justification>
  </clause>

  <clause id="2751">
    <literal><![CDATA[
      T(x * K(y,x),y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(2722(a,1),1609(a,1,1))].">
      <j1 rule="para" parents="2722 1609"/>
    </justification>
  </clause>

  <clause id="2752">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x / K(z,y)
    ]]></literal>
    <justification jstring="[para(2722(a,2),2071(a,1,2))].">
      <j1 rule="para" parents="2722 2071"/>
    </justification>
  </clause>

  <clause id="2753">
    <literal><![CDATA[
      K(x,y) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(136,a,2723,a(flip),b,1978,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 2723 1978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2754">
    <literal><![CDATA[
      K(x,y) \ (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(133,a,2723,a(flip),b,1978,a(flip))].">
      <j1 rule="hyper" parents="133 2723 1978"/>
    </justification>
  </clause>

  <clause id="2756">
    <literal><![CDATA[
      T(x * y,K(y,x)) = x * y
    ]]></literal>
    <justification jstring="[hyper(253,a,94,a,b,2728,a)].">
      <j1 rule="hyper" parents="253 94 2728"/>
    </justification>
  </clause>

  <clause id="2757">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * x) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1938,a(flip),b,2728,a)].">
      <j1 rule="hyper" parents="63 1938 2728"/>
    </justification>
  </clause>

  <clause id="2758">
    <literal><![CDATA[
      (x * y) * ((y * x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,2728,a(flip),b,478,a)].">
      <j1 rule="hyper" parents="138 2728 478"/>
    </justification>
  </clause>

  <clause id="2759">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,2728,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 2728 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2760">
    <literal><![CDATA[
      K(x,y) = (x * y) * ((y * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(138,a,2728,a(flip),b,378,a),flip(a)].">
      <j1 rule="hyper" parents="138 2728 378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2761">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,2728,a(flip),b,479,a)].">
      <j1 rule="hyper" parents="136 2728 479"/>
    </justification>
  </clause>

  <clause id="2762">
    <literal><![CDATA[
      ((x \ y) * x) / y = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(136,a,2728,a(flip),b,160,a(flip))].">
      <j1 rule="hyper" parents="136 2728 160"/>
    </justification>
  </clause>

  <clause id="2763">
    <literal><![CDATA[
      (K(x,y) * z) \ (x * y) = z \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2728,a(flip),b,479,a)].">
      <j1 rule="hyper" parents="133 2728 479"/>
    </justification>
  </clause>

  <clause id="2764">
    <literal><![CDATA[
      K(L(x,y,z),z * y) * (z * (y * x)) = L(x,y,z) * (z * y)
    ]]></literal>
    <justification jstring="[para(100(a,1),2728(a,1,2))].">
      <j1 rule="para" parents="100 2728"/>
    </justification>
  </clause>

  <clause id="2765">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(2728(a,1),477(a,1,1))].">
      <j1 rule="para" parents="2728 477"/>
    </justification>
  </clause>

  <clause id="2766">
    <literal><![CDATA[
      K(x,y) * ((y * x) / z) = (x * y) / z
    ]]></literal>
    <justification jstring="[para(2728(a,1),660(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2728 660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2770">
    <literal><![CDATA[
      L(x,y,(z * u) * w) = L(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[para(2728(a,1),1675(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2728 1675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2771">
    <literal><![CDATA[
      a(x * y,z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(2728(a,1),1806(a,1,1))].">
      <j1 rule="para" parents="2728 1806"/>
    </justification>
  </clause>

  <clause id="2772">
    <literal><![CDATA[
      K(x,y \ 1) * (((y \ z) / z) * x) = x * ((y \ z) / z)
    ]]></literal>
    <justification jstring="[para(1956(a,1),2728(a,1,1))].">
      <j1 rule="para" parents="1956 2728"/>
    </justification>
  </clause>

  <clause id="2773">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ z) = K(y,y \ x) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,2721,a(flip),b,478,a)].">
      <j1 rule="hyper" parents="138 2721 478"/>
    </justification>
  </clause>

  <clause id="2774">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,2721,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 2721 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2776">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) / z) = (y / x) / z
    ]]></literal>
    <justification jstring="[para(2721(a,1),660(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2721 660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2777">
    <literal><![CDATA[
      K(x,x \ y) * (((x \ y) * z) * u) = ((y / x) * z) * u
    ]]></literal>
    <justification jstring="[para(2721(a,1),656(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2721 656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2778">
    <literal><![CDATA[
      K(x,x \ y) * R(x \ y,z,u) = R(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(2721(a,1),1028(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2721 1028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2779">
    <literal><![CDATA[
      K(x \ y,x) * (y * z) = ((x \ y) * x) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,2727,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 2727 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2780">
    <literal><![CDATA[
      K(x \ y,x) * (y / z) = ((x \ y) * x) / z
    ]]></literal>
    <justification jstring="[para(2727(a,1),660(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2727 660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2781">
    <literal><![CDATA[
      L(x,y,z * ((u \ w) * u)) = L(x,y,w * z)
    ]]></literal>
    <justification jstring="[para(2727(a,1),1675(a,1,3,2))].">
      <j1 rule="para" parents="2727 1675"/>
    </justification>
  </clause>

  <clause id="2782">
    <literal><![CDATA[
      L(x,y,z * ((u \ w) * u)) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(2727(a,1),1684(a,1,3,2))].">
      <j1 rule="para" parents="2727 1684"/>
    </justification>
  </clause>

  <clause id="2783">
    <literal><![CDATA[
      a((x \ y) * x,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(2727(a,1),1806(a,1,1))].">
      <j1 rule="para" parents="2727 1806"/>
    </justification>
  </clause>

  <clause id="2784">
    <literal><![CDATA[
      (K(x,x \ y) * z) \ y = z \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2730,a(flip),b,479,a)].">
      <j1 rule="hyper" parents="133 2730 479"/>
    </justification>
  </clause>

  <clause id="2785">
    <literal><![CDATA[
      x \ (K(y,y \ x) * z) = ((y \ x) * y) \ z
    ]]></literal>
    <justification jstring="[para(2730(a,1),477(a,1,1))].">
      <j1 rule="para" parents="2730 477"/>
    </justification>
  </clause>

  <clause id="2786">
    <literal><![CDATA[
      T(x * K(x * y,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,1625,a,b,2734,a),flip(a)].">
      <j1 rule="hyper" parents="40 1625 2734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2787">
    <literal><![CDATA[
      a((x * x) * (x \ y),z,u) = a((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,1828,a(flip),b,2771,a),flip(a)].">
      <j1 rule="hyper" parents="316 1828 2771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2788">
    <literal><![CDATA[
      a(x * K(y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,1806,a(flip),b,2771,a),flip(a)].">
      <j1 rule="hyper" parents="316 1806 2771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2789">
    <literal><![CDATA[
      a((x * x) * (y * z),u,w) = a(y * (z * (x * x)),u,w)
    ]]></literal>
    <justification jstring="[para(32(a,1),2771(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32 2771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2790">
    <literal><![CDATA[
      a(L(x,y,z) * (z * y),u,w) = a(z * (y * x),u,w)
    ]]></literal>
    <justification jstring="[para(100(a,1),2771(a,1,1)),flip(a)].">
      <j1 rule="para" parents="100 2771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2791">
    <literal><![CDATA[
      a(L(x * y,z,u),w,v5) = a(L(y * x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(1360(a,1),2783(a,1,1))].">
      <j1 rule="para" parents="1360 2783"/>
    </justification>
  </clause>

  <clause id="2792">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = T(R(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(2786(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2786 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2793">
    <literal><![CDATA[
      a(L(x * K(x * y,x),z,u),w,v5) = a(L(R(x,y,x),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(2786(a,1),1812(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2786 1812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2794">
    <literal><![CDATA[
      T(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,1239,a,b,2724,a)].">
      <j1 rule="hyper" parents="63 1239 2724"/>
    </justification>
  </clause>

  <clause id="2795">
    <literal><![CDATA[
      K(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(136,a,1239,a,b,2724,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 1239 2724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2796">
    <literal><![CDATA[
      ((x * y) / x) * z = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(2724(a,1),1234(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2724 1234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2797">
    <literal><![CDATA[
      (x \ y) \ y = K(x,x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(384,a,2794,a)].">
      <j1 rule="hyper" parents="384 2794"/>
    </justification>
  </clause>

  <clause id="2798">
    <literal><![CDATA[
      (K(x * y,z) * x) * y = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,406,a,b,2794,a)].">
      <j1 rule="hyper" parents="316 406 2794"/>
    </justification>
  </clause>

  <clause id="2799">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,2794,a,b,478,a)].">
      <j1 rule="hyper" parents="138 2794 478"/>
    </justification>
  </clause>

  <clause id="2800">
    <literal><![CDATA[
      K(x,y) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,2794,a,b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 2794 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2801">
    <literal><![CDATA[
      T(x,y) / (z \ x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(136,a,2794,a,b,479,a)].">
      <j1 rule="hyper" parents="136 2794 479"/>
    </justification>
  </clause>

  <clause id="2802">
    <literal><![CDATA[
      T(x * y,z) / y = K(x * y,z) * x
    ]]></literal>
    <justification jstring="[hyper(136,a,2794,a,b,406,a)].">
      <j1 rule="hyper" parents="136 2794 406"/>
    </justification>
  </clause>

  <clause id="2803">
    <literal><![CDATA[
      (K(x,y) * z) \ T(x,y) = z \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,2794,a,b,479,a)].">
      <j1 rule="hyper" parents="133 2794 479"/>
    </justification>
  </clause>

  <clause id="2804">
    <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,2794,a),flip(a)].">
      <j1 rule="hyper" parents="63 25 2794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2806">
    <literal><![CDATA[
      K(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1330,a,b,2794,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 1330 2794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2808">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2794(a,2),266(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2794 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2809">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) * z) = x \ z
    ]]></literal>
    <justification jstring="[para(2794(a,2),477(a,1,1))].">
      <j1 rule="para" parents="2794 477"/>
    </justification>
  </clause>

  <clause id="2810">
    <literal><![CDATA[
      K(x,y) * (x / z) = T(x,y) / z
    ]]></literal>
    <justification jstring="[para(2794(a,2),660(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2794 660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2811">
    <literal><![CDATA[
      K(x,y) * ((x * z) * u) = (T(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(2794(a,2),656(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2794 656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2812">
    <literal><![CDATA[
      K(x,y) * R(x,z,u) = R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2794(a,2),1028(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2794 1028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2813">
    <literal><![CDATA[
      K(x,y) * (R(x,z,u) * w) = R(T(x,y),z,u) * w
    ]]></literal>
    <justification jstring="[para(2794(a,2),1029(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2794 1029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2814">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,856,a(flip),b,2795,a)].">
      <j1 rule="hyper" parents="316 856 2795"/>
    </justification>
  </clause>

  <clause id="2815">
    <literal><![CDATA[
      T(x,y) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,2795,a,b,1329,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 2795 1329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2816">
    <literal><![CDATA[
      K(x,y) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(136,a,2795,a,b,1310,a)].">
      <j1 rule="hyper" parents="136 2795 1310"/>
    </justification>
  </clause>

  <clause id="2817">
    <literal><![CDATA[
      T(1 / x,K(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(2795(a,2),1326(a,1,2))].">
      <j1 rule="para" parents="2795 1326"/>
    </justification>
  </clause>

  <clause id="2819">
    <literal><![CDATA[
      (x \ y) \ y = x * K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,2806,a,b,311,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 2806 311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2820">
    <literal><![CDATA[
      T(x,R(y,z,u)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,1935,a(flip),b,2806,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 1935 2806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2821">
    <literal><![CDATA[
      x * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2806(a,2),270(a,1,2))].">
      <j1 rule="para" parents="2806 270"/>
    </justification>
  </clause>

  <clause id="2822">
    <literal><![CDATA[
      x * (y * K(y,x)) = y * x
    ]]></literal>
    <justification jstring="[para(2806(a,2),243(a,1,2,2))].">
      <j1 rule="para" parents="2806 243"/>
    </justification>
  </clause>

  <clause id="2823">
    <literal><![CDATA[
      L(x \ K(y,z),x,y) = (y * x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(2806(a,2),298(a,1,1,2))].">
      <j1 rule="para" parents="2806 298"/>
    </justification>
  </clause>

  <clause id="2824">
    <literal><![CDATA[
      T(x,y) * (x \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(2806(a,2),2691(a,2,2))].">
      <j1 rule="para" parents="2806 2691"/>
    </justification>
  </clause>

  <clause id="2825">
    <literal><![CDATA[
      x \ (y * x) = y * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(383,a,2815,a)].">
      <j1 rule="hyper" parents="383 2815"/>
    </justification>
  </clause>

  <clause id="2829">
    <literal><![CDATA[
      T(K(x,y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(253,a,2794,a(flip),b,2815,a(flip))].">
      <j1 rule="hyper" parents="253 2794 2815"/>
    </justification>
  </clause>

  <clause id="2830">
    <literal><![CDATA[
      T(x,K(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(253,a,2815,a(flip),b,2794,a(flip))].">
      <j1 rule="hyper" parents="253 2815 2794"/>
    </justification>
  </clause>

  <clause id="2831">
    <literal><![CDATA[
      T(x,y) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2815(a,2),43(a,1))].">
      <j1 rule="para" parents="2815 43"/>
    </justification>
  </clause>

  <clause id="2832">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2815(a,2),321(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2815 321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2833">
    <literal><![CDATA[
      x * (y * K(x,y)) = T(x,y) * y
    ]]></literal>
    <justification jstring="[para(2815(a,2),2070(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2815 2070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2834">
    <literal><![CDATA[
      T(x,K(T(x,y),z)) = x
    ]]></literal>
    <justification jstring="[hyper(154,a,2830,a)].">
      <j1 rule="hyper" parents="154 2830"/>
    </justification>
  </clause>

  <clause id="2835">
    <literal><![CDATA[
      T(x / (x / y),K(y,z)) = x / (x / y)
    ]]></literal>
    <justification jstring="[para(258(a,1),2834(a,1,2,1))].">
      <j1 rule="para" parents="258 2834"/>
    </justification>
  </clause>

  <clause id="2836">
    <literal><![CDATA[
      K(x,y) * (1 / x) = (1 / x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,2817,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 2817 22"/>
    </justification>
  </clause>

  <clause id="2837">
    <literal><![CDATA[
      T(x,R(y,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2815,a,b,2820,a),flip(a)].">
      <j1 rule="hyper" parents="316 2815 2820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2838">
    <literal><![CDATA[
      T(x / R(y,z,u),y) = R(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(377,a,2837,a),flip(a)].">
      <j1 rule="hyper" parents="377 2837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2839">
    <literal><![CDATA[
      T(x,R(1 / y,z,u)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,2595,a(flip),b,2837,a),flip(a)].">
      <j1 rule="hyper" parents="316 2595 2837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2842">
    <literal><![CDATA[
      R(x,y,z) * T(u,x) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,2837,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 2837 22"/>
    </justification>
  </clause>

  <clause id="2843">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(506(a,1),2837(a,1,2)),flip(a)].">
      <j1 rule="para" parents="506 2837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2844">
    <literal><![CDATA[
      T(x,y * (z \ 1)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(507(a,1),2837(a,1,2))].">
      <j1 rule="para" parents="507 2837"/>
    </justification>
  </clause>

  <clause id="2845">
    <literal><![CDATA[
      T(x,(y * z) / u) = T(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(509(a,1),2837(a,1,2))].">
      <j1 rule="para" parents="509 2837"/>
    </justification>
  </clause>

  <clause id="2846">
    <literal><![CDATA[
      T(x,T(y * (z \ 1),u)) = T(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[para(553(a,1),2837(a,1,2))].">
      <j1 rule="para" parents="553 2837"/>
    </justification>
  </clause>

  <clause id="2848">
    <literal><![CDATA[
      T(x,T(1 / y,z)) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(827(a,1),2837(a,1,2)),flip(a)].">
      <j1 rule="para" parents="827 2837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2849">
    <literal><![CDATA[
      T(x,y \ (z * (u \ y))) = T(x,T(z / u,y))
    ]]></literal>
    <justification jstring="[para(826(a,1),2837(a,1,2))].">
      <j1 rule="para" parents="826 2837"/>
    </justification>
  </clause>

  <clause id="2850">
    <literal><![CDATA[
      T(x,T(y / z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(830(a,1),2837(a,1,2)),flip(a)].">
      <j1 rule="para" parents="830 2837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2851">
    <literal><![CDATA[
      L((x \ y) \ 1,y,(x \ y) \ 1) * y = y * T((x \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(2837(a,1),1650(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2837 1650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2852">
    <literal><![CDATA[
      T(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(2820(a,2),2821(a,1))].">
      <j1 rule="para" parents="2820 2821"/>
    </justification>
  </clause>

  <clause id="2853">
    <literal><![CDATA[
      K(x,x \ y) * (x * z) = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,2797,a,b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 2797 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2857">
    <literal><![CDATA[
      T(x,y) * (x \ (z * u)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(316,a,406,a,b,2799,a),flip(a)].">
      <j1 rule="hyper" parents="316 406 2799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2859">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,1183,a(flip),b,2799,a),flip(a)].">
      <j1 rule="hyper" parents="63 1183 2799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2860">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) = T(K(x,z),x * y)
    ]]></literal>
    <justification jstring="[hyper(390,a,161,a(flip),b,2799,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="390 161 2799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2861">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(136,a,161,a(flip),b,2799,a(flip))].">
      <j1 rule="hyper" parents="136 161 2799"/>
    </justification>
  </clause>

  <clause id="2862">
    <literal><![CDATA[
      K(x,y) \ (x \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(133,a,1183,a(flip),b,2799,a(flip))].">
      <j1 rule="hyper" parents="133 1183 2799"/>
    </justification>
  </clause>

  <clause id="2863">
    <literal><![CDATA[
      K(x,y) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(133,a,161,a(flip),b,2799,a(flip))].">
      <j1 rule="hyper" parents="133 161 2799"/>
    </justification>
  </clause>

  <clause id="2864">
    <literal><![CDATA[
      K(x,y) * (z * x) = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(22(a,2),2799(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22 2799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2867">
    <literal><![CDATA[
      x * (K(x,y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(2799(a,1),1182(a,1,2))].">
      <j1 rule="para" parents="2799 1182"/>
    </justification>
  </clause>

  <clause id="2868">
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * x) = T(x,y) * L(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,412,a(flip),b,2800,a)].">
      <j1 rule="hyper" parents="63 412 2800"/>
    </justification>
  </clause>

  <clause id="2869">
    <literal><![CDATA[
      K(R(x,y,z),u) * (R(x,y,z) * w) = R(T(x,u),y,z) * w
    ]]></literal>
    <justification jstring="[para(27(a,2),2800(a,2,1))].">
      <j1 rule="para" parents="27 2800"/>
    </justification>
  </clause>

  <clause id="2870">
    <literal><![CDATA[
      (T(x,y) * z) \ (K(x,y) * u) = (x * z) \ u
    ]]></literal>
    <justification jstring="[para(2800(a,1),477(a,1,1))].">
      <j1 rule="para" parents="2800 477"/>
    </justification>
  </clause>

  <clause id="2871">
    <literal><![CDATA[
      K(x,y) * ((x * z) / u) = (T(x,y) * z) / u
    ]]></literal>
    <justification jstring="[para(2800(a,1),660(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2800 660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2872">
    <literal><![CDATA[
      a(T(x,y) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(2800(a,1),1806(a,1,1))].">
      <j1 rule="para" parents="2800 1806"/>
    </justification>
  </clause>

  <clause id="2873">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(316,a,424,a(flip),b,2801,a),flip(a)].">
      <j1 rule="hyper" parents="316 424 2801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2874">
    <literal><![CDATA[
      K(x * y,z) * (y * K(x,y)) = T(x * y,z) / x
    ]]></literal>
    <justification jstring="[para(2736(a,1),2801(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2736 2801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2875">
    <literal><![CDATA[
      (x * y) \ T(x,y) = (y * x) \ x
    ]]></literal>
    <justification jstring="[para(2728(a,1),2803(a,1,1))].">
      <j1 rule="para" parents="2728 2803"/>
    </justification>
  </clause>

  <clause id="2876">
    <literal><![CDATA[
      ((x \ y) * x) \ x = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(2730(a,1),2803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2730 2803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2877">
    <literal><![CDATA[
      (T(x,y) * z) \ T(x,y) = (x * z) \ x
    ]]></literal>
    <justification jstring="[para(2800(a,1),2803(a,1,1))].">
      <j1 rule="para" parents="2800 2803"/>
    </justification>
  </clause>

  <clause id="2878">
    <literal><![CDATA[
      K(x,y) * ((x / z) * u) = (T(x,y) / z) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,2810,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 2810 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2879">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / z) = x \ (x / z)
    ]]></literal>
    <justification jstring="[hyper(133,a,2810,a(flip),b,2799,a)].">
      <j1 rule="hyper" parents="133 2810 2799"/>
    </justification>
  </clause>

  <clause id="2880">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2046,a(flip),b,2814,a)].">
      <j1 rule="hyper" parents="63 2046 2814"/>
    </justification>
  </clause>

  <clause id="2881">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(T(x,z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1734,a(flip),b,2814,a)].">
      <j1 rule="hyper" parents="63 1734 2814"/>
    </justification>
  </clause>

  <clause id="2882">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1343,a(flip),b,2814,a)].">
      <j1 rule="hyper" parents="63 1343 2814"/>
    </justification>
  </clause>

  <clause id="2883">
    <literal><![CDATA[
      (x / y) * K(y \ 1,z) = x * T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(139,a,2814,a(flip),b,955,a)].">
      <j1 rule="hyper" parents="139 2814 955"/>
    </justification>
  </clause>

  <clause id="2884">
    <literal><![CDATA[
      K((x / y) \ 1,z) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,2814,a(flip),b,1343,a(flip))].">
      <j1 rule="hyper" parents="138 2814 1343"/>
    </justification>
  </clause>

  <clause id="2885">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(2814(a,1),712(a,2,2))].">
      <j1 rule="para" parents="2814 712"/>
    </justification>
  </clause>

  <clause id="2886">
    <literal><![CDATA[
      T(x,K(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(2814(a,1),1222(a,1,2))].">
      <j1 rule="para" parents="2814 1222"/>
    </justification>
  </clause>

  <clause id="2888">
    <literal><![CDATA[
      L(T(x \ 1,y),x,x \ z) = z \ ((z / x) * K(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(2814(a,1),1598(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2814 1598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2889">
    <literal><![CDATA[
      T(K(x \ 1,y),x) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,2886,a)].">
      <j1 rule="hyper" parents="54 2886"/>
    </justification>
  </clause>

  <clause id="2891">
    <literal><![CDATA[
      T(x,y) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(2722(a,2),2833(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2722 2833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2892">
    <literal><![CDATA[
      1 / T(x \ (1 / y),x * y) = (x \ (1 / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(209,a,2843,a(flip),b,2427,a(flip))].">
      <j1 rule="hyper" parents="209 2843 2427"/>
    </justification>
  </clause>

  <clause id="2893">
    <literal><![CDATA[
      T(x,y / R(z / u,u,z \ 1)) = T(x,y * (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(349(a,2),2843(a,1,2,2))].">
      <j1 rule="para" parents="349 2843"/>
    </justification>
  </clause>

  <clause id="2894">
    <literal><![CDATA[
      T(x,y / (z \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2643,a(flip),b,2844,a),flip(a)].">
      <j1 rule="hyper" parents="63 2643 2844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      L(x,y \ 1,z) * (z * (y \ 1)) = z * ((y \ 1) * T(x,z / y))
    ]]></literal>
    <justification jstring="[para(2844(a,1),598(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2844 598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2896">
    <literal><![CDATA[
      T(x,T(R(y,z,u) / w,y)) = T(x,w \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(2837(a,1),2850(a,1,2))].">
      <j1 rule="para" parents="2837 2850"/>
    </justification>
  </clause>

  <clause id="2897">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(539,a,2859,a),flip(a)].">
      <j1 rule="hyper" parents="539 2859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2898">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(133,a,9,a(flip),b,2859,a),flip(a)].">
      <j1 rule="hyper" parents="133 9 2859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2899">
    <literal><![CDATA[
      T(x,x \ (x \ y)) \ y = (x \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(34,a,2730,a,b,2859,a),flip(a)].">
      <j1 rule="hyper" parents="34 2730 2859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2901">
    <literal><![CDATA[
      T(x,y) * (K(x,y) \ z) = x * z
    ]]></literal>
    <justification jstring="[hyper(139,a,75,a(flip),b,2859,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 75 2859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2902">
    <literal><![CDATA[
      K(x,y) * ((T(x,y) \ z) * u) = (x \ z) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,2859,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 2859 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2903">
    <literal><![CDATA[
      K(L(x,y,z),u) * (L(T(x,u),y,z) \ w) = L(x,y,z) \ w
    ]]></literal>
    <justification jstring="[para(25(a,2),2859(a,1,2,1))].">
      <j1 rule="para" parents="25 2859"/>
    </justification>
  </clause>

  <clause id="2904">
    <literal><![CDATA[
      K(R(x,y,z),u) * (R(T(x,u),y,z) \ w) = R(x,y,z) \ w
    ]]></literal>
    <justification jstring="[para(27(a,2),2859(a,1,2,1))].">
      <j1 rule="para" parents="27 2859"/>
    </justification>
  </clause>

  <clause id="2905">
    <literal><![CDATA[
      K(x,x \ y) * (((x \ y) \ y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[para(115(a,1),2859(a,1,2,1))].">
      <j1 rule="para" parents="115 2859"/>
    </justification>
  </clause>

  <clause id="2906">
    <literal><![CDATA[
      (x \ y) \ (K(x,z) * u) = (T(x,z) \ y) \ u
    ]]></literal>
    <justification jstring="[para(2859(a,1),477(a,1,1))].">
      <j1 rule="para" parents="2859 477"/>
    </justification>
  </clause>

  <clause id="2907">
    <literal><![CDATA[
      K(x,y) * (((T(x,y) \ z) * u) * w) = ((x \ z) * u) * w
    ]]></literal>
    <justification jstring="[para(2859(a,1),656(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2859 656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2908">
    <literal><![CDATA[
      a(T(x,y) \ z,u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(2859(a,1),1806(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2859 1806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2909">
    <literal><![CDATA[
      x \ (K(x,y) * z) = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(2809(a,1),2859(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2809 2859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2910">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[para(2806(a,1),2862(a,1,1))].">
      <j1 rule="para" parents="2806 2862"/>
    </justification>
  </clause>

  <clause id="2911">
    <literal><![CDATA[
      K(x,y) * (x * z) = x * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2800,a,b,2867,a)].">
      <j1 rule="hyper" parents="316 2800 2867"/>
    </justification>
  </clause>

  <clause id="2912">
    <literal><![CDATA[
      T(x,y) * (z \ (z * u)) = x * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(316,a,161,a,b,2867,a)].">
      <j1 rule="hyper" parents="316 161 2867"/>
    </justification>
  </clause>

  <clause id="2913">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,238,a(flip),b,2867,a),flip(a)].">
      <j1 rule="hyper" parents="63 238 2867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2914">
    <literal><![CDATA[
      K(x / y,z) * x = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,1198,a,b,2867,a),flip(a)].">
      <j1 rule="hyper" parents="34 1198 2867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2915">
    <literal><![CDATA[
      T(x,y) = x / (K(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(136,a,73,a(flip),b,2867,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 73 2867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2916">
    <literal><![CDATA[
      x * R(K(x,y) * z,u,w) = T(x,y) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(1028(a,2),2867(a,1,2))].">
      <j1 rule="para" parents="1028 2867"/>
    </justification>
  </clause>

  <clause id="2918">
    <literal><![CDATA[
      T(x,y) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(2728(a,1),2867(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2728 2867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2919">
    <literal><![CDATA[
      (x * (y / x)) \ (y / x) = y \ T(y / x,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),2875(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 2875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2920">
    <literal><![CDATA[
      (L(x,y,z) * u) \ L(T(x,u),y,z) = (u * L(x,y,z)) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),2875(a,1,2))].">
      <j1 rule="para" parents="25 2875"/>
    </justification>
  </clause>

  <clause id="2921">
    <literal><![CDATA[
      (K(x,y) * (z * u)) \ T(K(x,y) * z,u) = (u * (K(x,y) * z)) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(406(a,1),2875(a,1,1))].">
      <j1 rule="para" parents="406 2875"/>
    </justification>
  </clause>

  <clause id="2923">
    <literal><![CDATA[
      T(x,y) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(34,a,1185,a,b,2918,a(flip))].">
      <j1 rule="hyper" parents="34 1185 2918"/>
    </justification>
  </clause>

  <clause id="2924">
    <literal><![CDATA[
      (x * (x * y)) \ (T(x,y) * ((y * x) * z)) = L(z,y * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(2918(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2918 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2925">
    <literal><![CDATA[
      T(x,T(y,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(253,a,114,a,b,2923,a)].">
      <j1 rule="hyper" parents="253 114 2923"/>
    </justification>
  </clause>

  <clause id="2927">
    <literal><![CDATA[
      (T(x,y) * T(y,x)) / y = x
    ]]></literal>
    <justification jstring="[hyper(136,a,2923,a,b,xx)].">
      <j1 rule="hyper" parents="136 2923"/>
    </justification>
  </clause>

  <clause id="2928">
    <literal><![CDATA[
      T(x,y) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(34,a,2901,a,b,2923,a),flip(a)].">
      <j1 rule="hyper" parents="34 2901 2923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2929">
    <literal><![CDATA[
      K(x,y) * T(y,x) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,2867,a,b,2923,a(flip))].">
      <j1 rule="hyper" parents="34 2867 2923"/>
    </justification>
  </clause>

  <clause id="2930">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) \ ((x * y) * z) = T(x,y) * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[para(2923(a,1),2315(a,1,2,1))].">
      <j1 rule="para" parents="2923 2315"/>
    </justification>
  </clause>

  <clause id="2931">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,1632,a,b,2925,a)].">
      <j1 rule="hyper" parents="316 1632 2925"/>
    </justification>
  </clause>

  <clause id="2932">
    <literal><![CDATA[
      T(x,x / y) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2850,a(flip),b,2925,a),flip(a)].">
      <j1 rule="hyper" parents="63 2850 2925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2933">
    <literal><![CDATA[
      T(x,y) / y = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(209,a,2925,a(flip),b,1313,a),flip(a)].">
      <j1 rule="hyper" parents="209 2925 1313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2934">
    <literal><![CDATA[
      T(x,y) \ y = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2925,a(flip),b,1197,a),flip(a)].">
      <j1 rule="hyper" parents="133 2925 1197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2937">
    <literal><![CDATA[
      K(x,y) = y / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(209,a,2928,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="209 2928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2938">
    <literal><![CDATA[
      K(x,y) \ y = 1 \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2928,a,b,7,a),flip(a)].">
      <j1 rule="hyper" parents="133 2928 7"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2941">
    <literal><![CDATA[
      K(x,y / x) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(139,a,116,a(flip),b,2928,a(flip))].">
      <j1 rule="hyper" parents="139 116 2928"/>
    </justification>
  </clause>

  <clause id="2943">
    <literal><![CDATA[
      x / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2928(a,2),291(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2928 291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2944">
    <literal><![CDATA[
      T(x,y) \ 1 = x \ K(y,x)
    ]]></literal>
    <justification jstring="[para(2928(a,2),425(a,1,1))].">
      <j1 rule="para" parents="2928 425"/>
    </justification>
  </clause>

  <clause id="2945">
    <literal><![CDATA[
      L(T(x,y),K(y,x),z) = (z * K(y,x)) \ (z * x)
    ]]></literal>
    <justification jstring="[para(2928(a,2),102(a,1,1))].">
      <j1 rule="para" parents="2928 102"/>
    </justification>
  </clause>

  <clause id="2946">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(2928(a,2),640(a,1,2,1))].">
      <j1 rule="para" parents="2928 640"/>
    </justification>
  </clause>

  <clause id="2947">
    <literal><![CDATA[
      T(x,y) * K(y,x) = x
    ]]></literal>
    <justification jstring="[para(2928(a,2),1977(a,1,1))].">
      <j1 rule="para" parents="2928 1977"/>
    </justification>
  </clause>

  <clause id="2948">
    <literal><![CDATA[
      K(x,y) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,1995,a,b,2929,a),flip(a)].">
      <j1 rule="hyper" parents="35 1995 2929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2949">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,2929,a(flip),b,478,a)].">
      <j1 rule="hyper" parents="138 2929 478"/>
    </justification>
  </clause>

  <clause id="2950">
    <literal><![CDATA[
      (K(x,y) * z) \ y = z \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2929,a(flip),b,479,a)].">
      <j1 rule="hyper" parents="133 2929 479"/>
    </justification>
  </clause>

  <clause id="2951">
    <literal><![CDATA[
      x / T(x * x,y) = x \ K(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2937,a,b,696,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 2937 696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2952">
    <literal><![CDATA[
      T(x,y) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(149,a,2947,a),flip(a)].">
      <j1 rule="hyper" parents="149 2947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2953">
    <literal><![CDATA[
      K(x,y) * (x * K(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,2800,a,b,2947,a)].">
      <j1 rule="hyper" parents="63 2800 2947"/>
    </justification>
  </clause>

  <clause id="2955">
    <literal><![CDATA[
      K(x,T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,2733,a,b,2947,a)].">
      <j1 rule="hyper" parents="34 2733 2947"/>
    </justification>
  </clause>

  <clause id="2957">
    <literal><![CDATA[
      (x \ y) \ y = x / K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(136,a,2947,a(flip),b,313,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 2947 313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2958">
    <literal><![CDATA[
      K(x,y) \ x = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2947,a(flip),b,2800,a)].">
      <j1 rule="hyper" parents="133 2947 2800"/>
    </justification>
  </clause>

  <clause id="2959">
    <literal><![CDATA[
      K(x,y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(132,a,2947,a(flip),b,2867,a),flip(a)].">
      <j1 rule="hyper" parents="132 2947 2867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2962">
    <literal><![CDATA[
      x / K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2947(a,1),266(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2947 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2963">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2947(a,1),321(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2947 321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2964">
    <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),2948(a,2,1)),flip(a)].">
      <j1 rule="para" parents="27 2948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2965">
    <literal><![CDATA[
      T(x,y) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(2948(a,2),1997(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2948 1997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2966">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(2948(a,2),2587(a,1,2))].">
      <j1 rule="para" parents="2948 2587"/>
    </justification>
  </clause>

  <clause id="2967">
    <literal><![CDATA[
      K(x,y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,2915,a(flip),b,2952,a(flip))].">
      <j1 rule="hyper" parents="36 2915 2952"/>
    </justification>
  </clause>

  <clause id="2968">
    <literal><![CDATA[
      K(x,x \ (y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),2955(a,1,2))].">
      <j1 rule="para" parents="22 2955"/>
    </justification>
  </clause>

  <clause id="2969">
    <literal><![CDATA[
      K(x,y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(116(a,1),2955(a,1,2)),flip(a)].">
      <j1 rule="para" parents="116 2955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2971">
    <literal><![CDATA[
      1 / K(x,y) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(149,a,2959,a)].">
      <j1 rule="hyper" parents="149 2959"/>
    </justification>
  </clause>

  <clause id="2972">
    <literal><![CDATA[
      x * (K(y,z) * K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,2959,a,b,67,a)].">
      <j1 rule="hyper" parents="139 2959 67"/>
    </justification>
  </clause>

  <clause id="2973">
    <literal><![CDATA[
      1 / (x \ K(y,z)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(136,a,2959,a(flip),b,479,a)].">
      <j1 rule="hyper" parents="136 2959 479"/>
    </justification>
  </clause>

  <clause id="2974">
    <literal><![CDATA[
      ((x * y) / x) \ 1 = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2959,a(flip),b,2724,a)].">
      <j1 rule="hyper" parents="133 2959 2724"/>
    </justification>
  </clause>

  <clause id="2975">
    <literal><![CDATA[
      (K(x,y) * z) \ 1 = z \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2959,a(flip),b,479,a)].">
      <j1 rule="hyper" parents="133 2959 479"/>
    </justification>
  </clause>

  <clause id="2976">
    <literal><![CDATA[
      K(x,y) != 1 / z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2959(a,1),150(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2959 150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2977">
    <literal><![CDATA[
      K(x,y) != z \ 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2959(a,1),153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2959 153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2978">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2959(a,1),321(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2959 321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2979">
    <literal><![CDATA[
      K(x,y) * (K(y,x) / z) = 1 / z
    ]]></literal>
    <justification jstring="[para(2959(a,1),660(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2959 660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2980">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ K(y,x)) = a(z,u,w) \ 1
    ]]></literal>
    <justification jstring="[para(2959(a,1),2397(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2959 2397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2981">
    <literal><![CDATA[
      K(x,y) \ z = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(2967(a,1),526(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2967 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2982">
    <literal><![CDATA[
      T(x,K(y,z) \ 1) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(2967(a,1),2594(a,1,2,1))].">
      <j1 rule="para" parents="2967 2594"/>
    </justification>
  </clause>

  <clause id="2983">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,868,a,b,2932,a)].">
      <j1 rule="hyper" parents="63 868 2932"/>
    </justification>
  </clause>

  <clause id="2984">
    <literal><![CDATA[
      T(x,(y \ x) \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(80(a,1),2932(a,1,2)),flip(a)].">
      <j1 rule="para" parents="80 2932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2985">
    <literal><![CDATA[
      x * (T(y,z) \ 1) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,2944,a,b,9,a)].">
      <j1 rule="hyper" parents="139 2944 9"/>
    </justification>
  </clause>

  <clause id="2986">
    <literal><![CDATA[
      K(x,y) * ((y * x) / y) = x
    ]]></literal>
    <justification jstring="[para(2722(a,2),2953(a,1,2))].">
      <j1 rule="para" parents="2722 2953"/>
    </justification>
  </clause>

  <clause id="2987">
    <literal><![CDATA[
      K(x \ y,x) * (y / x) = x \ y
    ]]></literal>
    <justification jstring="[para(2732(a,1),2953(a,1,2))].">
      <j1 rule="para" parents="2732 2953"/>
    </justification>
  </clause>

  <clause id="2988">
    <literal><![CDATA[
      K(x,y) = x / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(209,a,2722,a,b,2958,a),flip(a)].">
      <j1 rule="hyper" parents="209 2722 2958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2991">
    <literal><![CDATA[
      x * K(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,2969,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="139 2969 97"/>
    </justification>
  </clause>

  <clause id="2992">
    <literal><![CDATA[
      K(x,x \ y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2969(a,1),2726(a,1,1))].">
      <j1 rule="para" parents="2969 2726"/>
    </justification>
  </clause>

  <clause id="2993">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(390,a,2981,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="390 2981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2994">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(325,a,2981,a),flip(a)].">
      <j1 rule="hyper" parents="325 2981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2995">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = z
    ]]></literal>
    <justification jstring="[hyper(322,a,2981,a),flip(a)].">
      <j1 rule="hyper" parents="322 2981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2996">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(316,a,2799,a,b,2981,a)].">
      <j1 rule="hyper" parents="316 2799 2981"/>
    </justification>
  </clause>

  <clause id="2997">
    <literal><![CDATA[
      K(x,y) \ (y * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(316,a,2800,a(flip),b,2981,a),flip(a)].">
      <j1 rule="hyper" parents="316 2800 2981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2998">
    <literal><![CDATA[
      (K(x,y) \ z) / z = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(209,a,10,a(flip),b,2981,a)].">
      <j1 rule="hyper" parents="209 10 2981"/>
    </justification>
  </clause>

  <clause id="2999">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) / z) * L(z,u,w)) = z \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,1461,a,b,2981,a)].">
      <j1 rule="hyper" parents="139 1461 2981"/>
    </justification>
  </clause>

  <clause id="3000">
    <literal><![CDATA[
      K(x,y) * R(K(y,x) * z,u,w) = R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,1028,a,b,2981,a)].">
      <j1 rule="hyper" parents="139 1028 2981"/>
    </justification>
  </clause>

  <clause id="3001">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) * z) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(139,a,406,a,b,2981,a)].">
      <j1 rule="hyper" parents="139 406 2981"/>
    </justification>
  </clause>

  <clause id="3002">
    <literal><![CDATA[
      K(x,y) * (y \ z) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,2859,a(flip),b,2981,a)].">
      <j1 rule="hyper" parents="139 2859 2981"/>
    </justification>
  </clause>

  <clause id="3003">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,2898,a,b,2981,a)].">
      <j1 rule="hyper" parents="63 2898 2981"/>
    </justification>
  </clause>

  <clause id="3004">
    <literal><![CDATA[
      K(x,y) * (z * (K(y,x) * u)) = u * T(z,K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,645,a(flip),b,2981,a),flip(a)].">
      <j1 rule="hyper" parents="63 645 2981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3005">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(139,a,2981,a(flip),b,2898,a)].">
      <j1 rule="hyper" parents="139 2981 2898"/>
    </justification>
  </clause>

  <clause id="3006">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * u = z
    ]]></literal>
    <justification jstring="[para(2981(a,1),152(a,1))].">
      <j1 rule="para" parents="2981 152"/>
    </justification>
  </clause>

  <clause id="3007">
    <literal><![CDATA[
      (K(x,y) * z) \ z = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(2981(a,1),668(a,1,1))].">
      <j1 rule="para" parents="2981 668"/>
    </justification>
  </clause>

  <clause id="3008">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(2981(a,1),643(a,1,1))].">
      <j1 rule="para" parents="2981 643"/>
    </justification>
  </clause>

  <clause id="3009">
    <literal><![CDATA[
      (K(x,y) * z) \ u = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(2981(a,1),664(a,1,1))].">
      <j1 rule="para" parents="2981 664"/>
    </justification>
  </clause>

  <clause id="3010">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,2986,a(flip),b,478,a)].">
      <j1 rule="hyper" parents="138 2986 478"/>
    </justification>
  </clause>

  <clause id="3012">
    <literal><![CDATA[
      K(x,y) / x = 1 / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(136,a,2988,a,b,1398,a)].">
      <j1 rule="hyper" parents="136 2988 1398"/>
    </justification>
  </clause>

  <clause id="3014">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(2995(a,1),321(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2995 321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3015">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ 1 = z
    ]]></literal>
    <justification jstring="[para(2998(a,1),186(a,1)),flip(b)].">
      <j1 rule="para" parents="2998 186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3016">
    <literal><![CDATA[
      K(x,y \ 1) * (x \ (y \ x)) = (y \ x) / x
    ]]></literal>
    <justification jstring="[para(1956(a,1),2941(a,1,1))].">
      <j1 rule="para" parents="1956 2941"/>
    </justification>
  </clause>

  <clause id="3018">
    <literal><![CDATA[
      K(x,y) * (z * T(y,x)) = y * T(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,238,a(flip),b,2946,a)].">
      <j1 rule="hyper" parents="63 238 2946"/>
    </justification>
  </clause>

  <clause id="3019">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,2946,a(flip),b,2897,a),flip(a)].">
      <j1 rule="hyper" parents="139 2946 2897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3020">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (L(T(y,x),z,u) * w) = L(y,z,u) * w
    ]]></literal>
    <justification jstring="[para(25(a,2),2946(a,1,2,1))].">
      <j1 rule="para" parents="25 2946"/>
    </justification>
  </clause>

  <clause id="3021">
    <literal><![CDATA[
      (x * y) \ (K(z,x) * u) = (T(x,z) * y) \ u
    ]]></literal>
    <justification jstring="[para(2946(a,1),477(a,1,1))].">
      <j1 rule="para" parents="2946 477"/>
    </justification>
  </clause>

  <clause id="3022">
    <literal><![CDATA[
      K(x,y) * T(T(y,x),z) = y * K(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(2815(a,2),2946(a,1,2))].">
      <j1 rule="para" parents="2815 2946"/>
    </justification>
  </clause>

  <clause id="3023">
    <literal><![CDATA[
      T(x,y) \ (y * x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(253,a,2800,a(flip),b,2949,a),flip(a)].">
      <j1 rule="hyper" parents="253 2800 2949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3026">
    <literal><![CDATA[
      x / R(y,y \ x,y) = K(y,x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(209,a,1637,a,b,2950,a)].">
      <j1 rule="hyper" parents="209 1637 2950"/>
    </justification>
  </clause>

  <clause id="3028">
    <literal><![CDATA[
      (x \ y) \ K(x \ y,x) = (y / x) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),2974(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 2974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3029">
    <literal><![CDATA[
      T(x \ y,x) * (y / x) = (x \ y) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,2987,a(flip),b,2897,a),flip(a)].">
      <j1 rule="hyper" parents="139 2987 2897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3030">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,2987,a(flip),b,478,a)].">
      <j1 rule="hyper" parents="138 2987 478"/>
    </justification>
  </clause>

  <clause id="3031">
    <literal><![CDATA[
      K(x \ y,x) * ((y / x) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,2987,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 2987 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3032">
    <literal><![CDATA[
      (x \ y) \ (K(x \ y,x) * z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[para(2987(a,1),477(a,1,1))].">
      <j1 rule="para" parents="2987 477"/>
    </justification>
  </clause>

  <clause id="3035">
    <literal><![CDATA[
      (x * (y / x)) / y = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(149,a,2992,a)].">
      <j1 rule="hyper" parents="149 2992"/>
    </justification>
  </clause>

  <clause id="3036">
    <literal><![CDATA[
      K(x,x \ y) * (y / z) = (x * (y / x)) / z
    ]]></literal>
    <justification jstring="[para(2992(a,1),660(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2992 660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3037">
    <literal><![CDATA[
      K(x \ y,x) \ (x * z) = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(316,a,313,a(flip),b,2997,a),flip(a)].">
      <j1 rule="hyper" parents="316 313 2997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3039">
    <literal><![CDATA[
      T(x,x \ 1) * R(y,x,x) = R(x * y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2576,a(flip),b,2997,a),flip(a)].">
      <j1 rule="hyper" parents="63 2576 2997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3041">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(2806(a,2),3002(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2806 3002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3042">
    <literal><![CDATA[
      K(x,y) * (T(y,x) \ z) = T(T(y,x),x) \ z
    ]]></literal>
    <justification jstring="[para(2955(a,1),3002(a,1,1))].">
      <j1 rule="para" parents="2955 3002"/>
    </justification>
  </clause>

  <clause id="3044">
    <literal><![CDATA[
      K(x,y) * (y * z) = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(3003(a,1),2949(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3003 2949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3046">
    <literal><![CDATA[
      K(x,y / z) * (z * T(z \ y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,1198,a(flip),b,3005,a),flip(a)].">
      <j1 rule="hyper" parents="34 1198 3005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3047">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * u = z
    ]]></literal>
    <justification jstring="[para(3005(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="3005 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3048">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(2722(a,1),3012(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2722 3012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3049">
    <literal><![CDATA[
      T(x,y / (z * y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(234(a,1),2839(a,1,2))].">
      <j1 rule="para" parents="234 2839"/>
    </justification>
  </clause>

  <clause id="3050">
    <literal><![CDATA[
      T(x,(y \ z) / z) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(370(a,1),2839(a,1,2))].">
      <j1 rule="para" parents="370 2839"/>
    </justification>
  </clause>

  <clause id="3051">
    <literal><![CDATA[
      T(x,(y / z) \ 1) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(371(a,1),2839(a,1,2)),flip(a)].">
      <j1 rule="para" parents="371 2839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      x \ T(y,x \ 1) = y * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[para(3049(a,1),919(a,1,2))].">
      <j1 rule="para" parents="3049 919"/>
    </justification>
  </clause>

  <clause id="3053">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(3050(a,1),1949(a,1,2))].">
      <j1 rule="para" parents="3050 1949"/>
    </justification>
  </clause>

  <clause id="3054">
    <literal><![CDATA[
      T(((1 / (x / y)) * z) * (x / y),y / x) = R(z,(x / y) \ 1,x / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2604,a(flip),b,3051,a),flip(a)].">
      <j1 rule="hyper" parents="63 2604 3051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3055">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,2806,a(flip),b,2739,a),flip(a)].">
      <j1 rule="hyper" parents="316 2806 2739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3056">
    <literal><![CDATA[
      (x \ K(y,x \ 1)) * y = y * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2739(a,1),85(a,1,1,2))].">
      <j1 rule="para" parents="2739 85"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      (x / ((y * z) / y)) * z = x / K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1397,a(flip),b,2752,a)].">
      <j1 rule="hyper" parents="63 1397 2752"/>
    </justification>
  </clause>

  <clause id="3059">
    <literal><![CDATA[
      L((x * y) \ z,y * x,(y * x) \ 1) = (1 / (y * x)) * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,2758,a(flip),b,886,a),flip(a)].">
      <j1 rule="hyper" parents="139 2758 886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3060">
    <literal><![CDATA[
      K(x,y) \ ((x * y) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,161,a(flip),b,2758,a(flip))].">
      <j1 rule="hyper" parents="133 161 2758"/>
    </justification>
  </clause>

  <clause id="3061">
    <literal><![CDATA[
      K(x * y,z) * ((z * x) * y) = ((x * y) * z) * a(z,x,y)
    ]]></literal>
    <justification jstring="[para(14(a,2),2758(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14 2758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3062">
    <literal><![CDATA[
      K(x,y) * (y * (x * z)) = (x * y) * L(z,x,y)
    ]]></literal>
    <justification jstring="[para(18(a,2),2758(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 2758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      K(x,y) * (z * (y * x)) = (x * y) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(22(a,2),2758(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22 2758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3064">
    <literal><![CDATA[
      T(x,y) * ((y * x) * z) = x * ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,2759,a(flip),b,3003,a)].">
      <j1 rule="hyper" parents="139 2759 3003"/>
    </justification>
  </clause>

  <clause id="3065">
    <literal><![CDATA[
      ((x * y) * z) \ (K(x,y) * u) = ((y * x) * z) \ u
    ]]></literal>
    <justification jstring="[para(2759(a,1),477(a,1,1))].">
      <j1 rule="para" parents="2759 477"/>
    </justification>
  </clause>

  <clause id="3066">
    <literal><![CDATA[
      a((x * y) * z,u,w) = a((y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(2759(a,1),1806(a,1,1))].">
      <j1 rule="para" parents="2759 1806"/>
    </justification>
  </clause>

  <clause id="3067">
    <literal><![CDATA[
      a((x \ (y * z)) \ (z * y),u,w) = a(K(z,y) * x,u,w)
    ]]></literal>
    <justification jstring="[para(2761(a,1),1813(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2761 1813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3068">
    <literal><![CDATA[
      L(x,y,z) = (y * z) \ (K(y,z) * (z * (y * x)))
    ]]></literal>
    <justification jstring="[hyper(316,a,18,a,b,2765,a)].">
      <j1 rule="hyper" parents="316 18 2765"/>
    </justification>
  </clause>

  <clause id="3069">
    <literal><![CDATA[
      (x * y) \ ((x * y) / z) = (y * x) \ ((y * x) / z)
    ]]></literal>
    <justification jstring="[hyper(133,a,2766,a(flip),b,2758,a)].">
      <j1 rule="hyper" parents="133 2766 2758"/>
    </justification>
  </clause>

  <clause id="3070">
    <literal><![CDATA[
      L(x,y,(z * u) / w) = L(x,y,(u * z) / w)
    ]]></literal>
    <justification jstring="[para(2766(a,1),1575(a,1,3))].">
      <j1 rule="para" parents="2766 1575"/>
    </justification>
  </clause>

  <clause id="3071">
    <literal><![CDATA[
      K(x,y) * (((x * y) / x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(375,a,2796,a),flip(a)].">
      <j1 rule="hyper" parents="375 2796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3072">
    <literal><![CDATA[
      (x * y) / x = y / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(136,a,2972,a(flip),b,2796,a),flip(a)].">
      <j1 rule="hyper" parents="136 2972 2796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3074">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),2796(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 2796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3075">
    <literal><![CDATA[
      (x * K(y,x)) * z = x * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(2722(a,1),2796(a,1,1))].">
      <j1 rule="para" parents="2722 2796"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      ((x * y) / x) * (x * z) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(2800(a,1),2796(a,2,2))].">
      <j1 rule="para" parents="2800 2796"/>
    </justification>
  </clause>

  <clause id="3078">
    <literal><![CDATA[
      x * K(T(x,y),y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,241,a(flip),b,3072,a(flip))].">
      <j1 rule="hyper" parents="138 241 3072"/>
    </justification>
  </clause>

  <clause id="3079">
    <literal><![CDATA[
      (x / y) * K(y \ x,y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(138,a,163,a(flip),b,3072,a(flip))].">
      <j1 rule="hyper" parents="138 163 3072"/>
    </justification>
  </clause>

  <clause id="3083">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,2815,a(flip),b,3078,a),flip(a)].">
      <j1 rule="hyper" parents="34 2815 3078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3084">
    <literal><![CDATA[
      (x * y) * K(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,3083,a(flip),b,246,a)].">
      <j1 rule="hyper" parents="139 3083 246"/>
    </justification>
  </clause>

  <clause id="3085">
    <literal><![CDATA[
      K(x / y,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(116(a,1),3083(a,1,1)),flip(a)].">
      <j1 rule="para" parents="116 3083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3087">
    <literal><![CDATA[
      K(T(x,R(y,z,u)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2837(a,2),3083(a,1,1))].">
      <j1 rule="para" parents="2837 3083"/>
    </justification>
  </clause>

  <clause id="3088">
    <literal><![CDATA[
      x * K(x / y,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,3085,a,b,95,a)].">
      <j1 rule="hyper" parents="139 3085 95"/>
    </justification>
  </clause>

  <clause id="3090">
    <literal><![CDATA[
      x / (x / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,3085,a(flip),b,2742,a),flip(a)].">
      <j1 rule="hyper" parents="139 3085 2742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3091">
    <literal><![CDATA[
      (x * (y / x)) * K(x \ y,x) = y
    ]]></literal>
    <justification jstring="[hyper(139,a,3085,a(flip),b,98,a)].">
      <j1 rule="hyper" parents="139 3085 98"/>
    </justification>
  </clause>

  <clause id="3095">
    <literal><![CDATA[
      x / (x / y) = K(y \ x,y) * y
    ]]></literal>
    <justification jstring="[hyper(316,a,1974,a,b,3090,a),flip(a)].">
      <j1 rule="hyper" parents="316 1974 3090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3096">
    <literal><![CDATA[
      (x * K(x \ y,x)) \ y = y / x
    ]]></literal>
    <justification jstring="[hyper(204,a,3090,a)].">
      <j1 rule="hyper" parents="204 3090"/>
    </justification>
  </clause>

  <clause id="3097">
    <literal><![CDATA[
      K(x,x \ y) * (y / (y / x)) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,3090,a,b,2958,a)].">
      <j1 rule="hyper" parents="139 3090 2958"/>
    </justification>
  </clause>

  <clause id="3104">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,u) = x \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,2812,a(flip),b,2799,a)].">
      <j1 rule="hyper" parents="133 2812 2799"/>
    </justification>
  </clause>

  <clause id="3105">
    <literal><![CDATA[
      (x * y) \ R(T(x,y),z,u) = (y * x) \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,2812,a(flip),b,2758,a)].">
      <j1 rule="hyper" parents="133 2812 2758"/>
    </justification>
  </clause>

  <clause id="3107">
    <literal><![CDATA[
      K(x,y) * (z / (z / x)) = (z / (z / x)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,2835,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 2835 22"/>
    </justification>
  </clause>

  <clause id="3108">
    <literal><![CDATA[
      (1 / x) * K(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,424,a(flip),b,2836,a),flip(a)].">
      <j1 rule="hyper" parents="63 424 2836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3109">
    <literal><![CDATA[
      (x * (R(x,y,z) \ u)) / x = u / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(285,a,2838,a)].">
      <j1 rule="hyper" parents="285 2838"/>
    </justification>
  </clause>

  <clause id="3110">
    <literal><![CDATA[
      (x / R(y,z,u)) * y = y * (R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,2838,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 2838 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3111">
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = (u / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(116(a,1),2842(a,1,2))].">
      <j1 rule="para" parents="116 2842"/>
    </justification>
  </clause>

  <clause id="3112">
    <literal><![CDATA[
      R(x,y,z) * (u * x) = x * (u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(2842(a,1),1172(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2842 1172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3113">
    <literal><![CDATA[
      T(x,(y * z) / (y / (z \ 1))) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,2476,a(flip),b,2845,a),flip(a)].">
      <j1 rule="hyper" parents="316 2476 2845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3114">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2602,a(flip),b,2848,a)].">
      <j1 rule="hyper" parents="63 2602 2848"/>
    </justification>
  </clause>

  <clause id="3115">
    <literal><![CDATA[
      ((K(x,y) * (z * x)) * (T(x,y) \ 1)) \ ((1 / (1 / T(x,y))) * T(z,x)) = L(T(x,y),T(x,y) \ 1,T(x,y) * T(z,x))
    ]]></literal>
    <justification jstring="[para(2864(a,2),2453(a,1,1,1))].">
      <j1 rule="para" parents="2864 2453"/>
    </justification>
  </clause>

  <clause id="3116">
    <literal><![CDATA[
      a(x * T(y,z),u,w) = a(y * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2771,a,b,2872,a)].">
      <j1 rule="hyper" parents="63 2771 2872"/>
    </justification>
  </clause>

  <clause id="3117">
    <literal><![CDATA[
      a((x / y) * z,u,w) = a((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(116(a,1),2872(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="116 2872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3119">
    <literal><![CDATA[
      K(x,y) * (x \ (x / z)) = x \ (T(x,y) / z)
    ]]></literal>
    <justification jstring="[hyper(139,a,2879,a(flip),b,2862,a)].">
      <j1 rule="hyper" parents="139 2879 2862"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      a(L(T(x,y),z,u) \ w,v5,v6) = a(L(x,z,u) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(25(a,2),2908(a,1,1,1))].">
      <j1 rule="para" parents="25 2908"/>
    </justification>
  </clause>

  <clause id="3121">
    <literal><![CDATA[
      a((x / y) \ z,u,w) = a((y \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(116(a,1),2908(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="116 2908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3122">
    <literal><![CDATA[
      a(((x \ y) \ y) \ z,u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(115(a,1),2908(a,1,1,1))].">
      <j1 rule="para" parents="115 2908"/>
    </justification>
  </clause>

  <clause id="3123">
    <literal><![CDATA[
      K(x,x \ y) * (x \ (x \ y)) = x \ (y / x)
    ]]></literal>
    <justification jstring="[para(2721(a,1),2909(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2721 2909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3124">
    <literal><![CDATA[
      K(x,y) * (x \ (y \ z)) = x \ (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[para(3002(a,1),2909(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3002 2909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      (T(x,y) \ 1) * (x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(2910(a,1),2108(a,1,1))].">
      <j1 rule="para" parents="2910 2108"/>
    </justification>
  </clause>

  <clause id="3128">
    <literal><![CDATA[
      K((x * y) / x,z) * (x * y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),2914(a,2,2,1))].">
      <j1 rule="para" parents="9 2914"/>
    </justification>
  </clause>

  <clause id="3129">
    <literal><![CDATA[
      K((x * (y * z)) / (x * z),u) * (x * (y * z)) = (x * z) * T(L(T(y,z),z,x),u)
    ]]></literal>
    <justification jstring="[para(247(a,1),2914(a,2,2,1))].">
      <j1 rule="para" parents="247 2914"/>
    </justification>
  </clause>

  <clause id="3130">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (K(u,w) * v5) = (a(x,y,z) \ K(w,u)) \ v5
    ]]></literal>
    <justification jstring="[para(2466(a,1),3009(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2466 3009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3131">
    <literal><![CDATA[
      (x * y) / (((z * x) / z) * y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(136,a,161,a(flip),b,3010,a(flip))].">
      <j1 rule="hyper" parents="136 161 3010"/>
    </justification>
  </clause>

  <clause id="3132">
    <literal><![CDATA[
      a(x,y,z) \ ((x * y) * z) = T(x,y) * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2315,a,b,3019,a)].">
      <j1 rule="hyper" parents="316 2315 3019"/>
    </justification>
  </clause>

  <clause id="3133">
    <literal><![CDATA[
      x * (y * (K(x,y) * z)) = T(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(3005(a,1),3019(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3005 3019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3135">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) * y) = y * (K(x,y) * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,2293,a,b,3044,a)].">
      <j1 rule="hyper" parents="63 2293 3044"/>
    </justification>
  </clause>

  <clause id="3136">
    <literal><![CDATA[
      (K(x,y) * (z * y)) \ (K(x,y) * (y * z)) = K(y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(3044(a,2),650(a,1,2))].">
      <j1 rule="para" parents="3044 650"/>
    </justification>
  </clause>

  <clause id="3137">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ 1)) * (y \ T(z,x)) = y \ z
    ]]></literal>
    <justification jstring="[para(848(a,1),3046(a,1,2))].">
      <j1 rule="para" parents="848 3046"/>
    </justification>
  </clause>

  <clause id="3138">
    <literal><![CDATA[
      x \ (y \ T(x,y \ 1)) = (y \ x) / x
    ]]></literal>
    <justification jstring="[hyper(517,a,3052,a)].">
      <j1 rule="hyper" parents="517 3052"/>
    </justification>
  </clause>

  <clause id="3139">
    <literal><![CDATA[
      x * R(1 / y,y,y \ x) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(370(a,2),3052(a,2,2)),flip(a)].">
      <j1 rule="para" parents="370 3052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3141">
    <literal><![CDATA[
      (x * ((y * z) / y)) / K(y,z) = x * z
    ]]></literal>
    <justification jstring="[para(11(a,1),3057(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 3057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3142">
    <literal><![CDATA[
      ((x * y) / x) \ z = K(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(3006,a,3071,a),flip(a)].">
      <j1 rule="hyper" parents="3006 3071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3143">
    <literal><![CDATA[
      K(x,x \ y) * ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),3071(a,1,2,1,1))].">
      <j1 rule="para" parents="10 3071"/>
    </justification>
  </clause>

  <clause id="3144">
    <literal><![CDATA[
      (x / (x / y)) * z = y * (K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(3090(a,2),3075(a,1,1))].">
      <j1 rule="para" parents="3090 3075"/>
    </justification>
  </clause>

  <clause id="3145">
    <literal><![CDATA[
      a(x * T(y,z),u,w) = a(x * y,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,2771,a,b,3116,a),flip(a)].">
      <j1 rule="hyper" parents="316 2771 3116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3146">
    <literal><![CDATA[
      a(x * ((y \ z) \ z),u,w) = a(y * x,u,w)
    ]]></literal>
    <justification jstring="[para(115(a,1),3116(a,1,1,2))].">
      <j1 rule="para" parents="115 3116"/>
    </justification>
  </clause>

  <clause id="3147">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,y) = x \ 1
    ]]></literal>
    <justification jstring="[para(2806(a,2),3125(a,1,2))].">
      <j1 rule="para" parents="2806 3125"/>
    </justification>
  </clause>

  <clause id="3148">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * ((z * y) / z)
    ]]></literal>
    <justification jstring="[hyper(151,a,3141,a)].">
      <j1 rule="hyper" parents="151 3141"/>
    </justification>
  </clause>

  <clause id="3149">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),3142(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3150">
    <literal><![CDATA[
      a(x * (y / z),u,w) = a(x * (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(116(a,1),3145(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="116 3145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3151">
    <literal><![CDATA[
      (x * (y \ z)) * K(y,y \ z) = x * (z / y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3148(a,2,2,1))].">
      <j1 rule="para" parents="10 3148"/>
    </justification>
  </clause>

  <clause id="3152">
    <literal><![CDATA[
      R(x * K(y * (z \ 1),x),y * (z \ 1),y * z) = ((y * (z \ 1)) * x) * ((y * (z \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1711,a(flip),b,2748,a)].">
      <j1 rule="hyper" parents="63 1711 2748"/>
    </justification>
  </clause>

  <clause id="3153">
    <literal><![CDATA[
      L(x * K(y,x),x,y) = (y / (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(136,a,1445,a(flip),b,2737,a),flip(a)].">
      <j1 rule="hyper" parents="136 1445 2737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3155">
    <literal><![CDATA[
      x * L(x \ K(y,x),x,y) = x \ ((y / (x \ 1)) / y)
    ]]></literal>
    <justification jstring="[hyper(133,a,3153,a(flip),b,1356,a),flip(a)].">
      <j1 rule="hyper" parents="133 3153 1356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3156">
    <literal><![CDATA[
      L(K(x,y) * y,y,x) = (x / (y \ 1)) / x
    ]]></literal>
    <justification jstring="[para(1974(a,2),3153(a,1,1))].">
      <j1 rule="para" parents="1974 3153"/>
    </justification>
  </clause>

  <clause id="3157">
    <literal><![CDATA[
      ((1 / x) * y) / (1 / x) = ((x \ 1) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,2722,a,b,2740,a)].">
      <j1 rule="hyper" parents="316 2722 2740"/>
    </justification>
  </clause>

  <clause id="3158">
    <literal><![CDATA[
      (x * y) \ (R(x,z,u) * y) = (y * x) \ (y * R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,2757,a(flip),b,2758,a),flip(a)].">
      <j1 rule="hyper" parents="133 2757 2758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3159">
    <literal><![CDATA[
      K(x * y,z) * ((z * x) * y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[para(109(a,1),2757(a,1,2))].">
      <j1 rule="para" parents="109 2757"/>
    </justification>
  </clause>

  <clause id="3160">
    <literal><![CDATA[
      L(x,y,(z * z) * (u * w)) = L(x,y,w * (u * (z * z)))
    ]]></literal>
    <justification jstring="[para(32(a,1),2770(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32 2770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3162">
    <literal><![CDATA[
      T(x,y / x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(253,a,2992,a(flip),b,2773,a)].">
      <j1 rule="hyper" parents="253 2992 2773"/>
    </justification>
  </clause>

  <clause id="3164">
    <literal><![CDATA[
      (x / y) \ R(T(y,y \ x),z,u) = (y \ x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,2812,a(flip),b,2773,a)].">
      <j1 rule="hyper" parents="133 2812 2773"/>
    </justification>
  </clause>

  <clause id="3165">
    <literal><![CDATA[
      x / T(y * x,y \ 1) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(209,a,3049,a(flip),b,3162,a(flip))].">
      <j1 rule="hyper" parents="209 3049 3162"/>
    </justification>
  </clause>

  <clause id="3166">
    <literal><![CDATA[
      (x \ (y \ x)) * T(x,y \ 1) = y \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,3050,a(flip),b,3162,a(flip))].">
      <j1 rule="hyper" parents="139 3050 3162"/>
    </justification>
  </clause>

  <clause id="3167">
    <literal><![CDATA[
      T(x,y) = (x \ (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),3162(a,1,2))].">
      <j1 rule="para" parents="11 3162"/>
    </justification>
  </clause>

  <clause id="3168">
    <literal><![CDATA[
      T(x \ y,x) = ((x \ y) \ y) \ y
    ]]></literal>
    <justification jstring="[para(80(a,1),3162(a,1,2))].">
      <j1 rule="para" parents="80 3162"/>
    </justification>
  </clause>

  <clause id="3169">
    <literal><![CDATA[
      (x / y) * L((y \ x) \ x,z,u) = L(y,z,u) * (x / y)
    ]]></literal>
    <justification jstring="[para(3162(a,1),251(a,1,2,1))].">
      <j1 rule="para" parents="3162 251"/>
    </justification>
  </clause>

  <clause id="3170">
    <literal><![CDATA[
      T(x * y,T(y,x)) = T(x * y,y)
    ]]></literal>
    <justification jstring="[para(3167(a,2),2984(a,1,2))].">
      <j1 rule="para" parents="3167 2984"/>
    </justification>
  </clause>

  <clause id="3171">
    <literal><![CDATA[
      T((x / y) \ x,x / y) = (y \ x) \ x
    ]]></literal>
    <justification jstring="[para(83(a,1),3168(a,2,1,1))].">
      <j1 rule="para" parents="83 3168"/>
    </justification>
  </clause>

  <clause id="3172">
    <literal><![CDATA[
      T((x \ y) \ y,x \ y) = T(x \ y,x) \ y
    ]]></literal>
    <justification jstring="[para(3168(a,2),3168(a,2,1))].">
      <j1 rule="para" parents="3168 3168"/>
    </justification>
  </clause>

  <clause id="3173">
    <literal><![CDATA[
      T(x,y) * L(T(y * x,x),z,u) = L(y * x,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3170(a,1),251(a,1,2,1))].">
      <j1 rule="para" parents="3170 251"/>
    </justification>
  </clause>

  <clause id="3175">
    <literal><![CDATA[
      T(x,x \ y) * ((x \ y) * z) = x * ((y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,2774,a(flip),b,2897,a),flip(a)].">
      <j1 rule="hyper" parents="139 2774 2897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3176">
    <literal><![CDATA[
      ((x \ y) * z) \ (K(x \ y,x) * u) = ((y / x) * z) \ u
    ]]></literal>
    <justification jstring="[para(2774(a,1),3009(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2774 3009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      (x / y) \ ((x / y) / z) = (y \ x) \ ((y \ x) / z)
    ]]></literal>
    <justification jstring="[hyper(133,a,2776,a(flip),b,2773,a)].">
      <j1 rule="hyper" parents="133 2776 2773"/>
    </justification>
  </clause>

  <clause id="3179">
    <literal><![CDATA[
      L(x,y,(z / u) / w) = L(x,y,(u \ z) / w)
    ]]></literal>
    <justification jstring="[para(2776(a,1),1575(a,1,3))].">
      <j1 rule="para" parents="2776 1575"/>
    </justification>
  </clause>

  <clause id="3180">
    <literal><![CDATA[
      K(x \ y,x) * ((y / z) * u) = (((x \ y) * x) / z) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,2780,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 2780 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3181">
    <literal><![CDATA[
      (T(x,y) * z) * T(u,x * z) = K(x,y) * (u * (x * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,238,a(flip),b,2811,a),flip(a)].">
      <j1 rule="hyper" parents="63 238 2811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3182">
    <literal><![CDATA[
      T(x,y) * ((x * z) * u) = x * ((T(x,y) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,2811,a(flip),b,2897,a),flip(a)].">
      <j1 rule="hyper" parents="139 2811 2897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3183">
    <literal><![CDATA[
      ((T(x,y) * z) * u) \ (K(x,y) * w) = ((x * z) * u) \ w
    ]]></literal>
    <justification jstring="[para(2811(a,1),477(a,1,1))].">
      <j1 rule="para" parents="2811 477"/>
    </justification>
  </clause>

  <clause id="3184">
    <literal><![CDATA[
      T(x,T(y * (z \ 1),y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2850,a(flip),b,2846,a),flip(a)].">
      <j1 rule="hyper" parents="316 2850 2846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3186">
    <literal><![CDATA[
      T(x,R(y,z,u) * (y \ (w \ y))) = T(x,T(R(y,z,u) / w,y))
    ]]></literal>
    <justification jstring="[para(1167(a,1),2849(a,1,2))].">
      <j1 rule="para" parents="1167 2849"/>
    </justification>
  </clause>

  <clause id="3187">
    <literal><![CDATA[
      (T(x,y) * z) \ ((T(x,y) * u) * w) = (x * z) \ ((x * u) * w)
    ]]></literal>
    <justification jstring="[para(2811(a,1),2870(a,1,2))].">
      <j1 rule="para" parents="2811 2870"/>
    </justification>
  </clause>

  <clause id="3188">
    <literal><![CDATA[
      (x * y) \ ((T(x,y) * z) / u) = (y * x) \ ((x * z) / u)
    ]]></literal>
    <justification jstring="[hyper(133,a,2871,a(flip),b,2758,a)].">
      <j1 rule="hyper" parents="133 2871 2758"/>
    </justification>
  </clause>

  <clause id="3189">
    <literal><![CDATA[
      K(x,y) * (x \ ((x / z) * u)) = x \ ((T(x,y) / z) * u)
    ]]></literal>
    <justification jstring="[para(2878(a,1),2909(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2878 2909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3190">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(2814(a,1),2881(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2814 2881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3191">
    <literal><![CDATA[
      K(T(x \ 1,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(2613(a,1),3190(a,2,1))].">
      <j1 rule="para" parents="2613 3190"/>
    </justification>
  </clause>

  <clause id="3192">
    <literal><![CDATA[
      K((x / y) \ 1,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,2914,a,b,2884,a),flip(a)].">
      <j1 rule="hyper" parents="35 2914 2884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3195">
    <literal><![CDATA[
      K(x / (y * x),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),3192(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 3192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3196">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(3195(a,1),3088(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3195 3088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3197">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) \ y = (((x / y) \ z) \ z) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,83,a(flip),b,2905,a)].">
      <j1 rule="hyper" parents="133 83 2905"/>
    </justification>
  </clause>

  <clause id="3198">
    <literal><![CDATA[
      (x * (y / x)) \ (y / x) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(116(a,1),2919(a,2,2))].">
      <j1 rule="para" parents="116 2919"/>
    </justification>
  </clause>

  <clause id="3200">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) * x) * z) = (y / x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,2779,a(flip),b,3030,a)].">
      <j1 rule="hyper" parents="133 2779 3030"/>
    </justification>
  </clause>

  <clause id="3202">
    <literal><![CDATA[
      (x / y) * (K(y \ x,y) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[hyper(34,a,2911,a,b,3031,a),flip(a)].">
      <j1 rule="hyper" parents="34 2911 3031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3203">
    <literal><![CDATA[
      x \ ((y \ z) \ (K(y \ z,y) * u)) = x \ ((z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,3032,a,b,10,a)].">
      <j1 rule="hyper" parents="133 3032 10"/>
    </justification>
  </clause>

  <clause id="3204">
    <literal><![CDATA[
      ((x \ y) * x) \ (y / z) = y \ ((x * (y / x)) / z)
    ]]></literal>
    <justification jstring="[para(3036(a,1),2785(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3036 2785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3205">
    <literal><![CDATA[
      L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2163,a(flip),b,3055,a)].">
      <j1 rule="hyper" parents="63 2163 3055"/>
    </justification>
  </clause>

  <clause id="3207">
    <literal><![CDATA[
      a((x * y) * z,u,w) = a(z * (y * x),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,2771,a,b,3066,a),flip(a)].">
      <j1 rule="hyper" parents="316 2771 3066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3208">
    <literal><![CDATA[
      L(x,y,(z * u) / w) = L(x,y,w \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,1586,a(flip),b,3070,a),flip(a)].">
      <j1 rule="hyper" parents="316 1586 3070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3209">
    <literal><![CDATA[
      L(x,y,(z * u) / (z * z)) = L(x,y,u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(562(a,1),3070(a,1,3)),flip(a)].">
      <j1 rule="para" parents="562 3070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3210">
    <literal><![CDATA[
      (x * (R(x,y,z) \ u)) * R(x,y,z) = u * x
    ]]></literal>
    <justification jstring="[hyper(138,a,3110,a(flip),b,1551,a)].">
      <j1 rule="hyper" parents="138 3110 1551"/>
    </justification>
  </clause>

  <clause id="3212">
    <literal><![CDATA[
      x \ (R(y,z,u) * (y \ w)) = x \ ((w / y) * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,3111,a,b,10,a)].">
      <j1 rule="hyper" parents="133 3111 10"/>
    </justification>
  </clause>

  <clause id="3213">
    <literal><![CDATA[
      x * ((y / x) * R(x,z,u)) = R(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,3111,a(flip),b,1167,a)].">
      <j1 rule="hyper" parents="139 3111 1167"/>
    </justification>
  </clause>

  <clause id="3214">
    <literal><![CDATA[
      a(((x \ 1) \ y) * x,z,u) = a(y * (x * x),z,u)
    ]]></literal>
    <justification jstring="[para(576(a,1),3117(a,1,1)),flip(a)].">
      <j1 rule="para" parents="576 3117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3215">
    <literal><![CDATA[
      (x / y) \ (y \ (x / y)) = (y \ x) \ (y \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(133,a,3123,a(flip),b,2773,a)].">
      <j1 rule="hyper" parents="133 3123 2773"/>
    </justification>
  </clause>

  <clause id="3216">
    <literal><![CDATA[
      K(x,x \ y) * (((y / x) \ z) * u) = ((x \ y) \ z) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,3143,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 3143 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3217">
    <literal><![CDATA[
      ((x \ y) \ z) \ (K(x,x \ y) * u) = ((y / x) \ z) \ u
    ]]></literal>
    <justification jstring="[para(3143(a,1),477(a,1,1))].">
      <j1 rule="para" parents="3143 477"/>
    </justification>
  </clause>

  <clause id="3218">
    <literal><![CDATA[
      L(x,y,(z / u) \ w) = L(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(3143(a,1),1575(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3143 1575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3219">
    <literal><![CDATA[
      L(x,y,z * ((u / w) \ v5)) = L(x,y,z * ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(3143(a,1),1684(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3143 1684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3221">
    <literal><![CDATA[
      (x / (x / y)) * x = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(2727(a,1),3144(a,2,2))].">
      <j1 rule="para" parents="2727 3144"/>
    </justification>
  </clause>

  <clause id="3223">
    <literal><![CDATA[
      T(x / (x / y),x) = L(y,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(253,a,3221,a,b,405,a)].">
      <j1 rule="hyper" parents="253 3221 405"/>
    </justification>
  </clause>

  <clause id="3224">
    <literal><![CDATA[
      K(x \ y,x) * ((((x \ y) \ z) * u) * w) = (((y / x) \ z) * u) * w
    ]]></literal>
    <justification jstring="[para(3149(a,1),656(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3149 656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3225">
    <literal><![CDATA[
      a((x * x) \ (y * z),u,w) = a(y * ((x * x) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1821,a,b,3150,a)].">
      <j1 rule="hyper" parents="63 1821 3150"/>
    </justification>
  </clause>

  <clause id="3226">
    <literal><![CDATA[
      a(((x / y) \ z) * (y \ x),u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2783,a(flip),b,3150,a),flip(a)].">
      <j1 rule="hyper" parents="63 2783 3150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3227">
    <literal><![CDATA[
      (x / (y \ z)) * (z / y) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(630,a,3151,a),flip(a)].">
      <j1 rule="hyper" parents="630 3151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3229">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(x,x \ 1) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(969(a,1),3151(a,1,1))].">
      <j1 rule="para" parents="969 3151"/>
    </justification>
  </clause>

  <clause id="3231">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) * (w / ((x \ y) \ w)) = (x \ y) * L(T(x \ y,x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(3172(a,1),597(a,2,2,1))].">
      <j1 rule="para" parents="3172 597"/>
    </justification>
  </clause>

  <clause id="3232">
    <literal><![CDATA[
      L(x,y,(z \ u) / w) = L(x,y,w \ (u / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1586,a(flip),b,3179,a),flip(a)].">
      <j1 rule="hyper" parents="63 1586 3179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3233">
    <literal><![CDATA[
      a((x * x) * (y * z),u,w) = a(z * (y * (x * x)),u,w)
    ]]></literal>
    <justification jstring="[para(32(a,1),3207(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32 3207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3234">
    <literal><![CDATA[
      a(((x \ 1) * (y / x)) * z,u,w) = a(z * (y / (x * x)),u,w)
    ]]></literal>
    <justification jstring="[para(566(a,1),3207(a,2,1,2))].">
      <j1 rule="para" parents="566 3207"/>
    </justification>
  </clause>

  <clause id="3235">
    <literal><![CDATA[
      L(x,y,z \ (u * w)) = L(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1586,a(flip),b,3208,a)].">
      <j1 rule="hyper" parents="63 1586 3208"/>
    </justification>
  </clause>

  <clause id="3236">
    <literal><![CDATA[
      L(x,y,(z * u) \ (u * (w * z))) = L(x,y,R(w,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),3208(a,1,3)),flip(a)].">
      <j1 rule="para" parents="20 3208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3237">
    <literal><![CDATA[
      T(x * (R(x,y,z) \ u),x) = R(x,y,z) \ (u * x)
    ]]></literal>
    <justification jstring="[hyper(133,a,3210,a(flip),b,2842,a),flip(a)].">
      <j1 rule="hyper" parents="133 3210 2842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3238">
    <literal><![CDATA[
      (R(x,y,z) \ u) * R(x,y,z) = (x \ u) * x
    ]]></literal>
    <justification jstring="[para(1170(a,1),3210(a,1,1))].">
      <j1 rule="para" parents="1170 3210"/>
    </justification>
  </clause>

  <clause id="3239">
    <literal><![CDATA[
      L(x,y,z / (u / w)) = L(x,y,(w \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1586,a,b,3218,a)].">
      <j1 rule="hyper" parents="63 1586 3218"/>
    </justification>
  </clause>

  <clause id="3240">
    <literal><![CDATA[
      a((x * y) * (x \ 1),z,u) = a(L(y,x,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(886(a,1),3226(a,1,1,1))].">
      <j1 rule="para" parents="886 3226"/>
    </justification>
  </clause>

  <clause id="3241">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) / (1 / x) = (x \ y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(136,a,2236,a(flip),b,3227,a)].">
      <j1 rule="hyper" parents="136 2236 3227"/>
    </justification>
  </clause>

  <clause id="3242">
    <literal><![CDATA[
      (x * (y / z)) / (z \ y) = x * K(z,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1347,a,b,3227,a)].">
      <j1 rule="hyper" parents="63 1347 3227"/>
    </justification>
  </clause>

  <clause id="3243">
    <literal><![CDATA[
      L(x,y,z \ (u / w)) = L(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1586,a(flip),b,3232,a),flip(a)].">
      <j1 rule="hyper" parents="63 1586 3232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3244">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((u * w) * z)) = L(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[para(18(a,2),3235(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18 3235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3245">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((w * u) * z)) = L(x,y,L(T(w,u),u,z))
    ]]></literal>
    <justification jstring="[para(247(a,1),3235(a,1,3)),flip(a)].">
      <j1 rule="para" parents="247 3235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3246">
    <literal><![CDATA[
      ((x * (y \ 1)) \ z) * R(x / y,y,y) = ((x / y) \ z) * (x / y)
    ]]></literal>
    <justification jstring="[para(563(a,1),3238(a,1,1,1))].">
      <j1 rule="para" parents="563 3238"/>
    </justification>
  </clause>

  <clause id="3247">
    <literal><![CDATA[
      L(R(x,y,z) \ u,R(x,y,z),R(x,y,z) \ 1) * R(x,y,z) = R(x,y,z) * ((1 / R(x,y,z)) * ((x \ u) * x))
    ]]></literal>
    <justification jstring="[para(3238(a,1),895(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3238 895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3248">
    <literal><![CDATA[
      (x \ (x \ R(x,y,z))) * x = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(979(a,1),3238(a,1,1)),flip(a)].">
      <j1 rule="para" parents="979 3238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3249">
    <literal><![CDATA[
      (x / (y / z)) * K(z,z \ y) = x / (z \ y)
    ]]></literal>
    <justification jstring="[hyper(376,a,3242,a),flip(a)].">
      <j1 rule="hyper" parents="376 3242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3250">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(138,a,2235,a(flip),b,3242,a),flip(a)].">
      <j1 rule="hyper" parents="138 2235 3242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3251">
    <literal><![CDATA[
      (x / y) * L(z,u,u \ (y \ x)) = ((x / y) / u) * (u * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,3243,a(flip),b,1598,a)].">
      <j1 rule="hyper" parents="139 3243 1598"/>
    </justification>
  </clause>

  <clause id="3252">
    <literal><![CDATA[
      L(x,y,z \ (u / (w * (v5 * v5)))) = L(x,y,z \ (w \ (u / (v5 * v5))))
    ]]></literal>
    <justification jstring="[para(393(a,1),3243(a,1,3,2))].">
      <j1 rule="para" parents="393 3243"/>
    </justification>
  </clause>

  <clause id="3253">
    <literal><![CDATA[
      L(x,y,z \ ((u \ 1) \ (w * (v5 * (u \ 1))))) = L(x,y,z \ ((w * (v5 * u)) / u))
    ]]></literal>
    <justification jstring="[para(964(a,1),3243(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="964 3243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3254">
    <literal><![CDATA[
      L(x,y,L(z,z,u)) = L(x,y,u \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(1447(a,2),3243(a,1,3))].">
      <j1 rule="para" parents="1447 3243"/>
    </justification>
  </clause>

  <clause id="3256">
    <literal><![CDATA[
      a(R(x * K(y,x),y,z) * u,w,v5) = a(((y * z) \ ((y * x) * z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(2746(a,2),3117(a,1,1,1))].">
      <j1 rule="para" parents="2746 3117"/>
    </justification>
  </clause>

  <clause id="3257">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,27,a,b,2792,a),flip(a)].">
      <j1 rule="hyper" parents="316 27 2792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3258">
    <literal><![CDATA[
      (x * y) / T(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(209,a,2076,a(flip),b,2945,a(flip))].">
      <j1 rule="hyper" parents="209 2076 2945"/>
    </justification>
  </clause>

  <clause id="3259">
    <literal><![CDATA[
      (x / y) * K(z,y) = x / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(376,a,3258,a),flip(a)].">
      <j1 rule="hyper" parents="376 3258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3260">
    <literal><![CDATA[
      (x / T(y,z)) * y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1319,a(flip),b,3258,a)].">
      <j1 rule="hyper" parents="63 1319 3258"/>
    </justification>
  </clause>

  <clause id="3262">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,x \ y)) = y / T(T(x,x \ y),z)
    ]]></literal>
    <justification jstring="[para(236(a,1),3258(a,1,1)),flip(a)].">
      <j1 rule="para" parents="236 3258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3263">
    <literal><![CDATA[
      (K(x,y) / x) * K(y,x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(316,a,2816,a(flip),b,3259,a),flip(a)].">
      <j1 rule="hyper" parents="316 2816 3259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3265">
    <literal><![CDATA[
      x * (K(y,x) * K(z,y)) = (y * x) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2796,a(flip),b,3259,a)].">
      <j1 rule="hyper" parents="63 2796 3259"/>
    </justification>
  </clause>

  <clause id="3266">
    <literal><![CDATA[
      x / ((y \ z) \ z) = (x / y) * K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(115(a,1),3259(a,2,2)),flip(a)].">
      <j1 rule="para" parents="115 3259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3268">
    <literal><![CDATA[
      (x * T(y,z)) * K(z,y) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),3260(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 3260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3269">
    <literal><![CDATA[
      ((x / y) * K(z,y)) * y = x * K(z,y)
    ]]></literal>
    <justification jstring="[para(3259(a,2),3260(a,1,1))].">
      <j1 rule="para" parents="3259 3260"/>
    </justification>
  </clause>

  <clause id="3271">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(133,a,10,a(flip),b,3268,a)].">
      <j1 rule="hyper" parents="133 10 3268"/>
    </justification>
  </clause>

  <clause id="3272">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) * K(y \ z,y) = x * y
    ]]></literal>
    <justification jstring="[para(115(a,1),3268(a,1,1,2))].">
      <j1 rule="para" parents="115 3268"/>
    </justification>
  </clause>

  <clause id="3274">
    <literal><![CDATA[
      (x \ (y \ x)) * x = (y \ x) * K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(3166(a,1),3268(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3166 3268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3275">
    <literal><![CDATA[
      (L(1 / x,x,y) * K(z,x)) * x = (x * ((y * x) \ y)) * K(z,x)
    ]]></literal>
    <justification jstring="[para(746(a,1),3269(a,1,1,1))].">
      <j1 rule="para" parents="746 3269"/>
    </justification>
  </clause>

  <clause id="3276">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(781(a,1),3271(a,1,1))].">
      <j1 rule="para" parents="781 3271"/>
    </justification>
  </clause>

  <clause id="3277">
    <literal><![CDATA[
      x * (K(y,x) * K(y * x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[hyper(316,a,2933,a,b,3265,a),flip(a)].">
      <j1 rule="hyper" parents="316 2933 3265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3278">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x,y) = (y \ ((x \ 1) \ y)) * y
    ]]></literal>
    <justification jstring="[para(2613(a,1),3274(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2613 3274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3279">
    <literal><![CDATA[
      R(T(x,y),z,u) * K(y,x) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,1935,a(flip),b,2964,a)].">
      <j1 rule="hyper" parents="139 1935 2964"/>
    </justification>
  </clause>

  <clause id="3280">
    <literal><![CDATA[
      T(x,y) * K(x * y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(1632(a,1),3279(a,1,1))].">
      <j1 rule="para" parents="1632 3279"/>
    </justification>
  </clause>

  <clause id="3281">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,3280,a(flip),b,2867,a),flip(a)].">
      <j1 rule="hyper" parents="133 3280 2867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3282">
    <literal><![CDATA[
      x * (K(y,x) * (y * z)) = (y * x) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3044,a(flip),b,3062,a)].">
      <j1 rule="hyper" parents="63 3044 3062"/>
    </justification>
  </clause>

  <clause id="3285">
    <literal><![CDATA[
      (x * y) * L(z,x,y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(2800(a,1),3282(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2800 3282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3286">
    <literal><![CDATA[
      L(x,y,z) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[hyper(144,a,3285,a),flip(a)].">
      <j1 rule="hyper" parents="144 3285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3288">
    <literal><![CDATA[
      L(T(x,y) \ z,x,y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,160,a(flip),b,3285,a),flip(a)].">
      <j1 rule="hyper" parents="133 160 3285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3289">
    <literal><![CDATA[
      (x * y) * L(L(z,x,y),u,w) = y * (T(x,y) * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,159,a,b,3285,a)].">
      <j1 rule="hyper" parents="63 159 3285"/>
    </justification>
  </clause>

  <clause id="3290">
    <literal><![CDATA[
      x * (y * L(y \ (x \ z),x,y)) = y * (T(x,y) * ((x * y) \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,879,a(flip),b,3285,a)].">
      <j1 rule="hyper" parents="63 879 3285"/>
    </justification>
  </clause>

  <clause id="3291">
    <literal><![CDATA[
      x * (T(y,x) * L(z,x,y)) = y * (x * L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,403,a(flip),b,3285,a),flip(a)].">
      <j1 rule="hyper" parents="63 403 3285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3292">
    <literal><![CDATA[
      x * (T(y,x) * T(z,y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,251,a(flip),b,3285,a),flip(a)].">
      <j1 rule="hyper" parents="63 251 3285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3293">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,450,a,b,3285,a)].">
      <j1 rule="hyper" parents="34 450 3285"/>
    </justification>
  </clause>

  <clause id="3294">
    <literal><![CDATA[
      ((x * y) / z) * L(z,x,y) = (y * (T(x,y) * z)) / z
    ]]></literal>
    <justification jstring="[hyper(136,a,3285,a(flip),b,1436,a),flip(a)].">
      <j1 rule="hyper" parents="136 3285 1436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3295">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * (T(y,z) * u))) = L(L(u,y,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(3285(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3285 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3296">
    <literal><![CDATA[
      L(x,y / z,z) = L(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(116(a,1),3293(a,1,2)),flip(a)].">
      <j1 rule="para" parents="116 3293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3298">
    <literal><![CDATA[
      (L(x,y,z) * (y * z)) \ (x * (y * z)) = a(z,T(y,z),T(x,y * z))
    ]]></literal>
    <justification jstring="[para(3293(a,1),1880(a,1,1,1))].">
      <j1 rule="para" parents="3293 1880"/>
    </justification>
  </clause>

  <clause id="3299">
    <literal><![CDATA[
      (x * y) \ (y * (x * z)) = L(K(y,x) * z,x,y)
    ]]></literal>
    <justification jstring="[para(3005(a,1),3286(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3005 3286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3300">
    <literal><![CDATA[
      ((x * y) \ y) * (x * x) = L(K(y,x) * x,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,388,a(flip),b,3299,a)].">
      <j1 rule="hyper" parents="63 388 3299"/>
    </justification>
  </clause>

  <clause id="3301">
    <literal><![CDATA[
      (x * L(a(y,z,u),w,v5)) \ ((x * v6) * L(a(y,z,u),w,v5)) = L(K(L(a(y,z,u),w,v5),x) * v6,x,L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(2304(a,1),3299(a,1,2))].">
      <j1 rule="para" parents="2304 3299"/>
    </justification>
  </clause>

  <clause id="3302">
    <literal><![CDATA[
      ((x * y) \ y) * (x * x) = (y / (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(316,a,3156,a(flip),b,3300,a),flip(a)].">
      <j1 rule="hyper" parents="316 3156 3300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3303">
    <literal><![CDATA[
      ((x / (y \ 1)) / x) * a((y * x) \ x,y,y) = (((y * x) \ x) * y) * y
    ]]></literal>
    <justification jstring="[hyper(138,a,3302,a(flip),b,200,a)].">
      <j1 rule="hyper" parents="138 3302 200"/>
    </justification>
  </clause>

  <clause id="3304">
    <literal><![CDATA[
      R(x,y,(z / (u \ 1)) / z) = R(x,y,(u * z) \ z)
    ]]></literal>
    <justification jstring="[para(3302(a,1),1701(a,1,3))].">
      <j1 rule="para" parents="3302 1701"/>
    </justification>
  </clause>

  <clause id="3305">
    <literal><![CDATA[
      R(x,y,z * ((u / (w \ 1)) / u)) = R(x,y,z * ((w * u) \ u))
    ]]></literal>
    <justification jstring="[para(3302(a,1),1703(a,1,3,2))].">
      <j1 rule="para" parents="3302 1703"/>
    </justification>
  </clause>

  <clause id="3306">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) = y * ((x \ (y \ z)) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1261,a,b,2714,a)].">
      <j1 rule="hyper" parents="63 1261 2714"/>
    </justification>
  </clause>

  <clause id="3307">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = y * (x \ T(x * (y \ z),y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1263,a(flip),b,2714,a),flip(a)].">
      <j1 rule="hyper" parents="63 1263 2714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3308">
    <literal><![CDATA[
      R(x \ y,z,u) \ ((x \ y) * x) = R(y / x,z,u) \ y
    ]]></literal>
    <justification jstring="[para(2778(a,1),2784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2778 2784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3310">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2814(a,1),2880(a,1,1))].">
      <j1 rule="para" parents="2814 2880"/>
    </justification>
  </clause>

  <clause id="3312">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(2613(a,1),3310(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2613 3310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3313">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,z) = x * T(x \ (x / (y \ 1)),z)
    ]]></literal>
    <justification jstring="[para(2613(a,1),2883(a,1,2))].">
      <j1 rule="para" parents="2613 2883"/>
    </justification>
  </clause>

  <clause id="3314">
    <literal><![CDATA[
      K(((x * y) / x) \ 1,z) = (x * K(y \ 1,z)) / x
    ]]></literal>
    <justification jstring="[hyper(136,a,2885,a(flip),b,2884,a),flip(a)].">
      <j1 rule="hyper" parents="136 2885 2884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3315">
    <literal><![CDATA[
      (x * y) * (y * T(y \ 1,z)) = (x * K(y \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(2885(a,1),1403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2885 1403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3316">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ z,u,w) = x * R(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(2859(a,1),2916(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2859 2916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3317">
    <literal><![CDATA[
      (((x \ y) * x) * (x \ 1)) \ ((((x \ y) * x) * (x \ 1)) / z) = T((x \ 1) * y,x) \ (((x \ 1) * ((x \ y) * x)) / z)
    ]]></literal>
    <justification jstring="[para(1386(a,1),3069(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1386 3069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3318">
    <literal><![CDATA[
      (R(x,y,z) * u) \ R(T(x,(u / x) * R(x,y,z)),w,v5) = (((u / x) * R(x,y,z)) * x) \ R(x,w,v5)
    ]]></literal>
    <justification jstring="[para(3213(a,1),3105(a,1,1))].">
      <j1 rule="para" parents="3213 3105"/>
    </justification>
  </clause>

  <clause id="3319">
    <literal><![CDATA[
      L(x,y,z \ T(u,w)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(3137(a,1),1575(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3137 1575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3320">
    <literal><![CDATA[
      a(x \ T(y,z),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[para(3137(a,1),1806(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3137 1806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3321">
    <literal><![CDATA[
      L(x,y,z \ L(T(u,w),v5,v6)) = L(x,y,z \ L(u,v5,v6))
    ]]></literal>
    <justification jstring="[para(25(a,2),3319(a,1,3,2))].">
      <j1 rule="para" parents="25 3319"/>
    </justification>
  </clause>

  <clause id="3322">
    <literal><![CDATA[
      a(x \ L(T(y,z),u,w),v5,v6) = a(x \ L(y,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(25(a,2),3320(a,1,1,2))].">
      <j1 rule="para" parents="25 3320"/>
    </justification>
  </clause>

  <clause id="3323">
    <literal><![CDATA[
      a(x \ (y / z),u,w) = a(x \ (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(116(a,1),3320(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="116 3320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3324">
    <literal><![CDATA[
      a((x * (y * y)) \ z,u,w) = a(x \ ((y * y) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1825,a,b,3323,a)].">
      <j1 rule="hyper" parents="63 1825 3323"/>
    </justification>
  </clause>

  <clause id="3325">
    <literal><![CDATA[
      a(L(x,x,y),z,u) = a(y \ ((x \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1824,a,b,3323,a)].">
      <j1 rule="hyper" parents="63 1824 3323"/>
    </justification>
  </clause>

  <clause id="3326">
    <literal><![CDATA[
      (((x / y) / z) * (z * y)) \ x = a(z \ (y \ x),z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1820,a,b,3323,a)].">
      <j1 rule="hyper" parents="63 1820 3323"/>
    </justification>
  </clause>

  <clause id="3327">
    <literal><![CDATA[
      a(x \ ((y * y) \ (z * u)),w,v5) = a(x \ (z * (u / (y * y))),w,v5)
    ]]></literal>
    <justification jstring="[para(683(a,1),3323(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="683 3323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3329">
    <literal><![CDATA[
      (x \ L(y,z,u)) \ (((x \ L(y,z,u)) * x) * (y * w)) = (L(y,z,u) / x) \ (y * (L(y,z,u) * w))
    ]]></literal>
    <justification jstring="[para(1124(a,1),3200(a,2,2))].">
      <j1 rule="para" parents="1124 3200"/>
    </justification>
  </clause>

  <clause id="3330">
    <literal><![CDATA[
      L(x,y,z * (u / (z * z))) = L(x,y,u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(683(a,1),3209(a,1,3))].">
      <j1 rule="para" parents="683 3209"/>
    </justification>
  </clause>

  <clause id="3331">
    <literal><![CDATA[
      T(x / (1 / (1 / y)),1 / (1 / y)) / (1 / y) = (y \ x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(116(a,2),3241(a,1,1))].">
      <j1 rule="para" parents="116 3241"/>
    </justification>
  </clause>

  <clause id="3332">
    <literal><![CDATA[
      a(x,y,z) * (u * L(w,a(x,y,z),u)) = u * (a(x,y,z) * L(w,u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(2273(a,1),3291(a,1,2,1))].">
      <j1 rule="para" parents="2273 3291"/>
    </justification>
  </clause>

  <clause id="3333">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / x = K((y / x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),3314(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3334">
    <literal><![CDATA[
      L(x,y,z * ((z * z) \ u)) = L(x,y,u * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,1682,a(flip),b,3330,a)].">
      <j1 rule="hyper" parents="63 1682 3330"/>
    </justification>
  </clause>

  <clause id="3335">
    <literal><![CDATA[
      L(x,y,z \ L(u,z,z)) = L(x,y,u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(1118(a,1),3334(a,1,3))].">
      <j1 rule="para" parents="1118 3334"/>
    </justification>
  </clause>

  <clause id="3336">
    <literal><![CDATA[
      L((1 / x) * K(y * (x \ 1),1 / x),x \ 1,y) = (y * (x \ (x \ 1))) / (y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(633(a,1),2749(a,2,1,2))].">
      <j1 rule="para" parents="633 2749"/>
    </justification>
  </clause>

  <clause id="3338">
    <literal><![CDATA[
      x \ ((y / (x \ 1)) / y) = x * ((y * x) \ T(y,x))
    ]]></literal>
    <justification jstring="[para(2823(a,1),3155(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2823 3155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3339">
    <literal><![CDATA[
      x \ ((y / (x \ 1)) / y) = x * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(2875(a,1),3338(a,2,2))].">
      <j1 rule="para" parents="2875 3338"/>
    </justification>
  </clause>

  <clause id="3340">
    <literal><![CDATA[
      x * (x * ((x * y) \ y)) = (y / (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(152,a,3339,a)].">
      <j1 rule="hyper" parents="152 3339"/>
    </justification>
  </clause>

  <clause id="3341">
    <literal><![CDATA[
      ((x \ 1) * ((1 / x) * (((1 / x) * y) \ y))) / (x \ 1) = ((y / ((1 / x) \ 1)) / y) / (1 / x)
    ]]></literal>
    <justification jstring="[para(3340(a,1),3157(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3340 3157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3343">
    <literal><![CDATA[
      a(R(x,y,y \ 1),z,u) = a(L(x,y,y \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1816,a(flip),b,3240,a)].">
      <j1 rule="hyper" parents="63 1816 3240"/>
    </justification>
  </clause>

  <clause id="3344">
    <literal><![CDATA[
      a(L(x,y,y \ 1),z,u) = a(R(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[para(573(a,1),3343(a,1,1)),flip(a)].">
      <j1 rule="para" parents="573 3343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3346">
    <literal><![CDATA[
      (((x / y) / (y \ 1)) * K(y \ 1,y)) \ x = a((y \ 1) \ (y \ x),y \ 1,y)
    ]]></literal>
    <justification jstring="[para(272(a,2),3326(a,1,1,2))].">
      <j1 rule="para" parents="272 3326"/>
    </justification>
  </clause>

  <clause id="3348">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) / y) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1212,a(flip),b,2772,a)].">
      <j1 rule="hyper" parents="63 1212 2772"/>
    </justification>
  </clause>

  <clause id="3349">
    <literal><![CDATA[
      R(1 / x,x,(x \ y) / y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,369,a,b,3348,a)].">
      <j1 rule="hyper" parents="39 369 3348"/>
    </justification>
  </clause>

  <clause id="3350">
    <literal><![CDATA[
      R(1 / x,x,y / (x * y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),3349(a,1,3,1))].">
      <j1 rule="para" parents="9 3349"/>
    </justification>
  </clause>

  <clause id="3351">
    <literal><![CDATA[
      (x \ 1) \ (y / (x * y)) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(3350(a,1),369(a,1,1))].">
      <j1 rule="para" parents="3350 369"/>
    </justification>
  </clause>

  <clause id="3352">
    <literal><![CDATA[
      (x / y) \ (((x / y) * z) * u) = (y \ x) \ (((y \ x) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(133,a,2777,a(flip),b,2773,a)].">
      <j1 rule="hyper" parents="133 2777 2773"/>
    </justification>
  </clause>

  <clause id="3353">
    <literal><![CDATA[
      L(x,y,(((z / u) * w) * v5) * v6) = L(x,y,(((u \ z) * w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(2777(a,1),1578(a,1,3,1))].">
      <j1 rule="para" parents="2777 1578"/>
    </justification>
  </clause>

  <clause id="3354">
    <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(80(a,1),2999(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="80 2999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3355">
    <literal><![CDATA[
      a((x \ (y * z)) \ (z * y),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,1806,a(flip),b,3067,a),flip(a)].">
      <j1 rule="hyper" parents="316 1806 3067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3357">
    <literal><![CDATA[
      a(x \ (y * z),u,w) = a(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3122,a(flip),b,3355,a)].">
      <j1 rule="hyper" parents="63 3122 3355"/>
    </justification>
  </clause>

  <clause id="3358">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,w) = a(R(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[para(199(a,1),3355(a,1,1,1))].">
      <j1 rule="para" parents="199 3355"/>
    </justification>
  </clause>

  <clause id="3359">
    <literal><![CDATA[
      a(x \ (L(y,z,u) * (u * z)),w,v5) = a(x \ (u * (z * y)),w,v5)
    ]]></literal>
    <justification jstring="[para(100(a,1),3357(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="100 3357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3360">
    <literal><![CDATA[
      a(x \ (L(y,z \ u,z) * u),w,v5) = a(x \ (z * ((z \ u) * y)),w,v5)
    ]]></literal>
    <justification jstring="[para(405(a,1),3357(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="405 3357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3361">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,u) = (x * u) \ (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(316,a,102,a,b,3158,a)].">
      <j1 rule="hyper" parents="316 102 3158"/>
    </justification>
  </clause>

  <clause id="3362">
    <literal><![CDATA[
      (x \ 1) \ R(x,y,z) = x * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1247,a(flip),b,3164,a),flip(a)].">
      <j1 rule="hyper" parents="63 1247 3164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3363">
    <literal><![CDATA[
      ((x / y) * z) \ (x / y) = ((y \ x) * z) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(2987(a,1),3176(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2987 3176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3364">
    <literal><![CDATA[
      ((x / y) / x) / (1 / y) = ((x / y) / x) * y
    ]]></literal>
    <justification jstring="[hyper(209,a,1762,a(flip),b,3363,a)].">
      <j1 rule="hyper" parents="209 1762 3363"/>
    </justification>
  </clause>

  <clause id="3365">
    <literal><![CDATA[
      (x * y) \ ((y * (T(x,y) * z)) / u) = (y * x) \ ((y * (x * z)) / u)
    ]]></literal>
    <justification jstring="[para(3019(a,1),3188(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3019 3188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3366">
    <literal><![CDATA[
      K(x \ 1,x) \ (x * y) = (((y / (x * y)) \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(1920(a,1),3197(a,1,1))].">
      <j1 rule="para" parents="1920 3197"/>
    </justification>
  </clause>

  <clause id="3367">
    <literal><![CDATA[
      x \ ((y \ 1) \ (((y \ 1) * y) * z)) = x \ ((1 / y) \ z)
    ]]></literal>
    <justification jstring="[para(272(a,1),3203(a,1,2,2,1))].">
      <j1 rule="para" parents="272 3203"/>
    </justification>
  </clause>

  <clause id="3368">
    <literal><![CDATA[
      x \ ((y \ z) \ (T(y,y \ z) \ u)) = x \ ((z / y) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(3002(a,1),3203(a,1,2,2))].">
      <j1 rule="para" parents="3002 3203"/>
    </justification>
  </clause>

  <clause id="3370">
    <literal><![CDATA[
      a(((T(x,y) \ 1) * (x \ K(y,x))) * (z * u),w,v5) = a(u * (z * ((T(x,y) \ 1) * (T(x,y) \ 1))),w,v5)
    ]]></literal>
    <justification jstring="[para(2985(a,1),3233(a,1,1,1))].">
      <j1 rule="para" parents="2985 3233"/>
    </justification>
  </clause>

  <clause id="3371">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = (x / (y \ 1)) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,114,a(flip),b,3313,a)].">
      <j1 rule="hyper" parents="316 114 3313"/>
    </justification>
  </clause>

  <clause id="3372">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(2814(a,1),3315(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2814 3315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3373">
    <literal><![CDATA[
      (x * K(y \ 1,z)) / y = (x / y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(136,a,157,a(flip),b,3372,a)].">
      <j1 rule="hyper" parents="136 157 3372"/>
    </justification>
  </clause>

  <clause id="3374">
    <literal><![CDATA[
      (x * K(y \ 1,z)) / (((y * x) * K(y \ 1,z)) / y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3373(a,2),3131(a,1,2))].">
      <j1 rule="para" parents="3373 3131"/>
    </justification>
  </clause>

  <clause id="3375">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ z,x,x) = (z * (x \ 1)) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,624,a(flip),b,3316,a),flip(a)].">
      <j1 rule="hyper" parents="316 624 3316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3376">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (y * z)),u,w)) = y * (x * R(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(3316(a,1),1840(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3316 1840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3377">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) * T(w,y) = x * (w * R(w \ (x \ (w * y)),z,u))
    ]]></literal>
    <justification jstring="[para(3316(a,1),1560(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3316 1560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3379">
    <literal><![CDATA[
      a(x \ ((y * y) \ (x * ((y * y) * z))),u,w) = a(L(z,y * y,x),u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),3324(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 3324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3380">
    <literal><![CDATA[
      R(x \ 1,x,y) \ y = K(x \ 1,x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1791(a,2),3366(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1791 3366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3381">
    <literal><![CDATA[
      R(x \ 1,x,y) \ y = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(316,a,3037,a(flip),b,3380,a),flip(a)].">
      <j1 rule="hyper" parents="316 3037 3380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3382">
    <literal><![CDATA[
      R(x,1 / x,y) \ y = (((1 / x) \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(83(a,1),3381(a,1,1,1))].">
      <j1 rule="para" parents="83 3381"/>
    </justification>
  </clause>

  <clause id="3383">
    <literal><![CDATA[
      R(x,1 / x,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(83(a,1),3382(a,2,1,1))].">
      <j1 rule="para" parents="83 3382"/>
    </justification>
  </clause>

  <clause id="3384">
    <literal><![CDATA[
      R(x,1 / x,y) = R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,382,a,b,3383,a),flip(a)].">
      <j1 rule="hyper" parents="39 382 3383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3386">
    <literal><![CDATA[
      K(x,x \ 1) * (y / ((1 / x) * y)) = R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1106,a,b,3384,a)].">
      <j1 rule="hyper" parents="63 1106 3384"/>
    </justification>
  </clause>

  <clause id="3387">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,2813,a,b,2869,a),flip(a)].">
      <j1 rule="hyper" parents="35 2813 2869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3389">
    <literal><![CDATA[
      K(R(x,y,z),u) * x = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,3387,a,b,2795,a(flip))].">
      <j1 rule="hyper" parents="138 3387 2795"/>
    </justification>
  </clause>

  <clause id="3390">
    <literal><![CDATA[
      K((x / y) / z,u) = K(x / (z * y),u)
    ]]></literal>
    <justification jstring="[para(303(a,1),3387(a,1,1)),flip(a)].">
      <j1 rule="para" parents="303 3387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3391">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(506(a,1),3387(a,1,1)),flip(a)].">
      <j1 rule="para" parents="506 3387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3392">
    <literal><![CDATA[
      K(x * (y \ 1),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(507(a,1),3387(a,1,1))].">
      <j1 rule="para" parents="507 3387"/>
    </justification>
  </clause>

  <clause id="3393">
    <literal><![CDATA[
      K((x * y) / z,u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[para(509(a,1),3387(a,1,1))].">
      <j1 rule="para" parents="509 3387"/>
    </justification>
  </clause>

  <clause id="3395">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(1651(a,1),3387(a,1,1))].">
      <j1 rule="para" parents="1651 3387"/>
    </justification>
  </clause>

  <clause id="3397">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) \ y = R(y,z,u) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,3389,a(flip),b,3010,a),flip(a)].">
      <j1 rule="hyper" parents="133 3389 3010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3398">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = y * K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[para(3391(a,1),3088(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3391 3088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3399">
    <literal><![CDATA[
      x * K(x * (y \ 1),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(3392(a,2),3088(a,1,2))].">
      <j1 rule="para" parents="3392 3088"/>
    </justification>
  </clause>

  <clause id="3400">
    <literal><![CDATA[
      R((x * y) / x,z,u) \ y = R(y,z,u) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(756(a,2),3397(a,1,1))].">
      <j1 rule="para" parents="756 3397"/>
    </justification>
  </clause>

  <clause id="3401">
    <literal><![CDATA[
      R(x,y,y) \ T(x,y) = ((y * x) * (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(563(a,1),3400(a,1,1)),flip(a)].">
      <j1 rule="para" parents="563 3400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3402">
    <literal><![CDATA[
      L(T(x \ 1,x),x,x \ y) = y \ (y / T(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(2520(a,1),2888(a,2,2))].">
      <j1 rule="para" parents="2520 2888"/>
    </justification>
  </clause>

  <clause id="3403">
    <literal><![CDATA[
      L(T(x \ 1,x),x,x \ y) = L(x \ 1,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1453,a(flip),b,3402,a),flip(a)].">
      <j1 rule="hyper" parents="316 1453 3402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3404">
    <literal><![CDATA[
      L(x \ 1,x \ 1,x * y) = L(T(x \ 1,x),x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),3403(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 3403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3405">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z \ 1,u)) = L(x,y,L(z \ 1,z,z \ u))
    ]]></literal>
    <justification jstring="[para(3403(a,1),1585(a,1,3))].">
      <j1 rule="para" parents="3403 1585"/>
    </justification>
  </clause>

  <clause id="3406">
    <literal><![CDATA[
      L(L(x \ 1,x \ 1,x),x,y) = L(x \ 1,x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(636(a,2),3404(a,2,1)),flip(a)].">
      <j1 rule="para" parents="636 3404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3407">
    <literal><![CDATA[
      L(x,y,L(T(z,u),w,v5) \ v6) = L(x,y,L(z,w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(2903(a,1),1575(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2903 1575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3409">
    <literal><![CDATA[
      L(x,y,R(T(z,u),w,v5) \ v6) = L(x,y,R(z,w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(2904(a,1),1575(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2904 1575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3410">
    <literal><![CDATA[
      K(x,y) * (R(T(x,y),z,u) \ w) = R(x,z,u) \ w
    ]]></literal>
    <justification jstring="[para(3387(a,1),2904(a,1,1))].">
      <j1 rule="para" parents="3387 2904"/>
    </justification>
  </clause>

  <clause id="3411">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) \ w) = R(T(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(3006,a,3410,a)].">
      <j1 rule="hyper" parents="3006 3410"/>
    </justification>
  </clause>

  <clause id="3413">
    <literal><![CDATA[
      K(x,y) * ((R(y,z,u) \ w) * v5) = (R(T(y,x),z,u) \ w) * v5
    ]]></literal>
    <justification jstring="[para(3410(a,1),3001(a,1,2,1))].">
      <j1 rule="para" parents="3410 3001"/>
    </justification>
  </clause>

  <clause id="3415">
    <literal><![CDATA[
      K(x,L(y,z,u)) * ((L(T(y,x),z,u) * w) * v5) = (L(y,z,u) * w) * v5
    ]]></literal>
    <justification jstring="[hyper(138,a,3020,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 3020 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3416">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3159,a(flip),b,3061,a),flip(a)].">
      <j1 rule="hyper" parents="63 3159 3061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3417">
    <literal><![CDATA[
      a(x,y,z) = ((y * z) * x) \ ((y * z) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,3159,a(flip),b,3061,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 3159 3061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3418">
    <literal><![CDATA[
      a(x,y,z) * ((y * z) * x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a,b,3416,a)].">
      <j1 rule="hyper" parents="63 2290 3416"/>
    </justification>
  </clause>

  <clause id="3419">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) != (x * y) * u
    ]]></literal>
    <literal><![CDATA[
      R(z,x,y) = u
    ]]></literal>
    <justification jstring="[para(3416(a,2),43(a,1))].">
      <j1 rule="para" parents="3416 43"/>
    </justification>
  </clause>

  <clause id="3420">
    <literal><![CDATA[
      (x * (y * z)) * a(L(z,y,x),x,y) = (x * y) * R(L(z,y,x),x,y)
    ]]></literal>
    <justification jstring="[para(100(a,1),3416(a,1,1))].">
      <j1 rule="para" parents="100 3416"/>
    </justification>
  </clause>

  <clause id="3422">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,102,a,b,3417,a),flip(a)].">
      <j1 rule="hyper" parents="316 102 3417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3423">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),x,y * z) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3417(a,2),484(a,2,1))].">
      <j1 rule="para" parents="3417 484"/>
    </justification>
  </clause>

  <clause id="3424">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,z * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1668,a,b,3422,a),flip(a)].">
      <j1 rule="hyper" parents="316 1668 3422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3425">
    <literal><![CDATA[
      L(x \ R(x,y \ z,y),x,z) = a(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1667,a(flip),b,3422,a)].">
      <j1 rule="hyper" parents="316 1667 3422"/>
    </justification>
  </clause>

  <clause id="3426">
    <literal><![CDATA[
      L(x \ R(x,y,y \ z),x,z) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),3422(a,2,3)),flip(a)].">
      <j1 rule="para" parents="10 3422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3427">
    <literal><![CDATA[
      L((x * y) \ (x * R(y,z,u)),y,z * u) = L(a(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(3422(a,2),484(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3422 484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3428">
    <literal><![CDATA[
      a(x,y,z) = ((z * y) * x) \ ((z * y) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,102,a(flip),b,3424,a),flip(a)].">
      <j1 rule="hyper" parents="316 102 3424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3429">
    <literal><![CDATA[
      ((x * y) * z) * a(z,y,x) = (x * y) * R(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,3424,a,b,102,a(flip))].">
      <j1 rule="hyper" parents="139 3424 102"/>
    </justification>
  </clause>

  <clause id="3431">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),x,z * y) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3424(a,2),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3424 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3432">
    <literal><![CDATA[
      L(L(L(x \ R(x,y,z),u,w),v5,v6),x,z * y) = L(L(a(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(3424(a,2),122(a,2,1,1))].">
      <j1 rule="para" parents="3424 122"/>
    </justification>
  </clause>

  <clause id="3434">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((w * u) * z)) = L(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,1585,a(flip),b,3245,a),flip(a)].">
      <j1 rule="hyper" parents="316 1585 3245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3436">
    <literal><![CDATA[
      L(x,y,(z \ 1) * (u * z)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1678,a(flip),b,3434,a)].">
      <j1 rule="hyper" parents="63 1678 3434"/>
    </justification>
  </clause>

  <clause id="3437">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),3434(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 3434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3439">
    <literal><![CDATA[
      ((x * (y * x)) / x) * L(z,y,x) = L(x,y,x) * (y * z)
    ]]></literal>
    <justification jstring="[para(3437(a,1),1647(a,1,2))].">
      <j1 rule="para" parents="3437 1647"/>
    </justification>
  </clause>

  <clause id="3440">
    <literal><![CDATA[
      L(x \ R(x,y * z,z \ 1),x,L(y,z,z)) = a(x,y * z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3424,a,b,3436,a),flip(a)].">
      <j1 rule="hyper" parents="63 3424 3436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3441">
    <literal><![CDATA[
      L(x,y,(z * u) * (z \ 1)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2770,a,b,3436,a)].">
      <j1 rule="hyper" parents="63 2770 3436"/>
    </justification>
  </clause>

  <clause id="3442">
    <literal><![CDATA[
      L(x,y,L(z \ u,z,z)) = L(x,y,u * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,2781,a(flip),b,3436,a),flip(a)].">
      <j1 rule="hyper" parents="63 2781 3436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3444">
    <literal><![CDATA[
      x * (T(y,x) * L(L(R(x,y,x),z,u),w,v5)) = (y * x) * L(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(1618(a,1),3289(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1618 3289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3445">
    <literal><![CDATA[
      L(x * ((x \ 1) * (x \ 1)),x,y) = L(x \ 1,x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(271(a,2),3406(a,1,1))].">
      <j1 rule="para" parents="271 3406"/>
    </justification>
  </clause>

  <clause id="3446">
    <literal><![CDATA[
      L(x \ ((x / y) * R(y,z,u)),y,z * u) = L(a(y,z,u),y,y \ x)
    ]]></literal>
    <justification jstring="[para(1602(a,1),3423(a,1,1))].">
      <j1 rule="para" parents="1602 3423"/>
    </justification>
  </clause>

  <clause id="3447">
    <literal><![CDATA[
      K(x,y) * (L(y * x,z,u) * x) = L(y * x,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2868,a,b,3173,a)].">
      <j1 rule="hyper" parents="63 2868 3173"/>
    </justification>
  </clause>

  <clause id="3449">
    <literal><![CDATA[
      T(x,R(y,z,u) * (y \ (w \ y))) = T(x,w \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,2896,a(flip),b,3186,a),flip(a)].">
      <j1 rule="hyper" parents="316 2896 3186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3450">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(3055(a,1),3205(a,1,1))].">
      <j1 rule="para" parents="3055 3205"/>
    </justification>
  </clause>

  <clause id="3451">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,2806,a,b,3450,a),flip(a)].">
      <j1 rule="hyper" parents="316 2806 3450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3452">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(2806(a,2),3451(a,1,1))].">
      <j1 rule="para" parents="2806 3451"/>
    </justification>
  </clause>

  <clause id="3454">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(1950(a,1),3452(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1950 3452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3455">
    <literal><![CDATA[
      L(x,x,y) * ((x \ 1) * (x \ 1)) = L(x \ 1,x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1058,a(flip),b,3445,a)].">
      <j1 rule="hyper" parents="63 1058 3445"/>
    </justification>
  </clause>

  <clause id="3457">
    <literal><![CDATA[
      ((x * y) * (x \ 1)) \ (x * y) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,587,a,b,3455,a)].">
      <j1 rule="hyper" parents="35 587 3455"/>
    </justification>
  </clause>

  <clause id="3458">
    <literal><![CDATA[
      (L(x * (x * y),z,u) * (x \ 1)) \ (x * (x * L(y,z,u))) = L(x,x,x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1367(a,2),3457(a,1,1,1))].">
      <j1 rule="para" parents="1367 3457"/>
    </justification>
  </clause>

  <clause id="3460">
    <literal><![CDATA[
      (x * (x * y)) \ (x * ((x * y) * z)) = L(z,y * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(3064(a,1),2924(a,1,2))].">
      <j1 rule="para" parents="3064 2924"/>
    </justification>
  </clause>

  <clause id="3461">
    <literal><![CDATA[
      L(x,y * z,T(z,y)) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,18,a,b,3460,a),flip(a)].">
      <j1 rule="hyper" parents="63 18 3460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3462">
    <literal><![CDATA[
      L(x,y * z,z) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(1652,a,3461,a)].">
      <j1 rule="hyper" parents="1652 3461"/>
    </justification>
  </clause>

  <clause id="3464">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,3132,a,b,2930,a),flip(a)].">
      <j1 rule="hyper" parents="39 3132 2930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3465">
    <literal><![CDATA[
      a(x,T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1810,a(flip),b,3464,a)].">
      <j1 rule="hyper" parents="63 1810 3464"/>
    </justification>
  </clause>

  <clause id="3467">
    <literal><![CDATA[
      a(x,y / x,z) = a(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(116(a,1),3465(a,1,2)),flip(a)].">
      <j1 rule="para" parents="116 3465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3468">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / L((1 / x) * y,x,a(x,x \ 1,y)) = a(x,1 / x,y) * x
    ]]></literal>
    <justification jstring="[para(3467(a,1),2473(a,1,2,3))].">
      <j1 rule="para" parents="3467 2473"/>
    </justification>
  </clause>

  <clause id="3469">
    <literal><![CDATA[
      ((x * (y \ 1)) \ z) * (x * (y \ 1)) = ((x / y) \ z) * (x / y)
    ]]></literal>
    <justification jstring="[para(563(a,1),3246(a,1,2))].">
      <j1 rule="para" parents="563 3246"/>
    </justification>
  </clause>

  <clause id="3470">
    <literal><![CDATA[
      ((x \ 1) * (x * L(x \ 1,x,y))) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2246(a,1),3275(a,1,1))].">
      <j1 rule="para" parents="2246 3275"/>
    </justification>
  </clause>

  <clause id="3472">
    <literal><![CDATA[
      L(x,y,z \ ((u * (w * w)) \ v5)) = L(x,y,z \ (u \ (v5 / (w * w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,3243,a(flip),b,3252,a)].">
      <j1 rule="hyper" parents="63 3243 3252"/>
    </justification>
  </clause>

  <clause id="3474">
    <literal><![CDATA[
      (x * (y * z)) * a(L(z,y,x),x,y) = x * (y * R(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,404,a(flip),b,3420,a),flip(a)].">
      <j1 rule="hyper" parents="316 404 3420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3475">
    <literal><![CDATA[
      L(x \ R(x,y * z,z),x,L(y,z,z)) = a(x,y * z,z \ 1)
    ]]></literal>
    <justification jstring="[para(1033(a,1),3440(a,1,1,2))].">
      <j1 rule="para" parents="1033 3440"/>
    </justification>
  </clause>

  <clause id="3476">
    <literal><![CDATA[
      L(x \ R(x,y * z,z),x,L(y,z,z)) = a(x,y * z,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2534,a(flip),b,3475,a),flip(a)].">
      <j1 rule="hyper" parents="316 2534 3475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3481">
    <literal><![CDATA[
      T(x,y * R(y \ z,u,w)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(253,a,3376,a(flip),b,3377,a)].">
      <j1 rule="hyper" parents="253 3376 3377"/>
    </justification>
  </clause>

  <clause id="3483">
    <literal><![CDATA[
      T(x,y * R(z,u,w)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),3481(a,1,2,2,1))].">
      <j1 rule="para" parents="9 3481"/>
    </justification>
  </clause>

  <clause id="3484">
    <literal><![CDATA[
      T(x,y * R(z,u,w)) = x * K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2815,a(flip),b,3483,a),flip(a)].">
      <j1 rule="hyper" parents="316 2815 3483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3485">
    <literal><![CDATA[
      T(x,(y / R(z,u,w)) * z) = T(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),3483(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 3483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3486">
    <literal><![CDATA[
      T(x,y * (z * (u \ 1))) = T(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(507(a,1),3483(a,1,2,2))].">
      <j1 rule="para" parents="507 3483"/>
    </justification>
  </clause>

  <clause id="3487">
    <literal><![CDATA[
      T(x,T(y * z,y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(1636(a,1),3483(a,1,2))].">
      <j1 rule="para" parents="1636 3483"/>
    </justification>
  </clause>

  <clause id="3488">
    <literal><![CDATA[
      K(x * R(y,z,u),w) = T(w,x * y) \ w
    ]]></literal>
    <justification jstring="[para(3483(a,1),2948(a,2,1))].">
      <j1 rule="para" parents="3483 2948"/>
    </justification>
  </clause>

  <clause id="3489">
    <literal><![CDATA[
      T(x,(y \ 1) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3184,a(flip),b,3487,a),flip(a)].">
      <j1 rule="hyper" parents="63 3184 3487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3490">
    <literal><![CDATA[
      ((x \ 1) * y) * T(z,x \ y) = z * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,3489,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 3489 22"/>
    </justification>
  </clause>

  <clause id="3491">
    <literal><![CDATA[
      L(x \ 1,y,x \ 1) * y = y * T(x \ 1,x \ y)
    ]]></literal>
    <justification jstring="[para(3489(a,1),548(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3489 548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3492">
    <literal><![CDATA[
      L(x,y,z \ 1) * ((z \ 1) * y) = (z \ 1) * (y * T(x,z \ y))
    ]]></literal>
    <justification jstring="[para(3489(a,1),598(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3489 598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3493">
    <literal><![CDATA[
      K((x \ 1) * y,z) = T(z,x \ y) \ z
    ]]></literal>
    <justification jstring="[para(3489(a,1),2948(a,2,1))].">
      <j1 rule="para" parents="3489 2948"/>
    </justification>
  </clause>

  <clause id="3494">
    <literal><![CDATA[
      T(x,y / R(z,u,w)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(1554(a,1),3485(a,1,2))].">
      <j1 rule="para" parents="1554 3485"/>
    </justification>
  </clause>

  <clause id="3495">
    <literal><![CDATA[
      T(x,y * (R(y,z,u) \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[para(3110(a,1),3485(a,1,2))].">
      <j1 rule="para" parents="3110 3485"/>
    </justification>
  </clause>

  <clause id="3496">
    <literal><![CDATA[
      T(x,y * (z * (u \ 1))) = T(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2893,a(flip),b,3494,a)].">
      <j1 rule="hyper" parents="63 2893 3494"/>
    </justification>
  </clause>

  <clause id="3497">
    <literal><![CDATA[
      K(x,y / R(z,u,w)) = x \ T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(133,a,3494,a(flip),b,2815,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 3494 2815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3498">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(3026(a,1),3494(a,1,2))].">
      <j1 rule="para" parents="3026 3494"/>
    </justification>
  </clause>

  <clause id="3499">
    <literal><![CDATA[
      T(x,y * (R(y,z,u) \ w)) = x * K(x,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,2815,a(flip),b,3495,a),flip(a)].">
      <j1 rule="hyper" parents="316 2815 3495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3500">
    <literal><![CDATA[
      T(x,R(y,z,u) * w) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),3495(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 3495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3501">
    <literal><![CDATA[
      T(x,(y * z) * u) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(199(a,1),3495(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="199 3495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3502">
    <literal><![CDATA[
      T(x,y * ((y \ z) * u)) = T(x,z * u)
    ]]></literal>
    <justification jstring="[para(492(a,1),3495(a,1,2,2))].">
      <j1 rule="para" parents="492 3495"/>
    </justification>
  </clause>

  <clause id="3503">
    <literal><![CDATA[
      T(x,y * (T(z,y) * u)) = T(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(491(a,1),3495(a,1,2,2))].">
      <j1 rule="para" parents="491 3495"/>
    </justification>
  </clause>

  <clause id="3504">
    <literal><![CDATA[
      T(x,R(y,z,u) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[para(1170(a,1),3495(a,1,2))].">
      <j1 rule="para" parents="1170 3495"/>
    </justification>
  </clause>

  <clause id="3505">
    <literal><![CDATA[
      T(x,y \ R(z,u,w)) = T(x,z * (z \ (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3449,a(flip),b,3500,a)].">
      <j1 rule="hyper" parents="63 3449 3500"/>
    </justification>
  </clause>

  <clause id="3506">
    <literal><![CDATA[
      T(x,((y / z) / u) * w) = T(x,(y / (u * z)) * w)
    ]]></literal>
    <justification jstring="[para(303(a,1),3500(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="303 3500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3507">
    <literal><![CDATA[
      T(x,(y * z) * (z \ u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(495(a,1),3500(a,1,2))].">
      <j1 rule="para" parents="495 3500"/>
    </justification>
  </clause>

  <clause id="3509">
    <literal><![CDATA[
      T(x,R(y,z,u) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,215,a(flip),b,3504,a),flip(a)].">
      <j1 rule="hyper" parents="316 215 3504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3511">
    <literal><![CDATA[
      T(x,(y / z) \ u) = T(x,z * (y \ u))
    ]]></literal>
    <justification jstring="[para(490(a,1),3504(a,1,2)),flip(a)].">
      <j1 rule="para" parents="490 3504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3512">
    <literal><![CDATA[
      T(x,y \ (z * u)) = T(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[para(492(a,1),3504(a,1,2)),flip(a)].">
      <j1 rule="para" parents="492 3504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3513">
    <literal><![CDATA[
      x / R(T(y,y \ x),z,u) = R(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(3504(a,1),344(a,1,2,1))].">
      <j1 rule="para" parents="3504 344"/>
    </justification>
  </clause>

  <clause id="3514">
    <literal><![CDATA[
      x / (R(y,z,u) \ y) = (R(y,z,u) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(377,a,3509,a),flip(a)].">
      <j1 rule="hyper" parents="377 3509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3516">
    <literal><![CDATA[
      T(x,(y \ z) * (z \ y)) = x
    ]]></literal>
    <justification jstring="[para(698(a,1),3509(a,1,2))].">
      <j1 rule="para" parents="698 3509"/>
    </justification>
  </clause>

  <clause id="3519">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) * z = z * ((x \ y) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(139,a,3516,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 3516 22"/>
    </justification>
  </clause>

  <clause id="3520">
    <literal><![CDATA[
      K((x \ 1) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2948,a,b,3493,a),flip(a)].">
      <j1 rule="hyper" parents="316 2948 3493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3521">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),3520(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 3520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3523">
    <literal><![CDATA[
      T(x,(y / z) * u) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(333(a,1),3502(a,1,2,2))].">
      <j1 rule="para" parents="333 3502"/>
    </justification>
  </clause>

  <clause id="3524">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * w) = T(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[para(1496(a,1),3502(a,1,2))].">
      <j1 rule="para" parents="1496 3502"/>
    </justification>
  </clause>

  <clause id="3525">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(71(a,1),3507(a,1,2))].">
      <j1 rule="para" parents="71 3507"/>
    </justification>
  </clause>

  <clause id="3526">
    <literal><![CDATA[
      L(x,y \ z,u * y) * ((u * y) * (y \ z)) = (u * y) * ((y \ z) * T(x,u * z))
    ]]></literal>
    <justification jstring="[para(3507(a,1),598(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3507 598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3528">
    <literal><![CDATA[
      T(x,((y * z) * u) * ((y * (z * u)) \ w)) = T(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[para(2330(a,1),3507(a,1,2,1))].">
      <j1 rule="para" parents="2330 3507"/>
    </justification>
  </clause>

  <clause id="3529">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) \ w) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(1272(a,1),3511(a,1,2,1))].">
      <j1 rule="para" parents="1272 3511"/>
    </justification>
  </clause>

  <clause id="3530">
    <literal><![CDATA[
      T(x,(R(y,z,u) \ w) * v5) = T(x,y \ (w * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,3504,a(flip),b,3512,a),flip(a)].">
      <j1 rule="hyper" parents="63 3504 3512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3531">
    <literal><![CDATA[
      T(x,(y \ T(z,u)) * K(u,z)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2947(a,1),3512(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2947 3512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3532">
    <literal><![CDATA[
      R(T(x / y,x * (y \ z)),z,x / y) = T(x / y,z)
    ]]></literal>
    <justification jstring="[para(3523(a,1),1632(a,1,1))].">
      <j1 rule="para" parents="3523 1632"/>
    </justification>
  </clause>

  <clause id="3533">
    <literal><![CDATA[
      K(x,y * R(z,u,w)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(2831,a,3484,a)].">
      <j1 rule="hyper" parents="2831 3484"/>
    </justification>
  </clause>

  <clause id="3534">
    <literal><![CDATA[
      K(x,y * R(y \ z,u,w)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),3533(a,2,2))].">
      <j1 rule="para" parents="10 3533"/>
    </justification>
  </clause>

  <clause id="3535">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(1636(a,1),3533(a,1,2))].">
      <j1 rule="para" parents="1636 3533"/>
    </justification>
  </clause>

  <clause id="3537">
    <literal><![CDATA[
      K(x,y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2955,a(flip),b,3535,a),flip(a)].">
      <j1 rule="hyper" parents="63 2955 3535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3538">
    <literal><![CDATA[
      K(x,y \ R(y * z,u,w)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(901(a,1),3534(a,1,2))].">
      <j1 rule="para" parents="901 3534"/>
    </justification>
  </clause>

  <clause id="3539">
    <literal><![CDATA[
      K(x,y \ R(z,u,w)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),3538(a,1,2,2,1))].">
      <j1 rule="para" parents="10 3538"/>
    </justification>
  </clause>

  <clause id="3540">
    <literal><![CDATA[
      K(x,(y * z) \ y) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(570(a,1),3539(a,1,2)),flip(a)].">
      <j1 rule="para" parents="570 3539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3541">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3540(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3542">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ (y * z)) = K(x,L(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(100(a,1),3540(a,1,2,1))].">
      <j1 rule="para" parents="100 3540"/>
    </justification>
  </clause>

  <clause id="3543">
    <literal><![CDATA[
      K(x * R(y,z,u),w) = K(x * y,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,2948,a,b,3488,a),flip(a)].">
      <j1 rule="hyper" parents="316 2948 3488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3544">
    <literal><![CDATA[
      K(x \ R(y,z,u),w) = K((x \ 1) * y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3520,a(flip),b,3543,a)].">
      <j1 rule="hyper" parents="63 3520 3543"/>
    </justification>
  </clause>

  <clause id="3545">
    <literal><![CDATA[
      K((x / R(y,z,u)) * y,w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),3543(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 3543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3546">
    <literal><![CDATA[
      K(x * ((y \ 1) \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(1037(a,1),3543(a,1,1,2))].">
      <j1 rule="para" parents="1037 3543"/>
    </justification>
  </clause>

  <clause id="3547">
    <literal><![CDATA[
      K(T(x * y,x),z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[para(1636(a,1),3543(a,1,1))].">
      <j1 rule="para" parents="1636 3543"/>
    </justification>
  </clause>

  <clause id="3548">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) = K(u * R(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3087,a(flip),b,3547,a)].">
      <j1 rule="hyper" parents="63 3087 3547"/>
    </justification>
  </clause>

  <clause id="3549">
    <literal><![CDATA[
      K(x * y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3083,a(flip),b,3547,a),flip(a)].">
      <j1 rule="hyper" parents="63 3083 3547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3550">
    <literal><![CDATA[
      K(x * (R(x,y,z) \ u),w) = K(u,w)
    ]]></literal>
    <justification jstring="[para(3110(a,1),3545(a,1,1))].">
      <j1 rule="para" parents="3110 3545"/>
    </justification>
  </clause>

  <clause id="3551">
    <literal><![CDATA[
      K(R(x,y,z) * u,w) = K(x * u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),3550(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 3550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3552">
    <literal><![CDATA[
      K((x * y) * z,u) = K(x * (y * z),u)
    ]]></literal>
    <justification jstring="[para(199(a,1),3550(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="199 3550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3553">
    <literal><![CDATA[
      K(x * ((x \ y) * z),u) = K(y * z,u)
    ]]></literal>
    <justification jstring="[para(492(a,1),3550(a,1,1,2))].">
      <j1 rule="para" parents="492 3550"/>
    </justification>
  </clause>

  <clause id="3554">
    <literal><![CDATA[
      K(R(x,y,z) \ u,w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(1170(a,1),3550(a,1,1))].">
      <j1 rule="para" parents="1170 3550"/>
    </justification>
  </clause>

  <clause id="3555">
    <literal><![CDATA[
      K((x * y) * (y \ z),u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(495(a,1),3551(a,1,1))].">
      <j1 rule="para" parents="495 3551"/>
    </justification>
  </clause>

  <clause id="3556">
    <literal><![CDATA[
      K((x / y) \ z,u) = K(y * (x \ z),u)
    ]]></literal>
    <justification jstring="[para(490(a,1),3554(a,1,1)),flip(a)].">
      <j1 rule="para" parents="490 3554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3557">
    <literal><![CDATA[
      K(x \ (y * z),u) = K((x \ y) * z,u)
    ]]></literal>
    <justification jstring="[para(492(a,1),3554(a,1,1)),flip(a)].">
      <j1 rule="para" parents="492 3554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3559">
    <literal><![CDATA[
      K(x / (y \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3392,a(flip),b,3546,a)].">
      <j1 rule="hyper" parents="63 3392 3546"/>
    </justification>
  </clause>

  <clause id="3560">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x / (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(316,a,3391,a,b,3559,a)].">
      <j1 rule="hyper" parents="316 3391 3559"/>
    </justification>
  </clause>

  <clause id="3561">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),3559(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="83 3559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3562">
    <literal><![CDATA[
      K(x * R(1 / y,z,u),w) = K(x / y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3543,a,b,3561,a)].">
      <j1 rule="hyper" parents="63 3543 3561"/>
    </justification>
  </clause>

  <clause id="3563">
    <literal><![CDATA[
      K((x * y) * R(z,u,w),v5) = K(x * (y * z),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3543,a,b,3552,a)].">
      <j1 rule="hyper" parents="63 3543 3552"/>
    </justification>
  </clause>

  <clause id="3564">
    <literal><![CDATA[
      K((x / y) * z,u) = K(x * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(333(a,1),3553(a,1,1,2))].">
      <j1 rule="para" parents="333 3553"/>
    </justification>
  </clause>

  <clause id="3565">
    <literal><![CDATA[
      K((x \ 1) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(71(a,1),3555(a,1,1))].">
      <j1 rule="para" parents="71 3555"/>
    </justification>
  </clause>

  <clause id="3566">
    <literal><![CDATA[
      K((1 / x) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(81(a,1),3555(a,1,1)),flip(a)].">
      <j1 rule="para" parents="81 3555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3567">
    <literal><![CDATA[
      K((L(x,y,z) \ x) * u,w) = K(x * (L(x,y,z) \ u),w)
    ]]></literal>
    <justification jstring="[para(1375(a,1),3555(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1375 3555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3568">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,3521,a(flip),b,3566,a),flip(a)].">
      <j1 rule="hyper" parents="316 3521 3566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3569">
    <literal><![CDATA[
      K(x,y / R(z,u,w)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2806,a,b,3497,a),flip(a)].">
      <j1 rule="hyper" parents="316 2806 3497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3570">
    <literal><![CDATA[
      K(x,y * (R(y,z,u) \ w)) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(2831,a,3499,a)].">
      <j1 rule="hyper" parents="2831 3499"/>
    </justification>
  </clause>

  <clause id="3571">
    <literal><![CDATA[
      K(x,R(y,z,u) * w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),3570(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 3570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3572">
    <literal><![CDATA[
      K(x,(y * z) * u) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(199(a,1),3570(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="199 3570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3573">
    <literal><![CDATA[
      K(x,y * ((y \ z) * u)) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(492(a,1),3570(a,1,2,2))].">
      <j1 rule="para" parents="492 3570"/>
    </justification>
  </clause>

  <clause id="3574">
    <literal><![CDATA[
      K(x,R(y,z,u) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(1170(a,1),3570(a,1,2))].">
      <j1 rule="para" parents="1170 3570"/>
    </justification>
  </clause>

  <clause id="3575">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(1037(a,1),3571(a,1,2,1))].">
      <j1 rule="para" parents="1037 3571"/>
    </justification>
  </clause>

  <clause id="3576">
    <literal><![CDATA[
      K(R(x,y,z),R(u,w,v5) \ v6) = K(x,u \ v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,3387,a(flip),b,3574,a),flip(a)].">
      <j1 rule="hyper" parents="316 3387 3574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3578">
    <literal><![CDATA[
      K(x,(y \ 1) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(382(a,1),3574(a,1,2))].">
      <j1 rule="para" parents="382 3574"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      K(x,y \ (z * u)) = K(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[para(492(a,1),3574(a,1,2)),flip(a)].">
      <j1 rule="para" parents="492 3574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3580">
    <literal><![CDATA[
      K(x,((y * (z \ u)) / u) \ w) = K(x,(y / z) \ w)
    ]]></literal>
    <justification jstring="[para(508(a,1),3574(a,1,2,1))].">
      <j1 rule="para" parents="508 3574"/>
    </justification>
  </clause>

  <clause id="3582">
    <literal><![CDATA[
      K(x,(y / z) * u) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(333(a,1),3573(a,1,2,2))].">
      <j1 rule="para" parents="333 3573"/>
    </justification>
  </clause>

  <clause id="3583">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3578,a(flip),b,3575,a)].">
      <j1 rule="hyper" parents="63 3578 3575"/>
    </justification>
  </clause>

  <clause id="3584">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(83(a,1),3583(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 3583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      K(x,y \ ((1 / y) \ z)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),3584(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 3584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3587">
    <literal><![CDATA[
      K(x \ R(y,z,u),w) = K(x \ y,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,3520,a(flip),b,3544,a),flip(a)].">
      <j1 rule="hyper" parents="316 3520 3544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      K((x / y) \ R(x,z,u),w) = K(y,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,861,a(flip),b,3587,a),flip(a)].">
      <j1 rule="hyper" parents="316 861 3587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3589">
    <literal><![CDATA[
      K((x * y) \ x,z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(570(a,1),3587(a,1,1)),flip(a)].">
      <j1 rule="para" parents="570 3587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3590">
    <literal><![CDATA[
      K(x \ (1 / y),z) = K(x \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(1040(a,1),3587(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1040 3587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3592">
    <literal><![CDATA[
      (x * ((y * z) \ y)) * K(z \ 1,x) = ((y * z) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,3589,a(flip),b,16,a(flip))].">
      <j1 rule="hyper" parents="139 3589 16"/>
    </justification>
  </clause>

  <clause id="3593">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),3589(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3595">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,860,a(flip),b,3593,a),flip(a)].">
      <j1 rule="hyper" parents="316 860 3593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3597">
    <literal><![CDATA[
      K(L(x \ y,x,z) \ 1,u) = K((z * y) \ (z * x),u)
    ]]></literal>
    <justification jstring="[para(102(a,2),3593(a,1,1,1))].">
      <j1 rule="para" parents="102 3593"/>
    </justification>
  </clause>

  <clause id="3598">
    <literal><![CDATA[
      K(L(x \ y,z,u) \ 1,w) = L(K(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(3593(a,1),3310(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3593 3310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3599">
    <literal><![CDATA[
      (x * K(y \ x,z)) / x = K((y / x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(3593(a,1),3333(a,1,1,2))].">
      <j1 rule="para" parents="3593 3333"/>
    </justification>
  </clause>

  <clause id="3602">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) = ((x * y) \ x) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,3595,a(flip),b,2814,a),flip(a)].">
      <j1 rule="hyper" parents="133 3595 2814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3603">
    <literal><![CDATA[
      K(x * (y \ R(y,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3556,a(flip),b,3588,a)].">
      <j1 rule="hyper" parents="63 3556 3588"/>
    </justification>
  </clause>

  <clause id="3604">
    <literal><![CDATA[
      K(x / (y / z),u) = K(x * (z / y),u)
    ]]></literal>
    <justification jstring="[para(371(a,1),3562(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="371 3562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3606">
    <literal><![CDATA[
      T(x,y / (z / u)) = T(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3486,a(flip),b,3496,a),flip(a)].">
      <j1 rule="hyper" parents="63 3486 3496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3607">
    <literal><![CDATA[
      T(x,(y * z) / u) = T(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2845,a,b,3606,a)].">
      <j1 rule="hyper" parents="63 2845 3606"/>
    </justification>
  </clause>

  <clause id="3613">
    <literal><![CDATA[
      T(x,y * (T(z,y) * u)) = T(x,z * (y * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,3501,a(flip),b,3503,a),flip(a)].">
      <j1 rule="hyper" parents="316 3501 3503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3614">
    <literal><![CDATA[
      (x * y) / R(T(x,y),z,u) = R(x,z,u) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),3513(a,1,2,1,2))].">
      <j1 rule="para" parents="9 3513"/>
    </justification>
  </clause>

  <clause id="3615">
    <literal><![CDATA[
      x / R((y \ x) \ x,z,u) = R(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(115(a,1),3513(a,1,2,1))].">
      <j1 rule="para" parents="115 3513"/>
    </justification>
  </clause>

  <clause id="3618">
    <literal><![CDATA[
      ((x * R(y,z,u)) * y) / (x * R(y,z,u)) = y * K(R(y,z,u) * x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,3548,a,b,2720,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 3548 2720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3619">
    <literal><![CDATA[
      K(x / y,z) * x = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,3192,a(flip),b,3599,a)].">
      <j1 rule="hyper" parents="138 3192 3599"/>
    </justification>
  </clause>

  <clause id="3620">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,2882,a,b,3599,a)].">
      <j1 rule="hyper" parents="37 2882 3599"/>
    </justification>
  </clause>

  <clause id="3621">
    <literal><![CDATA[
      T(K(x / y,z),x) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(253,a,3619,a,b,xx)].">
      <j1 rule="hyper" parents="253 3619"/>
    </justification>
  </clause>

  <clause id="3622">
    <literal><![CDATA[
      K(x / (x / y),z) * x = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),3619(a,2,2,1))].">
      <j1 rule="para" parents="83 3619"/>
    </justification>
  </clause>

  <clause id="3623">
    <literal><![CDATA[
      K((x \ y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(80(a,1),3621(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 3621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3625">
    <literal><![CDATA[
      K((x \ (y \ x)) \ 1,z) = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3593,a,b,3623,a)].">
      <j1 rule="hyper" parents="63 3593 3623"/>
    </justification>
  </clause>

  <clause id="3626">
    <literal><![CDATA[
      K(T(x,y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3395,a(flip),b,3623,a)].">
      <j1 rule="hyper" parents="63 3395 3623"/>
    </justification>
  </clause>

  <clause id="3627">
    <literal><![CDATA[
      K(T(x,x \ y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(115(a,2),3623(a,1,1))].">
      <j1 rule="para" parents="115 3623"/>
    </justification>
  </clause>

  <clause id="3628">
    <literal><![CDATA[
      T(K(x,y),x * z) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(314(a,2),3623(a,1,1)),flip(a)].">
      <j1 rule="para" parents="314 3623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3631">
    <literal><![CDATA[
      (K(x,y) * z) * K(T(y,z),x) = z
    ]]></literal>
    <justification jstring="[hyper(139,a,3626,a,b,3007,a)].">
      <j1 rule="hyper" parents="139 3626 3007"/>
    </justification>
  </clause>

  <clause id="3632">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,3626,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="139 3626 22"/>
    </justification>
  </clause>

  <clause id="3633">
    <literal><![CDATA[
      T(K(x * y,z),x) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3547,a(flip),b,3626,a),flip(a)].">
      <j1 rule="hyper" parents="63 3547 3626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3634">
    <literal><![CDATA[
      T(K(x,y),K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1975(a,1),3626(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1975 3626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3635">
    <literal><![CDATA[
      K(x,y) * K(z,x) = K(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,3634,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 3634 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3638">
    <literal><![CDATA[
      (x * y) * K(T(x,y),z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,3628,a(flip),b,2860,a)].">
      <j1 rule="hyper" parents="139 3628 2860"/>
    </justification>
  </clause>

  <clause id="3640">
    <literal><![CDATA[
      K(x * y,z) * x = x * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(3547(a,1),3632(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3547 3632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3641">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,807,a(flip),b,3620,a)].">
      <j1 rule="hyper" parents="63 807 3620"/>
    </justification>
  </clause>

  <clause id="3642">
    <literal><![CDATA[
      x \ (T(a(y,z,u) \ x,w) * a(y,z,u)) = K(a(y,z,u) \ x,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,2290,a(flip),b,3620,a(flip))].">
      <j1 rule="hyper" parents="133 2290 3620"/>
    </justification>
  </clause>

  <clause id="3643">
    <literal><![CDATA[
      x * K((x \ (y \ x)) \ 1,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,3625,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="139 3625 22"/>
    </justification>
  </clause>

  <clause id="3644">
    <literal><![CDATA[
      T(x * y,z) / y = x * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2802,a,b,3640,a)].">
      <j1 rule="hyper" parents="63 2802 3640"/>
    </justification>
  </clause>

  <clause id="3645">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2707,a(flip),b,3644,a)].">
      <j1 rule="hyper" parents="63 2707 3644"/>
    </justification>
  </clause>

  <clause id="3647">
    <literal><![CDATA[
      x * (y * K(x * y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,3644,a(flip),b,2707,a(flip))].">
      <j1 rule="hyper" parents="139 3644 2707"/>
    </justification>
  </clause>

  <clause id="3648">
    <literal><![CDATA[
      T(x * K(y * x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(3644(a,1),116(a,1,1))].">
      <j1 rule="para" parents="3644 116"/>
    </justification>
  </clause>

  <clause id="3649">
    <literal><![CDATA[
      L(x * K(y * x,z),y,z) = (z * y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(3645(a,1),413(a,1,1))].">
      <j1 rule="para" parents="3645 413"/>
    </justification>
  </clause>

  <clause id="3650">
    <literal><![CDATA[
      T(x \ T(x * y,y),x * y) = y
    ]]></literal>
    <justification jstring="[para(3645(a,2),2731(a,1,1))].">
      <j1 rule="para" parents="3645 2731"/>
    </justification>
  </clause>

  <clause id="3651">
    <literal><![CDATA[
      x * ((y * K(x \ 1,x)) * K((1 / (1 / x)) * y,z)) = T(x * (y * K(x \ 1,x)),z)
    ]]></literal>
    <justification jstring="[para(2259(a,1),3647(a,1,2,2,1))].">
      <j1 rule="para" parents="2259 3647"/>
    </justification>
  </clause>

  <clause id="3652">
    <literal><![CDATA[
      T(x,a(y,z,u) * (w * v5)) = T(x,w * (a(y,z,u) * v5))
    ]]></literal>
    <justification jstring="[para(2273(a,1),3613(a,1,2,2,1))].">
      <j1 rule="para" parents="2273 3613"/>
    </justification>
  </clause>

  <clause id="3653">
    <literal><![CDATA[
      R((x \ y) \ y,z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(204,a,3615,a),flip(a)].">
      <j1 rule="hyper" parents="204 3615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3654">
    <literal><![CDATA[
      T(x * L(x \ (x * y),z,u),x) = x * L(y * K((x \ 1) \ y,x),z,u)
    ]]></literal>
    <justification jstring="[para(3641(a,1),1401(a,2,2,1))].">
      <j1 rule="para" parents="3641 1401"/>
    </justification>
  </clause>

  <clause id="3655">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (z * (K((z \ (x \ z)) \ 1,y) * u)) = a(z,K((z \ (x \ z)) \ 1,y),u)
    ]]></literal>
    <justification jstring="[para(3643(a,1),2329(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3643 2329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3657">
    <literal><![CDATA[
      T(x,y \ R(z,u,w)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),3505(a,2,2))].">
      <j1 rule="para" parents="10 3505"/>
    </justification>
  </clause>

  <clause id="3658">
    <literal><![CDATA[
      T(x,y * (z \ R(u,w,v5))) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3511,a(flip),b,3657,a)].">
      <j1 rule="hyper" parents="63 3511 3657"/>
    </justification>
  </clause>

  <clause id="3660">
    <literal><![CDATA[
      T(x,(y * z) \ y) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(570(a,1),3657(a,1,2)),flip(a)].">
      <j1 rule="para" parents="570 3657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3661">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ 1)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(1037(a,1),3657(a,1,2,2))].">
      <j1 rule="para" parents="1037 3657"/>
    </justification>
  </clause>

  <clause id="3662">
    <literal><![CDATA[
      T(x,y \ (1 / z)) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(1040(a,1),3657(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1040 3657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3663">
    <literal><![CDATA[
      T(x * y,y \ 1) = ((x * y) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(384,a,3660,a),flip(a)].">
      <j1 rule="hyper" parents="384 3660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3664">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3660(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3665">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[para(114(a,1),3660(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="114 3660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3666">
    <literal><![CDATA[
      T(x,(y * (z * u)) \ (y * z)) = T(x,L(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(100(a,1),3660(a,1,2,1))].">
      <j1 rule="para" parents="100 3660"/>
    </justification>
  </clause>

  <clause id="3667">
    <literal><![CDATA[
      T(x,((y * z) * u) \ (y * (z * u))) = T(x,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(89(a,1),3660(a,1,2,1))].">
      <j1 rule="para" parents="89 3660"/>
    </justification>
  </clause>

  <clause id="3668">
    <literal><![CDATA[
      T(x,y \ (a(z,u,w) \ y)) = T(x,a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(2274(a,1),3660(a,1,2,1))].">
      <j1 rule="para" parents="2274 3660"/>
    </justification>
  </clause>

  <clause id="3669">
    <literal><![CDATA[
      T(x / ((y \ z) \ 1),z \ y) = ((y \ z) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(377,a,3664,a),flip(a)].">
      <j1 rule="hyper" parents="377 3664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3670">
    <literal><![CDATA[
      T(x,1 / (y \ z)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2595,a,b,3664,a)].">
      <j1 rule="hyper" parents="63 2595 3664"/>
    </justification>
  </clause>

  <clause id="3671">
    <literal><![CDATA[
      T(x * a(y,z,u),a(y,z,u) \ 1) = ((a(y,z,u) * x) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,2396,a,b,3663,a),flip(a)].">
      <j1 rule="hyper" parents="316 2396 3663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3672">
    <literal><![CDATA[
      L(x \ 1,x,y) \ y = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,358,a,b,3663,a)].">
      <j1 rule="hyper" parents="316 358 3663"/>
    </justification>
  </clause>

  <clause id="3673">
    <literal><![CDATA[
      T(x * (y \ 1),y) = ((x * (y \ 1)) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,2594,a(flip),b,3663,a)].">
      <j1 rule="hyper" parents="63 2594 3663"/>
    </justification>
  </clause>

  <clause id="3674">
    <literal><![CDATA[
      T(x * (1 / y),y) = ((x * (1 / y)) \ x) \ x
    ]]></literal>
    <justification jstring="[para(83(a,1),3663(a,1,2))].">
      <j1 rule="para" parents="83 3663"/>
    </justification>
  </clause>

  <clause id="3675">
    <literal><![CDATA[
      T(x,(x * y) \ y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2445,a(flip),b,3665,a),flip(a)].">
      <j1 rule="hyper" parents="63 2445 3665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3676">
    <literal><![CDATA[
      (((x * y) \ y) * x) * T(x,x \ 1) = (x * ((x * y) \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,3675,a(flip),b,921,a(flip))].">
      <j1 rule="hyper" parents="139 3675 921"/>
    </justification>
  </clause>

  <clause id="3677">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,x,y) \ y) = R(y,x,x)
    ]]></literal>
    <justification jstring="[para(3672(a,2),572(a,1,2))].">
      <j1 rule="para" parents="3672 572"/>
    </justification>
  </clause>

  <clause id="3678">
    <literal><![CDATA[
      T((x * (y \ 1)) \ x,x * (y \ 1)) = T(x * (y \ 1),y) \ x
    ]]></literal>
    <justification jstring="[para(3673(a,2),3168(a,2,1))].">
      <j1 rule="para" parents="3673 3168"/>
    </justification>
  </clause>

  <clause id="3679">
    <literal><![CDATA[
      L(x,x \ 1,y) \ y = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(2674(a,2),3674(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2674 3674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3681">
    <literal><![CDATA[
      T(x,(R(y,z,u) \ y) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),3530(a,2,2))].">
      <j1 rule="para" parents="9 3530"/>
    </justification>
  </clause>

  <clause id="3683">
    <literal><![CDATA[
      T(x,((y \ z) * (z \ y)) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(698(a,1),3681(a,1,2,1))].">
      <j1 rule="para" parents="698 3681"/>
    </justification>
  </clause>

  <clause id="3684">
    <literal><![CDATA[
      T(x,(y \ z) \ u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3507,a(flip),b,3683,a),flip(a)].">
      <j1 rule="hyper" parents="63 3507 3683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3685">
    <literal><![CDATA[
      T(x,(y \ z) \ u) = T(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,3512,a,b,3684,a),flip(a)].">
      <j1 rule="hyper" parents="316 3512 3684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3686">
    <literal><![CDATA[
      T(x,((y \ z) \ u) * w) = T(x,(z \ y) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,3512,a(flip),b,3684,a)].">
      <j1 rule="hyper" parents="63 3512 3684"/>
    </justification>
  </clause>

  <clause id="3687">
    <literal><![CDATA[
      ((x \ y) \ z) * T(u,(y \ x) * z) = u * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,3684,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 3684 22"/>
    </justification>
  </clause>

  <clause id="3688">
    <literal><![CDATA[
      x * K(x,y \ (z * u)) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,2815,a(flip),b,3685,a)].">
      <j1 rule="hyper" parents="316 2815 3685"/>
    </justification>
  </clause>

  <clause id="3689">
    <literal><![CDATA[
      (x * y) / T(z,(x \ z) \ y) = z \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(209,a,3685,a,b,115,a(flip))].">
      <j1 rule="hyper" parents="209 3685 115"/>
    </justification>
  </clause>

  <clause id="3690">
    <literal><![CDATA[
      T(x,(y * z) \ (y * u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),3685(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3691">
    <literal><![CDATA[
      T(x,(y \ z) \ (y \ u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),3685(a,2,2,2))].">
      <j1 rule="para" parents="10 3685"/>
    </justification>
  </clause>

  <clause id="3692">
    <literal><![CDATA[
      T(x,(y * (z * u)) \ ((y * z) * w)) = T(x,L(u,z,y) \ w)
    ]]></literal>
    <justification jstring="[para(18(a,2),3685(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18 3685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3693">
    <literal><![CDATA[
      T(x,(y * z) \ (z * u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(22(a,2),3685(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="22 3685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      T(x,y \ ((y / z) * u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(83(a,1),3685(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 3685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3695">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[para(2981(a,1),3685(a,2,2))].">
      <j1 rule="para" parents="2981 3685"/>
    </justification>
  </clause>

  <clause id="3697">
    <literal><![CDATA[
      T(x * y,y \ z) = ((x * y) \ (x * z)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(384,a,3690,a),flip(a)].">
      <j1 rule="hyper" parents="384 3690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3698">
    <literal><![CDATA[
      T(x,(y * z) \ u) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),3690(a,1,2,2))].">
      <j1 rule="para" parents="10 3690"/>
    </justification>
  </clause>

  <clause id="3699">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(22(a,2),3691(a,1,2,1))].">
      <j1 rule="para" parents="22 3691"/>
    </justification>
  </clause>

  <clause id="3700">
    <literal><![CDATA[
      T(x,R(y,z,y) \ (z \ u)) = T(x,T(y * z,y) \ u)
    ]]></literal>
    <justification jstring="[para(1616(a,1),3691(a,1,2,1))].">
      <j1 rule="para" parents="1616 3691"/>
    </justification>
  </clause>

  <clause id="3702">
    <literal><![CDATA[
      ((x / y) * z) / T(x,y \ z) = x \ ((x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(209,a,3694,a(flip),b,115,a(flip))].">
      <j1 rule="hyper" parents="209 3694 115"/>
    </justification>
  </clause>

  <clause id="3703">
    <literal><![CDATA[
      T(x * y,y \ (x \ z)) = ((x * y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(384,a,3698,a),flip(a)].">
      <j1 rule="hyper" parents="384 3698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3704">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(316,a,3661,a(flip),b,3698,a),flip(a)].">
      <j1 rule="hyper" parents="316 3661 3698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3705">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ u) = T(x,z * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(316,a,3525,a(flip),b,3698,a),flip(a)].">
      <j1 rule="hyper" parents="316 3525 3698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3706">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3665,a,b,3698,a)].">
      <j1 rule="hyper" parents="63 3665 3698"/>
    </justification>
  </clause>

  <clause id="3707">
    <literal><![CDATA[
      x / T(y * z,z \ (y \ x)) = (y * z) \ x
    ]]></literal>
    <justification jstring="[hyper(209,a,3698,a(flip),b,115,a(flip))].">
      <j1 rule="hyper" parents="209 3698 115"/>
    </justification>
  </clause>

  <clause id="3708">
    <literal><![CDATA[
      (x * ((y * z) \ u)) / T(x,z \ (y \ u)) = (y * z) \ u
    ]]></literal>
    <justification jstring="[hyper(209,a,3698,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="209 3698 22"/>
    </justification>
  </clause>

  <clause id="3710">
    <literal><![CDATA[
      T(x,((y * (z * y)) / y) \ u) = T(x,z \ (L(y,z,y) \ u))
    ]]></literal>
    <justification jstring="[para(1623(a,2),3698(a,1,2,1))].">
      <j1 rule="para" parents="1623 3698"/>
    </justification>
  </clause>

  <clause id="3711">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,3114,a,b,3706,a)].">
      <j1 rule="hyper" parents="316 3114 3706"/>
    </justification>
  </clause>

  <clause id="3712">
    <literal><![CDATA[
      K(x,(y \ z) \ u) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(34,a,2815,a(flip),b,3688,a)].">
      <j1 rule="hyper" parents="34 2815 3688"/>
    </justification>
  </clause>

  <clause id="3713">
    <literal><![CDATA[
      K(x,(y \ z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(316,a,3579,a(flip),b,3712,a),flip(a)].">
      <j1 rule="hyper" parents="316 3579 3712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3714">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),3712(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3717">
    <literal><![CDATA[
      K(x,(y * z) \ u) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),3714(a,1,2,2))].">
      <j1 rule="para" parents="10 3714"/>
    </justification>
  </clause>

  <clause id="3719">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z = K(u,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3276,a,b,3717,a)].">
      <j1 rule="hyper" parents="63 3276 3717"/>
    </justification>
  </clause>

  <clause id="3720">
    <literal><![CDATA[
      (x * y) / T(z * x,T(z,x) \ y) = (z * x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(22(a,2),3689(a,1,2,2,1))].">
      <j1 rule="para" parents="22 3689"/>
    </justification>
  </clause>

  <clause id="3721">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * w) / T(u,a(x,y,z) \ w) = u \ ((a(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(2301(a,1),3689(a,1,2,2,1))].">
      <j1 rule="para" parents="2301 3689"/>
    </justification>
  </clause>

  <clause id="3722">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(316,a,3698,a(flip),b,3699,a),flip(a)].">
      <j1 rule="hyper" parents="316 3698 3699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3723">
    <literal><![CDATA[
      T((x / y) * z,z \ y) = (((x / y) * z) \ x) \ x
    ]]></literal>
    <justification jstring="[para(83(a,1),3703(a,1,2,2))].">
      <j1 rule="para" parents="83 3703"/>
    </justification>
  </clause>

  <clause id="3724">
    <literal><![CDATA[
      T(x,y * ((z * y) \ u)) = T(x,R(z,y,y) \ u)
    ]]></literal>
    <justification jstring="[para(565(a,1),3705(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="565 3705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3725">
    <literal><![CDATA[
      T(x,L(y \ z,u,w) \ (y \ v5)) = T(x,y \ (L(z / y,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(261(a,1),3722(a,1,2,1))].">
      <j1 rule="para" parents="261 3722"/>
    </justification>
  </clause>

  <clause id="3726">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (w \ v5)) = T(x,w \ (a(y,z,u) \ v5))
    ]]></literal>
    <justification jstring="[para(2273(a,1),3722(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2273 3722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3727">
    <literal><![CDATA[
      K((x * y) * L(R(z,u,w),v5,v6),v7) = K(x * (y * L(z,v5,v6)),v7)
    ]]></literal>
    <justification jstring="[para(29(a,1),3563(a,1,1,2))].">
      <j1 rule="para" parents="29 3563"/>
    </justification>
  </clause>

  <clause id="3728">
    <literal><![CDATA[
      T(x,y * (z \ R(z,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(83(a,1),3658(a,2,2))].">
      <j1 rule="para" parents="83 3658"/>
    </justification>
  </clause>

  <clause id="3729">
    <literal><![CDATA[
      T(x,(y \ R(y,z,u)) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[para(2198(a,2),3728(a,1,2))].">
      <j1 rule="para" parents="2198 3728"/>
    </justification>
  </clause>

  <clause id="3730">
    <literal><![CDATA[
      T(x,y * a(z,u,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2380(a,1),3728(a,1,2,2))].">
      <j1 rule="para" parents="2380 3728"/>
    </justification>
  </clause>

  <clause id="3731">
    <literal><![CDATA[
      T(x,y * a(z,u,u)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2815,a(flip),b,3730,a),flip(a)].">
      <j1 rule="hyper" parents="316 2815 3730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3732">
    <literal><![CDATA[
      K(x,y * a(z,u,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2831,a,3731,a)].">
      <j1 rule="hyper" parents="2831 3731"/>
    </justification>
  </clause>

  <clause id="3733">
    <literal><![CDATA[
      T(x,((y / z) / u) * w) = T(x,y * ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(316,a,3523,a(flip),b,3506,a),flip(a)].">
      <j1 rule="hyper" parents="316 3523 3506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3735">
    <literal><![CDATA[
      T(T(((x \ y) \ 1) * z,u) / ((x \ y) \ 1),y \ x) = T(z * ((x \ y) \ 1),u) / ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,2707,a,b,3669,a),flip(a)].">
      <j1 rule="hyper" parents="316 2707 3669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3736">
    <literal><![CDATA[
      T(x,((y \ z) \ u) * w) = T(x,((z \ y) * u) * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,3501,a,b,3686,a),flip(a)].">
      <j1 rule="hyper" parents="316 3501 3686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3737">
    <literal><![CDATA[
      (x * R(y,z,u)) / (x * y) = (x * y) \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(209,a,2191,a(flip),b,3697,a(flip))].">
      <j1 rule="hyper" parents="209 2191 3697"/>
    </justification>
  </clause>

  <clause id="3738">
    <literal><![CDATA[
      T(x * (y / z),z) = ((x * (y / z)) \ (x * y)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(83(a,1),3697(a,1,2))].">
      <j1 rule="para" parents="83 3697"/>
    </justification>
  </clause>

  <clause id="3739">
    <literal><![CDATA[
      L(x \ y,x,z / y) \ z = T((z / y) * x,x \ y)
    ]]></literal>
    <justification jstring="[para(481(a,2),3723(a,2,1)),flip(a)].">
      <j1 rule="para" parents="481 3723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3740">
    <literal><![CDATA[
      L(x \ y,x,y \ z) \ z = T((z / y) * x,x \ y)
    ]]></literal>
    <justification jstring="[para(1601(a,2),3723(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1601 3723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3741">
    <literal><![CDATA[
      T(x,(y / z) * (u \ w)) = T(x,y * ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,3523,a(flip),b,3733,a)].">
      <j1 rule="hyper" parents="63 3523 3733"/>
    </justification>
  </clause>

  <clause id="3742">
    <literal><![CDATA[
      T(x,y * ((z * u) \ w)) = T(x,y * (u \ (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3523,a(flip),b,3741,a),flip(a)].">
      <j1 rule="hyper" parents="63 3523 3741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3744">
    <literal><![CDATA[
      K(x,L(y,z,u) \ 1) = K(x,(z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3714,a(flip),b,3542,a),flip(a)].">
      <j1 rule="hyper" parents="63 3714 3542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3745">
    <literal><![CDATA[
      K(x,L(y,z,u) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,3540,a(flip),b,3744,a),flip(a)].">
      <j1 rule="hyper" parents="316 3540 3744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3747">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3452,a,b,3745,a)].">
      <j1 rule="hyper" parents="63 3452 3745"/>
    </justification>
  </clause>

  <clause id="3751">
    <literal><![CDATA[
      a(x,y,K(z,u \ 1)) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,3747,a)].">
      <j1 rule="hyper" parents="53 3747"/>
    </justification>
  </clause>

  <clause id="3754">
    <literal><![CDATA[
      a(x,y,K(z,u)) = 1
    ]]></literal>
    <justification jstring="[para(83(a,1),3751(a,1,3,2))].">
      <j1 rule="para" parents="83 3751"/>
    </justification>
  </clause>

  <clause id="3756">
    <literal><![CDATA[
      a(x,y,K(z,u)) = w \ w
    ]]></literal>
    <justification jstring="[hyper(316,a,67,a,b,3754,a),flip(a)].">
      <j1 rule="hyper" parents="316 67 3754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3757">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w
    ]]></literal>
    <justification jstring="[hyper(138,a,3754,a,b,77,a)].">
      <j1 rule="hyper" parents="138 3754 77"/>
    </justification>
  </clause>

  <clause id="3758">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(52,a,3754,a)].">
      <j1 rule="hyper" parents="52 3754"/>
    </justification>
  </clause>

  <clause id="3760">
    <literal><![CDATA[
      K(x \ 1,x) * K(y,z) = (x \ 1) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(39,a,340,a,b,3756,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 340 3756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3761">
    <literal><![CDATA[
      (x / y) * (y * K(z,u)) = x * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(39,a,93,a,b,3756,a(flip))].">
      <j1 rule="hyper" parents="39 93 3756"/>
    </justification>
  </clause>

  <clause id="3762">
    <literal><![CDATA[
      x * ((x \ y) * K(z,u)) = y * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(39,a,91,a,b,3756,a(flip))].">
      <j1 rule="hyper" parents="39 91 3756"/>
    </justification>
  </clause>

  <clause id="3763">
    <literal><![CDATA[
      (x * y) * K(z,u) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(39,a,1804,a(flip),b,3756,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 1804 3756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3764">
    <literal><![CDATA[
      (x * (y * K(z,u))) / K(z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(136,a,3757,a(flip),b,2330,a(flip))].">
      <j1 rule="hyper" parents="136 3757 2330"/>
    </justification>
  </clause>

  <clause id="3765">
    <literal><![CDATA[
      R(x,y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(34,a,3418,a(flip),b,3757,a(flip))].">
      <j1 rule="hyper" parents="34 3418 3757"/>
    </justification>
  </clause>

  <clause id="3771">
    <literal><![CDATA[
      (x * y) / (z * K(x,y)) = (y * x) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,513,a(flip),b,3765,a)].">
      <j1 rule="hyper" parents="63 513 3765"/>
    </justification>
  </clause>

  <clause id="3773">
    <literal><![CDATA[
      (x * K(y,z)) / (u * K(y,z)) = x / u
    ]]></literal>
    <justification jstring="[hyper(63,a,110,a(flip),b,3765,a)].">
      <j1 rule="hyper" parents="63 110 3765"/>
    </justification>
  </clause>

  <clause id="3774">
    <literal><![CDATA[
      K(x,x \ 1) * K(y,z) = x * ((1 / x) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(138,a,3765,a(flip),b,1089,a),flip(a)].">
      <j1 rule="hyper" parents="138 3765 1089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3776">
    <literal><![CDATA[
      x * (T(y,x) * K(z,u)) = (y * x) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,3765,a(flip),b,248,a)].">
      <j1 rule="hyper" parents="138 3765 248"/>
    </justification>
  </clause>

  <clause id="3777">
    <literal><![CDATA[
      R(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(3765(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="3765 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3779">
    <literal><![CDATA[
      (1 / x) \ K(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(3765(a,1),369(a,1,1))].">
      <j1 rule="para" parents="3765 369"/>
    </justification>
  </clause>

  <clause id="3780">
    <literal><![CDATA[
      (x \ 1) * K(y,z) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[para(3765(a,1),382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3765 382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3781">
    <literal><![CDATA[
      x \ (y * K(z,u)) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(3765(a,1),492(a,1,1))].">
      <j1 rule="para" parents="3765 492"/>
    </justification>
  </clause>

  <clause id="3785">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,2967,a,b,3758,a),flip(a)].">
      <j1 rule="hyper" parents="316 2967 3758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3788">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,u) = K(x \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3310,a(flip),b,3758,a)].">
      <j1 rule="hyper" parents="63 3310 3758"/>
    </justification>
  </clause>

  <clause id="3802">
    <literal><![CDATA[
      ((x * x) / y) \ K(z,u) = (y / (x * x)) * K(z,u)
    ]]></literal>
    <justification jstring="[para(441(a,1),3779(a,1,1))].">
      <j1 rule="para" parents="441 3779"/>
    </justification>
  </clause>

  <clause id="3803">
    <literal><![CDATA[
      (x \ K(y,z)) / K(y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(149,a,3780,a)].">
      <j1 rule="hyper" parents="149 3780"/>
    </justification>
  </clause>

  <clause id="3805">
    <literal><![CDATA[
      L(x,y,z \ K(u,w)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(3780(a,1),1676(a,1,3))].">
      <j1 rule="para" parents="3780 1676"/>
    </justification>
  </clause>

  <clause id="3806">
    <literal><![CDATA[
      a(x \ K(y,z),u,w) = a(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(3780(a,1),2788(a,1,1))].">
      <j1 rule="para" parents="3780 2788"/>
    </justification>
  </clause>

  <clause id="3807">
    <literal><![CDATA[
      (x \ K((x \ 1) \ y,x \ 1)) \ y = y / (x \ 1)
    ]]></literal>
    <justification jstring="[para(3780(a,1),3096(a,1,1))].">
      <j1 rule="para" parents="3780 3096"/>
    </justification>
  </clause>

  <clause id="3817">
    <literal><![CDATA[
      T(x,y) / (z * K(x,y)) = x / z
    ]]></literal>
    <justification jstring="[hyper(136,a,2815,a,b,3761,a)].">
      <j1 rule="hyper" parents="136 2815 3761"/>
    </justification>
  </clause>

  <clause id="3819">
    <literal><![CDATA[
      x / (y * K(z,x)) = T(x,z) / y
    ]]></literal>
    <justification jstring="[hyper(136,a,2947,a(flip),b,3761,a)].">
      <j1 rule="hyper" parents="136 2947 3761"/>
    </justification>
  </clause>

  <clause id="3820">
    <literal><![CDATA[
      (K(x,y) / z) \ 1 = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2959,a(flip),b,3761,a)].">
      <j1 rule="hyper" parents="133 2959 3761"/>
    </justification>
  </clause>

  <clause id="3821">
    <literal><![CDATA[
      (T(x,y) / z) \ x = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2947,a(flip),b,3761,a)].">
      <j1 rule="hyper" parents="133 2947 3761"/>
    </justification>
  </clause>

  <clause id="3822">
    <literal><![CDATA[
      ((x * y) / z) \ (y * x) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,94,a(flip),b,3761,a)].">
      <j1 rule="hyper" parents="133 94 3761"/>
    </justification>
  </clause>

  <clause id="3823">
    <literal><![CDATA[
      x / K(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2972,a(flip),b,3761,a)].">
      <j1 rule="hyper" parents="63 2972 3761"/>
    </justification>
  </clause>

  <clause id="3824">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) = x
    ]]></literal>
    <justification jstring="[hyper(138,a,3761,a(flip),b,2972,a(flip))].">
      <j1 rule="hyper" parents="138 3761 2972"/>
    </justification>
  </clause>

  <clause id="3825">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(2815(a,2),3761(a,1,2))].">
      <j1 rule="para" parents="2815 3761"/>
    </justification>
  </clause>

  <clause id="3826">
    <literal><![CDATA[
      (x / (y * (z / y))) * z = x * K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(3091(a,1),3761(a,1,2))].">
      <j1 rule="para" parents="3091 3761"/>
    </justification>
  </clause>

  <clause id="3827">
    <literal><![CDATA[
      (x * K(y,z)) \ x = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(204,a,3823,a)].">
      <j1 rule="hyper" parents="204 3823"/>
    </justification>
  </clause>

  <clause id="3828">
    <literal><![CDATA[
      (x \ K(y,z)) * K(z,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(138,a,3780,a(flip),b,3823,a)].">
      <j1 rule="hyper" parents="138 3780 3823"/>
    </justification>
  </clause>

  <clause id="3829">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,T(x,z)) = z
    ]]></literal>
    <justification jstring="[hyper(138,a,3632,a(flip),b,3823,a)].">
      <j1 rule="hyper" parents="138 3632 3823"/>
    </justification>
  </clause>

  <clause id="3830">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(138,a,3631,a(flip),b,3823,a)].">
      <j1 rule="hyper" parents="138 3631 3823"/>
    </justification>
  </clause>

  <clause id="3832">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,3268,a(flip),b,3823,a)].">
      <j1 rule="hyper" parents="138 3268 3823"/>
    </justification>
  </clause>

  <clause id="3833">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(138,a,3259,a(flip),b,3823,a)].">
      <j1 rule="hyper" parents="138 3259 3823"/>
    </justification>
  </clause>

  <clause id="3834">
    <literal><![CDATA[
      (x / (y \ z)) * K(y \ z,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[hyper(138,a,3249,a(flip),b,3823,a)].">
      <j1 rule="hyper" parents="138 3249 3823"/>
    </justification>
  </clause>

  <clause id="3835">
    <literal><![CDATA[
      T(x,K(y,z)) * K(z,y) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(138,a,3008,a(flip),b,3823,a)].">
      <j1 rule="hyper" parents="138 3008 3823"/>
    </justification>
  </clause>

  <clause id="3837">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(3823(a,1),151(a,1))].">
      <j1 rule="para" parents="3823 151"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(253,a,3824,a,b,2995,a)].">
      <j1 rule="hyper" parents="253 3824 2995"/>
    </justification>
  </clause>

  <clause id="3839">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,3824,a(flip),b,3258,a),flip(a)].">
      <j1 rule="hyper" parents="138 3824 3258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3840">
    <literal><![CDATA[
      (x * K(y \ z,y)) * (z / y) = x * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(138,a,3824,a(flip),b,3242,a),flip(a)].">
      <j1 rule="hyper" parents="138 3824 3242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3841">
    <literal><![CDATA[
      (x * K(y \ z,y)) / (y \ z) = x / (z / y)
    ]]></literal>
    <justification jstring="[hyper(136,a,3824,a(flip),b,3227,a),flip(a)].">
      <j1 rule="hyper" parents="136 3824 3227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3843">
    <literal><![CDATA[
      (x / (y * K(z,u))) * y = x * K(u,z)
    ]]></literal>
    <justification jstring="[para(3824(a,1),3761(a,1,2))].">
      <j1 rule="para" parents="3824 3761"/>
    </justification>
  </clause>

  <clause id="3844">
    <literal><![CDATA[
      (x * K(L(y \ 1,z,u) \ 1,w)) \ x = L(K(w,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,3454,a(flip),b,3827,a),flip(a)].">
      <j1 rule="hyper" parents="316 3454 3827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3846">
    <literal><![CDATA[
      (x \ y) * K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,195,a,b,3817,a),flip(a)].">
      <j1 rule="hyper" parents="36 195 3817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      T(x,y) / (x * y) = x / (y * x)
    ]]></literal>
    <justification jstring="[para(94(a,1),3817(a,1,2))].">
      <j1 rule="para" parents="94 3817"/>
    </justification>
  </clause>

  <clause id="3848">
    <literal><![CDATA[
      T(x,y) / (z / T(y,x)) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(3259(a,1),3817(a,1,2))].">
      <j1 rule="para" parents="3259 3817"/>
    </justification>
  </clause>

  <clause id="3849">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(36,a,195,a,b,3819,a),flip(a)].">
      <j1 rule="hyper" parents="36 195 3819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3850">
    <literal><![CDATA[
      T(x,y) / (z * T(x,y)) = x / (z * x)
    ]]></literal>
    <justification jstring="[para(3268(a,1),3819(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3268 3819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3851">
    <literal><![CDATA[
      (K(x,y) * (z * z)) \ 1 = (z \ (z \ 1)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(444(a,1),3820(a,1,1))].">
      <j1 rule="para" parents="444 3820"/>
    </justification>
  </clause>

  <clause id="3852">
    <literal><![CDATA[
      (K(x,y) * z) \ x = (z \ x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(2801(a,1),3821(a,1,1))].">
      <j1 rule="para" parents="2801 3821"/>
    </justification>
  </clause>

  <clause id="3853">
    <literal><![CDATA[
      ((1 / x) \ y) * K(z,y) = (K(y,z) / x) \ y
    ]]></literal>
    <justification jstring="[para(2873(a,1),3821(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2873 3821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3854">
    <literal><![CDATA[
      (x * T(y,z)) / z = (x * y) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(136,a,3268,a(flip),b,3825,a),flip(a)].">
      <j1 rule="hyper" parents="136 3268 3825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3855">
    <literal><![CDATA[
      (x * T(y,z)) / y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1306,a,b,3825,a)].">
      <j1 rule="hyper" parents="63 1306 3825"/>
    </justification>
  </clause>

  <clause id="3856">
    <literal><![CDATA[
      ((x * y) * (y \ z)) * K(z,u) = R(x,y,y \ z) * T(z,u)
    ]]></literal>
    <justification jstring="[para(108(a,1),3825(a,1,1)),flip(a)].">
      <j1 rule="para" parents="108 3825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3858">
    <literal><![CDATA[
      (x / (y \ K(z,u))) * (y \ 1) = x * K(u,z)
    ]]></literal>
    <justification jstring="[para(3828(a,1),3761(a,1,2))].">
      <j1 rule="para" parents="3828 3761"/>
    </justification>
  </clause>

  <clause id="3860">
    <literal><![CDATA[
      K(T(x,y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(34,a,3631,a,b,3829,a)].">
      <j1 rule="hyper" parents="34 3631 3829"/>
    </justification>
  </clause>

  <clause id="3861">
    <literal><![CDATA[
      x * K(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,3860,a,b,2806,a(flip))].">
      <j1 rule="hyper" parents="139 3860 2806"/>
    </justification>
  </clause>

  <clause id="3863">
    <literal><![CDATA[
      T(K(x,y),x * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3628,a,b,3860,a)].">
      <j1 rule="hyper" parents="63 3628 3860"/>
    </justification>
  </clause>

  <clause id="3865">
    <literal><![CDATA[
      K(x,T(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3626,a(flip),b,3860,a),flip(a)].">
      <j1 rule="hyper" parents="63 3626 3860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3866">
    <literal><![CDATA[
      K(x * y,T(z,x)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3547,a(flip),b,3860,a),flip(a)].">
      <j1 rule="hyper" parents="63 3547 3860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3868">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(188(a,1),3860(a,1,1)),flip(a)].">
      <j1 rule="para" parents="188 3860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3869">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(116(a,1),3860(a,1,1)),flip(a)].">
      <j1 rule="para" parents="116 3860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3870">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(240(a,1),3860(a,1,1)),flip(a)].">
      <j1 rule="para" parents="240 3860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3871">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(x,T(z,x \ y))
    ]]></literal>
    <justification jstring="[para(115(a,1),3860(a,1,1))].">
      <j1 rule="para" parents="115 3860"/>
    </justification>
  </clause>

  <clause id="3872">
    <literal><![CDATA[
      K(T(x,y),K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(2829(a,1),3860(a,2,2))].">
      <j1 rule="para" parents="2829 3860"/>
    </justification>
  </clause>

  <clause id="3873">
    <literal><![CDATA[
      K(x / y,T(z,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,3621,a(flip),b,3865,a),flip(a)].">
      <j1 rule="hyper" parents="316 3621 3865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3874">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1952,a,b,3865,a)].">
      <j1 rule="hyper" parents="63 1952 3865"/>
    </justification>
  </clause>

  <clause id="3875">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1945,a,b,3865,a)].">
      <j1 rule="hyper" parents="63 1945 3865"/>
    </justification>
  </clause>

  <clause id="3876">
    <literal><![CDATA[
      T(K(x,y * z),y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3535,a(flip),b,3865,a),flip(a)].">
      <j1 rule="hyper" parents="63 3535 3865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1948,a(flip),b,3865,a),flip(a)].">
      <j1 rule="hyper" parents="63 1948 3865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3878">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1946,a(flip),b,3865,a),flip(a)].">
      <j1 rule="hyper" parents="63 1946 3865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3880">
    <literal><![CDATA[
      x * T(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,3865,a(flip),b,2806,a(flip))].">
      <j1 rule="hyper" parents="139 3865 2806"/>
    </justification>
  </clause>

  <clause id="3881">
    <literal><![CDATA[
      K(x,y / L(x,z,u)) = K(x,L(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(116(a,1),3868(a,1,2)),flip(a)].">
      <j1 rule="para" parents="116 3868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3882">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,x \ y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(316,a,3002,a(flip),b,3830,a),flip(a)].">
      <j1 rule="hyper" parents="316 3002 3830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3883">
    <literal><![CDATA[
      x * K(y,T(T(z,x),u)) = K(y,T(z,u)) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),3830(a,1,2,2))].">
      <j1 rule="para" parents="23 3830"/>
    </justification>
  </clause>

  <clause id="3886">
    <literal><![CDATA[
      K(x,y) * (z * T(y,x)) = T(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(253,a,3832,a,b,2995,a),flip(a)].">
      <j1 rule="hyper" parents="253 3832 2995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,3832,a(flip),b,3258,a)].">
      <j1 rule="hyper" parents="138 3832 3258"/>
    </justification>
  </clause>

  <clause id="3889">
    <literal><![CDATA[
      (x * (y / z)) * K(y / z,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[para(116(a,1),3832(a,2,2))].">
      <j1 rule="para" parents="116 3832"/>
    </justification>
  </clause>

  <clause id="3891">
    <literal><![CDATA[
      (x * K(y,z)) * y = (x * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,3832,a,b,3839,a),flip(a)].">
      <j1 rule="hyper" parents="316 3832 3839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3892">
    <literal><![CDATA[
      (x * K(y,z)) \ ((x * y) * K(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(133,a,3832,a,b,3839,a)].">
      <j1 rule="hyper" parents="133 3832 3839"/>
    </justification>
  </clause>

  <clause id="3893">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(3148(a,1),3839(a,1,1))].">
      <j1 rule="para" parents="3148 3839"/>
    </justification>
  </clause>

  <clause id="3894">
    <literal><![CDATA[
      (x * (y \ z)) * T(y,y \ z) = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[para(3151(a,1),3839(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3151 3839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3895">
    <literal><![CDATA[
      ((x \ 1) \ (x \ y)) * (x \ 1) = (x \ y) * K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,851,a,b,3846,a)].">
      <j1 rule="hyper" parents="316 851 3846"/>
    </justification>
  </clause>

  <clause id="3896">
    <literal><![CDATA[
      x \ ((y \ z) \ z) = (x \ y) * K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,311,a(flip),b,3846,a)].">
      <j1 rule="hyper" parents="316 311 3846"/>
    </justification>
  </clause>

  <clause id="3897">
    <literal><![CDATA[
      K(x,y) * (z \ T(y,x)) = T(z \ y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(253,a,3846,a,b,2995,a),flip(a)].">
      <j1 rule="hyper" parents="253 3846 2995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3898">
    <literal><![CDATA[
      (x \ T(y,z)) / K(y,z) = x \ y
    ]]></literal>
    <justification jstring="[hyper(149,a,3846,a)].">
      <j1 rule="hyper" parents="149 3846"/>
    </justification>
  </clause>

  <clause id="3899">
    <literal><![CDATA[
      T(x,y) / (x * y) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,234,a,b,3847,a),flip(a)].">
      <j1 rule="hyper" parents="316 234 3847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3900">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3627(a,1),3861(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3627 3861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3901">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(y * x,K(y,z))
    ]]></literal>
    <justification jstring="[para(2829(a,1),3866(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2829 3866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3902">
    <literal><![CDATA[
      x * K(y,(z \ x) \ x) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,3874,a,b,2993,a)].">
      <j1 rule="hyper" parents="139 3874 2993"/>
    </justification>
  </clause>

  <clause id="3904">
    <literal><![CDATA[
      K(x,T(y,K(y,z) * u)) = T(K(x,y),T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(2897(a,1),3875(a,1,2,2))].">
      <j1 rule="para" parents="2897 3875"/>
    </justification>
  </clause>

  <clause id="3905">
    <literal><![CDATA[
      K(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2889,a(flip),b,3876,a),flip(a)].">
      <j1 rule="hyper" parents="63 2889 3876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3906">
    <literal><![CDATA[
      T(K(x,y),z * y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(316,a,3865,a(flip),b,3877,a),flip(a)].">
      <j1 rule="hyper" parents="316 3865 3877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3907">
    <literal><![CDATA[
      x * T(K(x,y \ 1),z) = T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,3711,a(flip),b,3880,a),flip(a)].">
      <j1 rule="hyper" parents="316 3711 3880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3908">
    <literal><![CDATA[
      T(K(x,y),z / y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(12(a,1),3906(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 3906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3909">
    <literal><![CDATA[
      T(K(x,L(T(y,y \ z),y \ z,u)),u * (y \ z)) = T(K(x,L(T(y,y \ z),y \ z,u)),u * z)
    ]]></literal>
    <justification jstring="[para(522(a,1),3908(a,1,2))].">
      <j1 rule="para" parents="522 3908"/>
    </justification>
  </clause>

  <clause id="3910">
    <literal><![CDATA[
      (x \ (y * x)) / (y * x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),3899(a,1,1))].">
      <j1 rule="para" parents="22 3899"/>
    </justification>
  </clause>

  <clause id="3911">
    <literal><![CDATA[
      x \ (y / (y / z)) = (x \ z) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,3090,a,b,3762,a)].">
      <j1 rule="hyper" parents="133 3090 3762"/>
    </justification>
  </clause>

  <clause id="3912">
    <literal><![CDATA[
      (x \ (y \ z)) * K(z,u) = x \ (y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,3846,a(flip),b,3762,a),flip(a)].">
      <j1 rule="hyper" parents="133 3846 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3913">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,u) = x \ (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,3832,a(flip),b,3762,a),flip(a)].">
      <j1 rule="hyper" parents="133 3832 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3914">
    <literal><![CDATA[
      (x \ y) * K(z,T(u,y)) = x \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,3830,a(flip),b,3762,a),flip(a)].">
      <j1 rule="hyper" parents="133 3830 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3915">
    <literal><![CDATA[
      (x \ (y \ 1)) * K(z,u) = x \ (y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,3780,a(flip),b,3762,a),flip(a)].">
      <j1 rule="hyper" parents="133 3780 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3917">
    <literal><![CDATA[
      (x \ (y / z)) * K(z \ y,z) = x \ (z \ y)
    ]]></literal>
    <justification jstring="[hyper(133,a,3079,a(flip),b,3762,a),flip(a)].">
      <j1 rule="hyper" parents="133 3079 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3918">
    <literal><![CDATA[
      (x \ y) * K(z,z \ y) = x \ (z * (y / z))
    ]]></literal>
    <justification jstring="[hyper(133,a,2991,a(flip),b,3762,a),flip(a)].">
      <j1 rule="hyper" parents="133 2991 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3919">
    <literal><![CDATA[
      (x \ (y \ z)) * K(y,y \ z) = x \ (z / y)
    ]]></literal>
    <justification jstring="[hyper(133,a,2732,a(flip),b,3762,a),flip(a)].">
      <j1 rule="hyper" parents="133 2732 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3920">
    <literal><![CDATA[
      x \ (K(y,z) * a(u,w,v5)) = (x \ a(u,w,v5)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,2290,a(flip),b,3762,a)].">
      <j1 rule="hyper" parents="133 2290 3762"/>
    </justification>
  </clause>

  <clause id="3921">
    <literal><![CDATA[
      (x \ y) * K(z \ y,z) = x \ ((z \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,307,a(flip),b,3762,a),flip(a)].">
      <j1 rule="hyper" parents="133 307 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3922">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,94,a(flip),b,3762,a),flip(a)].">
      <j1 rule="hyper" parents="133 94 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3926">
    <literal><![CDATA[
      x * K(y * (z \ x),u) = z * (y \ T(y * (z \ x),u))
    ]]></literal>
    <justification jstring="[para(3645(a,2),3762(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3645 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3927">
    <literal><![CDATA[
      (x * (y * K(z,u))) * K(u,z) = x * y
    ]]></literal>
    <justification jstring="[hyper(3837,a,3763,a)].">
      <j1 rule="hyper" parents="3837 3763"/>
    </justification>
  </clause>

  <clause id="3928">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (z * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,2208,a,b,3763,a)].">
      <j1 rule="hyper" parents="63 2208 3763"/>
    </justification>
  </clause>

  <clause id="3929">
    <literal><![CDATA[
      x * (y * K(z,T(u,x * y))) = K(z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3830,a(flip),b,3763,a),flip(a)].">
      <j1 rule="hyper" parents="63 3830 3763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3930">
    <literal><![CDATA[
      (x * (y * K(z,u))) * z = (x * y) * T(z,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,3763,a(flip),b,3855,a)].">
      <j1 rule="hyper" parents="138 3763 3855"/>
    </justification>
  </clause>

  <clause id="3931">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (w * K(z,u)) = (x * y) / w
    ]]></literal>
    <justification jstring="[hyper(136,a,3763,a(flip),b,3761,a)].">
      <j1 rule="hyper" parents="136 3763 3761"/>
    </justification>
  </clause>

  <clause id="3932">
    <literal><![CDATA[
      x \ (y * (z * K(u,w))) = (x \ (y * z)) * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,3763,a(flip),b,3762,a)].">
      <j1 rule="hyper" parents="133 3763 3762"/>
    </justification>
  </clause>

  <clause id="3933">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(94(a,1),3763(a,2,2))].">
      <j1 rule="para" parents="94 3763"/>
    </justification>
  </clause>

  <clause id="3934">
    <literal><![CDATA[
      (x * y) * K(z \ y,z) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(307(a,1),3763(a,2,2))].">
      <j1 rule="para" parents="307 3763"/>
    </justification>
  </clause>

  <clause id="3935">
    <literal><![CDATA[
      a(x * (y * K(z,u)),w,v5) = a(x * y,w,v5)
    ]]></literal>
    <justification jstring="[para(3763(a,1),2788(a,1,1))].">
      <j1 rule="para" parents="3763 2788"/>
    </justification>
  </clause>

  <clause id="3938">
    <literal><![CDATA[
      (x * K(y \ 1,z)) / ((y * (x * K(y \ 1,z))) / y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3763(a,1),3374(a,1,2,1))].">
      <j1 rule="para" parents="3763 3374"/>
    </justification>
  </clause>

  <clause id="3940">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,u) = x * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[para(3780(a,1),3763(a,2,2))].">
      <j1 rule="para" parents="3780 3763"/>
    </justification>
  </clause>

  <clause id="3941">
    <literal><![CDATA[
      (x * y) * K(z,T(u,y)) = x * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(3830(a,1),3763(a,2,2))].">
      <j1 rule="para" parents="3830 3763"/>
    </justification>
  </clause>

  <clause id="3942">
    <literal><![CDATA[
      (x * (y * z)) * K(z,u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[para(3832(a,1),3763(a,2,2))].">
      <j1 rule="para" parents="3832 3763"/>
    </justification>
  </clause>

  <clause id="3943">
    <literal><![CDATA[
      (x * y) * (K(z,u) * (w * w)) = x * (y * (K(z,u) * (w * w)))
    ]]></literal>
    <justification jstring="[hyper(138,a,3764,a(flip),b,1056,a)].">
      <j1 rule="hyper" parents="138 3764 1056"/>
    </justification>
  </clause>

  <clause id="3944">
    <literal><![CDATA[
      (x * y) / (z * T(x,y)) = (y * x) / (z * x)
    ]]></literal>
    <justification jstring="[para(3268(a,1),3771(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3268 3771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3945">
    <literal><![CDATA[
      (x * y) / R(T(x,y),z,u) = (y * x) / R(x,z,u)
    ]]></literal>
    <justification jstring="[para(3279(a,1),3771(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3279 3771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      (x * K(y,z)) / (y * z) = x / (z * y)
    ]]></literal>
    <justification jstring="[para(94(a,1),3773(a,1,2))].">
      <j1 rule="para" parents="94 3773"/>
    </justification>
  </clause>

  <clause id="3948">
    <literal><![CDATA[
      (x * K(y,z)) / (u * (w * K(y,z))) = x / (u * w)
    ]]></literal>
    <justification jstring="[para(3763(a,1),3773(a,1,2))].">
      <j1 rule="para" parents="3763 3773"/>
    </justification>
  </clause>

  <clause id="3949">
    <literal><![CDATA[
      L(x,y,z \ (u * K(w,v5))) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(3781(a,2),1676(a,1,3))].">
      <j1 rule="para" parents="3781 1676"/>
    </justification>
  </clause>

  <clause id="3950">
    <literal><![CDATA[
      (x \ y) * K(z,u \ ((1 / u) \ w)) = x \ (y * K(z,w))
    ]]></literal>
    <justification jstring="[para(3585(a,1),3781(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3585 3781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3951">
    <literal><![CDATA[
      ((x * y) / (z * u)) \ (y * x) = z * (u * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,3763,a(flip),b,3822,a),flip(a)].">
      <j1 rule="hyper" parents="316 3763 3822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3952">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = (y * z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(20(a,2),3822(a,1,1))].">
      <j1 rule="para" parents="20 3822"/>
    </justification>
  </clause>

  <clause id="3953">
    <literal><![CDATA[
      L(x,y,z) * K(y * x,z) = (z * y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(202(a,1),3822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="202 3822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3954">
    <literal><![CDATA[
      (x * (y * z)) \ (z * (x * y)) = a(x,y,z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(200(a,1),3822(a,1,1))].">
      <j1 rule="para" parents="200 3822"/>
    </justification>
  </clause>

  <clause id="3955">
    <literal><![CDATA[
      (L(x * y,z,u) \ (x * y)) \ (y * x) = L(x * y,z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[para(1378(a,1),3822(a,1,1))].">
      <j1 rule="para" parents="1378 3822"/>
    </justification>
  </clause>

  <clause id="3956">
    <literal><![CDATA[
      (x * ((x \ y) * z)) * K(z,y) = a(x,x \ y,z) \ (z * y)
    ]]></literal>
    <justification jstring="[para(2328(a,1),3822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2328 3822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3957">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(253,a,3835,a,b,xx)].">
      <j1 rule="hyper" parents="253 3835"/>
    </justification>
  </clause>

  <clause id="3958">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,2723,a,b,3835,a)].">
      <j1 rule="hyper" parents="35 2723 3835"/>
    </justification>
  </clause>

  <clause id="3959">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(34,a,2815,a(flip),b,3958,a),flip(a)].">
      <j1 rule="hyper" parents="34 2815 3958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3960">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(3958(a,1),2745(a,1,1))].">
      <j1 rule="para" parents="3958 2745"/>
    </justification>
  </clause>

  <clause id="3961">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3958(a,1),2744(a,1))].">
      <j1 rule="para" parents="3958 2744"/>
    </justification>
  </clause>

  <clause id="3962">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(3015,a,3959,a)].">
      <j1 rule="hyper" parents="3015 3959"/>
    </justification>
  </clause>

  <clause id="3963">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(139,a,3959,a(flip),b,2806,a(flip))].">
      <j1 rule="hyper" parents="139 3959 2806"/>
    </justification>
  </clause>

  <clause id="3964">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y),x) = u
    ]]></literal>
    <justification jstring="[para(3962(a,1),2978(a,1))].">
      <j1 rule="para" parents="3962 2978"/>
    </justification>
  </clause>

  <clause id="3965">
    <literal><![CDATA[
      T(x * K(y,z),u) * K(z,y) = K(z,y) * T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(3838(a,1),250(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3838 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3966">
    <literal><![CDATA[
      T(x * (y * K(z,u)),K(u,z)) = K(z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(3763(a,1),3838(a,1,1))].">
      <j1 rule="para" parents="3763 3838"/>
    </justification>
  </clause>

  <clause id="3967">
    <literal><![CDATA[
      (x * (y * K(z,u))) / w = (x * y) / (w * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(136,a,3763,a(flip),b,3843,a)].">
      <j1 rule="hyper" parents="136 3763 3843"/>
    </justification>
  </clause>

  <clause id="3968">
    <literal><![CDATA[
      (x \ y) / (z * T(y / x,x)) = (y / x) / (z * (y / x))
    ]]></literal>
    <justification jstring="[para(116(a,1),3850(a,1,1))].">
      <j1 rule="para" parents="116 3850"/>
    </justification>
  </clause>

  <clause id="3969">
    <literal><![CDATA[
      ((x \ y) * (x * x)) / (z * T(y / (x \ 1),x)) = (y / (x \ 1)) / (z * (y / (x \ 1)))
    ]]></literal>
    <justification jstring="[para(613(a,1),3850(a,1,1))].">
      <j1 rule="para" parents="613 3850"/>
    </justification>
  </clause>

  <clause id="3970">
    <literal><![CDATA[
      ((x \ y) \ z) * K(x,z) = (T(x,z) \ y) \ z
    ]]></literal>
    <justification jstring="[para(3002(a,1),3852(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3002 3852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3971">
    <literal><![CDATA[
      T(x * y,K(y,z)) = T(x,K(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(253,a,3891,a(flip),b,642,a)].">
      <j1 rule="hyper" parents="253 3891 642"/>
    </justification>
  </clause>

  <clause id="3972">
    <literal><![CDATA[
      R(T(x,y * K(x,z)),y,K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3892(a,1),916(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3892 916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3973">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,3880,a(flip),b,3900,a),flip(a)].">
      <j1 rule="hyper" parents="316 3880 3900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3974">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z * u) = x * (y * K(z \ 1,u * z))
    ]]></literal>
    <justification jstring="[para(3905(a,1),3763(a,1,2))].">
      <j1 rule="para" parents="3905 3763"/>
    </justification>
  </clause>

  <clause id="3975">
    <literal><![CDATA[
      (x \ (y * z)) / T(y,z) = (x \ (z * y)) / y
    ]]></literal>
    <justification jstring="[hyper(136,a,3922,a(flip),b,3825,a)].">
      <j1 rule="hyper" parents="136 3922 3825"/>
    </justification>
  </clause>

  <clause id="3976">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,z \ (y * z)) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(2968(a,2),3922(a,1,2))].">
      <j1 rule="para" parents="2968 3922"/>
    </justification>
  </clause>

  <clause id="3977">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,3933,a)].">
      <j1 rule="hyper" parents="144 3933"/>
    </justification>
  </clause>

  <clause id="3978">
    <literal><![CDATA[
      (x * (y * z)) / T(y,z) = (x * (z * y)) / y
    ]]></literal>
    <justification jstring="[hyper(136,a,3933,a(flip),b,3825,a)].">
      <j1 rule="hyper" parents="136 3933 3825"/>
    </justification>
  </clause>

  <clause id="3981">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = (x * y) / (z * y)
    ]]></literal>
    <justification jstring="[para(3268(a,1),3946(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3268 3946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3982">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,3865,a,b,3963,a),flip(a)].">
      <j1 rule="hyper" parents="316 3865 3963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3983">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(316,a,3626,a,b,3963,a),flip(a)].">
      <j1 rule="hyper" parents="316 3626 3963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3984">
    <literal><![CDATA[
      K(x,K(y,x) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3136,a(flip),b,3977,a)].">
      <j1 rule="hyper" parents="63 3136 3977"/>
    </justification>
  </clause>

  <clause id="3985">
    <literal><![CDATA[
      (x * (y * z)) \ ((z * y) * x) = K(z,y) * K(z * y,x)
    ]]></literal>
    <justification jstring="[para(3977(a,1),3922(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3977 3922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3988">
    <literal><![CDATA[
      K(x,y * K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3622(a,1),3984(a,1,2))].">
      <j1 rule="para" parents="3622 3984"/>
    </justification>
  </clause>

  <clause id="3989">
    <literal><![CDATA[
      K(x,y \ K(z,x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3578,a(flip),b,3988,a)].">
      <j1 rule="hyper" parents="63 3578 3988"/>
    </justification>
  </clause>

  <clause id="3990">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3824(a,1),3988(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3824 3988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3991">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,2967,a,b,3990,a),flip(a)].">
      <j1 rule="hyper" parents="316 2967 3990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3992">
    <literal><![CDATA[
      K(x * K(y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2977,a,3991,a)].">
      <j1 rule="hyper" parents="2977 3991"/>
    </justification>
  </clause>

  <clause id="3993">
    <literal><![CDATA[
      K(K(x,y) \ z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(3902(a,1),3992(a,1,1))].">
      <j1 rule="para" parents="3902 3992"/>
    </justification>
  </clause>

  <clause id="3994">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(3006,a,3982,a)].">
      <j1 rule="hyper" parents="3006 3982"/>
    </justification>
  </clause>

  <clause id="3995">
    <literal><![CDATA[
      K(x,K(K(x,y),z)) = 1
    ]]></literal>
    <justification jstring="[hyper(132,a,3872,a(flip),b,3983,a),flip(a)].">
      <j1 rule="hyper" parents="132 3872 3983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3996">
    <literal><![CDATA[
      T(x,K(K(x,y),z)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,3995,a)].">
      <j1 rule="hyper" parents="56 3995"/>
    </justification>
  </clause>

  <clause id="3997">
    <literal><![CDATA[
      T(x,K(y,K(z,x))) = x
    ]]></literal>
    <justification jstring="[para(3959(a,1),3996(a,1,2))].">
      <j1 rule="para" parents="3959 3996"/>
    </justification>
  </clause>

  <clause id="3998">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(x * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(1942(a,1),3994(a,1,2))].">
      <j1 rule="para" parents="1942 3994"/>
    </justification>
  </clause>

  <clause id="3999">
    <literal><![CDATA[
      T(x,y * K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3777,a,3972,a),flip(a)].">
      <j1 rule="hyper" parents="3777 3972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4001">
    <literal><![CDATA[
      T(x,K(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3830(a,1),3999(a,1,2))].">
      <j1 rule="para" parents="3830 3999"/>
    </justification>
  </clause>

  <clause id="4002">
    <literal><![CDATA[
      T(x,T(x,y) * z) = T(x,x * z)
    ]]></literal>
    <justification jstring="[para(2800(a,1),4001(a,1,2))].">
      <j1 rule="para" parents="2800 4001"/>
    </justification>
  </clause>

  <clause id="4004">
    <literal><![CDATA[
      x * (T(y,x) * K(z,u)) = y * (x * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,3763,a(flip),b,3776,a),flip(a)].">
      <j1 rule="hyper" parents="316 3763 3776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4007">
    <literal><![CDATA[
      x * (K(y \ K(z,u),y) * K(u,z)) = x / (y * (K(z,u) / y))
    ]]></literal>
    <justification jstring="[hyper(35,a,3927,a,b,3826,a)].">
      <j1 rule="hyper" parents="35 3927 3826"/>
    </justification>
  </clause>

  <clause id="4009">
    <literal><![CDATA[
      (x / ((y \ z) \ z)) / (y \ z) = (x / y) / (z / y)
    ]]></literal>
    <justification jstring="[para(3266(a,2),3841(a,1,1))].">
      <j1 rule="para" parents="3266 3841"/>
    </justification>
  </clause>

  <clause id="4010">
    <literal><![CDATA[
      (x \ K(y,z)) / (u \ 1) = (x \ 1) / (u \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(136,a,3780,a(flip),b,3858,a)].">
      <j1 rule="hyper" parents="136 3780 3858"/>
    </justification>
  </clause>

  <clause id="4011">
    <literal><![CDATA[
      x / T(T(y,y \ x),z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,3262,a(flip),b,3882,a)].">
      <j1 rule="hyper" parents="63 3262 3882"/>
    </justification>
  </clause>

  <clause id="4012">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(u,x) = T(x,u) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1269(a,1),3882(a,1,2,2))].">
      <j1 rule="para" parents="1269 3882"/>
    </justification>
  </clause>

  <clause id="4013">
    <literal><![CDATA[
      x / T((y \ x) \ x,z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(115(a,1),4011(a,1,2,1))].">
      <j1 rule="para" parents="115 4011"/>
    </justification>
  </clause>

  <clause id="4015">
    <literal><![CDATA[
      T(x / (x / y),z) \ x = x / T(y,z)
    ]]></literal>
    <justification jstring="[para(208(a,1),4013(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="208 4013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4016">
    <literal><![CDATA[
      x / (x / T(y,z)) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(210,a,4015,a)].">
      <j1 rule="hyper" parents="210 4015"/>
    </justification>
  </clause>

  <clause id="4017">
    <literal><![CDATA[
      T(x / (x / (y * K(z,y))),z) = x / (x / y)
    ]]></literal>
    <justification jstring="[para(2731(a,1),4016(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2731 4016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4018">
    <literal><![CDATA[
      T(x * y,K(y,z)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3018,a(flip),b,3886,a),flip(a)].">
      <j1 rule="hyper" parents="63 3018 3886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4019">
    <literal><![CDATA[
      T(T(x,K(y,z)),y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(253,a,3971,a(flip),b,4018,a(flip))].">
      <j1 rule="hyper" parents="253 3971 4018"/>
    </justification>
  </clause>

  <clause id="4020">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(386,a,4019,a)].">
      <j1 rule="hyper" parents="386 4019"/>
    </justification>
  </clause>

  <clause id="4021">
    <literal><![CDATA[
      T((x * y) / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,284,a(flip),b,4019,a),flip(a)].">
      <j1 rule="hyper" parents="63 284 4019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4022">
    <literal><![CDATA[
      T(x,T(y,K(z,x))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3997(a,1),4019(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3997 4019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4023">
    <literal><![CDATA[
      T(x,K(x,y) * (z * K(y,x))) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2994(a,2),4022(a,1,2))].">
      <j1 rule="para" parents="2994 4022"/>
    </justification>
  </clause>

  <clause id="4027">
    <literal><![CDATA[
      T(x,y) \ T(x,T(y,z)) = K(T(x,y),K(y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,4020,a(flip),b,2815,a(flip))].">
      <j1 rule="hyper" parents="133 4020 2815"/>
    </justification>
  </clause>

  <clause id="4028">
    <literal><![CDATA[
      (x * (y * (z / u))) * K(z / u,u) = x * (y * (u \ z))
    ]]></literal>
    <justification jstring="[para(3889(a,1),3763(a,2,2))].">
      <j1 rule="para" parents="3889 3763"/>
    </justification>
  </clause>

  <clause id="4029">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = T(K(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(34,a,2815,a(flip),b,3907,a)].">
      <j1 rule="hyper" parents="34 2815 3907"/>
    </justification>
  </clause>

  <clause id="4030">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(1950(a,1),4029(a,2,1))].">
      <j1 rule="para" parents="1950 4029"/>
    </justification>
  </clause>

  <clause id="4031">
    <literal><![CDATA[
      (x \ (1 / (1 / y))) \ 1 = (x \ y) \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3911(a,2),2258(a,1,1))].">
      <j1 rule="para" parents="3911 2258"/>
    </justification>
  </clause>

  <clause id="4032">
    <literal><![CDATA[
      L(x,y,z \ (u \ T(w,v5))) = L(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(3912(a,1),1676(a,1,3))].">
      <j1 rule="para" parents="3912 1676"/>
    </justification>
  </clause>

  <clause id="4033">
    <literal><![CDATA[
      (x \ (y \ (z * u))) * K(u,w) = x \ (y \ (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(133,a,3913,a(flip),b,3762,a),flip(a)].">
      <j1 rule="hyper" parents="133 3913 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4034">
    <literal><![CDATA[
      L(x,y,z \ (u * T(w,v5))) = L(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(3913(a,1),1676(a,1,3))].">
      <j1 rule="para" parents="3913 1676"/>
    </justification>
  </clause>

  <clause id="4035">
    <literal><![CDATA[
      a(x \ (y * T(z,u)),w,v5) = a(x \ (y * z),w,v5)
    ]]></literal>
    <justification jstring="[para(3913(a,1),2788(a,1,1))].">
      <j1 rule="para" parents="3913 2788"/>
    </justification>
  </clause>

  <clause id="4036">
    <literal><![CDATA[
      L(x,y,z \ (K(u,w) * v5)) = L(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(3914(a,1),1676(a,1,3))].">
      <j1 rule="para" parents="3914 1676"/>
    </justification>
  </clause>

  <clause id="4037">
    <literal><![CDATA[
      a(x \ (K(y,z) * u),w,v5) = a(x \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(3914(a,1),2788(a,1,1))].">
      <j1 rule="para" parents="3914 2788"/>
    </justification>
  </clause>

  <clause id="4038">
    <literal><![CDATA[
      (x \ (y \ z)) * K(u,u \ z) = x \ (y \ (u * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(133,a,3918,a(flip),b,3762,a),flip(a)].">
      <j1 rule="hyper" parents="133 3918 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4039">
    <literal><![CDATA[
      (x * (T(y,z) \ 1)) * T(y,z) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(3147(a,1),3930(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3147 3930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4040">
    <literal><![CDATA[
      a(x * (y * ((z \ u) \ u)),w,v5) = a(x * (y * z),w,v5)
    ]]></literal>
    <justification jstring="[para(3272(a,1),3935(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3272 3935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4041">
    <literal><![CDATA[
      a(x * (K(y,z) * u),w,v5) = a(x * u,w,v5)
    ]]></literal>
    <justification jstring="[para(3631(a,1),3935(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3631 3935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4042">
    <literal><![CDATA[
      a(x * (y \ K(z,u)),w,v5) = a(x * (y \ 1),w,v5)
    ]]></literal>
    <justification jstring="[para(3780(a,1),3935(a,1,1,2))].">
      <j1 rule="para" parents="3780 3935"/>
    </justification>
  </clause>

  <clause id="4043">
    <literal><![CDATA[
      a(x * (y \ (z / u)),w,v5) = a(x * (y \ (u \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(3917(a,1),3935(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3917 3935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4045">
    <literal><![CDATA[
      (x / (y * y)) * K(z,u) = x * ((y * y) \ K(z,u))
    ]]></literal>
    <justification jstring="[para(432(a,1),3940(a,1,1))].">
      <j1 rule="para" parents="432 3940"/>
    </justification>
  </clause>

  <clause id="4046">
    <literal><![CDATA[
      (x \ (y * z)) * K(u,T(w,z)) = x \ (y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(133,a,3941,a(flip),b,3762,a),flip(a)].">
      <j1 rule="hyper" parents="133 3941 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4048">
    <literal><![CDATA[
      (x * (y * T(z,u))) / T(z,u) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(136,a,3942,a(flip),b,3825,a)].">
      <j1 rule="hyper" parents="136 3942 3825"/>
    </justification>
  </clause>

  <clause id="4049">
    <literal><![CDATA[
      (x \ (y * (z * u))) * K(u,w) = x \ (y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(133,a,3942,a(flip),b,3762,a),flip(a)].">
      <j1 rule="hyper" parents="133 3942 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4050">
    <literal><![CDATA[
      R(x,y,z) = (z * (x * y)) / (y * T(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(316,a,20,a,b,3944,a)].">
      <j1 rule="hyper" parents="316 20 3944"/>
    </justification>
  </clause>

  <clause id="4051">
    <literal><![CDATA[
      L(x,y,z \ (u \ (w * v5))) = L(x,y,z \ (u \ (v5 * w)))
    ]]></literal>
    <justification jstring="[para(3922(a,1),3949(a,1,3,2))].">
      <j1 rule="para" parents="3922 3949"/>
    </justification>
  </clause>

  <clause id="4052">
    <literal><![CDATA[
      L(x,y,z \ (u \ (w / v5))) = L(x,y,z \ (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(3917(a,1),3949(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3917 3949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4053">
    <literal><![CDATA[
      (x \ ((y \ 1) \ x)) * x = (T(y,x) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,3278,a(flip),b,3970,a)].">
      <j1 rule="hyper" parents="63 3278 3970"/>
    </justification>
  </clause>

  <clause id="4054">
    <literal><![CDATA[
      R(x,y,z) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,301,a(flip),b,3978,a),flip(a)].">
      <j1 rule="hyper" parents="138 301 3978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4055">
    <literal><![CDATA[
      (x * (y \ z)) * T(y,y \ z) = R(x,y \ z,y) * z
    ]]></literal>
    <justification jstring="[hyper(323,a,4054,a),flip(a)].">
      <j1 rule="hyper" parents="323 4054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4056">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = R(x / z,z,y)
    ]]></literal>
    <justification jstring="[hyper(136,a,157,a(flip),b,4054,a)].">
      <j1 rule="hyper" parents="136 157 4054"/>
    </justification>
  </clause>

  <clause id="4057">
    <literal><![CDATA[
      (x * y) * R(a(z,u,w),y,x) = (a(z,u,w) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2305,a(flip),b,4054,a)].">
      <j1 rule="hyper" parents="63 2305 4054"/>
    </justification>
  </clause>

  <clause id="4058">
    <literal><![CDATA[
      R(x,y,T(z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,494,a,b,4054,a)].">
      <j1 rule="hyper" parents="35 494 4054"/>
    </justification>
  </clause>

  <clause id="4059">
    <literal><![CDATA[
      ((x * y) / z) * R(z,y,x) = z \ ((z * y) * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(133,a,4054,a(flip),b,3213,a),flip(a)].">
      <j1 rule="hyper" parents="133 4054 3213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4060">
    <literal><![CDATA[
      R(x,y,R(T(z,y),u,w)) = R(x,y,R(z,u,w))
    ]]></literal>
    <justification jstring="[para(27(a,2),4058(a,1,3))].">
      <j1 rule="para" parents="27 4058"/>
    </justification>
  </clause>

  <clause id="4061">
    <literal><![CDATA[
      R(x,y,z / y) = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(116(a,1),4058(a,1,3)),flip(a)].">
      <j1 rule="para" parents="116 4058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4062">
    <literal><![CDATA[
      R(x / (y \ z),y \ z,y) = (x * T(y,y \ z)) / z
    ]]></literal>
    <justification jstring="[para(10(a,1),4056(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 4056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4063">
    <literal><![CDATA[
      R(R(x,y,z) / x,x,u) = (u * R(x,y,z)) / (u * x)
    ]]></literal>
    <justification jstring="[para(2842(a,1),4056(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2842 4056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4064">
    <literal><![CDATA[
      R((x * T(y,z)) / y,y,z) = ((x * y) * z) / (z * y)
    ]]></literal>
    <justification jstring="[para(3887(a,1),4056(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3887 4056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3994,a(flip),b,3998,a),flip(a)].">
      <j1 rule="hyper" parents="63 3994 3998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4066">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3901,a,b,4065,a)].">
      <j1 rule="hyper" parents="63 3901 4065"/>
    </justification>
  </clause>

  <clause id="4067">
    <literal><![CDATA[
      T(x * K(y,z),z) = T(x,z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(253,a,2070,a,b,4004,a)].">
      <j1 rule="hyper" parents="253 2070 4004"/>
    </justification>
  </clause>

  <clause id="4068">
    <literal><![CDATA[
      x * (T(T(y,x),z) * K(u,w)) = T(y,z) * (x * K(u,w))
    ]]></literal>
    <justification jstring="[para(23(a,1),4004(a,1,2,1))].">
      <j1 rule="para" parents="23 4004"/>
    </justification>
  </clause>

  <clause id="4069">
    <literal><![CDATA[
      ((1 / x) * (T(y,x \ 1) * K(z,u))) * x = (y * ((x \ 1) * K(z,u))) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4004(a,1),2566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4004 2566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4070">
    <literal><![CDATA[
      (1 / x) * (T(y,x \ 1) * K(z,u)) = y * ((1 / x) * K(z,u))
    ]]></literal>
    <justification jstring="[para(2595(a,1),4004(a,1,2,1))].">
      <j1 rule="para" parents="2595 4004"/>
    </justification>
  </clause>

  <clause id="4071">
    <literal><![CDATA[
      T(1 / (K(x,y) / x),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(3048(a,1),4017(a,1,1,2))].">
      <j1 rule="para" parents="3048 4017"/>
    </justification>
  </clause>

  <clause id="4072">
    <literal><![CDATA[
      (1 / (K(x,y) / x)) * y = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(139,a,4071,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 4071 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4073">
    <literal><![CDATA[
      T(x,y) \ T(x,T(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,3872,a(flip),b,4027,a),flip(a)].">
      <j1 rule="hyper" parents="316 3872 4027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4074">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3041,a(flip),b,4073,a)].">
      <j1 rule="hyper" parents="63 3041 4073"/>
    </justification>
  </clause>

  <clause id="4075">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3994,a(flip),b,4074,a)].">
      <j1 rule="hyper" parents="63 3994 4074"/>
    </justification>
  </clause>

  <clause id="4076">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(3964,a,4075,a)].">
      <j1 rule="hyper" parents="3964 4075"/>
    </justification>
  </clause>

  <clause id="4077">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,4066,a(flip),b,4075,a),flip(a)].">
      <j1 rule="hyper" parents="316 4066 4075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4078">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,4075,a,b,2806,a(flip))].">
      <j1 rule="hyper" parents="139 4075 2806"/>
    </justification>
  </clause>

  <clause id="4079">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(138,a,4075,a,b,2795,a(flip))].">
      <j1 rule="hyper" parents="138 4075 2795"/>
    </justification>
  </clause>

  <clause id="4080">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(4075(a,1),3962(a,1,1))].">
      <j1 rule="para" parents="4075 3962"/>
    </justification>
  </clause>

  <clause id="4081">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = T(K(x,y),z) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,4076,a(flip),b,2861,a)].">
      <j1 rule="hyper" parents="138 4076 2861"/>
    </justification>
  </clause>

  <clause id="4082">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,4075,a,b,4077,a),flip(a)].">
      <j1 rule="hyper" parents="316 4075 4077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4083">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(2978,a,4080,a)].">
      <j1 rule="hyper" parents="2978 4080"/>
    </justification>
  </clause>

  <clause id="4084">
    <literal><![CDATA[
      K(x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3962,a(flip),b,4080,a)].">
      <j1 rule="hyper" parents="63 3962 4080"/>
    </justification>
  </clause>

  <clause id="4085">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,4075,a,b,4083,a),flip(a)].">
      <j1 rule="hyper" parents="316 4075 4083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4086">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4076,a(flip),b,4083,a),flip(a)].">
      <j1 rule="hyper" parents="63 4076 4083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4087">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,4077,a(flip),b,4084,a),flip(a)].">
      <j1 rule="hyper" parents="316 4077 4084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4088">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) = T(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,4084,a,b,2861,a)].">
      <j1 rule="hyper" parents="138 4084 2861"/>
    </justification>
  </clause>

  <clause id="4089">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4084(a,1),4078(a,1,2))].">
      <j1 rule="para" parents="4084 4078"/>
    </justification>
  </clause>

  <clause id="4090">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(4084(a,1),4079(a,1,1))].">
      <j1 rule="para" parents="4084 4079"/>
    </justification>
  </clause>

  <clause id="4091">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,4084,a,b,4085,a),flip(a)].">
      <j1 rule="hyper" parents="316 4084 4085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4092">
    <literal><![CDATA[
      K(x,K(y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4076,a(flip),b,4085,a)].">
      <j1 rule="hyper" parents="63 4076 4085"/>
    </justification>
  </clause>

  <clause id="4094">
    <literal><![CDATA[
      K(x,K(y,T(z,x))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,3872,a(flip),b,4086,a),flip(a)].">
      <j1 rule="hyper" parents="316 3872 4086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4095">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * u) = T(z,K(x,y)) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,4086,a,b,2861,a)].">
      <j1 rule="hyper" parents="138 4086 2861"/>
    </justification>
  </clause>

  <clause id="4096">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,4074,a,b,4086,a)].">
      <j1 rule="hyper" parents="63 4074 4086"/>
    </justification>
  </clause>

  <clause id="4097">
    <literal><![CDATA[
      K(x,K(y,z)) * y = T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(138,a,4086,a(flip),b,2795,a(flip))].">
      <j1 rule="hyper" parents="138 4086 2795"/>
    </justification>
  </clause>

  <clause id="4098">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4086(a,1),3982(a,1,2))].">
      <j1 rule="para" parents="4086 3982"/>
    </justification>
  </clause>

  <clause id="4100">
    <literal><![CDATA[
      (x * y) \ (K(x,K(z,u)) * w) = (T(x,K(z,u)) * y) \ w
    ]]></literal>
    <justification jstring="[para(4091(a,1),3021(a,1,2,1))].">
      <j1 rule="para" parents="4091 3021"/>
    </justification>
  </clause>

  <clause id="4101">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,4077,a,b,4092,a)].">
      <j1 rule="hyper" parents="316 4077 4092"/>
    </justification>
  </clause>

  <clause id="4102">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(3537(a,1),4082(a,1,2))].">
      <j1 rule="para" parents="3537 4082"/>
    </justification>
  </clause>

  <clause id="4103">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z \ y))
    ]]></literal>
    <justification jstring="[para(3578(a,1),4082(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3578 4082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4104">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,4086,a,b,4087,a),flip(a)].">
      <j1 rule="hyper" parents="316 4086 4087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4105">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,4084,a,b,4087,a),flip(a)].">
      <j1 rule="hyper" parents="316 4084 4087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4106">
    <literal><![CDATA[
      T(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4078,a(flip),b,4089,a)].">
      <j1 rule="hyper" parents="63 4078 4089"/>
    </justification>
  </clause>

  <clause id="4107">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3961,a,4106,a),flip(a)].">
      <j1 rule="hyper" parents="3961 4106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4108">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(T(x,u),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(386,a,4106,a)].">
      <j1 rule="hyper" parents="386 4106"/>
    </justification>
  </clause>

  <clause id="4109">
    <literal><![CDATA[
      K(x,y) * (z \ T(y,x)) = T(z \ y,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,3897,a,b,4106,a)].">
      <j1 rule="hyper" parents="316 3897 4106"/>
    </justification>
  </clause>

  <clause id="4110">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,3008,a,b,4106,a)].">
      <j1 rule="hyper" parents="316 3008 4106"/>
    </justification>
  </clause>

  <clause id="4111">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,2994,a,b,4106,a)].">
      <j1 rule="hyper" parents="316 2994 4106"/>
    </justification>
  </clause>

  <clause id="4114">
    <literal><![CDATA[
      T(x * y,K(z,y)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,4018,a(flip),b,4106,a),flip(a)].">
      <j1 rule="hyper" parents="316 4018 4106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4115">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,3838,a(flip),b,4106,a),flip(a)].">
      <j1 rule="hyper" parents="316 3838 4106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4116">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,4106,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="139 4106 22"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      K(x,y) * R(T(z,K(y,x)),u,w) = R(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4106(a,1),252(a,1,2,1))].">
      <j1 rule="para" parents="4106 252"/>
    </justification>
  </clause>

  <clause id="4118">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[para(4106(a,1),3835(a,1,1))].">
      <j1 rule="para" parents="4106 3835"/>
    </justification>
  </clause>

  <clause id="4119">
    <literal><![CDATA[
      (x * K(y,z)) / x = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(209,a,4107,a(flip),b,3023,a)].">
      <j1 rule="hyper" parents="209 4107 3023"/>
    </justification>
  </clause>

  <clause id="4120">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(4107(a,1),3960(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4107 3960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4121">
    <literal><![CDATA[
      K(x,K(y,T(z,x))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,4084,a,b,4094,a),flip(a)].">
      <j1 rule="hyper" parents="316 4084 4094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4122">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),4102(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 4102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4123">
    <literal><![CDATA[
      K(x,K(y,z * (u * x))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(3572(a,1),4104(a,1,2))].">
      <j1 rule="para" parents="3572 4104"/>
    </justification>
  </clause>

  <clause id="4124">
    <literal><![CDATA[
      T(x,K(y,z * x)) = x * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,4105,a(flip),b,2806,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 4105 2806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4126">
    <literal><![CDATA[
      (x * K(y,z)) / x = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,3865,a,b,4119,a),flip(a)].">
      <j1 rule="hyper" parents="316 3865 4119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4127">
    <literal><![CDATA[
      K(x,T(y,z)) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,3865,a,b,4119,a)].">
      <j1 rule="hyper" parents="138 3865 4119"/>
    </justification>
  </clause>

  <clause id="4128">
    <literal><![CDATA[
      K(T(x,y),z) * y = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,3626,a,b,4119,a)].">
      <j1 rule="hyper" parents="138 3626 4119"/>
    </justification>
  </clause>

  <clause id="4129">
    <literal><![CDATA[
      K(x,y * z) * z = z * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(138,a,3876,a(flip),b,4119,a)].">
      <j1 rule="hyper" parents="138 3876 4119"/>
    </justification>
  </clause>

  <clause id="4130">
    <literal><![CDATA[
      K(x * y,z) * y = y * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,3633,a(flip),b,4119,a)].">
      <j1 rule="hyper" parents="138 3633 4119"/>
    </justification>
  </clause>

  <clause id="4131">
    <literal><![CDATA[
      K(x \ y,z) * x = x * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,3869,a(flip),b,4126,a)].">
      <j1 rule="hyper" parents="138 3869 4126"/>
    </justification>
  </clause>

  <clause id="4132">
    <literal><![CDATA[
      K(((x * y) / x) \ 1,z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3314,a,b,4126,a)].">
      <j1 rule="hyper" parents="63 3314 4126"/>
    </justification>
  </clause>

  <clause id="4133">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4126(a,1),240(a,1,1))].">
      <j1 rule="para" parents="4126 240"/>
    </justification>
  </clause>

  <clause id="4134">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4126(a,1),326(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4126 326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4135">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (x * y) = L(K(z,T(u,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(4126(a,1),752(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4126 752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4136">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3865,a,b,4133,a)].">
      <j1 rule="hyper" parents="63 3865 4133"/>
    </justification>
  </clause>

  <clause id="4137">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3626,a,b,4133,a)].">
      <j1 rule="hyper" parents="63 3626 4133"/>
    </justification>
  </clause>

  <clause id="4140">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3621,a(flip),b,4133,a)].">
      <j1 rule="hyper" parents="63 3621 4133"/>
    </justification>
  </clause>

  <clause id="4141">
    <literal><![CDATA[
      K(x,T(y \ z,z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(40,a,3878,a,b,4133,a),flip(a)].">
      <j1 rule="hyper" parents="40 3878 4133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4144">
    <literal><![CDATA[
      K((x * y) / x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3870,a(flip),b,4136,a),flip(a)].">
      <j1 rule="hyper" parents="63 3870 4136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3869,a(flip),b,4136,a)].">
      <j1 rule="hyper" parents="63 3869 4136"/>
    </justification>
  </clause>

  <clause id="4146">
    <literal><![CDATA[
      K(x,T(y \ z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(116(a,1),4136(a,1,2,1))].">
      <j1 rule="para" parents="116 4136"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(116(a,1),4137(a,1,2))].">
      <j1 rule="para" parents="116 4137"/>
    </justification>
  </clause>

  <clause id="4150">
    <literal><![CDATA[
      x \ (K(y,T(z,x)) * u) = (x * K(z,y)) \ u
    ]]></literal>
    <justification jstring="[para(4128(a,1),3009(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4128 3009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4152">
    <literal><![CDATA[
      K(x / y,y / z) = K(y \ x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3869,a(flip),b,4141,a),flip(a)].">
      <j1 rule="hyper" parents="63 3869 4141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[para(4144(a,1),3128(a,1,1))].">
      <j1 rule="para" parents="4144 3128"/>
    </justification>
  </clause>

  <clause id="4154">
    <literal><![CDATA[
      x * K(T(x,y),y \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,4148,a,b,2806,a(flip))].">
      <j1 rule="hyper" parents="139 4148 2806"/>
    </justification>
  </clause>

  <clause id="4155">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3865(a,2),4134(a,1))].">
      <j1 rule="para" parents="3865 4134"/>
    </justification>
  </clause>

  <clause id="4156">
    <literal><![CDATA[
      K(x \ y,z) * K(z,y / x) = K(x,K(z,x \ y))
    ]]></literal>
    <justification jstring="[para(4146(a,1),4096(a,1,2))].">
      <j1 rule="para" parents="4146 4096"/>
    </justification>
  </clause>

  <clause id="4157">
    <literal><![CDATA[
      K(x,y) * ((z * K(y,x)) * u) = T(z,K(x,y)) * u
    ]]></literal>
    <justification jstring="[para(4110(a,1),656(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4110 656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4158">
    <literal><![CDATA[
      T(x \ K(y,z),K(y,z)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(3828(a,1),4111(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3828 4111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4159">
    <literal><![CDATA[
      K(x,y) * (z * (u * K(y,x))) = T(z * u,K(x,y))
    ]]></literal>
    <justification jstring="[para(3763(a,1),4111(a,1,2))].">
      <j1 rule="para" parents="3763 4111"/>
    </justification>
  </clause>

  <clause id="4160">
    <literal><![CDATA[
      T(x * (y * z),K(y,z)) = K(y,z) * (x * (z * y))
    ]]></literal>
    <justification jstring="[para(3933(a,1),4111(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3933 4111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4161">
    <literal><![CDATA[
      T(x * (y * T(z,u)),K(z,u)) = K(z,u) * (x * (y * z))
    ]]></literal>
    <justification jstring="[para(3942(a,1),4115(a,1,1))].">
      <j1 rule="para" parents="3942 4115"/>
    </justification>
  </clause>

  <clause id="4162">
    <literal><![CDATA[
      (x \ T(y,K(z,u))) * K(z,u) = x \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,4118,a(flip),b,3762,a),flip(a)].">
      <j1 rule="hyper" parents="133 4118 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4163">
    <literal><![CDATA[
      T(x,K(y,z * x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,2815,a,b,4124,a),flip(a)].">
      <j1 rule="hyper" parents="316 2815 4124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4165">
    <literal><![CDATA[
      K(x / (y / z),y / u) = K(y \ (x * z),u \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3393,a(flip),b,4152,a)].">
      <j1 rule="hyper" parents="63 3393 4152"/>
    </justification>
  </clause>

  <clause id="4166">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z * x) * u) = (z * T(x,y)) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,4153,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 4153 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4168">
    <literal><![CDATA[
      T(x,T(y \ z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3861,a(flip),b,4154,a)].">
      <j1 rule="hyper" parents="63 3861 4154"/>
    </justification>
  </clause>

  <clause id="4170">
    <literal><![CDATA[
      T(x * (y \ z),K(y,y \ z)) = (y \ z) * T(x,z / y)
    ]]></literal>
    <justification jstring="[para(4168(a,1),4114(a,2,2))].">
      <j1 rule="para" parents="4168 4114"/>
    </justification>
  </clause>

  <clause id="4172">
    <literal><![CDATA[
      L(x,y,(K(z,u) * w) \ v5) = L(x,y,w \ v5)
    ]]></literal>
    <justification jstring="[para(477(a,1),4036(a,1,3)),flip(a)].">
      <j1 rule="para" parents="477 4036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4173">
    <literal><![CDATA[
      L(x,y,(z * u) \ w) = L(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[para(2765(a,1),4036(a,1,3))].">
      <j1 rule="para" parents="2765 4036"/>
    </justification>
  </clause>

  <clause id="4174">
    <literal><![CDATA[
      L(x,y,z \ ((u / w) * v5)) = L(x,y,z \ ((w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(2774(a,1),4036(a,1,3,2))].">
      <j1 rule="para" parents="2774 4036"/>
    </justification>
  </clause>

  <clause id="4175">
    <literal><![CDATA[
      a(x \ (K(y,z) * (u * w)),v5,v6) = a(x \ (w * u),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,3357,a,b,4037,a),flip(a)].">
      <j1 rule="hyper" parents="316 3357 4037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4176">
    <literal><![CDATA[
      a((x * y) \ z,u,w) = a((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(2765(a,1),4037(a,1,1))].">
      <j1 rule="para" parents="2765 4037"/>
    </justification>
  </clause>

  <clause id="4177">
    <literal><![CDATA[
      a(x \ ((y / z) * u),w,v5) = a(x \ ((z \ y) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(2774(a,1),4037(a,1,1,2))].">
      <j1 rule="para" parents="2774 4037"/>
    </justification>
  </clause>

  <clause id="4178">
    <literal><![CDATA[
      a(x \ ((y / z) \ u),w,v5) = a(x \ ((z \ y) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(3143(a,1),4037(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3143 4037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4179">
    <literal><![CDATA[
      a(x * (K(y,z) * u),w,v5) = a(u * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,2771,a,b,4041,a),flip(a)].">
      <j1 rule="hyper" parents="316 2771 4041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4180">
    <literal><![CDATA[
      a(x * ((y / z) \ u),w,v5) = a(x * ((z \ y) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(3143(a,1),4041(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3143 4041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4181">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ y = (y \ (x \ y)) * y
    ]]></literal>
    <justification jstring="[para(83(a,1),4053(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 4053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4183">
    <literal><![CDATA[
      K(x \ K(x,y),z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[para(2974(a,1),4132(a,1,1))].">
      <j1 rule="para" parents="2974 4132"/>
    </justification>
  </clause>

  <clause id="4184">
    <literal><![CDATA[
      K(x \ K(x,y),T(z,y)) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,4136,a(flip),b,4183,a),flip(a)].">
      <j1 rule="hyper" parents="316 4136 4183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4185">
    <literal><![CDATA[
      K(x,K(y \ K(y,x),z)) = K(x,K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(4183(a,2),4121(a,1,2))].">
      <j1 rule="para" parents="4183 4121"/>
    </justification>
  </clause>

  <clause id="4187">
    <literal><![CDATA[
      L(x,y,(z * K(u,w)) \ v5) = L(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(4150(a,1),4036(a,1,3))].">
      <j1 rule="para" parents="4150 4036"/>
    </justification>
  </clause>

  <clause id="4188">
    <literal><![CDATA[
      a((x * K(y,z)) \ u,w,v5) = a(x \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(4150(a,1),4037(a,1,1))].">
      <j1 rule="para" parents="4150 4037"/>
    </justification>
  </clause>

  <clause id="4189">
    <literal><![CDATA[
      (K(x,y) * (z \ 1)) \ R(T(z \ K(x,y),K(x,y)),u,w) = (z \ K(x,y)) \ R(z \ K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(4158(a,1),3104(a,1,1))].">
      <j1 rule="para" parents="4158 3104"/>
    </justification>
  </clause>

  <clause id="4190">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((z * w) * u)) = L(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,3244,a(flip),b,4173,a),flip(a)].">
      <j1 rule="hyper" parents="316 3244 4173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4191">
    <literal><![CDATA[
      x / L(y,z,(y * z) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(209,a,4173,a,b,1604,a(flip))].">
      <j1 rule="hyper" parents="209 4173 1604"/>
    </justification>
  </clause>

  <clause id="4192">
    <literal><![CDATA[
      L(x,y,(z * u) \ (u * (w * z))) = L(x,y,L(T(w,z),z,u))
    ]]></literal>
    <justification jstring="[para(247(a,1),4173(a,1,3)),flip(a)].">
      <j1 rule="para" parents="247 4173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4193">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,w) = a(L(T(z,x),x,y),u,w)
    ]]></literal>
    <justification jstring="[para(247(a,1),4176(a,1,1)),flip(a)].">
      <j1 rule="para" parents="247 4176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4194">
    <literal><![CDATA[
      a(((T(x,y) \ z) * u) * w,v5,v6) = a(w * ((x \ z) * u),v5,v6)
    ]]></literal>
    <justification jstring="[para(2902(a,1),4179(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2902 4179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4195">
    <literal><![CDATA[
      K(x,y \ K(y,z)) \ K(z,K(x,y \ 1)) = K(y \ K(y,z),T(x,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,4185,a(flip),b,4096,a)].">
      <j1 rule="hyper" parents="133 4185 4096"/>
    </justification>
  </clause>

  <clause id="4196">
    <literal><![CDATA[
      L(x,y,(z \ K(u,w)) \ v5) = L(x,y,(z \ 1) \ v5)
    ]]></literal>
    <justification jstring="[para(3780(a,1),4187(a,1,3,1))].">
      <j1 rule="para" parents="3780 4187"/>
    </justification>
  </clause>

  <clause id="4197">
    <literal><![CDATA[
      L(x,y,(z * (u * w)) \ v5) = L(x,y,(z * (w * u)) \ v5)
    ]]></literal>
    <justification jstring="[para(3933(a,1),4187(a,1,3,1))].">
      <j1 rule="para" parents="3933 4187"/>
    </justification>
  </clause>

  <clause id="4198">
    <literal><![CDATA[
      L(x,y,(z \ (u / w)) \ v5) = L(x,y,(z \ (w \ u)) \ v5)
    ]]></literal>
    <justification jstring="[para(3917(a,1),4187(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="3917 4187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4199">
    <literal><![CDATA[
      a((x \ T(y,z)) \ u,w,v5) = a((x \ y) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(3846(a,1),4188(a,1,1,1))].">
      <j1 rule="para" parents="3846 4188"/>
    </justification>
  </clause>

  <clause id="4200">
    <literal><![CDATA[
      a((x \ (y * z)) \ u,w,v5) = a((x \ (z * y)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(3922(a,1),4188(a,1,1,1))].">
      <j1 rule="para" parents="3922 4188"/>
    </justification>
  </clause>

  <clause id="4201">
    <literal><![CDATA[
      a((x \ (K(y,z) * u)) \ w,v5,v6) = a((x \ u) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(3914(a,1),4188(a,1,1,1))].">
      <j1 rule="para" parents="3914 4188"/>
    </justification>
  </clause>

  <clause id="4202">
    <literal><![CDATA[
      a((x \ (y / z)) \ u,w,v5) = a((x \ (z \ y)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(3917(a,1),4188(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3917 4188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4204">
    <literal><![CDATA[
      R(x,y,z / (x * y)) \ z = y * T(z / (x * y),x * y)
    ]]></literal>
    <justification jstring="[para(4050(a,2),319(a,1,1))].">
      <j1 rule="para" parents="4050 319"/>
    </justification>
  </clause>

  <clause id="4205">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(z,u) = x * ((y \ 1) * (y * K(z,u)))
    ]]></literal>
    <justification jstring="[para(3760(a,1),3763(a,2,2))].">
      <j1 rule="para" parents="3760 3763"/>
    </justification>
  </clause>

  <clause id="4206">
    <literal><![CDATA[
      (x \ K(x * y,x \ 1)) \ y = y / (x \ 1)
    ]]></literal>
    <justification jstring="[para(3565(a,1),3807(a,1,1,2))].">
      <j1 rule="para" parents="3565 3807"/>
    </justification>
  </clause>

  <clause id="4207">
    <literal><![CDATA[
      (K(x,y) * (z * z)) \ 1 = z \ (z \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,3915,a(flip),b,3851,a),flip(a)].">
      <j1 rule="hyper" parents="316 3915 3851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      (x * x) \ K(y,z) = x \ (x \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2975,a(flip),b,4207,a)].">
      <j1 rule="hyper" parents="63 2975 4207"/>
    </justification>
  </clause>

  <clause id="4209">
    <literal><![CDATA[
      T(K(x,y),T(y,z) * u) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(4001(a,1),3904(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4001 3904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4210">
    <literal><![CDATA[
      K(x,T(y,K(y,z) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3904,a,b,4209,a)].">
      <j1 rule="hyper" parents="63 3904 4209"/>
    </justification>
  </clause>

  <clause id="4213">
    <literal><![CDATA[
      K(x,T(y,z * K(u,y))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4023(a,1),4210(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4023 4210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4215">
    <literal><![CDATA[
      K(x,T(y,z \ T(y,u))) = K(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(3531(a,1),4213(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3531 4213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4216">
    <literal><![CDATA[
      K(x,T(y,z \ y)) * (z \ T(y,u)) = (z \ T(y,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,4215,a(flip),b,4126,a)].">
      <j1 rule="hyper" parents="138 4215 4126"/>
    </justification>
  </clause>

  <clause id="4217">
    <literal><![CDATA[
      (x \ 1) * (y * (z * K(x,x \ 1))) = (1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(3928(a,1),1208(a,1,2))].">
      <j1 rule="para" parents="3928 1208"/>
    </justification>
  </clause>

  <clause id="4218">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * x)) = y * (z * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(2564(a,1),3928(a,2,2))].">
      <j1 rule="para" parents="2564 3928"/>
    </justification>
  </clause>

  <clause id="4219">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * (x \ 1))) = y * (z * (1 / x))
    ]]></literal>
    <justification jstring="[para(3151(a,1),3928(a,2,2))].">
      <j1 rule="para" parents="3151 3928"/>
    </justification>
  </clause>

  <clause id="4220">
    <literal><![CDATA[
      ((x * y) * (z * K(u,w))) / ((y * z) * K(u,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,20,a,b,3931,a),flip(a)].">
      <j1 rule="hyper" parents="316 20 3931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4221">
    <literal><![CDATA[
      (x * y) * (K(z,u) * K(w,v5)) = x * ((y * K(z,u)) * K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(138,a,3764,a(flip),b,3931,a)].">
      <j1 rule="hyper" parents="138 3764 3931"/>
    </justification>
  </clause>

  <clause id="4222">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * K(u,w)) = x * ((y * z) * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(138,a,202,a(flip),b,3931,a)].">
      <j1 rule="hyper" parents="138 202 3931"/>
    </justification>
  </clause>

  <clause id="4224">
    <literal><![CDATA[
      (x * (y * (z * K(u,w)))) / v5 = (x * (y * z)) / (v5 * K(w,u))
    ]]></literal>
    <justification jstring="[para(3927(a,1),3931(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3927 3931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4225">
    <literal><![CDATA[
      x \ (y * ((z / (u * u)) * K(w,v5))) = (x \ ((y * z) / (u * u))) * K(w,v5)
    ]]></literal>
    <justification jstring="[para(683(a,2),3932(a,2,1,2))].">
      <j1 rule="para" parents="683 3932"/>
    </justification>
  </clause>

  <clause id="4226">
    <literal><![CDATA[
      x \ (y * (z * (u * K(w,v5)))) = (x \ (y * (z * u))) * K(w,v5)
    ]]></literal>
    <justification jstring="[para(3763(a,1),3932(a,1,2,2))].">
      <j1 rule="para" parents="3763 3932"/>
    </justification>
  </clause>

  <clause id="4227">
    <literal><![CDATA[
      (x \ (y * (z * u))) * K(w,T(v5,u)) = x \ (y * (z * (K(w,v5) * u)))
    ]]></literal>
    <justification jstring="[para(3941(a,1),3932(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3941 3932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      (x * y) / R(y,z,u) = R(y,z,u) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3614,a(flip),b,3945,a),flip(a)].">
      <j1 rule="hyper" parents="63 3614 3945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4229">
    <literal><![CDATA[
      a(x,y,z) * (x * ((y * z) * K(u,w))) = ((x * y) * z) * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(138,a,2329,a,b,3948,a)].">
      <j1 rule="hyper" parents="138 2329 3948"/>
    </justification>
  </clause>

  <clause id="4230">
    <literal><![CDATA[
      (x * ((y \ z) * y)) / (u * (w * K(y \ z,y))) = (x * z) / (u * w)
    ]]></literal>
    <justification jstring="[para(3934(a,1),3948(a,1,1))].">
      <j1 rule="para" parents="3934 3948"/>
    </justification>
  </clause>

  <clause id="4231">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(u,z)) = K(z,u) * (x * (K(u,z) * y))
    ]]></literal>
    <justification jstring="[para(3008(a,1),3966(a,1,1,2))].">
      <j1 rule="para" parents="3008 3966"/>
    </justification>
  </clause>

  <clause id="4232">
    <literal><![CDATA[
      T((x / y) / (z / y),y \ z) = (y \ z) \ (x / ((y \ z) \ z))
    ]]></literal>
    <justification jstring="[para(4009(a,1),116(a,1,1))].">
      <j1 rule="para" parents="4009 116"/>
    </justification>
  </clause>

  <clause id="4233">
    <literal><![CDATA[
      L(x,1 / x,(1 / x) \ (y / x)) = (y / x) \ ((y / ((x \ 1) \ 1)) / (x \ 1))
    ]]></literal>
    <justification jstring="[para(4009(a,2),1642(a,2,2))].">
      <j1 rule="para" parents="4009 1642"/>
    </justification>
  </clause>

  <clause id="4234">
    <literal><![CDATA[
      a(x \ (y * (z / u)),w,v5) = a(x \ (y * (u \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(116(a,1),4035(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="116 4035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4235">
    <literal><![CDATA[
      a(x \ (y * ((z \ u) \ u)),w,v5) = a(x \ (y * z),w,v5)
    ]]></literal>
    <justification jstring="[para(115(a,1),4035(a,1,1,2,2))].">
      <j1 rule="para" parents="115 4035"/>
    </justification>
  </clause>

  <clause id="4236">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ z,x,x) = (z * (T(x,u) \ 1)) * T(x,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,3375,a,b,4039,a)].">
      <j1 rule="hyper" parents="316 3375 4039"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      ((x * x) / y) \ K(z,u) = y * ((x * x) \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3802,a,b,4045,a)].">
      <j1 rule="hyper" parents="63 3802 4045"/>
    </justification>
  </clause>

  <clause id="4238">
    <literal><![CDATA[
      x \ (y * ((z * z) \ K(u,w))) = (x \ (y / (z * z))) * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,4045,a(flip),b,3762,a)].">
      <j1 rule="hyper" parents="133 4045 3762"/>
    </justification>
  </clause>

  <clause id="4240">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * K(T(y,x),u)) = T(K(x,y),z) * T(T(y,x),u)
    ]]></literal>
    <justification jstring="[para(3022(a,1),4081(a,1,2))].">
      <j1 rule="para" parents="3022 4081"/>
    </justification>
  </clause>

  <clause id="4241">
    <literal><![CDATA[
      K(x \ y,z) * K(z,y / x) = K(z,K(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(316,a,4084,a,b,4156,a),flip(a)].">
      <j1 rule="hyper" parents="316 4084 4156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4242">
    <literal><![CDATA[
      K(x,y) * ((z \ (u \ T(y,x))) * w) = T(z \ (u \ y),K(x,y)) * w
    ]]></literal>
    <justification jstring="[para(3912(a,1),4157(a,1,2,1))].">
      <j1 rule="para" parents="3912 4157"/>
    </justification>
  </clause>

  <clause id="4243">
    <literal><![CDATA[
      x * (K(y,x) * (z * K(x,y))) = T(x * z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3044,a(flip),b,4159,a)].">
      <j1 rule="hyper" parents="63 3044 4159"/>
    </justification>
  </clause>

  <clause id="4244">
    <literal><![CDATA[
      T(x * (y * z),K(y,z)) = (y * z) * T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,3063,a(flip),b,4160,a),flip(a)].">
      <j1 rule="hyper" parents="316 3063 4160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4245">
    <literal><![CDATA[
      T(x \ (K(y,z) * u),K(y,z)) = K(y,z) * (x \ T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(4162(a,1),4115(a,1,1))].">
      <j1 rule="para" parents="4162 4115"/>
    </justification>
  </clause>

  <clause id="4246">
    <literal><![CDATA[
      K(x \ (y * z),u \ x) = K(y * (z / x),x / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3604,a(flip),b,4165,a),flip(a)].">
      <j1 rule="hyper" parents="63 3604 4165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4247">
    <literal><![CDATA[
      L(x,y,z \ ((u * T(w,v5)) * v6)) = L(x,y,z \ ((u * w) * v6))
    ]]></literal>
    <justification jstring="[para(4166(a,1),4036(a,1,3,2))].">
      <j1 rule="para" parents="4166 4036"/>
    </justification>
  </clause>

  <clause id="4249">
    <literal><![CDATA[
      ((x * x) / y) \ K(z,u) = y * (x \ (x \ K(z,u)))
    ]]></literal>
    <justification jstring="[para(4208(a,1),4237(a,2,2))].">
      <j1 rule="para" parents="4208 4237"/>
    </justification>
  </clause>

  <clause id="4250">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,x) = K(x,K(z,z \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3635,a,b,4241,a)].">
      <j1 rule="hyper" parents="63 3635 4241"/>
    </justification>
  </clause>

  <clause id="4251">
    <literal><![CDATA[
      T(x * y,K(z,x)) = x * T(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(4111(a,1),4243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4111 4243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4252">
    <literal><![CDATA[
      x * T(x \ y,K(z,x)) = T(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(10(a,1),4251(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4253">
    <literal><![CDATA[
      x * T(x \ y,K(x,z)) = T(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(4106(a,1),4252(a,1,2))].">
      <j1 rule="para" parents="4106 4252"/>
    </justification>
  </clause>

  <clause id="4254">
    <literal><![CDATA[
      x * T(x \ y,K(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,4106,a,b,4253,a),flip(a)].">
      <j1 rule="hyper" parents="316 4106 4253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4255">
    <literal><![CDATA[
      T(x * (y \ 1),K(y,z)) = T(x,K(y,z)) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(138,a,4254,a(flip),b,852,a),flip(a)].">
      <j1 rule="hyper" parents="138 4254 852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4256">
    <literal><![CDATA[
      (x * T(y,(z \ R(z,u,w)) * x)) \ T(y * (x * (z \ R(z,u,w))),K(x,z \ R(z,u,w))) = R(z \ R(z,u,w),x,T(y,(z \ R(z,u,w)) * x))
    ]]></literal>
    <justification jstring="[para(4244(a,2),2607(a,1,2))].">
      <j1 rule="para" parents="4244 2607"/>
    </justification>
  </clause>

  <clause id="4258">
    <literal><![CDATA[
      (x \ (y * y)) * (y \ (y \ K(z,u))) = x \ K(z,u)
    ]]></literal>
    <justification jstring="[para(80(a,1),4249(a,1,1)),flip(a)].">
      <j1 rule="para" parents="80 4249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4259">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,x) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,4122,a(flip),b,4250,a),flip(a)].">
      <j1 rule="hyper" parents="316 4122 4250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4260">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,4092,a,b,4259,a),flip(a)].">
      <j1 rule="hyper" parents="316 4092 4259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4261">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3598,a(flip),b,3597,a)].">
      <j1 rule="hyper" parents="63 3598 3597"/>
    </justification>
  </clause>

  <clause id="4263">
    <literal><![CDATA[
      L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),4261(a,2,1,1))].">
      <j1 rule="para" parents="10 4261"/>
    </justification>
  </clause>

  <clause id="4265">
    <literal><![CDATA[
      K((x * (y / z)) \ (x * y),u) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(83(a,1),4261(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 4261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4267">
    <literal><![CDATA[
      K((x \ y) \ z,u) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3758,a(flip),b,4263,a)].">
      <j1 rule="hyper" parents="63 3758 4263"/>
    </justification>
  </clause>

  <clause id="4268">
    <literal><![CDATA[
      K((x \ y) \ z,T(u,y)) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4145,a(flip),b,4267,a),flip(a)].">
      <j1 rule="hyper" parents="316 4145 4267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4269">
    <literal><![CDATA[
      K((x \ y) \ z,u) = K((y \ x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,3557,a(flip),b,4267,a),flip(a)].">
      <j1 rule="hyper" parents="316 3557 4267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4270">
    <literal><![CDATA[
      K(x \ (y * z),T(u,z)) = K(z / (y \ x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4140,a(flip),b,4267,a),flip(a)].">
      <j1 rule="hyper" parents="63 4140 4267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4271">
    <literal><![CDATA[
      x * K(y \ (z * x),z \ y) = ((z \ y) \ x) * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,4267,a(flip),b,95,a)].">
      <j1 rule="hyper" parents="139 4267 95"/>
    </justification>
  </clause>

  <clause id="4272">
    <literal><![CDATA[
      x * K((y \ z) * x,z \ y) = ((z \ y) \ x) * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,4269,a(flip),b,95,a)].">
      <j1 rule="hyper" parents="139 4269 95"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(104(a,2),4265(a,1,1))].">
      <j1 rule="para" parents="104 4265"/>
    </justification>
  </clause>

  <clause id="4276">
    <literal><![CDATA[
      L(K(x,y),z * x,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),4274(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 4274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4279">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3758,a(flip),b,4276,a),flip(a)].">
      <j1 rule="hyper" parents="63 3758 4276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4280">
    <literal><![CDATA[
      K(L(x,y,z),u) = 1 / K(u,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,2971,a,b,4279,a),flip(a)].">
      <j1 rule="hyper" parents="316 2971 4279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4281">
    <literal><![CDATA[
      (x * y) / x = y * K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(139,a,4279,a,b,2720,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 4279 2720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      T(x,L(y,z,u)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(209,a,4279,a(flip),b,2948,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="209 4279 2948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4284">
    <literal><![CDATA[
      (L(x,y,z) * u) / L(x,y,z) = u * K(x,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,4279,a(flip),b,2720,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 4279 2720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4285">
    <literal><![CDATA[
      K((x * y) \ z,u) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[para(298(a,1),4279(a,1,1))].">
      <j1 rule="para" parents="298 4279"/>
    </justification>
  </clause>

  <clause id="4286">
    <literal><![CDATA[
      K(x,x \ 1) * K(y \ (1 / x),x * y) = ((x * y) \ K(x,x \ 1)) * (x * y)
    ]]></literal>
    <justification jstring="[para(4279(a,1),1105(a,1,2))].">
      <j1 rule="para" parents="4279 1105"/>
    </justification>
  </clause>

  <clause id="4287">
    <literal><![CDATA[
      K(x,L(y,z,u)) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[para(4279(a,1),2967(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4279 2967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4288">
    <literal><![CDATA[
      R(x * K(y,x),L(y,z,u),L(y,z,u)) = (L(y,z,u) * x) * (L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4279(a,1),2748(a,1,1,2))].">
      <j1 rule="para" parents="4279 2748"/>
    </justification>
  </clause>

  <clause id="4289">
    <literal><![CDATA[
      K(x,y) * L(x,z,u) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4279(a,1),2804(a,1,1))].">
      <j1 rule="para" parents="4279 2804"/>
    </justification>
  </clause>

  <clause id="4290">
    <literal><![CDATA[
      K(x,y) * (L(T(x,y),z,u) \ w) = L(x,z,u) \ w
    ]]></literal>
    <justification jstring="[para(4279(a,1),2903(a,1,1))].">
      <j1 rule="para" parents="4279 2903"/>
    </justification>
  </clause>

  <clause id="4291">
    <literal><![CDATA[
      K(x,L(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2976,a,4280,a)].">
      <j1 rule="hyper" parents="2976 4280"/>
    </justification>
  </clause>

  <clause id="4292">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,3758,a,b,4291,a)].">
      <j1 rule="hyper" parents="316 3758 4291"/>
    </justification>
  </clause>

  <clause id="4295">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[hyper(138,a,4291,a,b,2753,a(flip))].">
      <j1 rule="hyper" parents="138 4291 2753"/>
    </justification>
  </clause>

  <clause id="4297">
    <literal><![CDATA[
      K(x,y) * T(L(y,z,u),x) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,4291,a(flip),b,2937,a(flip))].">
      <j1 rule="hyper" parents="138 4291 2937"/>
    </justification>
  </clause>

  <clause id="4298">
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) * x) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,4291,a(flip),b,2753,a(flip))].">
      <j1 rule="hyper" parents="138 4291 2753"/>
    </justification>
  </clause>

  <clause id="4299">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,w)) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[para(720(a,1),4291(a,1,2)),flip(a)].">
      <j1 rule="para" parents="720 4291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4301">
    <literal><![CDATA[
      (x * y) * K(z,L(u,w,v5)) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(4291(a,1),3763(a,2,2,2))].">
      <j1 rule="para" parents="4291 3763"/>
    </justification>
  </clause>

  <clause id="4302">
    <literal><![CDATA[
      (1 / (K(x,y) / x)) * L(y,z,u) = L(y,z,u) * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(4291(a,1),4072(a,1,1,2,1))].">
      <j1 rule="para" parents="4291 4072"/>
    </justification>
  </clause>

  <clause id="4303">
    <literal><![CDATA[
      T(x,L(x \ y,z,u)) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(316,a,2957,a,b,4282,a),flip(a)].">
      <j1 rule="hyper" parents="316 2957 4282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4304">
    <literal><![CDATA[
      T(x,L(y,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2952,a,b,4282,a),flip(a)].">
      <j1 rule="hyper" parents="316 2952 4282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4305">
    <literal><![CDATA[
      T(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(4282(a,2),2962(a,1))].">
      <j1 rule="para" parents="4282 2962"/>
    </justification>
  </clause>

  <clause id="4306">
    <literal><![CDATA[
      L(x,y,z) \ (u * L(x,y,z)) = T(u,x)
    ]]></literal>
    <justification jstring="[hyper(383,a,4304,a)].">
      <j1 rule="hyper" parents="383 4304"/>
    </justification>
  </clause>

  <clause id="4307">
    <literal><![CDATA[
      T(x / L(y,z,u),y) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(377,a,4304,a),flip(a)].">
      <j1 rule="hyper" parents="377 4304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4308">
    <literal><![CDATA[
      T(x,L(L(y,z,u),w,v5)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,4304,a(flip),b,4304,a),flip(a)].">
      <j1 rule="hyper" parents="316 4304 4304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4309">
    <literal><![CDATA[
      T(x / y,L(y,z,u)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,116,a(flip),b,4304,a),flip(a)].">
      <j1 rule="hyper" parents="316 116 4304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4310">
    <literal><![CDATA[
      T(x,L(y,z,u)) = y \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,22,a(flip),b,4304,a),flip(a)].">
      <j1 rule="hyper" parents="316 22 4304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4311">
    <literal><![CDATA[
      x * T(y,L(x,z,u)) = y * x
    ]]></literal>
    <justification jstring="[hyper(139,a,4304,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="139 4304 22"/>
    </justification>
  </clause>

  <clause id="4312">
    <literal><![CDATA[
      (1 / L(x,y,z)) * ((L(x,y,z) \ u) * L(x,y,z)) = T((1 / L(x,y,z)) * u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,793,a,b,4304,a)].">
      <j1 rule="hyper" parents="63 793 4304"/>
    </justification>
  </clause>

  <clause id="4313">
    <literal><![CDATA[
      L(x,y,z) * T(u,x) = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,4304,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 4304 22"/>
    </justification>
  </clause>

  <clause id="4315">
    <literal><![CDATA[
      L(x,y,z) * L(T(u,x),w,v5) = L(u,w,v5) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4304(a,1),251(a,1,2,1))].">
      <j1 rule="para" parents="4304 251"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      L(x,y,z) * R(T(u,x),w,v5) = R(u,w,v5) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4304(a,1),252(a,1,2,1))].">
      <j1 rule="para" parents="4304 252"/>
    </justification>
  </clause>

  <clause id="4317">
    <literal><![CDATA[
      L(R(x,y,L(x,z,u)),z,u) = y \ T(L(x,z,u) * y,x)
    ]]></literal>
    <justification jstring="[para(4304(a,1),1635(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4304 1635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4318">
    <literal><![CDATA[
      L(x,y,z) * (T(u,x) * T(w,u * L(x,y,z))) = L(w,u,L(x,y,z)) * (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(4304(a,1),3292(a,1,2,1))].">
      <j1 rule="para" parents="4304 3292"/>
    </justification>
  </clause>

  <clause id="4319">
    <literal><![CDATA[
      L(x,y,z) * (T(u,x) * K(w,v5)) = u * (L(x,y,z) * K(w,v5))
    ]]></literal>
    <justification jstring="[para(4304(a,1),4004(a,1,2,1))].">
      <j1 rule="para" parents="4304 4004"/>
    </justification>
  </clause>

  <clause id="4320">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4287(a,2),2982(a,1,2))].">
      <j1 rule="para" parents="4287 2982"/>
    </justification>
  </clause>

  <clause id="4324">
    <literal><![CDATA[
      R(L(x,y,z) \ u,L(x,y,z),L(x,y,z) \ x) = x \ (u * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,725,a(flip),b,4309,a)].">
      <j1 rule="hyper" parents="63 725 4309"/>
    </justification>
  </clause>

  <clause id="4325">
    <literal><![CDATA[
      L(x,y,z) * (x \ u) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,4309,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 4309 22"/>
    </justification>
  </clause>

  <clause id="4326">
    <literal><![CDATA[
      x * (L(y,z,u) * (y \ w)) = x * ((w / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(4309(a,1),238(a,1,2,2))].">
      <j1 rule="para" parents="4309 238"/>
    </justification>
  </clause>

  <clause id="4327">
    <literal><![CDATA[
      (x / L(y,z,u)) * y = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,116,a(flip),b,4310,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 116 4310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4328">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * L(x,y,z))) = u * x
    ]]></literal>
    <justification jstring="[hyper(139,a,22,a(flip),b,4310,a(flip))].">
      <j1 rule="hyper" parents="139 22 4310"/>
    </justification>
  </clause>

  <clause id="4329">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u * x)) = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,4310,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 4310 22"/>
    </justification>
  </clause>

  <clause id="4330">
    <literal><![CDATA[
      (x * y) / (L(x,z,u) * y) = (y * x) / (y * L(x,z,u))
    ]]></literal>
    <justification jstring="[para(4311(a,1),3981(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4311 3981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4332">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * T(v5,x) = v5 * L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,4308,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 4308 22"/>
    </justification>
  </clause>

  <clause id="4333">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) / x = u / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2732,a(flip),b,4281,a),flip(a)].">
      <j1 rule="hyper" parents="316 2732 4281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4334">
    <literal><![CDATA[
      ((x * y) / x) * L(x,z,u) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(138,a,4281,a,b,2722,a)].">
      <j1 rule="hyper" parents="138 4281 2722"/>
    </justification>
  </clause>

  <clause id="4335">
    <literal><![CDATA[
      R((x * y) / x,L(x,z,u),L(x,z,u)) = (L(x,z,u) * y) * (L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4281(a,2),2748(a,1,1))].">
      <j1 rule="para" parents="4281 2748"/>
    </justification>
  </clause>

  <clause id="4336">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (x * u) = (u * L(x,y,z)) \ (u * x)
    ]]></literal>
    <justification jstring="[hyper(133,a,4295,a(flip),b,2758,a),flip(a)].">
      <j1 rule="hyper" parents="133 4295 2758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4338">
    <literal><![CDATA[
      (x * y) \ (L(x,z,u) * y) = (y * x) \ (y * L(x,z,u))
    ]]></literal>
    <justification jstring="[para(4295(a,1),2763(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4295 2763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4339">
    <literal><![CDATA[
      (L(x \ y,z,u) * x) * ((x \ y) \ y) = (x * L(x \ y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,4303,a(flip),b,921,a(flip))].">
      <j1 rule="hyper" parents="139 4303 921"/>
    </justification>
  </clause>

  <clause id="4340">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ y) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,4303,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 4303 22"/>
    </justification>
  </clause>

  <clause id="4342">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,3993,a(flip),b,4285,a),flip(a)].">
      <j1 rule="hyper" parents="316 3993 4285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4344">
    <literal><![CDATA[
      K(x,y) * L(T(y,x),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(3006,a,4289,a)].">
      <j1 rule="hyper" parents="3006 4289"/>
    </justification>
  </clause>

  <clause id="4345">
    <literal><![CDATA[
      K(x,y) * (L(x,z,u) * w) = L(T(x,y),z,u) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,4289,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 4289 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4346">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,u) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,4289,a(flip),b,2799,a)].">
      <j1 rule="hyper" parents="133 4289 2799"/>
    </justification>
  </clause>

  <clause id="4347">
    <literal><![CDATA[
      (x / y) \ L(T(y,y \ x),z,u) = (y \ x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,4289,a(flip),b,2773,a)].">
      <j1 rule="hyper" parents="133 4289 2773"/>
    </justification>
  </clause>

  <clause id="4348">
    <literal><![CDATA[
      L(T(x,y),z,u) \ T(x,y) = L(x,z,u) \ x
    ]]></literal>
    <justification jstring="[para(4289(a,1),2803(a,1,1))].">
      <j1 rule="para" parents="4289 2803"/>
    </justification>
  </clause>

  <clause id="4349">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (x * y) = L(x,z,u) \ (y * x)
    ]]></literal>
    <justification jstring="[para(4289(a,1),2763(a,1,1))].">
      <j1 rule="para" parents="4289 2763"/>
    </justification>
  </clause>

  <clause id="4350">
    <literal><![CDATA[
      K(x,y) * (x \ L(x,z,u)) = x \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4289(a,1),2909(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4289 2909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4353">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (x \ v5) = (v5 / x) * L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,4309,a(flip),b,4306,a)].">
      <j1 rule="hyper" parents="139 4309 4306"/>
    </justification>
  </clause>

  <clause id="4354">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * T(v5,x) = v5 * L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,2837,a(flip),b,4306,a)].">
      <j1 rule="hyper" parents="139 2837 4306"/>
    </justification>
  </clause>

  <clause id="4355">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (a(v5,v6,v7) \ v8) = (v8 / a(v5,v6,v7)) * L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,2326,a(flip),b,4306,a)].">
      <j1 rule="hyper" parents="139 2326 4306"/>
    </justification>
  </clause>

  <clause id="4357">
    <literal><![CDATA[
      L(x,y,z) * (x \ T(u,x)) = x \ (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(4306(a,1),1131(a,1,2,2))].">
      <j1 rule="para" parents="4306 1131"/>
    </justification>
  </clause>

  <clause id="4358">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) / ((x \ L(x,y,z)) * x) = L(x,y,z) \ ((x \ L(x,y,z)) * (x * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1568,a,b,4307,a)].">
      <j1 rule="hyper" parents="63 1568 4307"/>
    </justification>
  </clause>

  <clause id="4359">
    <literal><![CDATA[
      x / L(R(y,z,u) \ y,w,v5) = L(R(y,z,u) \ y,w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,3509,a(flip),b,4307,a)].">
      <j1 rule="hyper" parents="63 3509 4307"/>
    </justification>
  </clause>

  <clause id="4360">
    <literal><![CDATA[
      L(x,y,z) * (L(x,u,w) \ v5) = (v5 / L(x,u,w)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,4307,a(flip),b,4306,a)].">
      <j1 rule="hyper" parents="139 4307 4306"/>
    </justification>
  </clause>

  <clause id="4361">
    <literal><![CDATA[
      L(x,y / x,z) \ (z * y) = T(z * (y / x),x)
    ]]></literal>
    <justification jstring="[para(521(a,1),4307(a,1,1)),flip(a)].">
      <j1 rule="para" parents="521 4307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4362">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) \ z = T((z / (y * x)) * y,x)
    ]]></literal>
    <justification jstring="[para(1605(a,1),4307(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1605 4307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4363">
    <literal><![CDATA[
      L(x,y,z) * T(z * y,x) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(316,a,100,a(flip),b,4313,a),flip(a)].">
      <j1 rule="hyper" parents="316 100 4313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4364">
    <literal><![CDATA[
      L(x,y,z) = (z * (T(y,z) * x)) / T(y * z,x)
    ]]></literal>
    <justification jstring="[hyper(136,a,3285,a(flip),b,4313,a),flip(a)].">
      <j1 rule="hyper" parents="136 3285 4313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4365">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * x)) / T(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(136,a,100,a(flip),b,4313,a),flip(a)].">
      <j1 rule="hyper" parents="136 100 4313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4366">
    <literal><![CDATA[
      K(T(x,y) \ z,T(x,y)) = K(x \ z,T(x,y))
    ]]></literal>
    <justification jstring="[para(2733(a,1),4342(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2733 4342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4367">
    <literal><![CDATA[
      L(x,y,z) * (L(T(x,u),y,z) \ w) = K(u,x) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,4344,a(flip),b,478,a)].">
      <j1 rule="hyper" parents="138 4344 478"/>
    </justification>
  </clause>

  <clause id="4369">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),v5,v6) * (v6 * v5) = v6 * (v5 * L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(2436(a,1),4363(a,1,2))].">
      <j1 rule="para" parents="2436 4363"/>
    </justification>
  </clause>

  <clause id="4371">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) / (x * (z * y)) = (z * (y * x)) / ((z * y) * x)
    ]]></literal>
    <justification jstring="[para(4363(a,1),3981(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4363 3981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4372">
    <literal><![CDATA[
      (x * (L(L(y,z,u),w,v5) * v6)) / T(x * L(L(y,w,v5),z,u),v6) = L(v6,L(L(y,z,u),w,v5),x)
    ]]></literal>
    <justification jstring="[para(159(a,1),4365(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="159 4365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4373">
    <literal><![CDATA[
      (L(L(x,y,z),u,w) * (x * v5)) / T(x * L(L(x,u,w),y,z),v5) = L(v5,x,L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(839(a,1),4365(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="839 4365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4374">
    <literal><![CDATA[
      ((x * y) / x) * L(L(x,z,u),w,v5) = L(L(x,z,u),w,v5) * y
    ]]></literal>
    <justification jstring="[hyper(138,a,4281,a,b,4284,a)].">
      <j1 rule="hyper" parents="138 4281 4284"/>
    </justification>
  </clause>

  <clause id="4376">
    <literal><![CDATA[
      (L(x \ y,z,u) * x) \ ((x \ y) * x) = (x * L(x \ y,z,u)) \ y
    ]]></literal>
    <justification jstring="[para(4298(a,1),2784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4298 2784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4377">
    <literal><![CDATA[
      (x * L(y,z,u)) / y = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,1438,a,b,4325,a)].">
      <j1 rule="hyper" parents="316 1438 4325"/>
    </justification>
  </clause>

  <clause id="4378">
    <literal><![CDATA[
      L(x,y,z) * (x \ (z * y)) = (z * (y * x)) / x
    ]]></literal>
    <justification jstring="[hyper(316,a,1465,a(flip),b,4325,a),flip(a)].">
      <j1 rule="hyper" parents="316 1465 4325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      L(x,y,z) * (x \ K(u,w)) = K(u,w) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,1461,a(flip),b,4325,a),flip(a)].">
      <j1 rule="hyper" parents="316 1461 4325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4380">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) * x = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,4325,a,b,1438,a)].">
      <j1 rule="hyper" parents="138 4325 1438"/>
    </justification>
  </clause>

  <clause id="4381">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) / w = ((u / x) * L(x,y,z)) / w
    ]]></literal>
    <justification jstring="[hyper(136,a,4325,a,b,12,a)].">
      <j1 rule="hyper" parents="136 4325 12"/>
    </justification>
  </clause>

  <clause id="4382">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1126,a,b,4325,a)].">
      <j1 rule="hyper" parents="63 1126 4325"/>
    </justification>
  </clause>

  <clause id="4383">
    <literal><![CDATA[
      (x \ y) * ((z * (x \ y)) \ (z * y)) = (y / x) * L(x,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,821,a(flip),b,4325,a)].">
      <j1 rule="hyper" parents="63 821 4325"/>
    </justification>
  </clause>

  <clause id="4384">
    <literal><![CDATA[
      (x * x) \ (((x * x) / y) * L(y,z,u)) = T(y \ L(y,z,u),x * x)
    ]]></literal>
    <justification jstring="[hyper(390,a,4325,a(flip),b,1136,a),flip(a)].">
      <j1 rule="hyper" parents="390 4325 1136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4385">
    <literal><![CDATA[
      x * ((y / x) * L(x,z,u)) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,4325,a(flip),b,1126,a)].">
      <j1 rule="hyper" parents="139 4325 1126"/>
    </justification>
  </clause>

  <clause id="4388">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ ((u / x) * L(x,y,z)) = a(x,x \ L(x,y,z),x \ u)
    ]]></literal>
    <justification jstring="[para(4325(a,1),1500(a,1,2))].">
      <j1 rule="para" parents="4325 1500"/>
    </justification>
  </clause>

  <clause id="4389">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ w)) = T(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(4325(a,2),3523(a,1,2))].">
      <j1 rule="para" parents="4325 3523"/>
    </justification>
  </clause>

  <clause id="4390">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1435,a,b,4327,a)].">
      <j1 rule="hyper" parents="63 1435 4327"/>
    </justification>
  </clause>

  <clause id="4391">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,z,u) \ x) = y / L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1442,a(flip),b,4327,a),flip(a)].">
      <j1 rule="hyper" parents="63 1442 4327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4393">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * L(x,y,z) = u * x
    ]]></literal>
    <justification jstring="[hyper(138,a,4327,a(flip),b,1435,a)].">
      <j1 rule="hyper" parents="138 4327 1435"/>
    </justification>
  </clause>

  <clause id="4394">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * (x \ 1) = R(u / L(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[hyper(138,a,4327,a(flip),b,569,a)].">
      <j1 rule="hyper" parents="138 4327 569"/>
    </justification>
  </clause>

  <clause id="4395">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ (u * x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4327(a,1),1443(a,1,1))].">
      <j1 rule="para" parents="4327 1443"/>
    </justification>
  </clause>

  <clause id="4396">
    <literal><![CDATA[
      (L(R(x,y,z),u,w) \ L(x,u,w)) * R(x,y,z) = R(x,y,z) * (L(R(x,y,z),u,w) \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(1795(a,1),4327(a,1,1))].">
      <j1 rule="para" parents="1795 4327"/>
    </justification>
  </clause>

  <clause id="4398">
    <literal><![CDATA[
      L(x,y,z) * (u * x) = x * (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,4328,a(flip),b,1129,a)].">
      <j1 rule="hyper" parents="139 4328 1129"/>
    </justification>
  </clause>

  <clause id="4399">
    <literal><![CDATA[
      (x / (L(y,z,u) * K(w,v5))) * y = y * (L(y,z,u) \ (x * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(3843(a,1),4328(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3843 4328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4400">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u / x)) = u / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,1464,a,b,4333,a),flip(a)].">
      <j1 rule="hyper" parents="37 1464 4333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4402">
    <literal><![CDATA[
      (x * (L(L(x,y,z),u,w) \ v5)) / x = v5 / L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(35,a,4327,a,b,4334,a),flip(a)].">
      <j1 rule="hyper" parents="35 4327 4334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4403">
    <literal><![CDATA[
      (L(x,y,z) * u) * x = (x * u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,4334,a(flip),b,1438,a)].">
      <j1 rule="hyper" parents="138 4334 1438"/>
    </justification>
  </clause>

  <clause id="4404">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) = (x * u) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(4334(a,1),1612(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4334 1612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4405">
    <literal><![CDATA[
      L(T(x,x \ y),z,u) \ ((x \ y) \ y) = L(x,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,311,a(flip),b,4348,a)].">
      <j1 rule="hyper" parents="63 311 4348"/>
    </justification>
  </clause>

  <clause id="4406">
    <literal><![CDATA[
      L(x \ y,z,u) \ T(y / x,x) = L(y / x,z,u) \ (y / x)
    ]]></literal>
    <justification jstring="[para(116(a,1),4348(a,1,1,1))].">
      <j1 rule="para" parents="116 4348"/>
    </justification>
  </clause>

  <clause id="4407">
    <literal><![CDATA[
      R(x * K(y \ x,T(y,z)),u,w) = (T(y,z) \ R(x,u,w)) * T(y,z)
    ]]></literal>
    <justification jstring="[para(4366(a,1),1771(a,1,1,2))].">
      <j1 rule="para" parents="4366 1771"/>
    </justification>
  </clause>

  <clause id="4408">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,1126,a,b,4377,a)].">
      <j1 rule="hyper" parents="138 1126 4377"/>
    </justification>
  </clause>

  <clause id="4409">
    <literal><![CDATA[
      (L(x,y,z) \ u) * L(x,y,z) = (x \ u) * x
    ]]></literal>
    <justification jstring="[hyper(138,a,1131,a(flip),b,4377,a),flip(a)].">
      <j1 rule="hyper" parents="138 1131 4377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4410">
    <literal><![CDATA[
      (x * ((y * L(y \ 1,z,u)) * y)) / y = L(y \ 1,z,u) * ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,995,a,b,4377,a)].">
      <j1 rule="hyper" parents="63 995 4377"/>
    </justification>
  </clause>

  <clause id="4411">
    <literal><![CDATA[
      (x * L(L(y,z,u),w,v5)) / L(y,w,v5) = L(L(y,w,v5),z,u) * (L(y,w,v5) \ x)
    ]]></literal>
    <justification jstring="[para(30(a,1),4377(a,1,1,2))].">
      <j1 rule="para" parents="30 4377"/>
    </justification>
  </clause>

  <clause id="4412">
    <literal><![CDATA[
      L(x,x,y) * (x \ y) = (y / (x \ 1)) / x
    ]]></literal>
    <justification jstring="[para(1445(a,1),4377(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1445 4377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4413">
    <literal><![CDATA[
      L(x,y,y \ z) * (x \ z) = ((z / y) * (y * x)) / x
    ]]></literal>
    <justification jstring="[para(1606(a,1),4377(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1606 4377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4414">
    <literal><![CDATA[
      T(L(L(x,y,z),u,w) * (L(x,y,z) \ v5),x) = L(x,y,z) \ (v5 * L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(4377(a,1),4307(a,1,1))].">
      <j1 rule="para" parents="4377 4307"/>
    </justification>
  </clause>

  <clause id="4415">
    <literal><![CDATA[
      L(x,y,z) * (z * y) = x * ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(139,a,1465,a(flip),b,4382,a),flip(a)].">
      <j1 rule="hyper" parents="139 1465 4382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4416">
    <literal><![CDATA[
      L(x,y,z) \ ((u / x) * L(x,w,v5)) = x \ (L(x,y,z) \ (L(x,w,v5) * u))
    ]]></literal>
    <justification jstring="[hyper(133,a,4382,a(flip),b,1131,a)].">
      <j1 rule="hyper" parents="133 4382 1131"/>
    </justification>
  </clause>

  <clause id="4417">
    <literal><![CDATA[
      K(x,y) * ((z / R(y,u,w)) * L(R(y,u,w),v5,v6)) = R(T(y,x),u,w) \ (L(R(y,u,w),v5,v6) * z)
    ]]></literal>
    <justification jstring="[para(4382(a,1),3411(a,1,2))].">
      <j1 rule="para" parents="4382 3411"/>
    </justification>
  </clause>

  <clause id="4418">
    <literal><![CDATA[
      (x / (y \ R(y,z,u))) * L(y \ R(y,z,u),y,u * z) = (y \ R(y,z,u)) \ (a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(3424(a,2),4382(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3424 4382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4419">
    <literal><![CDATA[
      (L(x,y,z) * u) / T(x * w,w \ ((u / x) * L(x,y,z))) = (x * w) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(4382(a,1),3707(a,1,2,2,2))].">
      <j1 rule="para" parents="4382 3707"/>
    </justification>
  </clause>

  <clause id="4420">
    <literal><![CDATA[
      (T(x,y) / y) * L(y,z,u) = y \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(4313(a,1),4382(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4313 4382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4421">
    <literal><![CDATA[
      x \ ((y / x) * L(x,z,u)) = ((x \ y) / x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4325(a,1),4382(a,1,2))].">
      <j1 rule="para" parents="4325 4382"/>
    </justification>
  </clause>

  <clause id="4422">
    <literal><![CDATA[
      ((x \ 1) / x) * L(x,y,z) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,1063,a(flip),b,4385,a),flip(a)].">
      <j1 rule="hyper" parents="34 1063 4385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4423">
    <literal><![CDATA[
      ((x \ y) * x) / L(x,z,u) = L(x,z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(316,a,1130,a(flip),b,4390,a),flip(a)].">
      <j1 rule="hyper" parents="316 1130 4390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4424">
    <literal><![CDATA[
      (L(x,y,z) \ (L(x,u,w) \ x)) * L(x,y,z) = (L(x,u,w) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(138,a,1140,a(flip),b,4390,a)].">
      <j1 rule="hyper" parents="138 1140 4390"/>
    </justification>
  </clause>

  <clause id="4425">
    <literal><![CDATA[
      (x * y) / (L(y \ 1,z,u) * (y * y)) = (y \ 1) * (L(y \ 1,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,639,a,b,4390,a)].">
      <j1 rule="hyper" parents="63 639 4390"/>
    </justification>
  </clause>

  <clause id="4426">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * (x \ L(x,y,z)))) = R(u,x \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1277,a(flip),b,4390,a),flip(a)].">
      <j1 rule="hyper" parents="63 1277 4390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4427">
    <literal><![CDATA[
      x * (L(x,y,R(z,y,x)) \ (z * y)) = R(z,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,498,a(flip),b,4390,a),flip(a)].">
      <j1 rule="hyper" parents="63 498 4390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4428">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * x = x * (L(x,y,z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(138,a,4390,a(flip),b,4333,a)].">
      <j1 rule="hyper" parents="138 4390 4333"/>
    </justification>
  </clause>

  <clause id="4430">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ 1 = L(x,y,z) / (x * x)
    ]]></literal>
    <justification jstring="[para(4390(a,1),429(a,1,1))].">
      <j1 rule="para" parents="4390 429"/>
    </justification>
  </clause>

  <clause id="4431">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u / (x \ 1))) = (u * (x * x)) / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(576(a,1),4390(a,1,1)),flip(a)].">
      <j1 rule="para" parents="576 4390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4432">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,z,u) \ T(x,w)) = (K(x,w) * y) / L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(2799(a,1),4390(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2799 4390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4433">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ (x * u) = L(x,y,z) * K(x,u)
    ]]></literal>
    <justification jstring="[para(4390(a,1),3822(a,1,1))].">
      <j1 rule="para" parents="4390 3822"/>
    </justification>
  </clause>

  <clause id="4434">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ u),x) = L(x,y,z) \ (u * x)
    ]]></literal>
    <justification jstring="[para(4390(a,1),4307(a,1,1))].">
      <j1 rule="para" parents="4390 4307"/>
    </justification>
  </clause>

  <clause id="4435">
    <literal><![CDATA[
      L(x,y,z) * ((x * (L(x,y,z) \ u)) * L(L(x,y,z),w,v5)) = L(L(x,y,z),w,v5) * (u * x)
    ]]></literal>
    <justification jstring="[para(4390(a,1),4385(a,1,2,1))].">
      <j1 rule="para" parents="4390 4385"/>
    </justification>
  </clause>

  <clause id="4436">
    <literal><![CDATA[
      (((x \ 1) \ 1) * (L((x \ 1) \ 1,y,z) \ ((x \ 1) * u))) * L((x \ 1) \ 1,y,z) = ((1 / x) * u) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,2566,a(flip),b,4393,a),flip(a)].">
      <j1 rule="hyper" parents="316 2566 4393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4437">
    <literal><![CDATA[
      L(x,y,z) \ (x * (u / x)) = u / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1129,a,b,4400,a)].">
      <j1 rule="hyper" parents="63 1129 4400"/>
    </justification>
  </clause>

  <clause id="4438">
    <literal><![CDATA[
      x \ ((x * y) * L(x,z,u)) = T(L(x,z,u) * y,x)
    ]]></literal>
    <justification jstring="[hyper(390,a,xx,b,4403,a),flip(a)].">
      <j1 rule="hyper" parents="390 4403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4439">
    <literal><![CDATA[
      (x \ (y * L(x,z,u))) * x = T(y,x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4313(a,1),4408(a,1,1,2))].">
      <j1 rule="para" parents="4313 4408"/>
    </justification>
  </clause>

  <clause id="4440">
    <literal><![CDATA[
      L(L(x,y,z),u,w) / x = x \ L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(136,a,1273,a(flip),b,4409,a(flip))].">
      <j1 rule="hyper" parents="136 1273 4409"/>
    </justification>
  </clause>

  <clause id="4441">
    <literal><![CDATA[
      ((x \ (y * z)) \ u) * L((y \ x) \ z,y \ x,y) = (((y \ x) \ z) \ u) * ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[para(475(a,1),4409(a,1,1,1))].">
      <j1 rule="para" parents="475 4409"/>
    </justification>
  </clause>

  <clause id="4442">
    <literal><![CDATA[
      L(x \ 1,y,z) * x = (x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,4422,a(flip),b,1438,a)].">
      <j1 rule="hyper" parents="138 4422 1438"/>
    </justification>
  </clause>

  <clause id="4443">
    <literal><![CDATA[
      K(x \ y,x) * ((y / L(x,z,u)) * w) = (L(x,z,u) \ y) * w
    ]]></literal>
    <justification jstring="[para(4423(a,1),3180(a,2,1))].">
      <j1 rule="para" parents="4423 3180"/>
    </justification>
  </clause>

  <clause id="4444">
    <literal><![CDATA[
      (x * y) \ x = (1 / y) * ((y \ 1) * L(y,y,x))
    ]]></literal>
    <justification jstring="[para(4442(a,1),1010(a,2,2))].">
      <j1 rule="para" parents="4442 1010"/>
    </justification>
  </clause>

  <clause id="4445">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(w,v5,v6)) = x * (y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(4301(a,1),3763(a,2,2))].">
      <j1 rule="para" parents="4301 3763"/>
    </justification>
  </clause>

  <clause id="4446">
    <literal><![CDATA[
      (x * (y * z)) / T(y * x,K(x,y) * z) = L(K(x,y) * z,y,x)
    ]]></literal>
    <justification jstring="[para(3005(a,1),4364(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3005 4364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4447">
    <literal><![CDATA[
      x * ((y * ((z \ 1) * x)) / x) = y * ((z \ 1) * T(x,y / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2895,a(flip),b,4415,a),flip(a)].">
      <j1 rule="hyper" parents="63 2895 4415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4448">
    <literal><![CDATA[
      L(x,y,x \ 1) * ((x \ 1) * y) = x * (L(x \ 1,y,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1648(a,1),4415(a,2,2))].">
      <j1 rule="para" parents="1648 4415"/>
    </justification>
  </clause>

  <clause id="4449">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,183,a(flip),b,4290,a(flip))].">
      <j1 rule="hyper" parents="139 183 4290"/>
    </justification>
  </clause>

  <clause id="4450">
    <literal><![CDATA[
      K(x,y) * ((L(y,z,u) \ w) * v5) = (L(T(y,x),z,u) \ w) * v5
    ]]></literal>
    <justification jstring="[para(4290(a,1),3001(a,1,2,1))].">
      <j1 rule="para" parents="4290 3001"/>
    </justification>
  </clause>

  <clause id="4452">
    <literal><![CDATA[
      (x \ L(y,z,u)) * K(y,w) = x \ L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,4449,a(flip),b,3762,a),flip(a)].">
      <j1 rule="hyper" parents="133 4449 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4453">
    <literal><![CDATA[
      (x * L(y,z,u)) * K(y,L(w,v5,v6)) = x * L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(4449(a,1),4301(a,2,2))].">
      <j1 rule="para" parents="4449 4301"/>
    </justification>
  </clause>

  <clause id="4454">
    <literal><![CDATA[
      K(x,T(y \ (z * u),u)) = K(x,u / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4141,a(flip),b,4299,a),flip(a)].">
      <j1 rule="hyper" parents="63 4141 4299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4456">
    <literal><![CDATA[
      L(T(x,y),z,u) * T(w,x) = K(x,y) * (w * L(x,z,u))
    ]]></literal>
    <justification jstring="[para(4313(a,1),4345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4313 4345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4457">
    <literal><![CDATA[
      K(x,y) * ((z / x) * L(x,u,w)) = L(T(x,y),u,w) * (x \ z)
    ]]></literal>
    <justification jstring="[para(4325(a,1),4345(a,1,2))].">
      <j1 rule="para" parents="4325 4345"/>
    </justification>
  </clause>

  <clause id="4458">
    <literal><![CDATA[
      L(x,y,z) * (T(x,u) \ u) = x \ (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2934(a,2),4357(a,1,2))].">
      <j1 rule="para" parents="2934 4357"/>
    </justification>
  </clause>

  <clause id="4459">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ 1 = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1110,a(flip),b,4430,a),flip(a)].">
      <j1 rule="hyper" parents="316 1110 4430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4460">
    <literal><![CDATA[
      T(L(x,y,z) * (L(L(x,y,z),u,w) \ L(x,u,w)),L(x,y,z)) = L(x,u,w) * (L(L(x,u,w),y,z) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,1143,a(flip),b,4434,a),flip(a)].">
      <j1 rule="hyper" parents="316 1143 4434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4463">
    <literal><![CDATA[
      x \ ((x * (L(x,y,z) \ u)) * (x \ 1)) = (L(x,y,z) \ (u * x)) / (x * x)
    ]]></literal>
    <justification jstring="[para(4434(a,1),680(a,2,1))].">
      <j1 rule="para" parents="4434 680"/>
    </justification>
  </clause>

  <clause id="4464">
    <literal><![CDATA[
      x \ T(L(y,z,u) * x,y) = L(R(y,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,4438,a(flip),b,1654,a(flip))].">
      <j1 rule="hyper" parents="133 4438 1654"/>
    </justification>
  </clause>

  <clause id="4465">
    <literal><![CDATA[
      x \ L(T(x,x \ 1),y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3229,a(flip),b,4452,a),flip(a)].">
      <j1 rule="hyper" parents="63 3229 4452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4466">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (T(R(x,y,z),v5) \ v5) = K(x,v6) * (R(T(x,v6),y,z) \ (v5 * L(R(x,y,z),u,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,3410,a,b,4458,a),flip(a)].">
      <j1 rule="hyper" parents="316 3410 4458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4467">
    <literal><![CDATA[
      (x * (L(R(x,y,z),u,w) * (T(R(x,y,z),v5) \ v5))) / x = (v5 * L(R(x,y,z),u,w)) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(4458(a,2),3109(a,1,1,2))].">
      <j1 rule="para" parents="4458 3109"/>
    </justification>
  </clause>

  <clause id="4468">
    <literal><![CDATA[
      x \ L(T(x,x \ 1),y,z) = x * L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1229,a(flip),b,4465,a),flip(a)].">
      <j1 rule="hyper" parents="316 1229 4465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4469">
    <literal><![CDATA[
      T(x,L(y,z,u) \ 1) = T(x,(z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3690,a(flip),b,3666,a),flip(a)].">
      <j1 rule="hyper" parents="63 3690 3666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4471">
    <literal><![CDATA[
      T(x,L(y,z,u) \ 1) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,3660,a(flip),b,4469,a),flip(a)].">
      <j1 rule="hyper" parents="316 3660 4469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4473">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * T(u,x \ 1) = u * (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,4471,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 4471 22"/>
    </justification>
  </clause>

  <clause id="4474">
    <literal><![CDATA[
      (x \ (L(y,z,u) \ x)) * T(x,y \ 1) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(4471(a,1),3166(a,1,2))].">
      <j1 rule="para" parents="4471 3166"/>
    </justification>
  </clause>

  <clause id="4475">
    <literal><![CDATA[
      T(x,T(y * z,y) \ u) = T(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3504,a(flip),b,3700,a),flip(a)].">
      <j1 rule="hyper" parents="63 3504 3700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4477">
    <literal><![CDATA[
      T((x / (x / y)) * z,z \ (x / y)) = L(z \ (x / y),z,y) \ x
    ]]></literal>
    <justification jstring="[para(1589(a,1),3739(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1589 3739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4479">
    <literal><![CDATA[
      R(x,y \ z,y) * z = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,3894,a(flip),b,4055,a),flip(a)].">
      <j1 rule="hyper" parents="63 3894 4055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4480">
    <literal><![CDATA[
      ((x * (y / z)) * z) / y = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(136,a,3894,a(flip),b,4055,a(flip))].">
      <j1 rule="hyper" parents="136 3894 4055"/>
    </justification>
  </clause>

  <clause id="4481">
    <literal><![CDATA[
      R(x / (y / z),z \ y,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[hyper(136,a,157,a(flip),b,4479,a),flip(a)].">
      <j1 rule="hyper" parents="136 157 4479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4482">
    <literal><![CDATA[
      R(x,(y * (z \ 1)) \ 1,y * (z \ 1)) * 1 = (x * R(z / y,y,z)) * (y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(728(a,2),4479(a,2,1,2))].">
      <j1 rule="para" parents="728 4479"/>
    </justification>
  </clause>

  <clause id="4484">
    <literal><![CDATA[
      (x * R(x,y,z)) / (x * x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,980,a(flip),b,4063,a),flip(a)].">
      <j1 rule="hyper" parents="63 980 4063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4485">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,u) = (u * R(x,y,z)) / (u * x)
    ]]></literal>
    <justification jstring="[para(1774(a,1),4063(a,1,1))].">
      <j1 rule="para" parents="1774 4063"/>
    </justification>
  </clause>

  <clause id="4486">
    <literal><![CDATA[
      R(x,y,z \ R(z,u,w)) = R(x,y,z * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(4484(a,1),1702(a,1,3))].">
      <j1 rule="para" parents="4484 1702"/>
    </justification>
  </clause>

  <clause id="4487">
    <literal><![CDATA[
      R(x,y,z * R(z,u,u)) = R(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(2380(a,1),4486(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2380 4486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4488">
    <literal><![CDATA[
      ((x * y) * z) / (z * y) = R(x * K(y,z),y,z)
    ]]></literal>
    <justification jstring="[para(3855(a,1),4064(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3855 4064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4489">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ ((v5 * w) * u))) = L(x,y,z * R(v5 * K(w,u),w,u))
    ]]></literal>
    <justification jstring="[para(4488(a,1),1682(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="4488 1682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4490">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((v5 * w) * u))) = L(x,y,z \ R(v5 * K(w,u),w,u))
    ]]></literal>
    <justification jstring="[para(4488(a,1),3243(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="4488 3243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4492">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) = (x * T(u,w)) \ (L(x,y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(1652,a,4404,a)].">
      <j1 rule="hyper" parents="1652 4404"/>
    </justification>
  </clause>

  <clause id="4493">
    <literal><![CDATA[
      (x * (y * z)) \ (L(x,z,y) * (y * z)) = ((y * z) * x) \ (y * (z * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,489,a(flip),b,4404,a),flip(a)].">
      <j1 rule="hyper" parents="63 489 4404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4494">
    <literal><![CDATA[
      L(x,y,y \ z) * z = x * (((z / y) * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(139,a,4413,a(flip),b,1126,a),flip(a)].">
      <j1 rule="hyper" parents="139 4413 1126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4497">
    <literal><![CDATA[
      (((x \ L(x,y,z)) \ 1) * u) * T(w,x * (L(x,y,z) \ u)) = w * (((x \ L(x,y,z)) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3529(a,1),3490(a,1,2))].">
      <j1 rule="para" parents="3529 3490"/>
    </justification>
  </clause>

  <clause id="4498">
    <literal><![CDATA[
      T(x,((y \ z) * u) * T(w,(y \ z) * u)) = T(x,w * ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(3687(a,1),3736(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3687 3736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4500">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(3306(a,1),3719(a,1,1))].">
      <j1 rule="para" parents="3306 3719"/>
    </justification>
  </clause>

  <clause id="4501">
    <literal><![CDATA[
      x * K(y \ (z \ x),z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[hyper(39,a,3827,a,b,4500,a)].">
      <j1 rule="hyper" parents="39 3827 4500"/>
    </justification>
  </clause>

  <clause id="4502">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = y * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,2714,a,b,4501,a)].">
      <j1 rule="hyper" parents="316 2714 4501"/>
    </justification>
  </clause>

  <clause id="4503">
    <literal><![CDATA[
      (x * K(y \ (z \ x),z)) * u = (y * ((z \ (y \ x)) * z)) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,4501,a,b,11,a)].">
      <j1 rule="hyper" parents="138 4501 11"/>
    </justification>
  </clause>

  <clause id="4504">
    <literal><![CDATA[
      (x \ y) * K(x \ (z \ y),z) = (z \ (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(34,a,3762,a,b,4501,a(flip))].">
      <j1 rule="hyper" parents="34 3762 4501"/>
    </justification>
  </clause>

  <clause id="4505">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (y * K((1 / z) \ (x \ y),x)) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,4502,a(flip),b,2570,a),flip(a)].">
      <j1 rule="hyper" parents="138 4502 2570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4506">
    <literal><![CDATA[
      (x * y) * K(y \ (z \ (x * y)),z) = ((z \ x) * z) * y
    ]]></literal>
    <justification jstring="[para(11(a,1),4502(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 4502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4507">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,u) = (u * x) \ (u * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4485,a,b,3737,a)].">
      <j1 rule="hyper" parents="63 4485 3737"/>
    </justification>
  </clause>

  <clause id="4508">
    <literal><![CDATA[
      (x * x) \ (x * R(x,y,z)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4484,a(flip),b,3737,a),flip(a)].">
      <j1 rule="hyper" parents="63 4484 3737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4509">
    <literal><![CDATA[
      (x * y) * a(x * y,y,x) = R(x * y,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,3428,a,b,4508,a(flip))].">
      <j1 rule="hyper" parents="139 3428 4508"/>
    </justification>
  </clause>

  <clause id="4510">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,u) = L(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,102,a,b,4507,a),flip(a)].">
      <j1 rule="hyper" parents="316 102 4507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4511">
    <literal><![CDATA[
      R(L(x,y,z) \ R(L(x,y,z),u,w),L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * R(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(100(a,1),4507(a,2,1))].">
      <j1 rule="para" parents="100 4507"/>
    </justification>
  </clause>

  <clause id="4512">
    <literal><![CDATA[
      T((R(x,y,z) * (x \ u)) / u,x) = L(x \ R(x,y,z),x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,725,a,b,4510,a)].">
      <j1 rule="hyper" parents="63 725 4510"/>
    </justification>
  </clause>

  <clause id="4514">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(3312(a,1),3844(a,1,1,2))].">
      <j1 rule="para" parents="3312 3844"/>
    </justification>
  </clause>

  <clause id="4516">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(210,a,4514,a)].">
      <j1 rule="hyper" parents="210 4514"/>
    </justification>
  </clause>

  <clause id="4519">
    <literal><![CDATA[
      x * L(K(T(y \ 1,z) \ 1,u),w,v5) = x / L(T(K(u,y),z),w,v5)
    ]]></literal>
    <justification jstring="[para(4030(a,1),4516(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4030 4516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4521">
    <literal><![CDATA[
      ((x \ 1) \ (x \ y)) * (x \ 1) = (x \ y) * K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(1951(a,2),3895(a,2,2))].">
      <j1 rule="para" parents="1951 3895"/>
    </justification>
  </clause>

  <clause id="4522">
    <literal><![CDATA[
      ((x * ((x \ K(y,z)) * a(u,w,v5))) \ a(u,w,v5)) * K(y,z) = a(x,x \ K(y,z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,91,a(flip),b,3920,a),flip(a)].">
      <j1 rule="hyper" parents="63 91 3920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4524">
    <literal><![CDATA[
      (x \ ((1 / y) \ z)) * K(u,w \ ((1 / w) \ z)) = x \ ((K(z,u) / y) \ z)
    ]]></literal>
    <justification jstring="[para(3853(a,1),3950(a,2,2))].">
      <j1 rule="para" parents="3853 3950"/>
    </justification>
  </clause>

  <clause id="4525">
    <literal><![CDATA[
      (x / y) / (z * (x / y)) = (y \ x) / (z * (y \ x))
    ]]></literal>
    <justification jstring="[para(116(a,1),3968(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="116 3968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4526">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,14,a,b,3985,a),flip(a)].">
      <j1 rule="hyper" parents="63 14 3985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4527">
    <literal><![CDATA[
      x \ R(x,y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3281,a(flip),b,4526,a)].">
      <j1 rule="hyper" parents="63 3281 4526"/>
    </justification>
  </clause>

  <clause id="4528">
    <literal><![CDATA[
      x * a(x,y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,4526,a(flip),b,3281,a(flip))].">
      <j1 rule="hyper" parents="139 4526 3281"/>
    </justification>
  </clause>

  <clause id="4529">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[para(4526(a,1),1576(a,1,3))].">
      <j1 rule="para" parents="4526 1576"/>
    </justification>
  </clause>

  <clause id="4530">
    <literal><![CDATA[
      T(x * y,x) / x = y * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(4526(a,1),3277(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4526 3277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4532">
    <literal><![CDATA[
      a(x,y,x) \ (a(x,y,x) / z) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(63,a,1452,a(flip),b,4529,a)].">
      <j1 rule="hyper" parents="63 1452 4529"/>
    </justification>
  </clause>

  <clause id="4533">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = z \ (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,475,a(flip),b,4529,a),flip(a)].">
      <j1 rule="hyper" parents="63 475 4529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4534">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,298,a(flip),b,4529,a)].">
      <j1 rule="hyper" parents="63 298 4529"/>
    </justification>
  </clause>

  <clause id="4535">
    <literal><![CDATA[
      a(x,y,x) * (1 / z) = a(x,y,x) / z
    ]]></literal>
    <justification jstring="[hyper(209,a,4529,a(flip),b,2674,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="209 4529 2674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4536">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = a(x,y,x) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(209,a,4529,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="209 4529 104"/>
    </justification>
  </clause>

  <clause id="4537">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = (x * u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,4529,a(flip),b,2494,a)].">
      <j1 rule="hyper" parents="139 4529 2494"/>
    </justification>
  </clause>

  <clause id="4538">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = a(y,z,y) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,4529,a(flip),b,2353,a)].">
      <j1 rule="hyper" parents="139 4529 2353"/>
    </justification>
  </clause>

  <clause id="4539">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(139,a,4529,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="139 4529 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4540">
    <literal><![CDATA[
      (a(x,y,x) * z) * u = a(x,y,x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,4529,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="139 4529 18"/>
    </justification>
  </clause>

  <clause id="4541">
    <literal><![CDATA[
      (a(x,y,x) \ 1) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(133,a,4529,a(flip),b,271,a),flip(a)].">
      <j1 rule="hyper" parents="133 4529 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4542">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(4529(a,1),50(a,2))].">
      <j1 rule="para" parents="4529 50"/>
    </justification>
  </clause>

  <clause id="4543">
    <literal><![CDATA[
      a(x,y,x) \ (z * u) = (a(x,y,x) \ z) * u
    ]]></literal>
    <justification jstring="[para(4529(a,1),456(a,1,2,2))].">
      <j1 rule="para" parents="4529 456"/>
    </justification>
  </clause>

  <clause id="4544">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ (x * (a(z,u,z) * (y * w))) = L(w,a(z,u,z) * y,x)
    ]]></literal>
    <justification jstring="[para(4529(a,1),2357(a,2,1))].">
      <j1 rule="para" parents="4529 2357"/>
    </justification>
  </clause>

  <clause id="4545">
    <literal><![CDATA[
      a(x,y,x) * x = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,4527,a)].">
      <j1 rule="hyper" parents="38 2295 4527"/>
    </justification>
  </clause>

  <clause id="4546">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(10(a,1),4530(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4547">
    <literal><![CDATA[
      R(x * a(y,x,y),z,u) * y = y * R(y \ T(y * x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4530(a,1),609(a,1,1,1))].">
      <j1 rule="para" parents="4530 609"/>
    </justification>
  </clause>

  <clause id="4548">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = (z / u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,2290,a(flip),b,4536,a),flip(a)].">
      <j1 rule="hyper" parents="316 2290 4536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4549">
    <literal><![CDATA[
      ((x * (a(y,z,y) * u)) * w) / (a(y,z,y) * (u * w)) = R(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(209,a,4540,a(flip),b,199,a)].">
      <j1 rule="hyper" parents="209 4540 199"/>
    </justification>
  </clause>

  <clause id="4550">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ ((x * (a(y,z,y) * u)) * w) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[para(4540(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4540 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4552">
    <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(4540(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4540 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4553">
    <literal><![CDATA[
      ((a(x,y,x) * (z * u)) * w) / (u * w) = R(a(x,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(4540(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4540 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4554">
    <literal><![CDATA[
      L(x,y,z * (u * (w / v5))) = L(x,y,z * (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(4028(a,1),1676(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4028 1676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4555">
    <literal><![CDATA[
      a(x * (y * (L(z \ 1,u,w) \ 1)),v5,v6) = a(x * (y * (z * (L(z,u,w) \ z))),v5,v6)
    ]]></literal>
    <justification jstring="[para(4459(a,1),4040(a,1,1,2,2,1))].">
      <j1 rule="para" parents="4459 4040"/>
    </justification>
  </clause>

  <clause id="4556">
    <literal><![CDATA[
      a(x \ (y * (K(z,u) * w)),v5,v6) = a(x \ (y * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(4046(a,1),2788(a,1,1))].">
      <j1 rule="para" parents="4046 2788"/>
    </justification>
  </clause>

  <clause id="4558">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((v5 * w) * u))) = L(x,y,z \ L(T(v5,w),w,u))
    ]]></literal>
    <justification jstring="[para(247(a,1),4051(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="247 4051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4559">
    <literal><![CDATA[
      L(x,y,z \ ((u * (w * w)) \ v5)) = L(x,y,z \ (u \ ((w * w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3472,a,b,4052,a)].">
      <j1 rule="hyper" parents="63 3472 4052"/>
    </justification>
  </clause>

  <clause id="4560">
    <literal><![CDATA[
      L(T(T(x,y),K(z,u)),K(z,u),y) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,815,a,b,4068,a(flip))].">
      <j1 rule="hyper" parents="35 815 4068"/>
    </justification>
  </clause>

  <clause id="4561">
    <literal><![CDATA[
      R(K(x,y) * T(z,K(y,x)),u,w) = R(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1028,a,b,4117,a)].">
      <j1 rule="hyper" parents="63 1028 4117"/>
    </justification>
  </clause>

  <clause id="4562">
    <literal><![CDATA[
      T(x * (y * L(z,u,w)),K(y,z)) = K(y,z) * (x * (L(z,u,w) * y))
    ]]></literal>
    <justification jstring="[para(4313(a,1),4161(a,1,1,2))].">
      <j1 rule="para" parents="4313 4161"/>
    </justification>
  </clause>

  <clause id="4563">
    <literal><![CDATA[
      a((x * y) \ ((x * z) * y),u,w) = a(L(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[para(3068(a,2),4175(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3068 4175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4564">
    <literal><![CDATA[
      L(x,y,(z * (T(u,z * w) * w)) \ v5) = L(x,y,(L(u,w,z) * (z * w)) \ v5)
    ]]></literal>
    <justification jstring="[para(598(a,1),4197(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="598 4197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4565">
    <literal><![CDATA[
      a(((x * y) \ ((z * y) * x)) \ u,w,v5) = a(L(T(z,y),y,x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(247(a,1),4200(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="247 4200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4566">
    <literal><![CDATA[
      a((x \ (K(y,z) * u)) \ w,v5,v6) = a((u / x) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,3121,a,b,4201,a),flip(a)].">
      <j1 rule="hyper" parents="316 3121 4201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4567">
    <literal><![CDATA[
      (x \ 1) * (y * (((x \ 1) \ 1) * z)) = (1 / x) * (y * (x * z))
    ]]></literal>
    <justification jstring="[para(2237(a,1),4217(a,1,2,2))].">
      <j1 rule="para" parents="2237 4217"/>
    </justification>
  </clause>

  <clause id="4568">
    <literal><![CDATA[
      T(x,y * (z * (1 / u))) = T(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(4219(a,1),2642(a,1,2))].">
      <j1 rule="para" parents="4219 2642"/>
    </justification>
  </clause>

  <clause id="4569">
    <literal><![CDATA[
      T(x,y * (z * (1 / u))) = T(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(316,a,3486,a(flip),b,4568,a),flip(a)].">
      <j1 rule="hyper" parents="316 3486 4568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4570">
    <literal><![CDATA[
      T(x,y * (z / (u \ 1))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(80(a,1),4569(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="80 4569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4571">
    <literal><![CDATA[
      a(x \ ((y * y) \ (z * u)),w,v5) = a(x \ (z * ((y * y) \ u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3327,a,b,4234,a)].">
      <j1 rule="hyper" parents="63 3327 4234"/>
    </justification>
  </clause>

  <clause id="4572">
    <literal><![CDATA[
      a(x \ (y * (L(z \ 1,u,w) \ 1)),v5,v6) = a(x \ (y * (z * (L(z,u,w) \ z))),v5,v6)
    ]]></literal>
    <justification jstring="[para(4459(a,1),4235(a,1,1,2,2,1))].">
      <j1 rule="para" parents="4459 4235"/>
    </justification>
  </clause>

  <clause id="4573">
    <literal><![CDATA[
      x * K(y * (x / z),z / y) = ((y \ z) \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4246(a,1),4271(a,1,2))].">
      <j1 rule="para" parents="4246 4271"/>
    </justification>
  </clause>

  <clause id="4574">
    <literal><![CDATA[
      x * K((y \ (z \ u)) * x,(u \ z) * y) = (((z \ u) \ y) \ x) * ((z \ u) \ y)
    ]]></literal>
    <justification jstring="[para(3713(a,1),4272(a,1,2))].">
      <j1 rule="para" parents="3713 4272"/>
    </justification>
  </clause>

  <clause id="4575">
    <literal><![CDATA[
      L(x,y,y \ L(z,u,w)) * L(z,u,w) = (L(z,u,w) / y) * (y * T(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1606,a(flip),b,4315,a),flip(a)].">
      <j1 rule="hyper" parents="63 1606 4315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4576">
    <literal><![CDATA[
      L(R(x,y,z) \ u,w,v5) * R(T(v6,x \ u),v7,v8) = R(v6,v7,v8) * L(R(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(3504(a,1),4316(a,1,2,1))].">
      <j1 rule="para" parents="3504 4316"/>
    </justification>
  </clause>

  <clause id="4577">
    <literal><![CDATA[
      R(x,y,L(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,4464,a(flip),b,4317,a),flip(a)].">
      <j1 rule="hyper" parents="41 4464 4317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4579">
    <literal><![CDATA[
      L(R(x,y,L(L(x,z,u),w,v5)),z,u) = R(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,29,a(flip),b,4577,a)].">
      <j1 rule="hyper" parents="63 29 4577"/>
    </justification>
  </clause>

  <clause id="4580">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,w,v5)) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(4577(a,1),29(a,2,1))].">
      <j1 rule="para" parents="4577 29"/>
    </justification>
  </clause>

  <clause id="4581">
    <literal><![CDATA[
      R(x,y,z \ (z / (x \ 1))) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(1447(a,1),4577(a,1,3))].">
      <j1 rule="para" parents="1447 4577"/>
    </justification>
  </clause>

  <clause id="4584">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * T(v5,x) = v5 * L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,159,a,b,4332,a),flip(a)].">
      <j1 rule="hyper" parents="316 159 4332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4585">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (L(x,v5,v6) \ v7) = (v7 / L(x,v5,v6)) * L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(4307(a,1),4332(a,1,2))].">
      <j1 rule="para" parents="4307 4332"/>
    </justification>
  </clause>

  <clause id="4586">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,y,z),u) = (L(x,y,z) * u) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(316,a,102,a,b,4336,a)].">
      <j1 rule="hyper" parents="316 102 4336"/>
    </justification>
  </clause>

  <clause id="4588">
    <literal><![CDATA[
      (x * y) \ (L(x,z,z \ y) * y) = (y * x) \ ((y / z) * (z * x))
    ]]></literal>
    <justification jstring="[para(1606(a,1),4338(a,2,2))].">
      <j1 rule="para" parents="1606 4338"/>
    </justification>
  </clause>

  <clause id="4589">
    <literal><![CDATA[
      (x \ 1) \ L(x,y,z) = L(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,1248,a(flip),b,4347,a),flip(a)].">
      <j1 rule="hyper" parents="63 1248 4347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4590">
    <literal><![CDATA[
      (x \ 1) \ L(x,y,z) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,257,a(flip),b,4589,a),flip(a)].">
      <j1 rule="hyper" parents="316 257 4589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4591">
    <literal><![CDATA[
      R(1 / x,x,L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,369,a,b,4590,a)].">
      <j1 rule="hyper" parents="39 369 4590"/>
    </justification>
  </clause>

  <clause id="4593">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * w) = T(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3524,a,b,4389,a)].">
      <j1 rule="hyper" parents="63 3524 4389"/>
    </justification>
  </clause>

  <clause id="4595">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) \ ((x \ y) \ y) = L(x,z,u) \ x
    ]]></literal>
    <justification jstring="[para(115(a,1),4405(a,1,1,1))].">
      <j1 rule="para" parents="115 4405"/>
    </justification>
  </clause>

  <clause id="4596">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ (x * u) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,4449,a(flip),b,4433,a),flip(a)].">
      <j1 rule="hyper" parents="316 4449 4433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4597">
    <literal><![CDATA[
      L(L(T(x,y),z,u),w,v5) * (((x * (L(x,z,u) \ y)) \ (x * y)) \ (x * y)) = (x * (L(x,z,u) \ y)) * L((x * (L(x,z,u) \ y)) \ (x * y),w,v5)
    ]]></literal>
    <justification jstring="[para(4596(a,1),4340(a,1,1,1))].">
      <j1 rule="para" parents="4596 4340"/>
    </justification>
  </clause>

  <clause id="4598">
    <literal><![CDATA[
      K(x,y) * (z * L(x,T(x,y) \ 1,T(x,y))) = (1 / (1 / T(x,y))) * T(z,x)
    ]]></literal>
    <justification jstring="[para(1288(a,1),4456(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1288 4456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4599">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * (x \ 1) = (x \ 1) * (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(113(a,1),4473(a,1,2))].">
      <j1 rule="para" parents="113 4473"/>
    </justification>
  </clause>

  <clause id="4600">
    <literal><![CDATA[
      (L(x \ y,z,u) \ 1) * T(w,y \ x) = w * (L(x \ y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(3664(a,1),4473(a,1,2))].">
      <j1 rule="para" parents="3664 4473"/>
    </justification>
  </clause>

  <clause id="4601">
    <literal><![CDATA[
      ((1 / x) \ (x \ y)) * (1 / x) = (x \ y) * K(y,1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3250,a,b,4521,a)].">
      <j1 rule="hyper" parents="63 3250 4521"/>
    </justification>
  </clause>

  <clause id="4602">
    <literal><![CDATA[
      L(x,y,z * ((u * u) \ (w * v5))) = L(x,y,z * (w * ((u * u) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,1685,a,b,4554,a)].">
      <j1 rule="hyper" parents="63 1685 4554"/>
    </justification>
  </clause>

  <clause id="4603">
    <literal><![CDATA[
      a(x \ (y * (z * u)),w,v5) = a(x \ (y * (u * z)),w,v5)
    ]]></literal>
    <justification jstring="[para(2728(a,1),4556(a,1,1,2,2))].">
      <j1 rule="para" parents="2728 4556"/>
    </justification>
  </clause>

  <clause id="4604">
    <literal><![CDATA[
      R(x * K(y,z),u,w) = R(x,u,w) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4116(a,1),4561(a,1,1))].">
      <j1 rule="para" parents="4116 4561"/>
    </justification>
  </clause>

  <clause id="4605">
    <literal><![CDATA[
      x \ R(y * K(z,u),w,v5) = (x \ R(y,w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,4604,a,b,3762,a)].">
      <j1 rule="hyper" parents="133 4604 3762"/>
    </justification>
  </clause>

  <clause id="4606">
    <literal><![CDATA[
      a((x / (y * z)) \ u,w,v5) = a(((z * y) \ x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(2765(a,1),4566(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2765 4566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4607">
    <literal><![CDATA[
      ((R(x,y,z) \ u) \ w) * (R(x,y,z) \ u) = w * K(R(x,y,z) * (w / u),u / x)
    ]]></literal>
    <justification jstring="[para(3569(a,1),4573(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3569 4573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4608">
    <literal><![CDATA[
      ((x * y) / x) * L(L(x,z,u),w,v5) = L(L(x,w,v5),z,u) * y
    ]]></literal>
    <justification jstring="[para(240(a,1),4584(a,1,2)),flip(a)].">
      <j1 rule="para" parents="240 4584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4609">
    <literal><![CDATA[
      T(x,y) * R(L(L(y,z,u),w,v5),T(x,y),L(L(y,z,u),w,v5)) = T(x * L(L(y,w,v5),z,u),L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(4584(a,1),1636(a,2,1))].">
      <j1 rule="para" parents="4584 1636"/>
    </justification>
  </clause>

  <clause id="4611">
    <literal><![CDATA[
      ((x \ 1) * (L(x,y,z) \ 1)) * (x * x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(138,a,4599,a(flip),b,562,a)].">
      <j1 rule="hyper" parents="138 4599 562"/>
    </justification>
  </clause>

  <clause id="4612">
    <literal><![CDATA[
      K((x \ y) * x,1 / x) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[hyper(34,a,3398,a(flip),b,4601,a(flip))].">
      <j1 rule="hyper" parents="34 3398 4601"/>
    </justification>
  </clause>

  <clause id="4613">
    <literal><![CDATA[
      a(x \ (L(y,z \ (u * w),z) * (w * u)),v5,v6) = a(x \ (z * ((z \ (u * w)) * y)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,3360,a(flip),b,4603,a),flip(a)].">
      <j1 rule="hyper" parents="316 3360 4603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4614">
    <literal><![CDATA[
      a(((x * y) \ ((z * y) * x)) \ u,w,v5) = a(R(z,y,x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(20(a,2),4606(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="20 4606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4615">
    <literal><![CDATA[
      T(x,y \ ((z * u) \ (z * (u * y)))) = T(x,a(z,u,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3698,a(flip),b,3667,a)].">
      <j1 rule="hyper" parents="63 3698 3667"/>
    </justification>
  </clause>

  <clause id="4616">
    <literal><![CDATA[
      (x * y) * ((y \ z) * K(z,u)) = R(x,y,y \ z) * T(z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3763,a(flip),b,3856,a)].">
      <j1 rule="hyper" parents="63 3763 3856"/>
    </justification>
  </clause>

  <clause id="4620">
    <literal><![CDATA[
      a(x \ ((y * y) \ (y * (x * y))),z,u) = a(a(x,y,y) * K(y,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(3954(a,1),3324(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3954 3324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4621">
    <literal><![CDATA[
      a(x,x \ y,z) \ (z * y) = x * ((x \ y) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3942,a(flip),b,3956,a),flip(a)].">
      <j1 rule="hyper" parents="63 3942 3956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4622">
    <literal><![CDATA[
      a(x,x \ y,z) \ (z * y) = L(z,x \ y,x) * y
    ]]></literal>
    <justification jstring="[hyper(316,a,713,a(flip),b,4621,a),flip(a)].">
      <j1 rule="hyper" parents="316 713 4621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4623">
    <literal><![CDATA[
      (x \ L(x,y,z)) * R(a(u,w,v5),L(x,y,z),1 / x) = (a(u,w,v5) * L(x,y,z)) * T(1 / x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1458(a,1),4057(a,1,1))].">
      <j1 rule="para" parents="1458 4057"/>
    </justification>
  </clause>

  <clause id="4625">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z)
    ]]></literal>
    <justification jstring="[para(3830(a,1),4135(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3830 4135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4626">
    <literal><![CDATA[
      L(x,y,(z * u) \ (u * (w * z))) = L(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,1585,a(flip),b,4192,a),flip(a)].">
      <j1 rule="hyper" parents="316 1585 4192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4628">
    <literal><![CDATA[
      L(x,y,R(z,u,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,3236,a(flip),b,4626,a)].">
      <j1 rule="hyper" parents="63 3236 4626"/>
    </justification>
  </clause>

  <clause id="4629">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,3437,a(flip),b,4628,a),flip(a)].">
      <j1 rule="hyper" parents="316 3437 4628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4630">
    <literal><![CDATA[
      L(x,x,L(y,x,x)) = R(y,x,x) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1448,a(flip),b,4628,a),flip(a)].">
      <j1 rule="hyper" parents="63 1448 4628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4631">
    <literal><![CDATA[
      x * L(y,R(z,u,w) \ x,L(z,u,w)) = R(z,u,w) * ((R(z,u,w) \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,4628,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="139 4628 101"/>
    </justification>
  </clause>

  <clause id="4632">
    <literal><![CDATA[
      R(x,y,y) * L(y,y,L(x,y,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(139,a,4628,a(flip),b,1448,a(flip))].">
      <j1 rule="hyper" parents="139 4628 1448"/>
    </justification>
  </clause>

  <clause id="4633">
    <literal><![CDATA[
      R(x,y,z) \ L(u,R(x,y,z) \ 1,L(x,y,z)) = (R(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(133,a,4628,a(flip),b,271,a)].">
      <j1 rule="hyper" parents="133 4628 271"/>
    </justification>
  </clause>

  <clause id="4634">
    <literal><![CDATA[
      L(x,y,L(z,u,w \ 1)) = L(x,y,R(z,u,w))
    ]]></literal>
    <justification jstring="[para(1033(a,1),4628(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1033 4628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4635">
    <literal><![CDATA[
      x * (L(x,y,L(z,y,x)) \ (z * y)) = R(z,y,x) * y
    ]]></literal>
    <justification jstring="[para(4628(a,1),4427(a,1,2,1))].">
      <j1 rule="para" parents="4628 4427"/>
    </justification>
  </clause>

  <clause id="4636">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,1611,a(flip),b,4629,a),flip(a)].">
      <j1 rule="hyper" parents="316 1611 4629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4638">
    <literal><![CDATA[
      L(x,y,L(z,u,w \ 1)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,4628,a(flip),b,4634,a),flip(a)].">
      <j1 rule="hyper" parents="316 4628 4634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4639">
    <literal><![CDATA[
      L(x,y,(z \ (z \ 1)) \ ((1 / z) * u)) = L(x,y,L(u / (z \ 1),z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1698,a(flip),b,4638,a)].">
      <j1 rule="hyper" parents="63 1698 4638"/>
    </justification>
  </clause>

  <clause id="4640">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,w) = a(L(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,1812,a(flip),b,4193,a),flip(a)].">
      <j1 rule="hyper" parents="316 1812 4193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4642">
    <literal><![CDATA[
      a((x * y) \ (L(x,z,y) * (y * z)),u,w) = a(L(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3359,a,b,4640,a)].">
      <j1 rule="hyper" parents="63 3359 4640"/>
    </justification>
  </clause>

  <clause id="4643">
    <literal><![CDATA[
      a(R(x,y,z),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3358,a(flip),b,4640,a)].">
      <j1 rule="hyper" parents="63 3358 4640"/>
    </justification>
  </clause>

  <clause id="4644">
    <literal><![CDATA[
      a(L(x,y,y \ 1),z,u) = a(L(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3344,a,b,4643,a)].">
      <j1 rule="hyper" parents="63 3344 4643"/>
    </justification>
  </clause>

  <clause id="4645">
    <literal><![CDATA[
      a(R(L(x,y,z),u,w),v5,v6) = a(L(L(x,u,w),y,z),v5,v6)
    ]]></literal>
    <justification jstring="[para(30(a,1),4643(a,2,1))].">
      <j1 rule="para" parents="30 4643"/>
    </justification>
  </clause>

  <clause id="4646">
    <literal><![CDATA[
      a(L(x / y,y,y),z,u) = a(x * (y \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(563(a,1),4643(a,1,1)),flip(a)].">
      <j1 rule="para" parents="563 4643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4647">
    <literal><![CDATA[
      a(L(x,y,z \ 1),u,w) = a(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1033(a,1),4643(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1033 4643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4648">
    <literal><![CDATA[
      a(L(x,y,z * (u * u)),w,v5) = a(R(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(1701(a,1),4643(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1701 4643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4649">
    <literal><![CDATA[
      a((x * y) * (x \ 1),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3240,a,b,4644,a)].">
      <j1 rule="hyper" parents="63 3240 4644"/>
    </justification>
  </clause>

  <clause id="4650">
    <literal><![CDATA[
      a(L(x,y,z \ 1),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,4643,a(flip),b,4647,a),flip(a)].">
      <j1 rule="hyper" parents="316 4643 4647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4651">
    <literal><![CDATA[
      a(L(x \ y,x,x),z,u) = a(y * (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1815,a(flip),b,4646,a)].">
      <j1 rule="hyper" parents="63 1815 4646"/>
    </justification>
  </clause>

  <clause id="4652">
    <literal><![CDATA[
      a(L(x,y,z * (u * u)),w,v5) = a(L(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,4643,a(flip),b,4648,a),flip(a)].">
      <j1 rule="hyper" parents="316 4643 4648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4653">
    <literal><![CDATA[
      a(L(R(x,y,z),u,w),v5,v6) = a(L(L(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(29(a,1),4645(a,1,1))].">
      <j1 rule="para" parents="29 4645"/>
    </justification>
  </clause>

  <clause id="4654">
    <literal><![CDATA[
      R(x,y,z / (x * y)) \ z = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(116(a,1),4204(a,2,2))].">
      <j1 rule="para" parents="116 4204"/>
    </justification>
  </clause>

  <clause id="4655">
    <literal><![CDATA[
      R(x,x,y) \ y = x * ((x * x) \ y)
    ]]></literal>
    <justification jstring="[para(1702(a,1),4654(a,1,1))].">
      <j1 rule="para" parents="1702 4654"/>
    </justification>
  </clause>

  <clause id="4656">
    <literal><![CDATA[
      x \ (R(x,x,y) \ y) = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(517,a,4655,a)].">
      <j1 rule="hyper" parents="517 4655"/>
    </justification>
  </clause>

  <clause id="4657">
    <literal><![CDATA[
      R(x,x,y) \ y = x \ L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,1118,a(flip),b,4655,a),flip(a)].">
      <j1 rule="hyper" parents="316 1118 4655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4658">
    <literal><![CDATA[
      x * (R(x,x,y) \ y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,4655,a,b,1118,a(flip))].">
      <j1 rule="hyper" parents="139 4655 1118"/>
    </justification>
  </clause>

  <clause id="4659">
    <literal><![CDATA[
      L(x,y,R(z,z,u) \ u) = L(x,y,u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(4655(a,2),3334(a,1,3))].">
      <j1 rule="para" parents="4655 3334"/>
    </justification>
  </clause>

  <clause id="4660">
    <literal><![CDATA[
      x * (L(x,y,z) \ (R(x,x,u) \ u)) = L(x,y,z) \ L(u,x,x)
    ]]></literal>
    <justification jstring="[para(4657(a,2),1130(a,1,2,2))].">
      <j1 rule="para" parents="4657 1130"/>
    </justification>
  </clause>

  <clause id="4661">
    <literal><![CDATA[
      R(x,x,y) * L(y,x,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(139,a,4658,a(flip),b,1169,a)].">
      <j1 rule="hyper" parents="139 4658 1169"/>
    </justification>
  </clause>

  <clause id="4662">
    <literal><![CDATA[
      x * (L(x,y,y) \ y) = R(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,4393,a,b,4661,a)].">
      <j1 rule="hyper" parents="35 4393 4661"/>
    </justification>
  </clause>

  <clause id="4663">
    <literal><![CDATA[
      R(x,x,y * L(y,z,u)) * L(y \ L(y,z,u),x,x) = x * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1718(a,1),4661(a,1,1))].">
      <j1 rule="para" parents="1718 4661"/>
    </justification>
  </clause>

  <clause id="4664">
    <literal><![CDATA[
      ((x * y) * (z * K(u,w))) / (y * (z * K(u,w))) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3763(a,1),4220(a,1,2))].">
      <j1 rule="para" parents="3763 4220"/>
    </justification>
  </clause>

  <clause id="4665">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * K(u,w)) = x * (y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(3763(a,1),4222(a,2,2))].">
      <j1 rule="para" parents="3763 4222"/>
    </justification>
  </clause>

  <clause id="4666">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = T(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[para(18(a,2),4615(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18 4615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4668">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * T(u,z \ L(z,y,x)) = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,4666,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 4666 22"/>
    </justification>
  </clause>

  <clause id="4670">
    <literal><![CDATA[
      L(T(x,a(y,z,u) \ 1),u \ L(u,z,y),u) = L(u,z,y) \ (u * (x * (u \ L(u,z,y))))
    ]]></literal>
    <justification jstring="[para(4666(a,2),694(a,1,1))].">
      <j1 rule="para" parents="4666 694"/>
    </justification>
  </clause>

  <clause id="4671">
    <literal><![CDATA[
      T(x,y * L(y \ 1,z,u)) = T(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(1064(a,2),4666(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1064 4666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4672">
    <literal><![CDATA[
      R(x,y,y \ z) * T(z,u) = (x * y) * (y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(3846(a,1),4616(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3846 4616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4673">
    <literal><![CDATA[
      (x * y) * (y \ T(z,x)) = z * R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2842,a(flip),b,4672,a),flip(a)].">
      <j1 rule="hyper" parents="63 2842 4672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4674">
    <literal><![CDATA[
      L(x,y,z) * R(u,x,L(x,y,z) * (x \ 1)) = (u * x) * (x \ T(L(x,y,z),u))
    ]]></literal>
    <justification jstring="[para(969(a,2),4673(a,2,2,3)),flip(a)].">
      <j1 rule="para" parents="969 4673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4675">
    <literal><![CDATA[
      R(x,y,z * K(u,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,20,a,b,4664,a)].">
      <j1 rule="hyper" parents="63 20 4664"/>
    </justification>
  </clause>

  <clause id="4676">
    <literal><![CDATA[
      R(x,y,z * u) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(94(a,1),4675(a,1,3))].">
      <j1 rule="para" parents="94 4675"/>
    </justification>
  </clause>

  <clause id="4677">
    <literal><![CDATA[
      R(x,y,(z \ u) * z) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(306(a,1),4675(a,1,3)),flip(a)].">
      <j1 rule="para" parents="306 4675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4678">
    <literal><![CDATA[
      R(x,y,L(z,u,w) * (w * u)) = R(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[para(455(a,1),4675(a,1,3))].">
      <j1 rule="para" parents="455 4675"/>
    </justification>
  </clause>

  <clause id="4679">
    <literal><![CDATA[
      R(x,y,T(z,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2733(a,1),4675(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2733 4675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4680">
    <literal><![CDATA[
      R(x,y,z / u) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(2732(a,1),4675(a,1,3))].">
      <j1 rule="para" parents="2732 4675"/>
    </justification>
  </clause>

  <clause id="4681">
    <literal><![CDATA[
      R(x,y,(z \ u) \ u) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2819(a,2),4675(a,1,3))].">
      <j1 rule="para" parents="2819 4675"/>
    </justification>
  </clause>

  <clause id="4682">
    <literal><![CDATA[
      R(x,y,z / (z / u)) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(3090(a,2),4675(a,1,3))].">
      <j1 rule="para" parents="3090 4675"/>
    </justification>
  </clause>

  <clause id="4683">
    <literal><![CDATA[
      R(x,y,z * (u / w)) = R(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[para(3151(a,1),4675(a,1,3))].">
      <j1 rule="para" parents="3151 4675"/>
    </justification>
  </clause>

  <clause id="4685">
    <literal><![CDATA[
      R(x,y,K(z,u) * w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[para(3631(a,1),4675(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3631 4675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4686">
    <literal><![CDATA[
      R(x,y,T(z,u) * w) = R(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(3638(a,1),4675(a,1,3))].">
      <j1 rule="para" parents="3638 4675"/>
    </justification>
  </clause>

  <clause id="4687">
    <literal><![CDATA[
      R(x,y,z \ K(u,w)) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(3780(a,1),4675(a,1,3))].">
      <j1 rule="para" parents="3780 4675"/>
    </justification>
  </clause>

  <clause id="4688">
    <literal><![CDATA[
      R(x,y,z * (u * K(w,v5))) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(3763(a,1),4675(a,1,3))].">
      <j1 rule="para" parents="3763 4675"/>
    </justification>
  </clause>

  <clause id="4689">
    <literal><![CDATA[
      R(x,y,z \ (u * w)) = R(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[para(3922(a,1),4675(a,1,3))].">
      <j1 rule="para" parents="3922 4675"/>
    </justification>
  </clause>

  <clause id="4690">
    <literal><![CDATA[
      R(x,y,z * (u * w)) = R(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[para(3933(a,1),4675(a,1,3))].">
      <j1 rule="para" parents="3933 4675"/>
    </justification>
  </clause>

  <clause id="4692">
    <literal><![CDATA[
      R(x,y,z \ (u \ T(w,v5))) = R(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(3912(a,1),4675(a,1,3))].">
      <j1 rule="para" parents="3912 4675"/>
    </justification>
  </clause>

  <clause id="4693">
    <literal><![CDATA[
      R(x,y,z \ (u * T(w,v5))) = R(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(3913(a,1),4675(a,1,3))].">
      <j1 rule="para" parents="3913 4675"/>
    </justification>
  </clause>

  <clause id="4694">
    <literal><![CDATA[
      R(x,y,z \ (K(u,w) * v5)) = R(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(3914(a,1),4675(a,1,3))].">
      <j1 rule="para" parents="3914 4675"/>
    </justification>
  </clause>

  <clause id="4695">
    <literal><![CDATA[
      R(x,y,z \ (u / w)) = R(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(3917(a,1),4675(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3917 4675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4697">
    <literal><![CDATA[
      R(x,y,z * (K(u,w) * v5)) = R(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(3941(a,1),4675(a,1,3))].">
      <j1 rule="para" parents="3941 4675"/>
    </justification>
  </clause>

  <clause id="4698">
    <literal><![CDATA[
      R(x,y,L(T(z,u),w,v5)) = R(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(4449(a,1),4675(a,1,3))].">
      <j1 rule="para" parents="4449 4675"/>
    </justification>
  </clause>

  <clause id="4699">
    <literal><![CDATA[
      R(x,y,z \ (u * (w * T(v5,v6)))) = R(x,y,z \ (u * (w * v5)))
    ]]></literal>
    <justification jstring="[para(4049(a,1),4675(a,1,3))].">
      <j1 rule="para" parents="4049 4675"/>
    </justification>
  </clause>

  <clause id="4701">
    <literal><![CDATA[
      R(R(x,y,z),u,K(w,v5)) = R(x,y,T(z,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,3765,a,b,4679,a)].">
      <j1 rule="hyper" parents="316 3765 4679"/>
    </justification>
  </clause>

  <clause id="4707">
    <literal><![CDATA[
      R(x,y,(z \ 1) * u) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1711,a(flip),b,4676,a),flip(a)].">
      <j1 rule="hyper" parents="316 1711 4676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4709">
    <literal><![CDATA[
      R(x / y,y,z * u) = (x * (u * z)) / (y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,110,a(flip),b,4676,a),flip(a)].">
      <j1 rule="hyper" parents="316 110 4676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4710">
    <literal><![CDATA[
      R(x,y,z \ (z * (u * w))) = R(x,y,w * u)
    ]]></literal>
    <justification jstring="[para(9(a,2),4676(a,1,3))].">
      <j1 rule="para" parents="9 4676"/>
    </justification>
  </clause>

  <clause id="4711">
    <literal><![CDATA[
      R(x,y,y * x) \ 1 = y * ((x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(4676(a,1),729(a,1,1))].">
      <j1 rule="para" parents="4676 729"/>
    </justification>
  </clause>

  <clause id="4712">
    <literal><![CDATA[
      R(x,y,(z * z) \ u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1701,a(flip),b,4677,a)].">
      <j1 rule="hyper" parents="63 1701 4677"/>
    </justification>
  </clause>

  <clause id="4713">
    <literal><![CDATA[
      R(x,y,L((z \ u) * z,w,v5)) = R(x,y,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(1369(a,2),4677(a,1,3))].">
      <j1 rule="para" parents="1369 4677"/>
    </justification>
  </clause>

  <clause id="4714">
    <literal><![CDATA[
      R(x,y,T(z / u,w)) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4679,a,b,4680,a)].">
      <j1 rule="hyper" parents="63 4679 4680"/>
    </justification>
  </clause>

  <clause id="4715">
    <literal><![CDATA[
      T(((1 / (x / y)) * z) * (x / y),y / x) = R(z,(x / y) \ 1,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3054,a,b,4680,a)].">
      <j1 rule="hyper" parents="63 3054 4680"/>
    </justification>
  </clause>

  <clause id="4716">
    <literal><![CDATA[
      (x * ((y / z) \ 1)) * T(y / z,y \ z) = R(x,(y / z) \ 1,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2448,a,b,4680,a)].">
      <j1 rule="hyper" parents="63 2448 4680"/>
    </justification>
  </clause>

  <clause id="4717">
    <literal><![CDATA[
      R(1 / x,x,y \ (x \ y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,3349,a(flip),b,4680,a),flip(a)].">
      <j1 rule="hyper" parents="63 3349 4680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4718">
    <literal><![CDATA[
      R(x,y,z \ (z / (u \ 1))) = R(x,y,(u * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3304,a(flip),b,4680,a),flip(a)].">
      <j1 rule="hyper" parents="63 3304 4680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4719">
    <literal><![CDATA[
      R(x,y,z / (u * (w * w))) = R(x,y,u \ (z / (w * w)))
    ]]></literal>
    <justification jstring="[para(393(a,1),4680(a,1,3))].">
      <j1 rule="para" parents="393 4680"/>
    </justification>
  </clause>

  <clause id="4721">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ a(z,u,w)) = R(x,y,z * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(2474(a,1),4680(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2474 4680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4724">
    <literal><![CDATA[
      R(x,x \ (y \ z),y) \ z = (x \ (y \ z)) * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[para(4681(a,1),698(a,1,1))].">
      <j1 rule="para" parents="4681 698"/>
    </justification>
  </clause>

  <clause id="4725">
    <literal><![CDATA[
      R(x,y,K(z,u) * (w * v5)) = R(x,y,v5 * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,4676,a,b,4685,a),flip(a)].">
      <j1 rule="hyper" parents="316 4676 4685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4726">
    <literal><![CDATA[
      R(x,y,(z / u) * w) = R(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(2774(a,1),4685(a,1,3))].">
      <j1 rule="para" parents="2774 4685"/>
    </justification>
  </clause>

  <clause id="4727">
    <literal><![CDATA[
      R(x,y,(T(z,u) \ w) * v5) = R(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[para(2902(a,1),4685(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2902 4685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4728">
    <literal><![CDATA[
      R(x,y,(z / u) \ w) = R(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(3143(a,1),4685(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3143 4685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4729">
    <literal><![CDATA[
      R(x,y,((z / u) \ w) * v5) = R(x,y,((u \ z) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(3216(a,1),4685(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3216 4685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4730">
    <literal><![CDATA[
      ((x * (y * y)) * ((y * y) \ z)) / z = R(x,y * y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,108,a,b,4712,a)].">
      <j1 rule="hyper" parents="63 108 4712"/>
    </justification>
  </clause>

  <clause id="4731">
    <literal><![CDATA[
      R(x,x,y) * ((x * x) \ y) = x \ y
    ]]></literal>
    <justification jstring="[para(4712(a,1),1165(a,1,1))].">
      <j1 rule="para" parents="4712 1165"/>
    </justification>
  </clause>

  <clause id="4732">
    <literal><![CDATA[
      R(x,y,a(z * u,z,u) * K(u,(z * u) * z)) = R(x,y,u * ((z * u) * z))
    ]]></literal>
    <justification jstring="[para(3954(a,1),4712(a,1,3))].">
      <j1 rule="para" parents="3954 4712"/>
    </justification>
  </clause>

  <clause id="4734">
    <literal><![CDATA[
      (x \ 1) \ (y \ (x \ y)) = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(4717(a,1),369(a,1,1))].">
      <j1 rule="para" parents="4717 369"/>
    </justification>
  </clause>

  <clause id="4736">
    <literal><![CDATA[
      R(x,y,z \ K(u,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1033,a(flip),b,4687,a),flip(a)].">
      <j1 rule="hyper" parents="316 1033 4687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4737">
    <literal><![CDATA[
      R(x,y,(z \ u) * (z * z)) = R(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(613(a,1),4714(a,1,3))].">
      <j1 rule="para" parents="613 4714"/>
    </justification>
  </clause>

  <clause id="4739">
    <literal><![CDATA[
      R(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(4701(a,1),1723(a,1))].">
      <j1 rule="para" parents="4701 1723"/>
    </justification>
  </clause>

  <clause id="4740">
    <literal><![CDATA[
      R(x,y,z * (u \ (u / (w \ 1)))) = R(x,y,z * ((w * u) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3305,a(flip),b,4683,a),flip(a)].">
      <j1 rule="hyper" parents="63 3305 4683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4741">
    <literal><![CDATA[
      R(x,y,z * ((u * u) \ w)) = R(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1712,a(flip),b,4683,a),flip(a)].">
      <j1 rule="hyper" parents="63 1712 4683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      R(x,y,z * (u / (w * (v5 * v5)))) = R(x,y,z * (w \ (u / (v5 * v5))))
    ]]></literal>
    <justification jstring="[para(393(a,1),4683(a,1,3,2))].">
      <j1 rule="para" parents="393 4683"/>
    </justification>
  </clause>

  <clause id="4743">
    <literal><![CDATA[
      R(x,y,z * ((u * u) \ (w \ v5))) = R(x,y,z * (w \ (v5 / (u * u))))
    ]]></literal>
    <justification jstring="[para(675(a,1),4683(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="675 4683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4744">
    <literal><![CDATA[
      R(x,y,z * L(u / (w \ 1),w \ 1,w)) = R(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[para(2743(a,1),4688(a,1,3,2))].">
      <j1 rule="para" parents="2743 4688"/>
    </justification>
  </clause>

  <clause id="4745">
    <literal><![CDATA[
      R(x,y,z * (u \ (w / v5))) = R(x,y,z * (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(3917(a,1),4688(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3917 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4746">
    <literal><![CDATA[
      R(x,y,z \ ((u \ 1) * w)) = R(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,1728,a(flip),b,4689,a),flip(a)].">
      <j1 rule="hyper" parents="316 1728 4689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      R(x,y,(z * u) \ ((w * u) * z)) = R(x,y,L(T(w,u),u,z))
    ]]></literal>
    <justification jstring="[para(247(a,1),4689(a,1,3)),flip(a)].">
      <j1 rule="para" parents="247 4689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4748">
    <literal><![CDATA[
      R(x,y,(z * u) * w) = R(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,4676,a,b,4690,a)].">
      <j1 rule="hyper" parents="316 4676 4690"/>
    </justification>
  </clause>

  <clause id="4749">
    <literal><![CDATA[
      R(x,y,z * ((u \ 1) * w)) = R(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,1729,a(flip),b,4690,a),flip(a)].">
      <j1 rule="hyper" parents="316 1729 4690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      R(x,y,z * ((z * u) * u)) = R(x,y,a(z,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,1716,a(flip),b,4690,a),flip(a)].">
      <j1 rule="hyper" parents="316 1716 4690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4751">
    <literal><![CDATA[
      R(x,y,z * ((u * u) * w)) = R(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,1703,a(flip),b,4690,a),flip(a)].">
      <j1 rule="hyper" parents="316 1703 4690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4752">
    <literal><![CDATA[
      R(x,y,(z * u) \ w) = R(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[para(2765(a,1),4694(a,1,3))].">
      <j1 rule="para" parents="2765 4694"/>
    </justification>
  </clause>

  <clause id="4753">
    <literal><![CDATA[
      R(x,y,((z \ u) * z) \ w) = R(x,y,u \ w)
    ]]></literal>
    <justification jstring="[para(2785(a,1),4694(a,1,3))].">
      <j1 rule="para" parents="2785 4694"/>
    </justification>
  </clause>

  <clause id="4754">
    <literal><![CDATA[
      R(x,y,((z * u) * w) \ v5) = R(x,y,((u * z) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(3065(a,1),4694(a,1,3))].">
      <j1 rule="para" parents="3065 4694"/>
    </justification>
  </clause>

  <clause id="4755">
    <literal><![CDATA[
      R(x,y,(z * K(u,w)) \ v5) = R(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(4150(a,1),4694(a,1,3))].">
      <j1 rule="para" parents="4150 4694"/>
    </justification>
  </clause>

  <clause id="4756">
    <literal><![CDATA[
      R(x,y,z \ ((u * u) \ w)) = R(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1708,a(flip),b,4695,a),flip(a)].">
      <j1 rule="hyper" parents="63 1708 4695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4758">
    <literal><![CDATA[
      R(x,y,z \ (u / (w / (v5 * v5)))) = R(x,y,z \ (w \ (u * (v5 * v5))))
    ]]></literal>
    <justification jstring="[para(676(a,1),4695(a,1,3,2))].">
      <j1 rule="para" parents="676 4695"/>
    </justification>
  </clause>

  <clause id="4759">
    <literal><![CDATA[
      R(x / y,y,x \ (z \ u)) \ (u / z) = y * (x \ (u / z))
    ]]></literal>
    <justification jstring="[para(4695(a,1),490(a,1,1))].">
      <j1 rule="para" parents="4695 490"/>
    </justification>
  </clause>

  <clause id="4760">
    <literal><![CDATA[
      R(x,y,z * ((u * w) * v5)) = R(x,y,z * ((w * u) * v5))
    ]]></literal>
    <justification jstring="[para(2759(a,1),4697(a,1,3,2))].">
      <j1 rule="para" parents="2759 4697"/>
    </justification>
  </clause>

  <clause id="4761">
    <literal><![CDATA[
      R(x,y,z * ((u / w) \ v5)) = R(x,y,z * ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(3143(a,1),4697(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3143 4697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4762">
    <literal><![CDATA[
      R(x,y,T(z / u,w) * v5) = R(x,y,(u \ z) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,4686,a,b,4726,a)].">
      <j1 rule="hyper" parents="63 4686 4726"/>
    </justification>
  </clause>

  <clause id="4764">
    <literal><![CDATA[
      R(x,y,(z \ u) * (z * u)) = R(x,y,a(z \ u,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2405,a(flip),b,4726,a),flip(a)].">
      <j1 rule="hyper" parents="63 2405 4726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4765">
    <literal><![CDATA[
      R(x,y,z * (u * (u * w))) = R(x,y,z * L(w,u,u))
    ]]></literal>
    <justification jstring="[para(18(a,2),4741(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="18 4741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4766">
    <literal><![CDATA[
      R(x,y,((z \ 1) * u) * w) = R(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,1729,a(flip),b,4748,a),flip(a)].">
      <j1 rule="hyper" parents="316 1729 4748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4767">
    <literal><![CDATA[
      R(x,y,z / (u * w)) = R(x,y,(w * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,4680,a,b,4752,a)].">
      <j1 rule="hyper" parents="316 4680 4752"/>
    </justification>
  </clause>

  <clause id="4768">
    <literal><![CDATA[
      R(x,y,(y * x) \ z) \ z = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(4752(a,1),348(a,1,1))].">
      <j1 rule="para" parents="4752 348"/>
    </justification>
  </clause>

  <clause id="4769">
    <literal><![CDATA[
      L(R(x,y,(z * u) \ w),v5,v6) * (y * ((u * z) \ w)) = (L(x,v5,v6) * y) * ((u * z) \ w)
    ]]></literal>
    <justification jstring="[para(4752(a,1),400(a,1,1,1))].">
      <j1 rule="para" parents="4752 400"/>
    </justification>
  </clause>

  <clause id="4770">
    <literal><![CDATA[
      R(x,y,(z \ K(u,w)) \ v5) = R(x,y,(z \ 1) \ v5)
    ]]></literal>
    <justification jstring="[para(3780(a,1),4755(a,1,3,1))].">
      <j1 rule="para" parents="3780 4755"/>
    </justification>
  </clause>

  <clause id="4771">
    <literal><![CDATA[
      R(x,y,z \ (u * (u * w))) = R(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[para(18(a,2),4756(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="18 4756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4772">
    <literal><![CDATA[
      R(x,y,(z * u) \ ((w * u) * z)) = R(x,y,R(w,u,z))
    ]]></literal>
    <justification jstring="[para(20(a,2),4767(a,1,3)),flip(a)].">
      <j1 rule="para" parents="20 4767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4773">
    <literal><![CDATA[
      (x / R(y,z,(z * y) \ x)) * L(R(y,z,(z * y) \ x),u,w) = L(R(y,z,(z * y) \ x),u,w) * (z * ((y * z) \ x))
    ]]></literal>
    <justification jstring="[para(4768(a,1),4325(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4768 4325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4774">
    <literal><![CDATA[
      R(x,y,z \ (u \ (w / v5))) = R(x,y,z \ (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(116(a,1),4692(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="116 4692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4775">
    <literal><![CDATA[
      R(x,y,z \ (u * (w / v5))) = R(x,y,z \ (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(116(a,1),4693(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="116 4693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4776">
    <literal><![CDATA[
      R(x,y,z \ ((u \ 1) \ z)) = R(x,y,(u * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4695,a(flip),b,4718,a)].">
      <j1 rule="hyper" parents="63 4695 4718"/>
    </justification>
  </clause>

  <clause id="4777">
    <literal><![CDATA[
      R(x,y,(x * z) \ z) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4581,a(flip),b,4718,a),flip(a)].">
      <j1 rule="hyper" parents="63 4581 4718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4778">
    <literal><![CDATA[
      R(x \ y,z,y \ x) = R(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4753,a(flip),b,4777,a)].">
      <j1 rule="hyper" parents="63 4753 4777"/>
    </justification>
  </clause>

  <clause id="4779">
    <literal><![CDATA[
      R(x,y,x) \ y = y * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(4777(a,1),348(a,1,1))].">
      <j1 rule="para" parents="4777 348"/>
    </justification>
  </clause>

  <clause id="4781">
    <literal><![CDATA[
      x * ((a(y,z,u) * x) \ x) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(2364(a,1),4779(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2364 4779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4782">
    <literal><![CDATA[
      ((x * T(x / y,y)) / ((x / y) * y)) \ y = y * (((x / y) * y) \ y)
    ]]></literal>
    <justification jstring="[para(4056(a,2),4779(a,1,1))].">
      <j1 rule="para" parents="4056 4779"/>
    </justification>
  </clause>

  <clause id="4783">
    <literal><![CDATA[
      R(x \ (y \ x),z,x \ (y \ x)) = R(x \ (y \ x),z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4681,a(flip),b,4778,a),flip(a)].">
      <j1 rule="hyper" parents="63 4681 4778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4784">
    <literal><![CDATA[
      (a(x,y,z) * u) \ u = u \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(144,a,4781,a),flip(a)].">
      <j1 rule="hyper" parents="144 4781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4785">
    <literal><![CDATA[
      x * ((x * a(y,z,u)) \ x) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,2394,a(flip),b,4781,a)].">
      <j1 rule="hyper" parents="63 2394 4781"/>
    </justification>
  </clause>

  <clause id="4786">
    <literal><![CDATA[
      (x * a(y,z,u)) \ x = x \ (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,4781,a(flip),b,2394,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 4781 2394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4787">
    <literal><![CDATA[
      x * L(a(y,z,u) \ 1,a(y,z,u),x) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,359,a,b,4785,a)].">
      <j1 rule="hyper" parents="63 359 4785"/>
    </justification>
  </clause>

  <clause id="4788">
    <literal><![CDATA[
      L(x \ (a(y,z,u) \ x),x * a(y,z,u),w) = (w * (x * a(y,z,u))) \ (w * x)
    ]]></literal>
    <justification jstring="[para(4786(a,1),102(a,1,1))].">
      <j1 rule="para" parents="4786 102"/>
    </justification>
  </clause>

  <clause id="4789">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ u) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1701,a(flip),b,4737,a),flip(a)].">
      <j1 rule="hyper" parents="63 1701 4737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4791">
    <literal><![CDATA[
      T((R(x \ 1,y,z) * ((x \ 1) \ u)) / u,x \ 1) = R(x * R(x \ 1,y,z),x \ 1,x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1512,a,b,4789,a)].">
      <j1 rule="hyper" parents="63 1512 4789"/>
    </justification>
  </clause>

  <clause id="4792">
    <literal><![CDATA[
      T((((x \ 1) \ y) * z) * (((x \ 1) \ y) \ 1),(x \ 1) \ y) = R(z,(x \ 1) \ y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,625,a,b,4789,a)].">
      <j1 rule="hyper" parents="63 625 4789"/>
    </justification>
  </clause>

  <clause id="4794">
    <literal><![CDATA[
      R(x,y,((z * z) / u) \ w) = R(x,y,(u / (z * z)) \ w)
    ]]></literal>
    <justification jstring="[para(429(a,1),4789(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="429 4789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4795">
    <literal><![CDATA[
      R(x,y,((z * u) \ ((z * w) * u)) * v5) = R(x,y,R(w,z,u) * v5)
    ]]></literal>
    <justification jstring="[para(734(a,2),4762(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="734 4762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4796">
    <literal><![CDATA[
      R(x,y,(z \ K(u,w)) \ v5) = R(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,4789,a(flip),b,4770,a),flip(a)].">
      <j1 rule="hyper" parents="316 4789 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4797">
    <literal><![CDATA[
      R(x,y \ K(z,u),y \ w) * w = (x * (y \ K(z,u))) * ((y \ K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(138,a,4796,a(flip),b,108,a)].">
      <j1 rule="hyper" parents="138 4796 108"/>
    </justification>
  </clause>

  <clause id="4798">
    <literal><![CDATA[
      R(x,y,L(z,u,w) * (w * u)) = R(x,y,w * (z * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,4690,a,b,4678,a),flip(a)].">
      <j1 rule="hyper" parents="316 4690 4678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4799">
    <literal><![CDATA[
      R(x,y,a(z,u,z * u)) = R(x,y,z * R(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1727,a(flip),b,4750,a),flip(a)].">
      <j1 rule="hyper" parents="63 1727 4750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4800">
    <literal><![CDATA[
      R(x,y,z * ((u * w) * u)) = R(x,y,z * L(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4690,a,b,4765,a)].">
      <j1 rule="hyper" parents="63 4690 4765"/>
    </justification>
  </clause>

  <clause id="4801">
    <literal><![CDATA[
      R(x,y,z \ L(u,z,z)) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4710,a(flip),b,4771,a),flip(a)].">
      <j1 rule="hyper" parents="63 4710 4771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4802">
    <literal><![CDATA[
      R(x,y,R(z,z,u) \ u) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(4657(a,2),4801(a,1,3))].">
      <j1 rule="para" parents="4657 4801"/>
    </justification>
  </clause>

  <clause id="4803">
    <literal><![CDATA[
      R(x,y,z * (u * z)) = R(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1701,a(flip),b,4798,a),flip(a)].">
      <j1 rule="hyper" parents="63 1701 4798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4804">
    <literal><![CDATA[
      R(x,y,L(z * u,u,u)) = R(x,y,u * R(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1727,a(flip),b,4803,a),flip(a)].">
      <j1 rule="hyper" parents="63 1727 4803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4805">
    <literal><![CDATA[
      R(x,y,L(z * u,u,u)) = R(x,y,R(z,u,u) * u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4676,a,b,4804,a),flip(a)].">
      <j1 rule="hyper" parents="316 4676 4804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4806">
    <literal><![CDATA[
      R(x,y,R(z \ u,z,z) * z) = R(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4713,a(flip),b,4805,a),flip(a)].">
      <j1 rule="hyper" parents="63 4713 4805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4807">
    <literal><![CDATA[
      R(x,y,(z * (u * u)) \ w) = R(x,y,z \ (w / (u * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,4680,a(flip),b,4719,a)].">
      <j1 rule="hyper" parents="63 4680 4719"/>
    </justification>
  </clause>

  <clause id="4809">
    <literal><![CDATA[
      R(x,y,z \ a(z,u,w)) = R(x,y,z * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,4789,a(flip),b,4721,a)].">
      <j1 rule="hyper" parents="63 4789 4721"/>
    </justification>
  </clause>

  <clause id="4810">
    <literal><![CDATA[
      R(x,y,((z * u) * w) \ v5) = R(x,y,(w * (u * z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,4752,a,b,4754,a),flip(a)].">
      <j1 rule="hyper" parents="316 4752 4754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4811">
    <literal><![CDATA[
      R(x,y,z * ((u * w) * u)) = R(x,y,z * R(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,1727,a(flip),b,4760,a),flip(a)].">
      <j1 rule="hyper" parents="316 1727 4760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4812">
    <literal><![CDATA[
      L(x,y,R(z \ (u \ z),w,u)) = L(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[para(4783(a,1),4629(a,1,3))].">
      <j1 rule="para" parents="4783 4629"/>
    </justification>
  </clause>

  <clause id="4813">
    <literal><![CDATA[
      L(x,y,L(z \ (u \ z),w,u)) = L(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4628,a(flip),b,4812,a)].">
      <j1 rule="hyper" parents="63 4628 4812"/>
    </justification>
  </clause>

  <clause id="4814">
    <literal><![CDATA[
      L(x,y,(z * u) \ u) = L(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[para(298(a,1),4813(a,1,3))].">
      <j1 rule="para" parents="298 4813"/>
    </justification>
  </clause>

  <clause id="4815">
    <literal><![CDATA[
      L(x,y,(z \ u) \ (z \ (z \ u))) = L(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),4814(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 4814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4816">
    <literal><![CDATA[
      L(x,y,L(z * (u * u),w,v5) \ (u * u)) = L(x,y,(u * u) \ (L(z,w,v5) \ (u * u)))
    ]]></literal>
    <justification jstring="[para(1058(a,2),4814(a,1,3,1))].">
      <j1 rule="para" parents="1058 4814"/>
    </justification>
  </clause>

  <clause id="4817">
    <literal><![CDATA[
      R(x,y,((z * z) / u) \ w) = R(x,y,((z * z) \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(316,a,4728,a(flip),b,4794,a),flip(a)].">
      <j1 rule="hyper" parents="316 4728 4794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4818">
    <literal><![CDATA[
      R(x,y,(z * (u * u)) \ w) = R(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(316,a,1708,a(flip),b,4807,a),flip(a)].">
      <j1 rule="hyper" parents="316 1708 4807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4820">
    <literal><![CDATA[
      R(x,y,((z * z) \ u) \ w) = R(x,y,u \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,4753,a(flip),b,4818,a),flip(a)].">
      <j1 rule="hyper" parents="63 4753 4818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4821">
    <literal><![CDATA[
      R(x,y,(z * (u * (w * w))) \ v5) = R(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(32(a,1),4818(a,1,3,1))].">
      <j1 rule="para" parents="32 4818"/>
    </justification>
  </clause>

  <clause id="4822">
    <literal><![CDATA[
      R(x,y,(z \ (u \ 1)) \ w) = R(x,y,(z \ u) \ w)
    ]]></literal>
    <justification jstring="[para(584(a,1),4818(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="584 4818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4826">
    <literal><![CDATA[
      R(x,y,((z * u) * w) \ ((w * u) * z)) = R(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(14(a,2),4810(a,2,3))].">
      <j1 rule="para" parents="14 4810"/>
    </justification>
  </clause>

  <clause id="4827">
    <literal><![CDATA[
      R(x,y,((z * z) / u) \ w) = R(x,y,u \ w)
    ]]></literal>
    <justification jstring="[hyper(316,a,4820,a(flip),b,4817,a),flip(a)].">
      <j1 rule="hyper" parents="316 4820 4817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4829">
    <literal><![CDATA[
      R(x,y,(z * (L(z,u,w) \ z)) \ v5) = R(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(4390(a,1),4827(a,1,3,1))].">
      <j1 rule="para" parents="4390 4827"/>
    </justification>
  </clause>

  <clause id="4831">
    <literal><![CDATA[
      R(x,y,(z * (u * (w * (v5 * v5)))) \ v6) = R(x,y,(z * (u * w)) \ v6)
    ]]></literal>
    <justification jstring="[para(32(a,1),4821(a,1,3,1,2))].">
      <j1 rule="para" parents="32 4821"/>
    </justification>
  </clause>

  <clause id="4832">
    <literal><![CDATA[
      R(x,y,(z * (u \ 1)) \ w) = R(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[para(229(a,1),4821(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="229 4821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4833">
    <literal><![CDATA[
      R(x,y \ 1,(x * y) \ z) \ z = (y \ 1) * ((x * (y \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(4832(a,1),348(a,1,1))].">
      <j1 rule="para" parents="4832 348"/>
    </justification>
  </clause>

  <clause id="4837">
    <literal><![CDATA[
      L(x * K(y,z),u,w) = L(x,u,w) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(463,a,4665,a)].">
      <j1 rule="hyper" parents="463 4665"/>
    </justification>
  </clause>

  <clause id="4839">
    <literal><![CDATA[
      x * L(y * K(z,u),w,v5) = x * (L(y,w,v5) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,4837,a,b,9,a)].">
      <j1 rule="hyper" parents="139 4837 9"/>
    </justification>
  </clause>

  <clause id="4840">
    <literal><![CDATA[
      x \ L(y * K(z,u),w,v5) = (x \ L(y,w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,4837,a,b,3762,a)].">
      <j1 rule="hyper" parents="133 4837 3762"/>
    </justification>
  </clause>

  <clause id="4842">
    <literal><![CDATA[
      K(x,y) * L(K(x,y) \ z,u,w) = L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(35,a,1348,a,b,4837,a(flip))].">
      <j1 rule="hyper" parents="35 1348 4837"/>
    </justification>
  </clause>

  <clause id="4843">
    <literal><![CDATA[
      L(x,y,L(z * K(u,w),v5,v6)) = L(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(4837(a,2),1676(a,1,3))].">
      <j1 rule="para" parents="4837 1676"/>
    </justification>
  </clause>

  <clause id="4844">
    <literal><![CDATA[
      L(x \ y,z,u) * K(x,x \ y) = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(2732(a,1),4837(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2732 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4845">
    <literal><![CDATA[
      a(L(x * K(y,z),u,w),v5,v6) = a(L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(4837(a,2),2788(a,1,1))].">
      <j1 rule="para" parents="4837 2788"/>
    </justification>
  </clause>

  <clause id="4846">
    <literal><![CDATA[
      L(x \ 1,y,z) * K(u,w) = L(x \ K(u,w),y,z)
    ]]></literal>
    <justification jstring="[para(3780(a,1),4837(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3780 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4847">
    <literal><![CDATA[
      L(x * y,z,u) * K(y,w) = L(x * T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(3832(a,1),4837(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3832 4837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4850">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) = K(x,y) * L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,4842,a(flip),b,1355,a),flip(a)].">
      <j1 rule="hyper" parents="139 4842 1355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4851">
    <literal><![CDATA[
      (x * y) \ L(K(y,x) \ z,u,w) = (y * x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,4842,a(flip),b,2758,a),flip(a)].">
      <j1 rule="hyper" parents="133 4842 2758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4852">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(u,w) = x * L(x \ K(u,w),y,z)
    ]]></literal>
    <justification jstring="[para(4842(a,1),1495(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4842 1495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4853">
    <literal><![CDATA[
      (K(x,y) * z) * L((K(x,y) * z) \ u,w,v5) = L(u / z,w,v5) * z
    ]]></literal>
    <justification jstring="[para(4842(a,1),1533(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4842 1533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4854">
    <literal><![CDATA[
      K(x,y) * L(T(x,y) \ z,u,w) = L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(2862(a,1),4842(a,1,2,1))].">
      <j1 rule="para" parents="2862 4842"/>
    </justification>
  </clause>

  <clause id="4855">
    <literal><![CDATA[
      K(x,y) * L(x * z,u,w) = L(T(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(2863(a,1),4842(a,1,2,1))].">
      <j1 rule="para" parents="2863 4842"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) * v5 = K(x,y) * (L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(138,a,4850,a,b,410,a)].">
      <j1 rule="hyper" parents="138 4850 410"/>
    </justification>
  </clause>

  <clause id="4857">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) / v5 = K(x,y) * (L(z,u,w) / v5)
    ]]></literal>
    <justification jstring="[para(4850(a,2),660(a,1,1))].">
      <j1 rule="para" parents="4850 660"/>
    </justification>
  </clause>

  <clause id="4859">
    <literal><![CDATA[
      (x \ y) * L(K(x,x \ y) * z,u,w) = (y / x) * L(z,u,w)
    ]]></literal>
    <justification jstring="[para(4850(a,2),3074(a,1,2))].">
      <j1 rule="para" parents="4850 3074"/>
    </justification>
  </clause>

  <clause id="4860">
    <literal><![CDATA[
      L(x,y,L(z \ T(u,w),v5,v6)) = L(x,y,L(z \ u,v5,v6))
    ]]></literal>
    <justification jstring="[para(3846(a,1),4843(a,1,3,1))].">
      <j1 rule="para" parents="3846 4843"/>
    </justification>
  </clause>

  <clause id="4861">
    <literal><![CDATA[
      a(L(R(x,y,x),z,u),w,v5) = a(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,2793,a(flip),b,4845,a)].">
      <j1 rule="hyper" parents="63 2793 4845"/>
    </justification>
  </clause>

  <clause id="4863">
    <literal><![CDATA[
      a(L(L(x,y,x),z,u),w,v5) = a(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,4653,a(flip),b,4861,a)].">
      <j1 rule="hyper" parents="63 4653 4861"/>
    </justification>
  </clause>

  <clause id="4865">
    <literal><![CDATA[
      L(x \ K(y \ 1,y),y,y \ 1) = (y \ 1) * (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,2247,a(flip),b,4846,a),flip(a)].">
      <j1 rule="hyper" parents="63 2247 4846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4866">
    <literal><![CDATA[
      K(x,y) / L(z \ 1,u,w) = 1 / L(z \ K(y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(209,a,4846,a(flip),b,3820,a),flip(a)].">
      <j1 rule="hyper" parents="209 4846 3820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4867">
    <literal><![CDATA[
      (x * L(y \ 1,z,u)) * K(w,v5) = x * L(y \ K(w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(4846(a,1),3763(a,2,2))].">
      <j1 rule="para" parents="4846 3763"/>
    </justification>
  </clause>

  <clause id="4868">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ z,u,w) = x * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,4854,a(flip),b,2897,a),flip(a)].">
      <j1 rule="hyper" parents="139 4854 2897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4869">
    <literal><![CDATA[
      (T(x,y) \ z) \ L(T(x,y) \ u,w,v5) = (x \ z) \ L(x \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(4854(a,1),2906(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4854 2906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4870">
    <literal><![CDATA[
      (x \ y) * L(T(x \ y,x) \ z,u,w) = (y / x) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(4854(a,1),3202(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4854 3202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4871">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y) * z,u,w) = x \ L(x * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,4855,a(flip),b,2799,a)].">
      <j1 rule="hyper" parents="133 4855 2799"/>
    </justification>
  </clause>

  <clause id="4872">
    <literal><![CDATA[
      (x * L(y,z,u)) \ (x * L(y * K(w,v5),z,u)) = K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(133,a,4839,a,b,3763,a)].">
      <j1 rule="hyper" parents="133 4839 3763"/>
    </justification>
  </clause>

  <clause id="4873">
    <literal><![CDATA[
      L(x * K(y \ (z \ L(x,u,w)),y),u,w) = z * ((y \ (z \ L(x,u,w))) * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,307,a(flip),b,4840,a),flip(a)].">
      <j1 rule="hyper" parents="139 307 4840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4874">
    <literal><![CDATA[
      (x \ L(y,z,u)) * K(w,w \ y) = x \ L(w * (y / w),z,u)
    ]]></literal>
    <justification jstring="[para(2991(a,1),4840(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2991 4840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4875">
    <literal><![CDATA[
      x \ L(R(y * K(z,u),w,v5),v6,v7) = (x \ L(R(y,w,v5),v6,v7)) * K(z,u)
    ]]></literal>
    <justification jstring="[para(4604(a,2),4840(a,1,2,1))].">
      <j1 rule="para" parents="4604 4840"/>
    </justification>
  </clause>

  <clause id="4877">
    <literal><![CDATA[
      (x * y) \ L(x * y,z,u) = (y * x) \ L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(2754(a,1),4851(a,1,2,1))].">
      <j1 rule="para" parents="2754 4851"/>
    </justification>
  </clause>

  <clause id="4878">
    <literal><![CDATA[
      K(x,y) * (L(y * x,z,u) * w) = L(x * y,z,u) * w
    ]]></literal>
    <justification jstring="[para(2728(a,1),4856(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2728 4856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4879">
    <literal><![CDATA[
      K(x,x \ y) * (L(y,z,u) / w) = L(x * (y / x),z,u) / w
    ]]></literal>
    <justification jstring="[para(2992(a,1),4857(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2992 4857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4880">
    <literal><![CDATA[
      L(x,y,L((z * z) \ (u * z),w,v5)) = L(x,y,L(z \ R(u,z,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,1689,a(flip),b,4860,a),flip(a)].">
      <j1 rule="hyper" parents="63 1689 4860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4881">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),w) = x * L(x \ T(y,w),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1839,a(flip),b,4868,a)].">
      <j1 rule="hyper" parents="63 1839 4868"/>
    </justification>
  </clause>

  <clause id="4882">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (y * z),u,w) = y * (x * L(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(4868(a,1),1424(a,2,2))].">
      <j1 rule="para" parents="4868 1424"/>
    </justification>
  </clause>

  <clause id="4884">
    <literal><![CDATA[
      (x \ y) \ L(T(y / x,x) * z,u,w) = (y / x) \ L((y / x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(116(a,1),4871(a,1,1))].">
      <j1 rule="para" parents="116 4871"/>
    </justification>
  </clause>

  <clause id="4885">
    <literal><![CDATA[
      (x * L(y \ T(z,u),w,v5)) \ (x * L(y \ z,w,v5)) = K(u,z)
    ]]></literal>
    <justification jstring="[para(3849(a,1),4872(a,1,2,2,1))].">
      <j1 rule="para" parents="3849 4872"/>
    </justification>
  </clause>

  <clause id="4886">
    <literal><![CDATA[
      L(x * y,z,u) * T(y,x) = L(y * x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,3447,a(flip),b,4878,a)].">
      <j1 rule="hyper" parents="63 3447 4878"/>
    </justification>
  </clause>

  <clause id="4887">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ T(z,u),w,v5) = T(x * L(x \ z,w,v5),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4868,a,b,4881,a)].">
      <j1 rule="hyper" parents="316 4868 4881"/>
    </justification>
  </clause>

  <clause id="4888">
    <literal><![CDATA[
      x * (y * L(y \ T(z,x),u,w)) = (y * L(y \ z,u,w)) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,4881,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 4881 22"/>
    </justification>
  </clause>

  <clause id="4891">
    <literal><![CDATA[
      R(x,x \ (a(y,z,u) \ w),a(y,z,u)) \ w = a(y,z,u) * (x \ (a(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(316,a,2359,a(flip),b,4724,a),flip(a)].">
      <j1 rule="hyper" parents="316 2359 4724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4892">
    <literal><![CDATA[
      R(x,y,L(T(z,u),u,w)) = R(x,y,R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,4772,a(flip),b,4747,a),flip(a)].">
      <j1 rule="hyper" parents="63 4772 4747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4893">
    <literal><![CDATA[
      R(x,y,R(z,u,w)) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,4698,a(flip),b,4892,a),flip(a)].">
      <j1 rule="hyper" parents="63 4698 4892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4895">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,4577,a(flip),b,4893,a),flip(a)].">
      <j1 rule="hyper" parents="316 4577 4893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4896">
    <literal><![CDATA[
      R(1 / x,x,L(y,z,u)) \ R(y,z,u) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(4893(a,1),369(a,1,1))].">
      <j1 rule="para" parents="4893 369"/>
    </justification>
  </clause>

  <clause id="4899">
    <literal><![CDATA[
      R(x,y,((z * u) * w) \ (z * (w * u))) = R(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4689,a,b,4826,a)].">
      <j1 rule="hyper" parents="63 4689 4826"/>
    </justification>
  </clause>

  <clause id="4900">
    <literal><![CDATA[
      T((x * (y \ 1)) \ x,x / y) = T(x * (y \ 1),y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,2844,a(flip),b,3678,a)].">
      <j1 rule="hyper" parents="63 2844 3678"/>
    </justification>
  </clause>

  <clause id="4901">
    <literal><![CDATA[
      T((x * y) * ((x / (y \ 1)) \ 1),x / (y \ 1)) = (x * y) * ((x / (y \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(39,a,3113,a(flip),b,4900,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 3113 4900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4902">
    <literal><![CDATA[
      K(x * K(y \ 1,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2988,a,b,3938,a)].">
      <j1 rule="hyper" parents="63 2988 3938"/>
    </justification>
  </clause>

  <clause id="4903">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(3829(a,1),4902(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3829 4902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4904">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(1951(a,2),4903(a,1,1,1))].">
      <j1 rule="para" parents="1951 4903"/>
    </justification>
  </clause>

  <clause id="4905">
    <literal><![CDATA[
      K(T(x,1 / y) / z,y) = K(x / z,y)
    ]]></literal>
    <justification jstring="[para(2810(a,1),4904(a,1,1))].">
      <j1 rule="para" parents="2810 4904"/>
    </justification>
  </clause>

  <clause id="4906">
    <literal><![CDATA[
      (x * y) * (K(z,u) * (w * w)) = x * ((y * K(z,u)) * (w * w))
    ]]></literal>
    <justification jstring="[para(32(a,2),3943(a,2,2))].">
      <j1 rule="para" parents="32 3943"/>
    </justification>
  </clause>

  <clause id="4907">
    <literal><![CDATA[
      x \ (K(y,z) * T(K(z,y) * u,w)) = (x \ T(u * K(z,y),w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,3965,a(flip),b,3762,a)].">
      <j1 rule="hyper" parents="133 3965 3762"/>
    </justification>
  </clause>

  <clause id="4908">
    <literal><![CDATA[
      x * (y * K(x \ 1,y * x)) = L(y / (x \ 1),x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2743,a(flip),b,3974,a),flip(a)].">
      <j1 rule="hyper" parents="63 2743 3974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4909">
    <literal><![CDATA[
      x * ((y * K(z,u)) * K(w \ K(z,u),w)) = (x * y) * ((w \ K(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(307(a,1),4221(a,1,2)),flip(a)].">
      <j1 rule="para" parents="307 4221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4910">
    <literal><![CDATA[
      (x \ 1) \ (y / ((x \ 1) \ 1)) = (1 / x) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2598,a(flip),b,4232,a),flip(a)].">
      <j1 rule="hyper" parents="63 2598 4232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4911">
    <literal><![CDATA[
      L(x,y,z \ (u * (w * T(v5,v6)))) = L(x,y,z \ ((w * v5) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3235,a,b,4247,a)].">
      <j1 rule="hyper" parents="63 3235 4247"/>
    </justification>
  </clause>

  <clause id="4912">
    <literal><![CDATA[
      L(x,y,z) * (T(u,x) * K(w,v5)) = u * L(x * K(w,v5),y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,4839,a,b,4319,a),flip(a)].">
      <j1 rule="hyper" parents="316 4839 4319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4914">
    <literal><![CDATA[
      (1 / x) * L(L(x,y,z),u,w) = x \ L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1848,a(flip),b,4353,a),flip(a)].">
      <j1 rule="hyper" parents="63 1848 4353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4915">
    <literal><![CDATA[
      R(x,y,z \ ((L(L(u,w,v5),v6,v7) \ 1) * (1 / u))) = R(x,y,z \ (u \ L(L(u,w,v5),v6,v7)))
    ]]></literal>
    <justification jstring="[para(4914(a,1),4746(a,2,3,2))].">
      <j1 rule="para" parents="4914 4746"/>
    </justification>
  </clause>

  <clause id="4916">
    <literal><![CDATA[
      (1 / L(x,y,z)) * L(x,u,w) = L(x,y,z) \ L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1004,a(flip),b,4360,a),flip(a)].">
      <j1 rule="hyper" parents="63 1004 4360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4917">
    <literal><![CDATA[
      L(L(x,y,z),u,x) * (u * x) = L(x,u,x) * (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3439,a(flip),b,4374,a),flip(a)].">
      <j1 rule="hyper" parents="63 3439 4374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4918">
    <literal><![CDATA[
      L(x / y,z,u) \ (x / y) = L(y \ x,z,u) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(116(a,1),4406(a,1,2)),flip(a)].">
      <j1 rule="para" parents="116 4406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4919">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u / (x \ 1))) = u / (L(x,y,z) / (x * x))
    ]]></literal>
    <justification jstring="[hyper(316,a,676,a(flip),b,4431,a),flip(a)].">
      <j1 rule="hyper" parents="316 676 4431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4920">
    <literal><![CDATA[
      K(L(x,y,z) \ u,L(x,y,z)) = K(x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,3031,a,b,4443,a)].">
      <j1 rule="hyper" parents="35 3031 4443"/>
    </justification>
  </clause>

  <clause id="4922">
    <literal><![CDATA[
      (x / (L(y,z,u) \ w)) * K(y \ w,y) = x / (w / L(y,z,u))
    ]]></literal>
    <justification jstring="[para(4920(a,1),3834(a,1,2))].">
      <j1 rule="para" parents="4920 3834"/>
    </justification>
  </clause>

  <clause id="4923">
    <literal><![CDATA[
      K(L(x,y,z),u) * ((w / L(x,y,z)) * L(L(x,y,z),v5,v6)) = L(L(T(x,u),y,z),v5,v6) * (L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(25(a,2),4457(a,2,1,1))].">
      <j1 rule="para" parents="25 4457"/>
    </justification>
  </clause>

  <clause id="4924">
    <literal><![CDATA[
      K(R(x,y,z),u) * ((w / R(x,y,z)) * L(R(x,y,z),v5,v6)) = L(R(T(x,u),y,z),v5,v6) * (R(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(27(a,2),4457(a,2,1,1))].">
      <j1 rule="para" parents="27 4457"/>
    </justification>
  </clause>

  <clause id="4925">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * u = (z * K((x \ 1) \ (y \ z),y)) * u
    ]]></literal>
    <justification jstring="[para(1390(a,1),4503(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1390 4503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4926">
    <literal><![CDATA[
      (x \ 1) * (y * ((x \ 1) \ K(z,u))) = (1 / x) * (y * (x * K(z,u)))
    ]]></literal>
    <justification jstring="[para(3780(a,1),4567(a,1,2,2))].">
      <j1 rule="para" parents="3780 4567"/>
    </justification>
  </clause>

  <clause id="4927">
    <literal><![CDATA[
      a(x,y,z) = (L(z,y,x) * (x * y)) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1561,a,b,4586,a)].">
      <j1 rule="hyper" parents="63 1561 4586"/>
    </justification>
  </clause>

  <clause id="4928">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) * a(z,y,x) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,1561,a,b,4586,a(flip))].">
      <j1 rule="hyper" parents="139 1561 4586"/>
    </justification>
  </clause>

  <clause id="4929">
    <literal><![CDATA[
      R(L(x,y,z),u,L(L(x,y,z) \ x,L(x,y,z),u)) \ (x * u) = u * ((L(x,y,z) * u) \ (x * u))
    ]]></literal>
    <justification jstring="[para(4586(a,2),348(a,1,1,3))].">
      <j1 rule="para" parents="4586 348"/>
    </justification>
  </clause>

  <clause id="4930">
    <literal><![CDATA[
      a(x,y,z) \ (z * (x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,4927,a(flip))].">
      <j1 rule="hyper" parents="39 2301 4927"/>
    </justification>
  </clause>

  <clause id="4932">
    <literal><![CDATA[
      a(x,y,z) = (z * (x * y)) / (L(z,y,x) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(136,a,4928,a(flip),b,2290,a),flip(a)].">
      <j1 rule="hyper" parents="136 4928 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4933">
    <literal><![CDATA[
      L(x,y,x) * a(x,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,4537,a,b,4928,a(flip))].">
      <j1 rule="hyper" parents="35 4537 4928"/>
    </justification>
  </clause>

  <clause id="4934">
    <literal><![CDATA[
      a(x,y,x) * L(x,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a,b,4933,a)].">
      <j1 rule="hyper" parents="63 2290 4933"/>
    </justification>
  </clause>

  <clause id="4935">
    <literal><![CDATA[
      a(x,y,x) \ x = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,2274,a,b,4933,a)].">
      <j1 rule="hyper" parents="35 2274 4933"/>
    </justification>
  </clause>

  <clause id="4936">
    <literal><![CDATA[
      a(x,y,x) * (L(x,y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[para(4933(a,1),4538(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4933 4538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4937">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(133,a,10,a(flip),b,4936,a),flip(a)].">
      <j1 rule="hyper" parents="133 10 4936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4938">
    <literal><![CDATA[
      (L(x,y,x) * z) \ (x * z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,4936,a(flip),b,2290,a(flip))].">
      <j1 rule="hyper" parents="133 4936 2290"/>
    </justification>
  </clause>

  <clause id="4939">
    <literal><![CDATA[
      a(x,y,x) \ (z * x) = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4329,a(flip),b,4937,a),flip(a)].">
      <j1 rule="hyper" parents="63 4329 4937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4940">
    <literal><![CDATA[
      a(x,y,x) \ (L(x,y,x) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,1131,a(flip),b,4937,a),flip(a)].">
      <j1 rule="hyper" parents="63 1131 4937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4941">
    <literal><![CDATA[
      a(x,y,x) \ 1 = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,969,a(flip),b,4937,a),flip(a)].">
      <j1 rule="hyper" parents="63 969 4937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4942">
    <literal><![CDATA[
      x * (a(x,y,x) \ z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,4937,a(flip),b,1126,a)].">
      <j1 rule="hyper" parents="139 4937 1126"/>
    </justification>
  </clause>

  <clause id="4943">
    <literal><![CDATA[
      (x / y) \ (a(y,z,y) \ x) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,4937,a(flip),b,4325,a(flip))].">
      <j1 rule="hyper" parents="133 4937 4325"/>
    </justification>
  </clause>

  <clause id="4944">
    <literal><![CDATA[
      (x \ L(x,y,x)) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(4941(a,1),4541(a,1,1))].">
      <j1 rule="para" parents="4941 4541"/>
    </justification>
  </clause>

  <clause id="4945">
    <literal><![CDATA[
      L(x,y,x) * (a(x,y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(139,a,69,a(flip),b,4940,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 69 4940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4946">
    <literal><![CDATA[
      a(x,y,x) \ y = x \ ((x * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,1623,a,b,4942,a),flip(a)].">
      <j1 rule="hyper" parents="133 1623 4942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4947">
    <literal><![CDATA[
      a(x,y,x) \ (x \ y) = y * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1416,a(flip),b,4944,a),flip(a)].">
      <j1 rule="hyper" parents="63 1416 4944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4948">
    <literal><![CDATA[
      a(x,y,x) * (y * x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,4363,a,b,4945,a),flip(a)].">
      <j1 rule="hyper" parents="34 4363 4945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4949">
    <literal><![CDATA[
      (x * y) * a(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a(flip),b,4948,a)].">
      <j1 rule="hyper" parents="63 2290 4948"/>
    </justification>
  </clause>

  <clause id="4950">
    <literal><![CDATA[
      a(x,x,y) \ y = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,388,a(flip),b,4930,a(flip))].">
      <j1 rule="hyper" parents="35 388 4930"/>
    </justification>
  </clause>

  <clause id="4951">
    <literal><![CDATA[
      a(x,x,y) * L(y,x,x) = y
    ]]></literal>
    <justification jstring="[hyper(152,a,4950,a)].">
      <j1 rule="hyper" parents="152 4950"/>
    </justification>
  </clause>

  <clause id="4952">
    <literal><![CDATA[
      L(x,y,y) \ x = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,1379,a,b,4950,a)].">
      <j1 rule="hyper" parents="39 1379 4950"/>
    </justification>
  </clause>

  <clause id="4953">
    <literal><![CDATA[
      L(x,y,y) * a(y,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,2275,a,b,4950,a)].">
      <j1 rule="hyper" parents="38 2275 4950"/>
    </justification>
  </clause>

  <clause id="4955">
    <literal><![CDATA[
      a(x,x,y) \ (1 / y) = L(1 / y,x,x)
    ]]></literal>
    <justification jstring="[para(2535(a,1),4950(a,1,1))].">
      <j1 rule="para" parents="2535 4950"/>
    </justification>
  </clause>

  <clause id="4956">
    <literal><![CDATA[
      T((x / y) * a(z,z,y),a(z,z,y) \ y) = L(L(y,z,z),a(z,z,y),y \ x) \ x
    ]]></literal>
    <justification jstring="[para(4950(a,1),3740(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4950 3740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4957">
    <literal><![CDATA[
      L((a(x,x,y) * a(x,x,y)) * L(y,x,x),a(x,x,y),a(x,x,y)) = a(x,x,y) * y
    ]]></literal>
    <justification jstring="[para(4951(a,1),1114(a,2,2))].">
      <j1 rule="para" parents="4951 1114"/>
    </justification>
  </clause>

  <clause id="4958">
    <literal><![CDATA[
      (a(x,x,y) \ (y * z)) / (a(x,x,y) \ (L(y,x,x) * z)) = R(a(x,x,y),L(y,x,x),z)
    ]]></literal>
    <justification jstring="[para(4951(a,1),1176(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4951 1176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4959">
    <literal><![CDATA[
      a(a(x,x,y),L(y,x,x),z) \ (y * z) = a(x,x,y) * (L(y,x,x) * z)
    ]]></literal>
    <justification jstring="[para(4951(a,1),2315(a,1,2,1))].">
      <j1 rule="para" parents="4951 2315"/>
    </justification>
  </clause>

  <clause id="4960">
    <literal><![CDATA[
      (x * y) \ (a(z,z,y) * (x * L(y,z,z))) = a(x,L(y,z,z),a(z,z,y))
    ]]></literal>
    <justification jstring="[para(4951(a,1),2544(a,1,1,2))].">
      <j1 rule="para" parents="4951 2544"/>
    </justification>
  </clause>

  <clause id="4961">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) \ 1 = a(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2143,a(flip),b,4952,a)].">
      <j1 rule="hyper" parents="63 2143 4952"/>
    </justification>
  </clause>

  <clause id="4962">
    <literal><![CDATA[
      a(x,y,z * L(z,u,u)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(4952(a,1),2652(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4952 2652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4963">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,u),w,v5)) = a(x,y,L(a(u,u,z),w,v5))
    ]]></literal>
    <justification jstring="[para(4952(a,1),2656(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4952 2656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4964">
    <literal><![CDATA[
      L(x,y,y) \ ((z \ x) * z) = a(y,y,x) * K(z \ x,z)
    ]]></literal>
    <justification jstring="[para(4952(a,1),3921(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4952 3921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4965">
    <literal><![CDATA[
      (x * a(y,y,x)) \ 1 = L(x \ 1,y,y)
    ]]></literal>
    <justification jstring="[para(4952(a,1),4459(a,1,1,2))].">
      <j1 rule="para" parents="4952 4459"/>
    </justification>
  </clause>

  <clause id="4966">
    <literal><![CDATA[
      R(L(x,y,y),a(y,y,x),z) \ (x * z) = a(y,y,x) * z
    ]]></literal>
    <justification jstring="[para(4953(a,1),199(a,1,2,1))].">
      <j1 rule="para" parents="4953 199"/>
    </justification>
  </clause>

  <clause id="4968">
    <literal><![CDATA[
      a(L(x,y,y),a(y,y,x),z) \ (x * z) = L(x,y,y) * (a(y,y,x) * z)
    ]]></literal>
    <justification jstring="[para(4953(a,1),2315(a,1,2,1))].">
      <j1 rule="para" parents="4953 2315"/>
    </justification>
  </clause>

  <clause id="4969">
    <literal><![CDATA[
      ((x \ (1 / y)) * (y * x)) / (((y * x) \ K(y,y \ 1)) * (y * x)) = a(y,x,x \ (1 / y))
    ]]></literal>
    <justification jstring="[para(1090(a,1),4932(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1090 4932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4970">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,u),w,v5)) = a(x,y,a(u,u,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[para(4961(a,1),2534(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4961 2534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4971">
    <literal><![CDATA[
      L(R(x,a(y,y,x),z),y,y) \ (x * z) = a(y,y,x) * z
    ]]></literal>
    <justification jstring="[para(29(a,1),4966(a,1,1))].">
      <j1 rule="para" parents="29 4966"/>
    </justification>
  </clause>

  <clause id="4972">
    <literal><![CDATA[
      x \ (((y * K(z,u)) / y) * L(L(y,w,v5),v6,v7)) = (x \ L(L(y,v6,v7),w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,4608,a,b,3762,a)].">
      <j1 rule="hyper" parents="133 4608 3762"/>
    </justification>
  </clause>

  <clause id="4973">
    <literal><![CDATA[
      T(((x * y) / x) * L(L(x,z,u),w,v5),L(L(x,w,v5),z,u)) = y * R(L(L(x,w,v5),z,u),y,L(L(x,w,v5),z,u))
    ]]></literal>
    <justification jstring="[para(4608(a,2),1636(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4608 1636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4974">
    <literal><![CDATA[
      (x \ 1) * ((L(x,y,z) \ 1) * (x * x)) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,32,a(flip),b,4611,a)].">
      <j1 rule="hyper" parents="63 32 4611"/>
    </justification>
  </clause>

  <clause id="4976">
    <literal><![CDATA[
      R(x,y,z \ (u * (w * v5))) = R(x,y,z \ (u * (v5 * w)))
    ]]></literal>
    <justification jstring="[para(114(a,1),4699(a,1,3,2,2))].">
      <j1 rule="para" parents="114 4699"/>
    </justification>
  </clause>

  <clause id="4978">
    <literal><![CDATA[
      R(x,y,z * (u \ ((w \ 1) \ u))) = R(x,y,z * ((w * u) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4745,a(flip),b,4740,a)].">
      <j1 rule="hyper" parents="63 4745 4740"/>
    </justification>
  </clause>

  <clause id="4979">
    <literal><![CDATA[
      (x / y) * L((x / y) \ z,u,w) = (y \ x) * L((y \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(3143(a,1),4859(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3143 4859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4980">
    <literal><![CDATA[
      (x / y) * L(L(y \ x,z,u) * y,w,v5) = (y \ x) * L(y * L(y \ x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(4298(a,1),4859(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4298 4859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4981">
    <literal><![CDATA[
      K(x,x \ y) * (L(y,z,u) / w) = (x * (L(y,z,u) / x)) / w
    ]]></literal>
    <justification jstring="[para(1358(a,1),4879(a,2,1))].">
      <j1 rule="para" parents="1358 4879"/>
    </justification>
  </clause>

  <clause id="4982">
    <literal><![CDATA[
      (x * L(y \ T(y * z,u),w,v5)) \ (x * L(z,w,v5)) = K(u,y * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),4885(a,1,2,2,1))].">
      <j1 rule="para" parents="9 4885"/>
    </justification>
  </clause>

  <clause id="4983">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * x)),u,w)) = (y * L(y \ z,u,w)) * x
    ]]></literal>
    <justification jstring="[para(22(a,1),4888(a,1,2,2,1,2))].">
      <j1 rule="para" parents="22 4888"/>
    </justification>
  </clause>

  <clause id="4984">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * u = u * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(213(a,1),4888(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="213 4888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4985">
    <literal><![CDATA[
      x / (y * L(y \ 1,z,u)) = (y * L(y \ 1,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(346,a,4984,a)].">
      <j1 rule="hyper" parents="346 4984"/>
    </justification>
  </clause>

  <clause id="4986">
    <literal><![CDATA[
      T(x,y * L(y \ 1,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(255,a,4984,a)].">
      <j1 rule="hyper" parents="255 4984"/>
    </justification>
  </clause>

  <clause id="4987">
    <literal><![CDATA[
      K(x,y) * (z * L(z \ 1,u,w)) = z * L(z \ K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,4867,a(flip),b,4984,a),flip(a)].">
      <j1 rule="hyper" parents="63 4867 4984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4988">
    <literal><![CDATA[
      (x \ y) \ (y * L(y \ (x \ y),z,u)) = x * L(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,1412,a(flip),b,4984,a(flip))].">
      <j1 rule="hyper" parents="133 1412 4984"/>
    </justification>
  </clause>

  <clause id="4989">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,4671,a(flip),b,4986,a)].">
      <j1 rule="hyper" parents="63 4671 4986"/>
    </justification>
  </clause>

  <clause id="4990">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ (u * L(x \ 1,y,z)) = R(u / x,x,L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,512,a(flip),b,4986,a)].">
      <j1 rule="hyper" parents="63 512 4986"/>
    </justification>
  </clause>

  <clause id="4991">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(604(a,1),4986(a,1,2))].">
      <j1 rule="para" parents="604 4986"/>
    </justification>
  </clause>

  <clause id="4992">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) = x
    ]]></literal>
    <justification jstring="[para(968(a,1),4986(a,1,2))].">
      <j1 rule="para" parents="968 4986"/>
    </justification>
  </clause>

  <clause id="4993">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ u) * (a(x,y,z) \ 1) = u
    ]]></literal>
    <justification jstring="[hyper(795,a,4989,a)].">
      <j1 rule="hyper" parents="795 4989"/>
    </justification>
  </clause>

  <clause id="4994">
    <literal><![CDATA[
      x / (a(y,z,u) \ 1) = (a(y,z,u) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(377,a,4989,a),flip(a)].">
      <j1 rule="hyper" parents="377 4989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4997">
    <literal><![CDATA[
      T(a(x,y,z) \ 1,u) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(137,a,4989,a,b,2927,a)].">
      <j1 rule="hyper" parents="137 4989 2927"/>
    </justification>
  </clause>

  <clause id="4998">
    <literal><![CDATA[
      K(a(x,y,z) \ 1,u) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,4989,a,b,4297,a),flip(a)].">
      <j1 rule="hyper" parents="134 4989 4297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4999">
    <literal><![CDATA[
      T(x,y \ (a(z,u,w) \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,3668,a,b,4989,a)].">
      <j1 rule="hyper" parents="63 3668 4989"/>
    </justification>
  </clause>

  <clause id="5000">
    <literal><![CDATA[
      R((a(x,y,z) \ 1) \ u,a(x,y,z),a(x,y,z)) = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2666,a,b,4989,a)].">
      <j1 rule="hyper" parents="63 2666 4989"/>
    </justification>
  </clause>

  <clause id="5002">
    <literal><![CDATA[
      x / L(a(y,z,u) \ 1,w,v5) = L(a(y,z,u) \ 1,w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,4307,a(flip),b,4989,a),flip(a)].">
      <j1 rule="hyper" parents="63 4307 4989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5003">
    <literal><![CDATA[
      K(x,a(y,z,u) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,4989,a)].">
      <j1 rule="hyper" parents="55 4989"/>
    </justification>
  </clause>

  <clause id="5004">
    <literal><![CDATA[
      (x * (a(y,z,u) \ 1)) / x = a(y,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(209,a,4989,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="209 4989 22"/>
    </justification>
  </clause>

  <clause id="5005">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * v5 = v5 * L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,4989,a(flip),b,4306,a)].">
      <j1 rule="hyper" parents="139 4989 4306"/>
    </justification>
  </clause>

  <clause id="5006">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * u = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,4989,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 4989 22"/>
    </justification>
  </clause>

  <clause id="5008">
    <literal><![CDATA[
      x / (a(y,z,u) * x) = (a(y,z,u) * x) \ x
    ]]></literal>
    <justification jstring="[para(4989(a,1),3165(a,1,2))].">
      <j1 rule="para" parents="4989 3165"/>
    </justification>
  </clause>

  <clause id="5010">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * (w * u) = w * (u * (a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(4989(a,1),4363(a,1,2))].">
      <j1 rule="para" parents="4989 4363"/>
    </justification>
  </clause>

  <clause id="5011">
    <literal><![CDATA[
      (x * (y * (a(z,u,w) \ 1))) / (x * y) = L(a(z,u,w) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(4989(a,1),4365(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4989 4365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5012">
    <literal><![CDATA[
      (x \ (L(a(y,z,u),w,v5) \ x)) * x = L(a(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[para(4989(a,1),4474(a,1,2))].">
      <j1 rule="para" parents="4989 4474"/>
    </justification>
  </clause>

  <clause id="5013">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ u) * (x \ L(x,y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(795,a,4992,a)].">
      <j1 rule="hyper" parents="795 4992"/>
    </justification>
  </clause>

  <clause id="5014">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (u * (x \ L(x,y,z))) = u
    ]]></literal>
    <justification jstring="[hyper(383,a,4992,a)].">
      <j1 rule="hyper" parents="383 4992"/>
    </justification>
  </clause>

  <clause id="5015">
    <literal><![CDATA[
      x / (y \ L(y,z,u)) = (y \ L(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(377,a,4992,a),flip(a)].">
      <j1 rule="hyper" parents="377 4992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5017">
    <literal><![CDATA[
      T(x \ L(x,y,z),u) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,4992,a,b,2927,a)].">
      <j1 rule="hyper" parents="137 4992 2927"/>
    </justification>
  </clause>

  <clause id="5018">
    <literal><![CDATA[
      K(x \ L(x,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,4992,a,b,4297,a),flip(a)].">
      <j1 rule="hyper" parents="134 4992 4297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5019">
    <literal><![CDATA[
      x / L(y \ L(y,z,u),w,v5) = L(y \ L(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,4307,a(flip),b,4992,a),flip(a)].">
      <j1 rule="hyper" parents="63 4307 4992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5021">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) / x = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(209,a,4992,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="209 4992 22"/>
    </justification>
  </clause>

  <clause id="5022">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * v5 = v5 * L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,4992,a(flip),b,4306,a)].">
      <j1 rule="hyper" parents="139 4992 4306"/>
    </justification>
  </clause>

  <clause id="5023">
    <literal><![CDATA[
      (x \ L(x,y,z)) * u = u * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,4992,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 4992 22"/>
    </justification>
  </clause>

  <clause id="5024">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(4992(a,1),49(a,2))].">
      <j1 rule="para" parents="4992 49"/>
    </justification>
  </clause>

  <clause id="5025">
    <literal><![CDATA[
      x \ ((y \ L(y,z,u)) * w) = x \ (w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(4992(a,1),237(a,1,2,2))].">
      <j1 rule="para" parents="4992 237"/>
    </justification>
  </clause>

  <clause id="5026">
    <literal><![CDATA[
      L(x,y,z) * (u \ L(u,w,v5)) = (u \ L(u,w,v5)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4992(a,1),251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4992 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5027">
    <literal><![CDATA[
      R(x,y,z) * (u \ L(u,w,v5)) = (u \ L(u,w,v5)) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(4992(a,1),252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4992 252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5028">
    <literal><![CDATA[
      L(x \ y,x,z \ L(z,u,w)) = (x * (z \ L(z,u,w))) \ ((z \ L(z,u,w)) * y)
    ]]></literal>
    <justification jstring="[para(4992(a,1),3288(a,1,1,1))].">
      <j1 rule="para" parents="4992 3288"/>
    </justification>
  </clause>

  <clause id="5029">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / y = y \ (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(4992(a,1),3689(a,1,2))].">
      <j1 rule="para" parents="4992 3689"/>
    </justification>
  </clause>

  <clause id="5030">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) / x = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(4992(a,1),3702(a,1,2))].">
      <j1 rule="para" parents="4992 3702"/>
    </justification>
  </clause>

  <clause id="5031">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * (w * u) = w * (u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(4992(a,1),4363(a,1,2))].">
      <j1 rule="para" parents="4992 4363"/>
    </justification>
  </clause>

  <clause id="5032">
    <literal><![CDATA[
      x * K(a(y,z,u) \ 1,w) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,4998,a,b,67,a)].">
      <j1 rule="hyper" parents="139 4998 67"/>
    </justification>
  </clause>

  <clause id="5033">
    <literal><![CDATA[
      x * K(y \ L(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,5018,a,b,67,a)].">
      <j1 rule="hyper" parents="139 5018 67"/>
    </justification>
  </clause>

  <clause id="5035">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * (u * w)) / (w * (a(x,y,z) \ 1)) = R(u,w,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(209,a,5032,a(flip),b,3952,a)].">
      <j1 rule="hyper" parents="209 5032 3952"/>
    </justification>
  </clause>

  <clause id="5037">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * w)) / (w * (x \ L(x,y,z))) = R(u,w,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(209,a,5033,a(flip),b,3952,a)].">
      <j1 rule="hyper" parents="209 5033 3952"/>
    </justification>
  </clause>

  <clause id="5038">
    <literal><![CDATA[
      (L(a(x,y,z) \ 1,u,w) \ v5) \ v5 = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(4997(a,1),310(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4997 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5039">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) / w) * R(w,u,a(x,y,z) \ 1) = w \ ((w * u) * (a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(4997(a,1),4059(a,2,2,2))].">
      <j1 rule="para" parents="4997 4059"/>
    </justification>
  </clause>

  <clause id="5040">
    <literal><![CDATA[
      T((x * y) \ L(x * y,z,u),w) = (y * x) \ L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4877,a,b,5017,a),flip(a)].">
      <j1 rule="hyper" parents="316 4877 5017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5041">
    <literal><![CDATA[
      (L(x \ L(x,y,z),u,w) \ v5) \ v5 = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(5017(a,1),310(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5017 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5043">
    <literal><![CDATA[
      T(x \ L(x,y,z),u) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(5017(a,2),1894(a,1,1))].">
      <j1 rule="para" parents="5017 1894"/>
    </justification>
  </clause>

  <clause id="5045">
    <literal><![CDATA[
      L(T(x \ L(x,y,z),u),x,w) = (x * w) \ (L(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(5017(a,2),4404(a,1,1))].">
      <j1 rule="para" parents="5017 4404"/>
    </justification>
  </clause>

  <clause id="5046">
    <literal><![CDATA[
      a(x,y,z) * ((a(x,y,z) \ 1) \ u) = u * (a(x,y,z) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(138,a,4993,a(flip),b,2333,a),flip(a)].">
      <j1 rule="hyper" parents="138 4993 2333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5047">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ u) * a(x,y,z) = u * (a(x,y,z) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(138,a,4993,a(flip),b,562,a),flip(a)].">
      <j1 rule="hyper" parents="138 4993 562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5048">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ u) / (a(x,y,z) * a(x,y,z)) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(133,a,4993,a(flip),b,2542,a),flip(a)].">
      <j1 rule="hyper" parents="133 4993 2542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5051">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u * (w * (a(x,y,z) \ 1))) = (u * (w * a(x,y,z))) / a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,964,a(flip),b,4994,a),flip(a)].">
      <j1 rule="hyper" parents="63 964 4994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5052">
    <literal><![CDATA[
      L(x \ ((a(y,z,u) \ 1) \ w),x,a(y,z,u)) = (a(y,z,u) * x) \ (w * (a(y,z,u) * a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(4994(a,1),2493(a,1,1,2))].">
      <j1 rule="para" parents="4994 2493"/>
    </justification>
  </clause>

  <clause id="5053">
    <literal><![CDATA[
      (1 / a(x,y,z)) * u = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(138,a,2276,a,b,5004,a)].">
      <j1 rule="hyper" parents="138 2276 5004"/>
    </justification>
  </clause>

  <clause id="5054">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u \ a(x,y,z)) = a(x,y,z) * (u \ (a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(316,a,2547,a(flip),b,5006,a),flip(a)].">
      <j1 rule="hyper" parents="316 2547 5006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5055">
    <literal><![CDATA[
      L(x,y,z) \ ((a(u,w,v5) \ 1) * x) = x * (L(x,y,z) \ (a(u,w,v5) \ 1))
    ]]></literal>
    <justification jstring="[hyper(133,a,5006,a,b,1128,a)].">
      <j1 rule="hyper" parents="133 5006 1128"/>
    </justification>
  </clause>

  <clause id="5056">
    <literal><![CDATA[
      (x * ((a(y,z,u) \ 1) * w)) \ (((a(y,z,u) \ 1) * x) * w) = a(x,a(y,z,u) \ 1,w)
    ]]></literal>
    <justification jstring="[para(5006(a,2),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5006 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5057">
    <literal><![CDATA[
      (x \ ((a(y,z,u) \ 1) * w)) * (v5 * v5) = x \ (w * (a(y,z,u) \ (v5 * v5)))
    ]]></literal>
    <justification jstring="[para(5006(a,2),838(a,1,1,2))].">
      <j1 rule="para" parents="5006 838"/>
    </justification>
  </clause>

  <clause id="5058">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * u) \ (u * (w * (a(x,y,z) \ 1))) = L(K(u,a(x,y,z) \ 1) * w,a(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(5006(a,1),3299(a,1,2,2))].">
      <j1 rule="para" parents="5006 3299"/>
    </justification>
  </clause>

  <clause id="5060">
    <literal><![CDATA[
      L(x,a(y,z,u) \ 1,w) * ((a(y,z,u) \ 1) * w) = x * ((w * ((a(y,z,u) \ 1) * x)) / x)
    ]]></literal>
    <justification jstring="[para(5006(a,2),4415(a,1,2))].">
      <j1 rule="para" parents="5006 4415"/>
    </justification>
  </clause>

  <clause id="5061">
    <literal><![CDATA[
      x / (a(y,z,u) * x) = x \ (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,4784,a(flip),b,5008,a),flip(a)].">
      <j1 rule="hyper" parents="316 4784 5008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5062">
    <literal><![CDATA[
      T((x \ L(x,y,z)) * u,w) = T(u * (x \ L(x,y,z)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2705,a(flip),b,5013,a),flip(a)].">
      <j1 rule="hyper" parents="63 2705 5013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5063">
    <literal><![CDATA[
      (((x \ L(x,y,z)) \ 1) * T(((x \ L(x,y,z)) \ 1) \ u,w)) * (x \ L(x,y,z)) = T((x \ L(x,y,z)) * u,w)
    ]]></literal>
    <justification jstring="[para(807(a,2),5013(a,1,1))].">
      <j1 rule="para" parents="807 5013"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      L(x,x,y \ L(y,z,u)) * (y \ L(y,z,u)) = (y \ L(y,z,u)) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(1447(a,2),5013(a,1,1))].">
      <j1 rule="para" parents="1447 5013"/>
    </justification>
  </clause>

  <clause id="5066">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ w = (u * (x \ L(x,y,z))) \ w
    ]]></literal>
    <justification jstring="[para(5014(a,1),165(a,1,1,2))].">
      <j1 rule="para" parents="5014 165"/>
    </justification>
  </clause>

  <clause id="5067">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x * (u * (x \ L(x,y,z)))) = x * u
    ]]></literal>
    <justification jstring="[para(5014(a,1),1504(a,2,2))].">
      <j1 rule="para" parents="5014 1504"/>
    </justification>
  </clause>

  <clause id="5068">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * (x \ L(x,y,z)))) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5014(a,1),1557(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5014 1557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5069">
    <literal><![CDATA[
      1 / (x \ L(x,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,1894,a(flip),b,5015,a),flip(a)].">
      <j1 rule="hyper" parents="316 1894 5015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5070">
    <literal><![CDATA[
      (x * (y * ((z \ L(z,u,w)) \ 1))) / ((z \ L(z,u,w)) \ 1) = (z \ L(z,u,w)) \ (x * (y * (z \ L(z,u,w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,964,a,b,5015,a)].">
      <j1 rule="hyper" parents="63 964 5015"/>
    </justification>
  </clause>

  <clause id="5071">
    <literal><![CDATA[
      (x \ ((y \ L(y,z,u)) \ 1)) / ((y \ L(y,z,u)) \ 1) = (y \ L(y,z,u)) \ (x \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,590,a,b,5015,a)].">
      <j1 rule="hyper" parents="63 590 5015"/>
    </justification>
  </clause>

  <clause id="5072">
    <literal><![CDATA[
      (x \ 1) / (L(x,y,z) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(209,a,2094,a(flip),b,5015,a(flip))].">
      <j1 rule="hyper" parents="209 2094 5015"/>
    </justification>
  </clause>

  <clause id="5075">
    <literal><![CDATA[
      x / ((y \ L(y,z,u)) * (y \ L(y,z,u))) = ((y \ L(y,z,u)) \ x) * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(5015(a,1),1896(a,2,1))].">
      <j1 rule="para" parents="5015 1896"/>
    </justification>
  </clause>

  <clause id="5076">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ 1 = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(204,a,5069,a)].">
      <j1 rule="hyper" parents="204 5069"/>
    </justification>
  </clause>

  <clause id="5080">
    <literal><![CDATA[
      (L(x * L(x,y,z),u,w) \ (x * L(x,y,z))) \ 1 = x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,1877,a(flip),b,5076,a),flip(a)].">
      <j1 rule="hyper" parents="316 1877 5076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5081">
    <literal><![CDATA[
      x * ((L(x,y,z) \ x) \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,5076,a,b,xx)].">
      <j1 rule="hyper" parents="139 5076"/>
    </justification>
  </clause>

  <clause id="5082">
    <literal><![CDATA[
      L(x * y,y,x) \ (x * y) = a(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(39,a,2538,a(flip),b,5076,a),flip(a)].">
      <j1 rule="hyper" parents="39 2538 5076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5083">
    <literal><![CDATA[
      x / ((L(y,z,u) \ y) \ (y \ L(y,z,u))) = x * ((L(y,z,u) \ y) * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(5076(a,1),444(a,1,2,2))].">
      <j1 rule="para" parents="5076 444"/>
    </justification>
  </clause>

  <clause id="5084">
    <literal><![CDATA[
      (((x * y) \ (x * z)) \ (y \ z)) \ 1 = (y \ z) \ L(y \ z,y,x)
    ]]></literal>
    <justification jstring="[para(102(a,1),5076(a,1,1,1))].">
      <j1 rule="para" parents="102 5076"/>
    </justification>
  </clause>

  <clause id="5085">
    <literal><![CDATA[
      (L(x \ (1 / y),x,y) \ (x \ (1 / y))) \ 1 = (x \ (1 / y)) \ ((y * x) \ K(y,y \ 1))
    ]]></literal>
    <justification jstring="[para(1090(a,1),5076(a,2,2))].">
      <j1 rule="para" parents="1090 5076"/>
    </justification>
  </clause>

  <clause id="5086">
    <literal><![CDATA[
      (x \ (x \ L(x,y,z))) * L((x \ ((L(x,y,z) \ x) \ 1)) \ u,w,v5) = (L(x,y,z) \ 1) * L((x \ (L(x,y,z) \ x)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(5076(a,1),1856(a,1,1,2))].">
      <j1 rule="para" parents="5076 1856"/>
    </justification>
  </clause>

  <clause id="5087">
    <literal><![CDATA[
      a(x \ 1,x,y) \ 1 = y \ L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2408(a,1),5076(a,1,1))].">
      <j1 rule="para" parents="2408 5076"/>
    </justification>
  </clause>

  <clause id="5088">
    <literal><![CDATA[
      a(x,x,y) \ 1 = y \ L(y,x,x)
    ]]></literal>
    <justification jstring="[para(4952(a,1),5076(a,1,1))].">
      <j1 rule="para" parents="4952 5076"/>
    </justification>
  </clause>

  <clause id="5090">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,u,u),y,z) = a(u,u,L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,167,a,b,5088,a)].">
      <j1 rule="hyper" parents="316 167 5088"/>
    </justification>
  </clause>

  <clause id="5093">
    <literal><![CDATA[
      x * (a(y,y,x) \ 1) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,5088,a,b,xx)].">
      <j1 rule="hyper" parents="139 5088"/>
    </justification>
  </clause>

  <clause id="5094">
    <literal><![CDATA[
      x \ (a(y,y,x) \ 1) = L(x \ 1,y,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,5088,a,b,1064,a)].">
      <j1 rule="hyper" parents="133 5088 1064"/>
    </justification>
  </clause>

  <clause id="5097">
    <literal><![CDATA[
      R(x,a(y,y,x) \ 1,z) \ (L(x,y,y) * z) = (x \ L(x,y,y)) * z
    ]]></literal>
    <justification jstring="[para(5088(a,2),492(a,1,1,2))].">
      <j1 rule="para" parents="5088 492"/>
    </justification>
  </clause>

  <clause id="5098">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,y,y \ z) = z \ ((z / y) * L(y,x,x))
    ]]></literal>
    <justification jstring="[para(5088(a,2),1602(a,1,1))].">
      <j1 rule="para" parents="5088 1602"/>
    </justification>
  </clause>

  <clause id="5099">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) \ 1 = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5088(a,2),4961(a,1,1,1))].">
      <j1 rule="para" parents="5088 4961"/>
    </justification>
  </clause>

  <clause id="5100">
    <literal><![CDATA[
      a(x,y,z * a(u,u,z)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[para(5093(a,1),2651(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5093 2651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5101">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * u) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(5093(a,1),2654(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5093 2654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5102">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,y,y \ z) * ((a(x,x,y) \ 1) \ z) = ((z / y) * L(y,x,x)) / (a(x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(5093(a,1),4413(a,2,1,2))].">
      <j1 rule="para" parents="5093 4413"/>
    </justification>
  </clause>

  <clause id="5103">
    <literal><![CDATA[
      ((x * (y \ L(y,z,u))) * w) / (x * w) = R(y \ L(y,z,u),x,w)
    ]]></literal>
    <justification jstring="[para(5021(a,1),110(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5021 110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5105">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = y * (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1495,a,b,5023,a)].">
      <j1 rule="hyper" parents="63 1495 5023"/>
    </justification>
  </clause>

  <clause id="5106">
    <literal><![CDATA[
      L(x,y,z) * L(u,x,x \ L(x,y,z)) = (x * u) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1278,a,b,5023,a)].">
      <j1 rule="hyper" parents="63 1278 5023"/>
    </justification>
  </clause>

  <clause id="5107">
    <literal><![CDATA[
      (x \ y) * (x \ L(x,z,u)) = y * L(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1415,a(flip),b,5023,a),flip(a)].">
      <j1 rule="hyper" parents="63 1415 5023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5108">
    <literal><![CDATA[
      (x * x) * (y \ L(y,z,u)) = y * L(y \ (x * x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1361,a(flip),b,5023,a),flip(a)].">
      <j1 rule="hyper" parents="63 1361 5023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5109">
    <literal><![CDATA[
      (x \ y) \ (y * L(y \ (x \ y),z,u)) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,1415,a(flip),b,5023,a(flip))].">
      <j1 rule="hyper" parents="133 1415 5023"/>
    </justification>
  </clause>

  <clause id="5110">
    <literal><![CDATA[
      x \ ((y \ x) * (y \ L(y,z,u))) = L(x \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,5023,a(flip),b,1415,a(flip))].">
      <j1 rule="hyper" parents="133 5023 1415"/>
    </justification>
  </clause>

  <clause id="5111">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ (u * (w * (x \ L(x,y,z)))) = L(T(w,x \ L(x,y,z)),x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5023(a,2),247(a,1,1))].">
      <j1 rule="para" parents="5023 247"/>
    </justification>
  </clause>

  <clause id="5112">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * u) = x * (u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(5023(a,1),1499(a,2,2))].">
      <j1 rule="para" parents="5023 1499"/>
    </justification>
  </clause>

  <clause id="5113">
    <literal><![CDATA[
      L(x,y,z) \ (x * (u * (x \ L(x,y,z)))) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5023(a,1),1526(a,1,2,2))].">
      <j1 rule="para" parents="5023 1526"/>
    </justification>
  </clause>

  <clause id="5114">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x \ 1) * u) = (x \ 1) * (u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(5023(a,1),1889(a,2,2))].">
      <j1 rule="para" parents="5023 1889"/>
    </justification>
  </clause>

  <clause id="5115">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * w)) * a(x \ L(x,y,z),w,u) = (u * w) * R(x \ L(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[para(5023(a,2),3429(a,1,1))].">
      <j1 rule="para" parents="5023 3429"/>
    </justification>
  </clause>

  <clause id="5116">
    <literal><![CDATA[
      K(x * (y * (x \ L(x,z,u))),w) = K(L(x,z,u) * y,w)
    ]]></literal>
    <justification jstring="[para(5023(a,1),3553(a,1,1,2))].">
      <j1 rule="para" parents="5023 3553"/>
    </justification>
  </clause>

  <clause id="5117">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ T((x \ L(x,y,z)) * u,w) = u * K(u * (x \ L(x,y,z)),w)
    ]]></literal>
    <justification jstring="[para(5023(a,1),3645(a,2,2,1))].">
      <j1 rule="para" parents="5023 3645"/>
    </justification>
  </clause>

  <clause id="5118">
    <literal><![CDATA[
      (x * (K(y,z) * (u \ L(u,w,v5)))) / v6 = (x * (u \ L(u,w,v5))) / (v6 * K(z,y))
    ]]></literal>
    <justification jstring="[para(5023(a,1),3967(a,1,1,2))].">
      <j1 rule="para" parents="5023 3967"/>
    </justification>
  </clause>

  <clause id="5119">
    <literal><![CDATA[
      (x * (y * (z \ L(z,u,w)))) / T(x * (z \ L(z,u,w)),y) = L(y,z \ L(z,u,w),x)
    ]]></literal>
    <justification jstring="[para(5023(a,1),4365(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5023 4365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5121">
    <literal><![CDATA[
      R(x / (y \ L(y,z,u)),(L(y,z,u) \ 1) \ (y \ 1),L(y,z,u) \ 1) = (x * (L(y,z,u) \ 1)) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(5072(a,1),4481(a,1,1,2))].">
      <j1 rule="para" parents="5072 4481"/>
    </justification>
  </clause>

  <clause id="5122">
    <literal><![CDATA[
      a(x,y,(z * u) * L(z * u,u,z)) = a(x,y,a(z,u,z * u))
    ]]></literal>
    <justification jstring="[para(5082(a,1),2652(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5082 2652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5123">
    <literal><![CDATA[
      L(a(x \ 1,x,y) \ 1,z,u) \ 1 = a(x \ 1,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5087(a,2),2409(a,1,1,1))].">
      <j1 rule="para" parents="5087 2409"/>
    </justification>
  </clause>

  <clause id="5124">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) = a(x,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,5099,a),flip(a)].">
      <j1 rule="hyper" parents="39 2301 5099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5125">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ x = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,2099,a(flip),b,4985,a),flip(a)].">
      <j1 rule="hyper" parents="63 2099 4985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5126">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = (x \ L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(1064(a,1),5125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1064 5125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5127">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) \ (x \ y) = L(1 / (x \ y),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(1216(a,1),5125(a,1,1))].">
      <j1 rule="para" parents="1216 5125"/>
    </justification>
  </clause>

  <clause id="5128">
    <literal><![CDATA[
      (x / y) * L((x / y) \ 1,z,u) = y \ (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1860,a,b,5029,a)].">
      <j1 rule="hyper" parents="63 1860 5029"/>
    </justification>
  </clause>

  <clause id="5129">
    <literal><![CDATA[
      x \ ((y \ x) * L((y \ x) \ x,z,u)) = (L(y,z,u) * (y \ x)) / x
    ]]></literal>
    <justification jstring="[para(604(a,1),5029(a,1,1)),flip(a)].">
      <j1 rule="para" parents="604 5029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5130">
    <literal><![CDATA[
      (x \ ((x / y) * L(y,z,u))) * x = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(151,a,5030,a)].">
      <j1 rule="hyper" parents="151 5030"/>
    </justification>
  </clause>

  <clause id="5131">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (a(u,w,v5) * x) = x * (a(u,w,v5) * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(139,a,2290,a,b,5067,a)].">
      <j1 rule="hyper" parents="139 2290 5067"/>
    </justification>
  </clause>

  <clause id="5132">
    <literal><![CDATA[
      (x * y) * (x \ L(x,z,u)) = x * (y * (x \ L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(38,a,5014,a,b,5067,a)].">
      <j1 rule="hyper" parents="38 5014 5067"/>
    </justification>
  </clause>

  <clause id="5133">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ L(x,u,w)) = L(x,y,z) * L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(971(a,1),5107(a,2,2,1))].">
      <j1 rule="para" parents="971 5107"/>
    </justification>
  </clause>

  <clause id="5134">
    <literal><![CDATA[
      ((x \ y) \ z) * (x \ (y * L(y \ x,u,w))) = z * L(z \ ((x \ y) \ z),u,w)
    ]]></literal>
    <justification jstring="[para(1252(a,1),5107(a,1,2))].">
      <j1 rule="para" parents="1252 5107"/>
    </justification>
  </clause>

  <clause id="5135">
    <literal><![CDATA[
      (L(x,y,z) \ u) * L(x \ L(x,w,v5),y,z) = u * L(u \ (L(x,y,z) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(2136(a,1),5107(a,1,2))].">
      <j1 rule="para" parents="2136 5107"/>
    </justification>
  </clause>

  <clause id="5137">
    <literal><![CDATA[
      (x * x) * (x \ L(x,y,z)) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5108(a,2,2,1))].">
      <j1 rule="para" parents="9 5108"/>
    </justification>
  </clause>

  <clause id="5138">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x \ u) \ u) = L((x \ u) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(5109(a,1),1276(a,1,1))].">
      <j1 rule="para" parents="5109 1276"/>
    </justification>
  </clause>

  <clause id="5139">
    <literal><![CDATA[
      x \ ((x / (y \ 1)) * ((y \ K(y * x,y \ 1)) \ L(y \ K(y * x,y \ 1),z,u))) = L(x \ ((y \ K(y * x,y \ 1)) \ x),z,u)
    ]]></literal>
    <justification jstring="[para(4206(a,1),5110(a,1,2,1))].">
      <j1 rule="para" parents="4206 5110"/>
    </justification>
  </clause>

  <clause id="5140">
    <literal><![CDATA[
      x \ ((x \ L(x,y,z)) * u) = (x \ u) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(543,a,5112,a)].">
      <j1 rule="hyper" parents="543 5112"/>
    </justification>
  </clause>

  <clause id="5141">
    <literal><![CDATA[
      (x \ K(L(x,y,z) * u,x \ 1)) \ (u * (x \ L(x,y,z))) = (u * (x \ L(x,y,z))) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(5116(a,1),4206(a,1,1,2))].">
      <j1 rule="para" parents="5116 4206"/>
    </justification>
  </clause>

  <clause id="5142">
    <literal><![CDATA[
      R(x \ ((x / y) * L(y,z,u)),x,x \ ((x / y) * L(y,z,u))) \ x = x * (((x / y) * L(y,z,u)) \ x)
    ]]></literal>
    <justification jstring="[para(5130(a,1),4779(a,2,2,1))].">
      <j1 rule="para" parents="5130 4779"/>
    </justification>
  </clause>

  <clause id="5143">
    <literal><![CDATA[
      R(x,y,x \ L(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(501,a,5132,a)].">
      <j1 rule="hyper" parents="501 5132"/>
    </justification>
  </clause>

  <clause id="5144">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(463,a,5132,a)].">
      <j1 rule="hyper" parents="463 5132"/>
    </justification>
  </clause>

  <clause id="5145">
    <literal><![CDATA[
      a(x,y,x \ L(x,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,5132,a(flip),b,2330,a),flip(a)].">
      <j1 rule="hyper" parents="134 5132 2330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5146">
    <literal><![CDATA[
      x \ (y * (x \ L(x,z,u))) = (x \ y) * (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,158,a(flip),b,5132,a(flip))].">
      <j1 rule="hyper" parents="133 158 5132"/>
    </justification>
  </clause>

  <clause id="5147">
    <literal><![CDATA[
      R(x,y,x * L(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,1718,a(flip),b,5143,a)].">
      <j1 rule="hyper" parents="63 1718 5143"/>
    </justification>
  </clause>

  <clause id="5149">
    <literal><![CDATA[
      L(x,y,z) \ (u * (x \ L(x,w,v5))) = (L(x,y,z) \ u) * (x \ L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(5143(a,1),723(a,1,1,1))].">
      <j1 rule="para" parents="5143 723"/>
    </justification>
  </clause>

  <clause id="5150">
    <literal><![CDATA[
      R(x,y,L(x,z,u) \ x) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,1721,a,b,5147,a)].">
      <j1 rule="hyper" parents="63 1721 5147"/>
    </justification>
  </clause>

  <clause id="5151">
    <literal><![CDATA[
      (x * y) * (L(x,z,u) \ x) = x * (y * (L(x,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(138,a,5150,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="138 5150 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5152">
    <literal><![CDATA[
      x \ (y * (L(x,z,u) \ x)) = (x \ y) * (L(x,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(5150(a,1),492(a,1,1))].">
      <j1 rule="para" parents="5150 492"/>
    </justification>
  </clause>

  <clause id="5153">
    <literal><![CDATA[
      (L(x,y,z) * u) * (L(x,w,v5) \ x) = L(x,y,z) * (u * (L(x,w,v5) \ x))
    ]]></literal>
    <justification jstring="[para(5150(a,1),400(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5150 400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5154">
    <literal><![CDATA[
      L(x,y,x) \ L(L(x,y,x),z,u) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2136,a,b,5144,a)].">
      <j1 rule="hyper" parents="63 2136 5144"/>
    </justification>
  </clause>

  <clause id="5155">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ L(x \ L(x,y,z),u,w) = x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,1557,a(flip),b,5144,a),flip(a)].">
      <j1 rule="hyper" parents="63 1557 5144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5156">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),v5,x) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(5144(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5144 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5157">
    <literal><![CDATA[
      (x * y) * L(x \ L(x,z,u),w,v5) = x * (y * L(x \ L(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(5144(a,1),403(a,1,2,1))].">
      <j1 rule="para" parents="5144 403"/>
    </justification>
  </clause>

  <clause id="5158">
    <literal><![CDATA[
      R(x / (y \ L(y,z,u)),y \ L(y,z,u),(y \ w) \ w) = (x * ((y \ w) \ w)) / L((y \ w) \ w,z,u)
    ]]></literal>
    <justification jstring="[hyper(209,a,5138,a(flip),b,493,a),flip(a)].">
      <j1 rule="hyper" parents="209 5138 493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5159">
    <literal><![CDATA[
      ((1 / x) \ y) * ((1 / x) \ L(1 / x,z,u)) = (1 / x) \ (y * (x \ L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(1066(a,1),5146(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1066 5146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5160">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,x) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(463,a,5151,a)].">
      <j1 rule="hyper" parents="463 5151"/>
    </justification>
  </clause>

  <clause id="5161">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (x * x) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,160,a(flip),b,5151,a)].">
      <j1 rule="hyper" parents="133 160 5151"/>
    </justification>
  </clause>

  <clause id="5162">
    <literal><![CDATA[
      (x * (y * (L(x,z,u) \ x))) * a(L(x,z,u) \ x,x,y) = x * (y * R(L(x,z,u) \ x,x,y))
    ]]></literal>
    <justification jstring="[para(5160(a,1),3474(a,1,2,1))].">
      <j1 rule="para" parents="5160 3474"/>
    </justification>
  </clause>

  <clause id="5165">
    <literal><![CDATA[
      T((x * y) \ (x * L(y,z,u)),w) = (y * x) \ (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,483,a,b,5045,a)].">
      <j1 rule="hyper" parents="63 483 5045"/>
    </justification>
  </clause>

  <clause id="5166">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,y,y \ z) = z \ (L(y,x,x) * (y \ z))
    ]]></literal>
    <justification jstring="[para(4325(a,2),5098(a,2,2))].">
      <j1 rule="para" parents="4325 5098"/>
    </justification>
  </clause>

  <clause id="5168">
    <literal><![CDATA[
      x * (1 / L(x \ L(x,y,z),u,w)) = x / L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(209,a,5156,a(flip),b,2674,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="209 5156 2674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5169">
    <literal><![CDATA[
      x / (L(x \ L(x,y,z),u,w) \ 1) = x * L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,5156,a(flip),b,1447,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 5156 1447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5171">
    <literal><![CDATA[
      (x \ 1) * L(L(x \ L(x,y,z),u,w),v5,v6) = x \ L(L(x \ L(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(5156(a,1),524(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5156 524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5173">
    <literal><![CDATA[
      L(x,y,z \ T(u / (T(w,v5) \ 1),T(w,v5))) = L(x,y,z \ ((T(w,v5) * w) * (T(w,v5) \ u)))
    ]]></literal>
    <justification jstring="[para(613(a,2),4911(a,1,3,2))].">
      <j1 rule="para" parents="613 4911"/>
    </justification>
  </clause>

  <clause id="5174">
    <literal><![CDATA[
      x * L(y * K(x * y,x),z,u) = L(y,z,u) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(3280(a,1),4912(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3280 4912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5175">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u / (x \ 1))) = u / L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1110(a,1),4919(a,2,2))].">
      <j1 rule="para" parents="1110 4919"/>
    </justification>
  </clause>

  <clause id="5176">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u / L(x \ 1,y,z))) = u / (x \ 1)
    ]]></literal>
    <justification jstring="[para(5175(a,1),75(a,1,2,2))].">
      <j1 rule="para" parents="5175 75"/>
    </justification>
  </clause>

  <clause id="5177">
    <literal><![CDATA[
      (x / (y / L(z,u,w))) * (y / z) = (x / (L(z,u,w) \ y)) * (z \ y)
    ]]></literal>
    <justification jstring="[para(4922(a,1),3840(a,1,1))].">
      <j1 rule="para" parents="4922 3840"/>
    </justification>
  </clause>

  <clause id="5178">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,w,v5))) = a(x,y,L(a(z,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,4963,a(flip),b,4970,a),flip(a)].">
      <j1 rule="hyper" parents="63 4963 4970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5179">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ (x * x)) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(389(a,1),4974(a,1,2))].">
      <j1 rule="para" parents="389 4974"/>
    </justification>
  </clause>

  <clause id="5180">
    <literal><![CDATA[
      K(x,x \ L(y,z,u)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(35,a,3036,a,b,4981,a)].">
      <j1 rule="hyper" parents="35 3036 4981"/>
    </justification>
  </clause>

  <clause id="5181">
    <literal><![CDATA[
      K(x,y) * (z * L(z \ K(y,x),u,w)) = z * L(z \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(3006,a,4987,a)].">
      <j1 rule="hyper" parents="3006 4987"/>
    </justification>
  </clause>

  <clause id="5182">
    <literal><![CDATA[
      K(L(L(x,y,z) \ 1,u,w),x) * ((L(x,y,z) \ v5) \ (v5 * L(v5 \ (L(x,y,z) \ v5),u,w))) = L(L(x,y,z) \ 1,u,w) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4988(a,2),4298(a,1,2))].">
      <j1 rule="para" parents="4988 4298"/>
    </justification>
  </clause>

  <clause id="5185">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z),u,w) \ a(x,y,z)) = L(a(x,y,z) \ 1,u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,4459,a,b,5038,a)].">
      <j1 rule="hyper" parents="39 4459 5038"/>
    </justification>
  </clause>

  <clause id="5186">
    <literal><![CDATA[
      L((x * y) \ L(x * y,z,u),w,v5) = L((y * x) \ L(y * x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(5040(a,1),2281(a,1,1))].">
      <j1 rule="para" parents="5040 2281"/>
    </justification>
  </clause>

  <clause id="5187">
    <literal><![CDATA[
      a(x,y,z * (u * (z * u))) = a(x,y,a(z,u,z * u))
    ]]></literal>
    <justification jstring="[para(100(a,1),5122(a,1,3))].">
      <j1 rule="para" parents="100 5122"/>
    </justification>
  </clause>

  <clause id="5188">
    <literal><![CDATA[
      L(a(x \ 1,x,y) \ 1,z,u) = a(x \ 1,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,5123,a),flip(a)].">
      <j1 rule="hyper" parents="39 2301 5123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5189">
    <literal><![CDATA[
      (x / y) \ L(x / y,z,u) = y \ (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1064,a(flip),b,5128,a)].">
      <j1 rule="hyper" parents="63 1064 5128"/>
    </justification>
  </clause>

  <clause id="5190">
    <literal><![CDATA[
      (x / y) \ L(x / y,z,u) = (y \ x) \ L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,1252,a,b,5189,a),flip(a)].">
      <j1 rule="hyper" parents="316 1252 5189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5191">
    <literal><![CDATA[
      L(x \ y,x,z) \ L((z * x) \ (z * y),u,w) = ((z * y) / (z * x)) \ L((z * y) / (z * x),u,w)
    ]]></literal>
    <justification jstring="[para(102(a,2),5190(a,2,1)),flip(a)].">
      <j1 rule="para" parents="102 5190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5192">
    <literal><![CDATA[
      ((x * (y * y)) / z) \ L((x * (y * y)) / z,u,w) = ((z \ x) * (y * y)) \ L(z \ (x * (y * y)),u,w)
    ]]></literal>
    <justification jstring="[para(388(a,1),5190(a,2,1))].">
      <j1 rule="para" parents="388 5190"/>
    </justification>
  </clause>

  <clause id="5193">
    <literal><![CDATA[
      R(x,y,(z \ u) \ L(z \ u,w,v5)) = R(x,y,(u / z) * L(u / z,w,v5))
    ]]></literal>
    <justification jstring="[para(5190(a,1),1718(a,1,3))].">
      <j1 rule="para" parents="5190 1718"/>
    </justification>
  </clause>

  <clause id="5195">
    <literal><![CDATA[
      R(T((x * y) \ (x * L(y,z,u)),((x * y) \ (x * L(y,z,u))) * w),w,(x * y) \ (x * L(y,z,u))) = (y * x) \ (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2931,a,b,5165,a)].">
      <j1 rule="hyper" parents="63 2931 5165"/>
    </justification>
  </clause>

  <clause id="5196">
    <literal><![CDATA[
      K(x,y) * (z * L(z \ K(y,x),u,w)) = z \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,1064,a(flip),b,5181,a),flip(a)].">
      <j1 rule="hyper" parents="316 1064 5181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5198">
    <literal><![CDATA[
      (x * L(x \ K(y,z),u,w)) * T(v5,K(z,y) * (x * L(x \ K(y,z),u,w))) = K(y,z) * (v5 * (x * L(x \ 1,u,w)))
    ]]></literal>
    <justification jstring="[para(5181(a,1),3004(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5181 3004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5199">
    <literal><![CDATA[
      K(x,y) * (z * (u * L(u \ (z \ K(y,x)),w,v5))) = (z * u) \ L(z * u,w,v5)
    ]]></literal>
    <justification jstring="[para(879(a,1),5196(a,1,2))].">
      <j1 rule="para" parents="879 5196"/>
    </justification>
  </clause>

  <clause id="5204">
    <literal><![CDATA[
      T(x,((y * z) * u) * ((z * u) \ (y \ w))) = T(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3742,a(flip),b,3528,a)].">
      <j1 rule="hyper" parents="63 3742 3528"/>
    </justification>
  </clause>

  <clause id="5205">
    <literal><![CDATA[
      ((a(x,y,z) * u) \ u) \ u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4989,a(flip),b,3671,a),flip(a)].">
      <j1 rule="hyper" parents="63 4989 3671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5207">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ x)) \ x = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(4784(a,1),5205(a,1,1))].">
      <j1 rule="para" parents="4784 5205"/>
    </justification>
  </clause>

  <clause id="5208">
    <literal><![CDATA[
      a(x,y,z) * (x * (y * (z * K(u,w)))) = ((x * y) * z) * K(u,w)
    ]]></literal>
    <justification jstring="[para(3763(a,1),4229(a,1,2,2))].">
      <j1 rule="para" parents="3763 4229"/>
    </justification>
  </clause>

  <clause id="5209">
    <literal><![CDATA[
      R(x / T(y,z),y,y) = x * (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,609,a,b,4236,a(flip))].">
      <j1 rule="hyper" parents="35 609 4236"/>
    </justification>
  </clause>

  <clause id="5210">
    <literal><![CDATA[
      T((1 / (1 / x)) * y,y \ (x \ 1)) = L(y \ (1 / x),y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,3662,a(flip),b,4477,a)].">
      <j1 rule="hyper" parents="63 3662 4477"/>
    </justification>
  </clause>

  <clause id="5211">
    <literal><![CDATA[
      ((x * y) * x) \ (L(y * x,z,u) * T(x,y)) = L((y * x) \ L(y * x,z,u),y * x,x)
    ]]></literal>
    <justification jstring="[para(922(a,1),4492(a,2,1)),flip(a)].">
      <j1 rule="para" parents="922 4492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5212">
    <literal><![CDATA[
      T(x * R(x \ (x * y),z,u),x) = R(y * a(x,y,x),z,u) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,1544,a,b,4547,a)].">
      <j1 rule="hyper" parents="316 1544 4547"/>
    </justification>
  </clause>

  <clause id="5213">
    <literal><![CDATA[
      (a(x,y,x) * ((z * u) * w)) / (u * w) = R(a(x,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(4540(a,1),4553(a,1,1))].">
      <j1 rule="para" parents="4540 4553"/>
    </justification>
  </clause>

  <clause id="5214">
    <literal><![CDATA[
      L(R(x,y,L(L(x,z,u),w,v5)),z,u) = L(R(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4580,a(flip),b,4579,a),flip(a)].">
      <j1 rule="hyper" parents="316 4580 4579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5216">
    <literal><![CDATA[
      K(x,y) * ((y / z) * (z * x)) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[hyper(38,a,2765,a,b,4588,a)].">
      <j1 rule="hyper" parents="38 2765 4588"/>
    </justification>
  </clause>

  <clause id="5217">
    <literal><![CDATA[
      K(x,y) * ((y / L(y,z,z \ 1)) * (L(y,z,z \ 1) * x)) = L(x,L(y,z,z \ 1),a(z \ 1,z,y)) * y
    ]]></literal>
    <justification jstring="[para(2408(a,1),5216(a,2,1,3))].">
      <j1 rule="para" parents="2408 5216"/>
    </justification>
  </clause>

  <clause id="5221">
    <literal><![CDATA[
      R((a(x,y,z) \ 1) * K(T(u,z \ L(z,y,x)),w),T(u,z \ L(z,y,x)),w) = ((u * (a(x,y,z) \ 1)) * w) / (w * T(u,z \ L(z,y,x)))
    ]]></literal>
    <justification jstring="[para(4668(a,1),4488(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4668 4488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5224">
    <literal><![CDATA[
      K(x,y * (a(z,u,w) \ 1)) * (((y * (a(z,u,w) \ 1)) * x) / (x * y)) = L(a(z,u,w) \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2766,a,b,5011,a)].">
      <j1 rule="hyper" parents="63 2766 5011"/>
    </justification>
  </clause>

  <clause id="5225">
    <literal><![CDATA[
      (((x * y) \ (x * z)) \ (y \ z)) \ 1 = (y \ z) \ ((x * y) \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,476,a(flip),b,5084,a),flip(a)].">
      <j1 rule="hyper" parents="316 476 5084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5231">
    <literal><![CDATA[
      T(x,((y * z) * u) * (u \ (z \ (y \ w)))) = T(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3742,a(flip),b,5204,a)].">
      <j1 rule="hyper" parents="63 3742 5204"/>
    </justification>
  </clause>

  <clause id="5232">
    <literal><![CDATA[
      a(x,y,z) * (x * (y * (z * K(u,w)))) = (x * y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,3763,a(flip),b,5208,a),flip(a)].">
      <j1 rule="hyper" parents="316 3763 5208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5233">
    <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),5212(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 5212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5234">
    <literal><![CDATA[
      (((x * y) * z) / (y * z)) * a(u,w,u) = R(a(u,w,u) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4548,a(flip),b,5213,a)].">
      <j1 rule="hyper" parents="63 4548 5213"/>
    </justification>
  </clause>

  <clause id="5235">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,(y * z) * (z \ (y \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3507,a(flip),b,5231,a),flip(a)].">
      <j1 rule="hyper" parents="63 3507 5231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5237">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,y * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(316,a,3507,a(flip),b,5235,a),flip(a)].">
      <j1 rule="hyper" parents="316 3507 5235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5239">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),5237(a,2,2))].">
      <j1 rule="para" parents="10 5237"/>
    </justification>
  </clause>

  <clause id="5240">
    <literal><![CDATA[
      T(x / (a(y,z,u) * w),w) = (a(y,z,u) * w) \ x
    ]]></literal>
    <justification jstring="[hyper(377,a,5239,a),flip(a)].">
      <j1 rule="hyper" parents="377 5239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5241">
    <literal><![CDATA[
      x * T(y,a(z,u,w) * x) = y * x
    ]]></literal>
    <justification jstring="[hyper(139,a,5239,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="139 5239 22"/>
    </justification>
  </clause>

  <clause id="5242">
    <literal><![CDATA[
      T(x,y * (a(z,u,w) * v5)) = T(x,y * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3652,a(flip),b,5239,a)].">
      <j1 rule="hyper" parents="63 3652 5239"/>
    </justification>
  </clause>

  <clause id="5243">
    <literal><![CDATA[
      T(x,y * a(z,u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2518,a(flip),b,5239,a)].">
      <j1 rule="hyper" parents="63 2518 5239"/>
    </justification>
  </clause>

  <clause id="5244">
    <literal><![CDATA[
      T(a(x,y,z) / u,u \ 1) = a(x,y,z) / u
    ]]></literal>
    <justification jstring="[hyper(63,a,555,a(flip),b,5239,a),flip(a)].">
      <j1 rule="hyper" parents="63 555 5239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5245">
    <literal><![CDATA[
      (a(x,y,z) * u) / T(w * w,u) = (w * w) \ (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(209,a,5239,a(flip),b,825,a)].">
      <j1 rule="hyper" parents="209 5239 825"/>
    </justification>
  </clause>

  <clause id="5246">
    <literal><![CDATA[
      K(a(x,y,z) * u,w) = w / T(w,u)
    ]]></literal>
    <justification jstring="[hyper(209,a,5239,a(flip),b,2928,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="209 5239 2928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5247">
    <literal><![CDATA[
      (a(x,y,z) * u) * T(w,u) = w * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,5239,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 5239 22"/>
    </justification>
  </clause>

  <clause id="5248">
    <literal><![CDATA[
      K(x,a(y,z,u) * w) = T(x,w) / x
    ]]></literal>
    <justification jstring="[hyper(136,a,5239,a(flip),b,2794,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 5239 2794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5249">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),5239(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 5239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5251">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,u,w) * y) = a(z,u,w) * (y * T(x,y))
    ]]></literal>
    <justification jstring="[para(5239(a,1),598(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5239 598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5252">
    <literal><![CDATA[
      T(x,y / a(z,u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2289(a,1),5239(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2289 5239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5253">
    <literal><![CDATA[
      (a(x,y,z) * u) * T(w,u) = w * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(5239(a,1),2347(a,1,2))].">
      <j1 rule="para" parents="5239 2347"/>
    </justification>
  </clause>

  <clause id="5257">
    <literal><![CDATA[
      T(x,x * a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,113,a(flip),b,5243,a),flip(a)].">
      <j1 rule="hyper" parents="316 113 5243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5258">
    <literal><![CDATA[
      x * T(y,x * a(z,u,w)) = y * x
    ]]></literal>
    <justification jstring="[hyper(139,a,5243,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="139 5243 22"/>
    </justification>
  </clause>

  <clause id="5259">
    <literal><![CDATA[
      T(x,y * (z * a(u,w,v5))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3501,a(flip),b,5243,a)].">
      <j1 rule="hyper" parents="63 3501 5243"/>
    </justification>
  </clause>

  <clause id="5260">
    <literal><![CDATA[
      T(x,y \ a(z,u,w)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3489,a(flip),b,5243,a)].">
      <j1 rule="hyper" parents="63 3489 5243"/>
    </justification>
  </clause>

  <clause id="5261">
    <literal><![CDATA[
      (x * a(y,z,u)) \ ((x * w) * a(y,z,u)) = R(w,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(40,a,737,a(flip),b,5243,a),flip(a)].">
      <j1 rule="hyper" parents="40 737 5243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5262">
    <literal><![CDATA[
      (x * a(y,z,u)) * T(w,x) = w * (x * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,5243,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 5243 22"/>
    </justification>
  </clause>

  <clause id="5263">
    <literal><![CDATA[
      (x * a(y,z,u)) * x = x * (x * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,5257,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 5257 22"/>
    </justification>
  </clause>

  <clause id="5264">
    <literal><![CDATA[
      R(x,x,a(y,z,u)) = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(5257(a,1),2510(a,1,1))].">
      <j1 rule="para" parents="5257 2510"/>
    </justification>
  </clause>

  <clause id="5265">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(w,v5,v6) \ v7)) = T(x,v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,5249,a(flip),b,5249,a),flip(a)].">
      <j1 rule="hyper" parents="316 5249 5249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5266">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(w,v5,v6) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,4989,a(flip),b,5249,a),flip(a)].">
      <j1 rule="hyper" parents="316 4989 5249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5267">
    <literal><![CDATA[
      T(x,y \ (a(z,u,w) \ v5)) = T(x,y \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3726,a(flip),b,5249,a)].">
      <j1 rule="hyper" parents="63 3726 5249"/>
    </justification>
  </clause>

  <clause id="5268">
    <literal><![CDATA[
      (a(x,y,z) \ u) * T(w,u) = w * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,5249,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 5249 22"/>
    </justification>
  </clause>

  <clause id="5269">
    <literal><![CDATA[
      R(T(x,y),x \ (a(z,u,w) \ y),x) = (x \ (a(z,u,w) \ y)) \ (a(z,u,w) \ y)
    ]]></literal>
    <justification jstring="[para(5249(a,1),1651(a,1,1))].">
      <j1 rule="para" parents="5249 1651"/>
    </justification>
  </clause>

  <clause id="5271">
    <literal><![CDATA[
      T(x,x \ a(y,z,u)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1787,a(flip),b,5252,a),flip(a)].">
      <j1 rule="hyper" parents="63 1787 5252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5272">
    <literal><![CDATA[
      ((a(x,y,z) / u) \ 1) \ 1 = u \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,1790,a(flip),b,5252,a),flip(a)].">
      <j1 rule="hyper" parents="40 1790 5252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5273">
    <literal><![CDATA[
      x * ((y * ((a(z,u,w) \ 1) * x)) / x) = y * ((a(z,u,w) \ 1) * T(x,y))
    ]]></literal>
    <justification jstring="[para(5252(a,1),4447(a,2,2,2))].">
      <j1 rule="para" parents="5252 4447"/>
    </justification>
  </clause>

  <clause id="5274">
    <literal><![CDATA[
      (x / (a(y,z,u) * w)) * w = w * ((a(y,z,u) * w) \ x)
    ]]></literal>
    <justification jstring="[para(116(a,1),5241(a,1,2)),flip(a)].">
      <j1 rule="para" parents="116 5241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5275">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,u,w) * y) = a(z,u,w) * (x * y)
    ]]></literal>
    <justification jstring="[para(5241(a,1),598(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5241 598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5276">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,u,w) * y) = (x * y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(5241(a,1),2346(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5241 2346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5277">
    <literal><![CDATA[
      (x * y) / T(a(z,u,w) * x,y) = (y * x) / (a(z,u,w) * x)
    ]]></literal>
    <justification jstring="[para(5241(a,1),3854(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5241 3854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5278">
    <literal><![CDATA[
      K(a(x,y,z) * u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,2937,a,b,5246,a),flip(a)].">
      <j1 rule="hyper" parents="316 2937 5246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5279">
    <literal><![CDATA[
      K(a(x,y,z) \ u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),5278(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5280">
    <literal><![CDATA[
      K(x * a(y,z,u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(2290(a,1),5278(a,1,1))].">
      <j1 rule="para" parents="2290 5278"/>
    </justification>
  </clause>

  <clause id="5281">
    <literal><![CDATA[
      T(x * K(y,x),x * (a(z,u,w) * y)) = L(x,a(z,u,w) * y,x)
    ]]></literal>
    <justification jstring="[para(5278(a,1),2747(a,1,1,2))].">
      <j1 rule="para" parents="5278 2747"/>
    </justification>
  </clause>

  <clause id="5282">
    <literal><![CDATA[
      a(x,y,z) * K(u \ 1,u) = (u \ a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(5278(a,1),3399(a,1,2))].">
      <j1 rule="para" parents="5278 3399"/>
    </justification>
  </clause>

  <clause id="5284">
    <literal><![CDATA[
      K(a(x,y,z) \ u,w) = u \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,2806,a(flip),b,5279,a),flip(a)].">
      <j1 rule="hyper" parents="316 2806 5279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5285">
    <literal><![CDATA[
      ((a(x,y,z) \ u) \ w) * K(u,(a(x,y,z) \ u) \ w) = w / (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,5279,a(flip),b,2741,a)].">
      <j1 rule="hyper" parents="139 5279 2741"/>
    </justification>
  </clause>

  <clause id="5286">
    <literal><![CDATA[
      (a(x,y,z) \ u) * K(w \ u,w) = (w \ (a(x,y,z) \ u)) * w
    ]]></literal>
    <justification jstring="[para(5279(a,1),4504(a,1,2))].">
      <j1 rule="para" parents="5279 4504"/>
    </justification>
  </clause>

  <clause id="5287">
    <literal><![CDATA[
      K(x \ a(y,z,u),w) = K(x \ 1,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3520,a(flip),b,5280,a)].">
      <j1 rule="hyper" parents="63 3520 5280"/>
    </justification>
  </clause>

  <clause id="5288">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(4546(a,1),5280(a,1,1))].">
      <j1 rule="para" parents="4546 5280"/>
    </justification>
  </clause>

  <clause id="5289">
    <literal><![CDATA[
      K(x,a(y,z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,2795,a,b,5248,a),flip(a)].">
      <j1 rule="hyper" parents="316 2795 5248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5290">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),5289(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 5289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5291">
    <literal><![CDATA[
      K(x,y * a(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2290(a,1),5289(a,1,2))].">
      <j1 rule="para" parents="2290 5289"/>
    </justification>
  </clause>

  <clause id="5292">
    <literal><![CDATA[
      K(x,(y * a(z,u,z)) * w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(4538(a,2),5289(a,1,2))].">
      <j1 rule="para" parents="4538 5289"/>
    </justification>
  </clause>

  <clause id="5293">
    <literal><![CDATA[
      K(x,y \ a(z,u,w)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3578,a(flip),b,5291,a)].">
      <j1 rule="hyper" parents="63 3578 5291"/>
    </justification>
  </clause>

  <clause id="5295">
    <literal><![CDATA[
      (x / (y * a(z,u,w))) * y = y * ((y * a(z,u,w)) \ x)
    ]]></literal>
    <justification jstring="[para(116(a,1),5258(a,1,2)),flip(a)].">
      <j1 rule="para" parents="116 5258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5296">
    <literal><![CDATA[
      T(a(x,y,z) \ u,u \ 1) = ((a(x,y,z) \ u) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1078,a(flip),b,5260,a),flip(a)].">
      <j1 rule="hyper" parents="63 1078 5260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5297">
    <literal><![CDATA[
      (x \ a(y,z,u)) \ a(y,z,u) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(384,a,5271,a)].">
      <j1 rule="hyper" parents="384 5271"/>
    </justification>
  </clause>

  <clause id="5298">
    <literal><![CDATA[
      1 / (x \ a(y,z,u)) = (a(y,z,u) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(209,a,614,a(flip),b,5271,a(flip))].">
      <j1 rule="hyper" parents="209 614 5271"/>
    </justification>
  </clause>

  <clause id="5299">
    <literal><![CDATA[
      T(a(x,y,z) \ u,w) * a(x,y,z) = T(u,w)
    ]]></literal>
    <justification jstring="[hyper(38,a,3642,a,b,5284,a(flip))].">
      <j1 rule="hyper" parents="38 3642 5284"/>
    </justification>
  </clause>

  <clause id="5300">
    <literal><![CDATA[
      K(x \ 1,x) * a(y,z,u) = (x \ a(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(138,a,5287,a(flip),b,2762,a)].">
      <j1 rule="hyper" parents="138 5287 2762"/>
    </justification>
  </clause>

  <clause id="5301">
    <literal><![CDATA[
      K(x,x \ 1) * a(y,z,u) = x * (a(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(138,a,5293,a(flip),b,3035,a)].">
      <j1 rule="hyper" parents="138 5293 3035"/>
    </justification>
  </clause>

  <clause id="5303">
    <literal><![CDATA[
      (a(x,y,z) \ (a(u,w,v5) \ 1)) * v6 = v6 * (a(x,y,z) \ (a(u,w,v5) \ 1))
    ]]></literal>
    <justification jstring="[hyper(139,a,5266,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 5266 22"/>
    </justification>
  </clause>

  <clause id="5305">
    <literal><![CDATA[
      T((x * (a(y,z,u) * w)) / x,x * w) = L(a(y,z,u) * w,x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1609,a(flip),b,5242,a),flip(a)].">
      <j1 rule="hyper" parents="63 1609 5242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5306">
    <literal><![CDATA[
      T((x * (a(y,z,u) * w)) / x,x * w) = L(w * a(y,z,u),x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2392,a(flip),b,5259,a),flip(a)].">
      <j1 rule="hyper" parents="63 2392 5259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5308">
    <literal><![CDATA[
      T(T(x * K(x * (y \ (a(z,u,w) \ v5)),x),v6),y \ v5) = R(T(x,v6),y \ (a(z,u,w) \ v5),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3257,a(flip),b,5267,a),flip(a)].">
      <j1 rule="hyper" parents="63 3257 5267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5309">
    <literal><![CDATA[
      T(x,y \ (L(z,u,z) \ w)) = T(x,y \ (z \ w))
    ]]></literal>
    <justification jstring="[para(4940(a,1),5267(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4940 5267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5310">
    <literal><![CDATA[
      K(x,T(y * z,y) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(4949(a,1),5292(a,1,2,1))].">
      <j1 rule="para" parents="4949 5292"/>
    </justification>
  </clause>

  <clause id="5311">
    <literal><![CDATA[
      T(a(x,y,z) / (u \ 1),u) = a(x,y,z) / (u \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2594,a(flip),b,5244,a)].">
      <j1 rule="hyper" parents="63 2594 5244"/>
    </justification>
  </clause>

  <clause id="5312">
    <literal><![CDATA[
      (x * a(y,z,u)) * x = x * (a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(316,a,2293,a,b,5263,a),flip(a)].">
      <j1 rule="hyper" parents="316 2293 5263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5313">
    <literal><![CDATA[
      (x * ((a(y,z,u) * a(w,v5,v6)) \ v7)) / T(x,v7) = (a(y,z,u) * a(w,v5,v6)) \ v7
    ]]></literal>
    <justification jstring="[para(5265(a,1),3708(a,1,2))].">
      <j1 rule="para" parents="5265 3708"/>
    </justification>
  </clause>

  <clause id="5314">
    <literal><![CDATA[
      K(x,(a(y,z,u) / w) * v5) = K(x,(w \ a(y,z,u)) * v5)
    ]]></literal>
    <justification jstring="[para(5272(a,1),3575(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5272 3575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5315">
    <literal><![CDATA[
      a(x,y,z) / (u \ 1) = (1 / u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(209,a,206,a(flip),b,5297,a)].">
      <j1 rule="hyper" parents="209 206 5297"/>
    </justification>
  </clause>

  <clause id="5316">
    <literal><![CDATA[
      T(a(x,y,z) \ u,w) = a(x,y,z) \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(35,a,2274,a,b,5299,a),flip(a)].">
      <j1 rule="hyper" parents="35 2274 5299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5317">
    <literal><![CDATA[
      T(x * a(y,z,u),w) = T(x,w) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(2275(a,1),5299(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2275 5299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5319">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),5310(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5320">
    <literal><![CDATA[
      R(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(501,a,5312,a)].">
      <j1 rule="hyper" parents="501 5312"/>
    </justification>
  </clause>

  <clause id="5321">
    <literal><![CDATA[
      L(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(463,a,5312,a)].">
      <j1 rule="hyper" parents="463 5312"/>
    </justification>
  </clause>

  <clause id="5323">
    <literal><![CDATA[
      a(x,a(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,5312,a(flip),b,2330,a),flip(a)].">
      <j1 rule="hyper" parents="134 5312 2330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5324">
    <literal><![CDATA[
      x * a(y,a(z,u,w),y) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,5323,a,b,67,a)].">
      <j1 rule="hyper" parents="139 5323 67"/>
    </justification>
  </clause>

  <clause id="5325">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ w = w
    ]]></literal>
    <justification jstring="[para(5323(a,2),66(a,1,1))].">
      <j1 rule="para" parents="5323 66"/>
    </justification>
  </clause>

  <clause id="5326">
    <literal><![CDATA[
      (x * a(y,z,u)) \ a(y,z,u) = a(y,z,u) \ (x \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,5325,a(flip),b,4947,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 5325 4947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5327">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) * a(y,z,u) = (1 / x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2322,a,b,5315,a)].">
      <j1 rule="hyper" parents="63 2322 5315"/>
    </justification>
  </clause>

  <clause id="5328">
    <literal><![CDATA[
      x * L(x \ ((1 / x) \ a(y,z,u)),w,v5) = L(a(y,z,u),w,v5) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(5315(a,1),993(a,1,2,1,2))].">
      <j1 rule="para" parents="5315 993"/>
    </justification>
  </clause>

  <clause id="5329">
    <literal><![CDATA[
      x * (a(y,z,u) \ T(w,x)) = (a(y,z,u) \ w) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,5316,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 5316 22"/>
    </justification>
  </clause>

  <clause id="5330">
    <literal><![CDATA[
      a(x,y,z) \ T(u * a(x,y,z),w) = T(u,w)
    ]]></literal>
    <justification jstring="[para(2275(a,1),5316(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2275 5316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5331">
    <literal><![CDATA[
      T(a(x,y,z) \ K(u,w),v5) = a(x,y,z) \ K(u,T(w,v5))
    ]]></literal>
    <justification jstring="[para(3865(a,2),5316(a,2,2))].">
      <j1 rule="para" parents="3865 5316"/>
    </justification>
  </clause>

  <clause id="5332">
    <literal><![CDATA[
      T(x * a(y,z,u),w) = a(y,z,u) * T(x,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,2290,a,b,5317,a),flip(a)].">
      <j1 rule="hyper" parents="316 2290 5317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5333">
    <literal><![CDATA[
      T((x / y) * a(z,u,w),y) = (y \ x) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(116(a,1),5317(a,2,1))].">
      <j1 rule="para" parents="116 5317"/>
    </justification>
  </clause>

  <clause id="5334">
    <literal><![CDATA[
      T(x * a(y,z,u),x * x) = L(x,x,x) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(117(a,1),5317(a,2,1))].">
      <j1 rule="para" parents="117 5317"/>
    </justification>
  </clause>

  <clause id="5335">
    <literal><![CDATA[
      T((x * K(y,x)) * a(z,u,w),y * x) = L(x,y,x) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(2751(a,1),5317(a,2,1))].">
      <j1 rule="para" parents="2751 5317"/>
    </justification>
  </clause>

  <clause id="5336">
    <literal><![CDATA[
      K(x,(y \ z) * (y * u)) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3572,a(flip),b,5319,a)].">
      <j1 rule="hyper" parents="63 3572 5319"/>
    </justification>
  </clause>

  <clause id="5337">
    <literal><![CDATA[
      T(a(x,y,z) * a(u,w,v5),v6) = a(u,w,v5) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,2286,a(flip),b,5330,a),flip(a)].">
      <j1 rule="hyper" parents="139 2286 5330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5338">
    <literal><![CDATA[
      T(a(x,y,z) * u,w) = a(x,y,z) * T(u,w)
    ]]></literal>
    <justification jstring="[para(2290(a,2),5332(a,1,1))].">
      <j1 rule="para" parents="2290 5332"/>
    </justification>
  </clause>

  <clause id="5339">
    <literal><![CDATA[
      K(x,T(y,z) * u) \ ((z \ y) * (z * u)) = 1 \ T((z \ y) * (z * u),x)
    ]]></literal>
    <justification jstring="[para(5336(a,1),2938(a,1,1))].">
      <j1 rule="para" parents="5336 2938"/>
    </justification>
  </clause>

  <clause id="5340">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ 1),w) = T(x,w) * (a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,846,a(flip),b,5338,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 846 5338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5341">
    <literal><![CDATA[
      T(a(x,y,z) * (u * w),K(w,u)) = a(x,y,z) * (u * w)
    ]]></literal>
    <justification jstring="[para(2756(a,1),5338(a,2,2))].">
      <j1 rule="para" parents="2756 5338"/>
    </justification>
  </clause>

  <clause id="5342">
    <literal><![CDATA[
      x / (a(y,z,u) * a(w,v5,v6)) = (a(y,z,u) * a(w,v5,v6)) \ x
    ]]></literal>
    <justification jstring="[hyper(2294,a,5240,a)].">
      <j1 rule="hyper" parents="2294 5240"/>
    </justification>
  </clause>

  <clause id="5343">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) / (a(x,y,z) * w) = L(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(40,a,708,a(flip),b,5240,a),flip(a)].">
      <j1 rule="hyper" parents="40 708 5240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5344">
    <literal><![CDATA[
      (x / y) * (a(z,u,w) * y) = (a(z,u,w) * y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(116(a,1),5247(a,1,2)),flip(a)].">
      <j1 rule="para" parents="116 5247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5345">
    <literal><![CDATA[
      (a(x,y,z) * a(u,w,v5)) * v6 = v6 * (a(x,y,z) * a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(2273(a,1),5247(a,1,2))].">
      <j1 rule="para" parents="2273 5247"/>
    </justification>
  </clause>

  <clause id="5346">
    <literal><![CDATA[
      (a(x,y,z) * (u / (a(x,y,z) \ 1))) * T(w,u / (a(x,y,z) \ 1)) = w * (u * (a(x,y,z) * a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(2288(a,1),5247(a,2,2))].">
      <j1 rule="para" parents="2288 5247"/>
    </justification>
  </clause>

  <clause id="5347">
    <literal><![CDATA[
      T(a(x,y,z) * (u / w),w) = (w \ u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(253,a,3894,a(flip),b,5253,a(flip))].">
      <j1 rule="hyper" parents="253 3894 5253"/>
    </justification>
  </clause>

  <clause id="5348">
    <literal><![CDATA[
      (x / y) * (y * a(z,u,w)) = (a(z,u,w) * y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(116(a,1),5253(a,1,2)),flip(a)].">
      <j1 rule="para" parents="116 5253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5349">
    <literal><![CDATA[
      (a(x,y,z) * a(u,w,v5)) * v6 = v6 * (a(u,w,v5) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(2273(a,1),5253(a,1,2))].">
      <j1 rule="para" parents="2273 5253"/>
    </justification>
  </clause>

  <clause id="5350">
    <literal><![CDATA[
      T(x * K((y * a(z,u,w)) * x,v5),y * a(z,u,w)) = (y * a(z,u,w)) \ T((a(z,u,w) * y) * T(x,y),v5)
    ]]></literal>
    <justification jstring="[para(5253(a,2),3648(a,2,2,1))].">
      <j1 rule="para" parents="5253 3648"/>
    </justification>
  </clause>

  <clause id="5351">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * v5) * T(v6,(v5 / a(x,y,z)) * L(a(x,y,z),u,w)) = v6 * (((v5 / a(x,y,z)) * L(a(x,y,z),u,w)) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(4385(a,1),5253(a,1,1))].">
      <j1 rule="para" parents="4385 5253"/>
    </justification>
  </clause>

  <clause id="5353">
    <literal><![CDATA[
      (x / y) * (y * a(z,u,w)) = (y * a(z,u,w)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(116(a,1),5262(a,1,2)),flip(a)].">
      <j1 rule="para" parents="116 5262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5354">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (u \ w) = (w / u) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(116(a,1),5268(a,1,2))].">
      <j1 rule="para" parents="116 5268"/>
    </justification>
  </clause>

  <clause id="5355">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * w) / T(u,w) = (w * (a(x,y,z) \ u)) / u
    ]]></literal>
    <justification jstring="[para(5268(a,1),3854(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5268 3854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5357">
    <literal><![CDATA[
      (x \ a(y,z,u)) * (x * x) = a(y,z,u) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,613,a(flip),b,5311,a)].">
      <j1 rule="hyper" parents="63 613 5311"/>
    </justification>
  </clause>

  <clause id="5358">
    <literal><![CDATA[
      ((x / y) * a(z,u,w)) * y = y * ((y \ x) * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,5333,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 5333 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5359">
    <literal><![CDATA[
      (x \ a(y,z,u)) * (x * x) = (1 / x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,5315,a(flip),b,5357,a),flip(a)].">
      <j1 rule="hyper" parents="316 5315 5357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5360">
    <literal><![CDATA[
      (x / (y \ L(a(z,u,w),y,y))) * (y \ 1) = (y \ 1) * ((a(z,u,w) * (y \ 1)) \ x)
    ]]></literal>
    <justification jstring="[para(2460(a,2),5274(a,1,1,2))].">
      <j1 rule="para" parents="2460 5274"/>
    </justification>
  </clause>

  <clause id="5361">
    <literal><![CDATA[
      K(x,(y \ a(z,u,w)) * v5) = K(x,a(z,u,w) * (y \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,3582,a(flip),b,5314,a),flip(a)].">
      <j1 rule="hyper" parents="63 3582 5314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5362">
    <literal><![CDATA[
      x / (a(y,z,u) * a(w,v5,v6)) = (a(w,v5,v6) * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(209,a,5337,a(flip),b,4303,a(flip))].">
      <j1 rule="hyper" parents="209 5337 4303"/>
    </justification>
  </clause>

  <clause id="5363">
    <literal><![CDATA[
      x \ ((a(y,z,u) * a(y,z,u)) * w) = (x \ w) * (a(y,z,u) * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(5337(a,1),822(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5337 822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5364">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ 1),w) = (a(y,z,u) \ 1) * T(x,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,5006,a,b,5340,a),flip(a)].">
      <j1 rule="hyper" parents="316 5006 5340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5365">
    <literal><![CDATA[
      T(a(x,y,z) * (u * L(w,v5,v6)),K(w,u)) = a(x,y,z) * (u * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(4279(a,1),5341(a,1,2))].">
      <j1 rule="para" parents="4279 5341"/>
    </justification>
  </clause>

  <clause id="5366">
    <literal><![CDATA[
      (1 / x) * (a(y,z,u) * x) = R(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,565,a(flip),b,5344,a),flip(a)].">
      <j1 rule="hyper" parents="316 565 5344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5367">
    <literal><![CDATA[
      K(x,(y \ a(z,u,w)) * v5) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,5289,a(flip),b,5361,a),flip(a)].">
      <j1 rule="hyper" parents="316 5289 5361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5370">
    <literal><![CDATA[
      a(x,y,z) * (u / T(w * w,u)) = (w * w) \ (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,696,a(flip),b,5245,a)].">
      <j1 rule="hyper" parents="63 696 5245"/>
    </justification>
  </clause>

  <clause id="5371">
    <literal><![CDATA[
      R(x,y,a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,2494,a(flip),b,5261,a),flip(a)].">
      <j1 rule="hyper" parents="63 2494 5261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5372">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,4529,a(flip),b,5371,a),flip(a)].">
      <j1 rule="hyper" parents="316 4529 5371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5373">
    <literal><![CDATA[
      R(x,y,((z * u) * w) \ (z * (w * u))) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4899,a,b,5371,a)].">
      <j1 rule="hyper" parents="63 4899 5371"/>
    </justification>
  </clause>

  <clause id="5374">
    <literal><![CDATA[
      R(x,y,(z \ u) * (z * u)) = L(x,y,a(z \ u,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4764,a,b,5371,a)].">
      <j1 rule="hyper" parents="63 4764 5371"/>
    </justification>
  </clause>

  <clause id="5375">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ 1)) = L(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2629,a,b,5371,a)].">
      <j1 rule="hyper" parents="63 2629 5371"/>
    </justification>
  </clause>

  <clause id="5376">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) \ u,a(x,y,z),a(x,y,z)) = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5000,a(flip),b,5371,a),flip(a)].">
      <j1 rule="hyper" parents="63 5000 5371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5377">
    <literal><![CDATA[
      R(x,y,z * R(z,u,u)) = L(x,y,a(z,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4799,a(flip),b,5371,a)].">
      <j1 rule="hyper" parents="63 4799 5371"/>
    </justification>
  </clause>

  <clause id="5378">
    <literal><![CDATA[
      L(x,a(y,z,u) \ 1,a(y,z,u)) = R(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2631,a(flip),b,5371,a),flip(a)].">
      <j1 rule="hyper" parents="63 2631 5371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5379">
    <literal><![CDATA[
      L(x,y * y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,2617,a(flip),b,5371,a),flip(a)].">
      <j1 rule="hyper" parents="63 2617 5371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5380">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),a(x,y,z)) = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2282,a(flip),b,5371,a),flip(a)].">
      <j1 rule="hyper" parents="63 2282 5371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5381">
    <literal><![CDATA[
      L(x / y,y,a(z,u,w)) = (x * (a(z,u,w) \ 1)) / (y * (a(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,1036,a(flip),b,5371,a),flip(a)].">
      <j1 rule="hyper" parents="63 1036 5371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5382">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (y * a(z,u,w)) = a(z,u,w) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(138,a,5371,a(flip),b,2341,a)].">
      <j1 rule="hyper" parents="138 5371 2341"/>
    </justification>
  </clause>

  <clause id="5383">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (y * a(z,u,w)) = (x * y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(138,a,5371,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="138 5371 20"/>
    </justification>
  </clause>

  <clause id="5384">
    <literal><![CDATA[
      a(x,y,z) \ L(u,a(x,y,z),a(x,y,z)) = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,5371,a(flip),b,2629,a)].">
      <j1 rule="hyper" parents="133 5371 2629"/>
    </justification>
  </clause>

  <clause id="5385">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,y * a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(5371(a,1),3422(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5371 3422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5386">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,a(z,u,w) * y) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(5371(a,1),3424(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5371 3424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5387">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(5371(a,2),4542(a,1))].">
      <j1 rule="para" parents="5371 4542"/>
    </justification>
  </clause>

  <clause id="5388">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(138,a,5372,a(flip),b,2497,a),flip(a)].">
      <j1 rule="hyper" parents="138 5372 2497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5389">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (u * a(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(138,a,5372,a(flip),b,2341,a),flip(a)].">
      <j1 rule="hyper" parents="138 5372 2341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5390">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,z)) = y * a(z,u,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,5372,a(flip),b,106,a(flip))].">
      <j1 rule="hyper" parents="138 5372 106"/>
    </justification>
  </clause>

  <clause id="5391">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(138,a,5372,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="138 5372 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5392">
    <literal><![CDATA[
      (x \ 1) * a(y,z,y) = x \ a(y,z,y)
    ]]></literal>
    <justification jstring="[para(5372(a,1),382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5372 382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5393">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = (x \ y) * a(z,u,z)
    ]]></literal>
    <justification jstring="[para(5372(a,1),492(a,1,1))].">
      <j1 rule="para" parents="5372 492"/>
    </justification>
  </clause>

  <clause id="5395">
    <literal><![CDATA[
      a(x,y,x) * (z \ 1) = z \ a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a,b,5392,a)].">
      <j1 rule="hyper" parents="63 2290 5392"/>
    </justification>
  </clause>

  <clause id="5396">
    <literal><![CDATA[
      a(x,y,x) \ (z * (a(x,y,x) * u)) = z * u
    ]]></literal>
    <justification jstring="[hyper(144,a,5388,a)].">
      <j1 rule="hyper" parents="144 5388"/>
    </justification>
  </clause>

  <clause id="5397">
    <literal><![CDATA[
      a(x,y,x) \ (z * u) = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,160,a(flip),b,5388,a)].">
      <j1 rule="hyper" parents="133 160 5388"/>
    </justification>
  </clause>

  <clause id="5398">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = x * (a(y,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4538,a,b,5388,a)].">
      <j1 rule="hyper" parents="63 4538 5388"/>
    </justification>
  </clause>

  <clause id="5399">
    <literal><![CDATA[
      (a(x,y,x) \ z) * (a(x,y,x) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(63,a,4539,a(flip),b,5388,a),flip(a)].">
      <j1 rule="hyper" parents="63 4539 5388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5400">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (a(z,u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a(flip),b,5388,a)].">
      <j1 rule="hyper" parents="63 2290 5388"/>
    </justification>
  </clause>

  <clause id="5401">
    <literal><![CDATA[
      a(x,y,x) * (z \ (a(x,y,x) \ u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(133,a,76,a(flip),b,5388,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 76 5388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5402">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ ((x * u) * (a(y,z,y) * w)) = a(x,u,a(y,z,y) * w)
    ]]></literal>
    <justification jstring="[para(5388(a,2),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5388 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5403">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) * w = a(y,z,y) * ((x * u) * w)
    ]]></literal>
    <justification jstring="[para(5388(a,1),4540(a,1,1))].">
      <j1 rule="para" parents="5388 4540"/>
    </justification>
  </clause>

  <clause id="5404">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = (x \ u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(543,a,5389,a)].">
      <j1 rule="hyper" parents="543 5389"/>
    </justification>
  </clause>

  <clause id="5405">
    <literal><![CDATA[
      (a(x,y,x) * z) * u = z * (u * a(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,4540,a,b,5389,a)].">
      <j1 rule="hyper" parents="63 4540 5389"/>
    </justification>
  </clause>

  <clause id="5407">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,2307,a,b,5389,a)].">
      <j1 rule="hyper" parents="35 2307 5389"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      (x * y) \ (x * (a(z,u,z) * (y * w))) = L(w * a(z,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(5389(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5389 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5409">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ w = (x * y) \ (a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(5389(a,1),4534(a,1,1))].">
      <j1 rule="para" parents="5389 4534"/>
    </justification>
  </clause>

  <clause id="5410">
    <literal><![CDATA[
      a(x,y,a(z,u,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,5407,a)].">
      <j1 rule="hyper" parents="53 5407"/>
    </justification>
  </clause>

  <clause id="5411">
    <literal><![CDATA[
      x * a(y,z,a(u,w,u)) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,5410,a,b,67,a)].">
      <j1 rule="hyper" parents="139 5410 67"/>
    </justification>
  </clause>

  <clause id="5412">
    <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(5391(a,1),500(a,1,1))].">
      <j1 rule="para" parents="5391 500"/>
    </justification>
  </clause>

  <clause id="5413">
    <literal><![CDATA[
      (a(x,y,x) \ z) * u = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4543,a(flip),b,5397,a)].">
      <j1 rule="hyper" parents="63 4543 5397"/>
    </justification>
  </clause>

  <clause id="5414">
    <literal><![CDATA[
      a(x,y,x) \ (z \ u) = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,168,a(flip),b,5397,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 168 5397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5415">
    <literal><![CDATA[
      a(x,y,x) \ (z \ (a(x,y,x) * u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(133,a,74,a(flip),b,5397,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 74 5397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5417">
    <literal><![CDATA[
      (x * a(y,z,y)) \ u = a(y,z,y) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,76,a(flip),b,5398,a)].">
      <j1 rule="hyper" parents="133 76 5398"/>
    </justification>
  </clause>

  <clause id="5418">
    <literal><![CDATA[
      a(x,a(y,z,y),u) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,5398,a(flip),b,2330,a),flip(a)].">
      <j1 rule="hyper" parents="134 5398 2330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5419">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ (((x * a(y,z,y)) * u) * w) = a(x * a(y,z,y),u,w)
    ]]></literal>
    <justification jstring="[para(5398(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5398 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5420">
    <literal><![CDATA[
      (x \ 1) * (a(y,z,y) * u) = (x \ a(y,z,y)) * u
    ]]></literal>
    <justification jstring="[para(5392(a,1),5398(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5392 5398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5421">
    <literal><![CDATA[
      x / (a(y,z,y) * u) = a(y,z,y) \ (x / u)
    ]]></literal>
    <justification jstring="[hyper(136,a,12,a(flip),b,5399,a)].">
      <j1 rule="hyper" parents="136 12 5399"/>
    </justification>
  </clause>

  <clause id="5422">
    <literal><![CDATA[
      x \ (y * (a(z,u,z) * w)) = (x \ (y * w)) * a(z,u,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,5400,a(flip),b,5390,a)].">
      <j1 rule="hyper" parents="133 5400 5390"/>
    </justification>
  </clause>

  <clause id="5423">
    <literal><![CDATA[
      x \ (y * (a(z,u,z) * w)) = a(z,u,z) * (x \ (y * w))
    ]]></literal>
    <justification jstring="[para(5396(a,1),5401(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5396 5401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5424">
    <literal><![CDATA[
      a(x,y,x) * (z \ (u * (a(x,y,x) \ w))) = z \ (u * w)
    ]]></literal>
    <justification jstring="[para(5397(a,1),5401(a,1,2,2))].">
      <j1 rule="para" parents="5397 5401"/>
    </justification>
  </clause>

  <clause id="5425">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = (z \ u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4533,a,b,5404,a)].">
      <j1 rule="hyper" parents="63 4533 5404"/>
    </justification>
  </clause>

  <clause id="5426">
    <literal><![CDATA[
      (1 / x) * (y * a(z,u,z)) = (a(z,u,z) / x) * y
    ]]></literal>
    <justification jstring="[para(4535(a,1),5405(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4535 5405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5427">
    <literal><![CDATA[
      (x \ 1) * (y * a(z,u,z)) = (x \ a(z,u,z)) * y
    ]]></literal>
    <justification jstring="[para(5395(a,1),5405(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5395 5405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5428">
    <literal><![CDATA[
      (a(x,y,x) / z) * (a(x,y,x) \ u) = (1 / z) * u
    ]]></literal>
    <justification jstring="[para(4532(a,1),5413(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4532 5413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5429">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = a(x,y,x) \ (z \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4534,a,b,5414,a)].">
      <j1 rule="hyper" parents="316 4534 5414"/>
    </justification>
  </clause>

  <clause id="5430">
    <literal><![CDATA[
      a(x,y,x) \ (x \ z) = R(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(4528(a,1),5417(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4528 5417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5431">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) \ w = a(y,z,y) \ ((x * u) \ w)
    ]]></literal>
    <justification jstring="[para(5400(a,1),5417(a,1,1))].">
      <j1 rule="para" parents="5400 5417"/>
    </justification>
  </clause>

  <clause id="5432">
    <literal><![CDATA[
      (R(x,y,x) \ z) * a(x,y,x) = x \ z
    ]]></literal>
    <justification jstring="[hyper(38,a,2275,a,b,5430,a)].">
      <j1 rule="hyper" parents="38 2275 5430"/>
    </justification>
  </clause>

  <clause id="5433">
    <literal><![CDATA[
      a(x,y,x) \ (z \ (x \ u)) = z \ (R(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(5430(a,1),5414(a,2,2))].">
      <j1 rule="para" parents="5430 5414"/>
    </justification>
  </clause>

  <clause id="5434">
    <literal><![CDATA[
      a(x,y,x) \ (z / x) = z / R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4545(a,1),5421(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4545 5421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5435">
    <literal><![CDATA[
      L(x,y,x) * (z / x) = x * (z / R(x,y,x))
    ]]></literal>
    <justification jstring="[para(5434(a,1),4942(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5434 4942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5437">
    <literal><![CDATA[
      a(x,y,x) \ ((L(x,y,x) * z) \ u) = (x * z) \ u
    ]]></literal>
    <justification jstring="[para(4936(a,1),5429(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4936 5429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5438">
    <literal><![CDATA[
      L(1 / x,y,x) = 1 / R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,1229,a(flip),b,5435,a(flip))].">
      <j1 rule="hyper" parents="34 1229 5435"/>
    </justification>
  </clause>

  <clause id="5439">
    <literal><![CDATA[
      R(T(L(1 / x,y,x),z),R(x,y,x),R(x,y,x) \ z) = z \ (1 * (R(x,y,x) \ z))
    ]]></literal>
    <justification jstring="[para(5438(a,2),826(a,1,1,1))].">
      <j1 rule="para" parents="5438 826"/>
    </justification>
  </clause>

  <clause id="5440">
    <literal><![CDATA[
      (x \ 1) \ (((x \ 1) * (y * a(z,u,z))) * w) = (1 / x) \ (((a(z,u,z) / x) * y) * w)
    ]]></literal>
    <justification jstring="[para(5426(a,1),3352(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5426 3352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5441">
    <literal><![CDATA[
      L(x \ (y \ z),x,y) = a(y,u,y) \ ((L(y,u,y) * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,298,a,b,5437,a)].">
      <j1 rule="hyper" parents="316 298 5437"/>
    </justification>
  </clause>

  <clause id="5442">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(5437(a,1),5290(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5437 5290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5443">
    <literal><![CDATA[
      R(x,y,(z * (u * w)) \ (u * (z * w))) = L(x,y,a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4752,a,b,5373,a)].">
      <j1 rule="hyper" parents="63 4752 5373"/>
    </justification>
  </clause>

  <clause id="5444">
    <literal><![CDATA[
      R(x,y,((z * (u * (w * (v5 * v5)))) \ (u * (z * w))) * (v5 * v5)) = L(x,y,a(z,w * (v5 * v5),u))
    ]]></literal>
    <justification jstring="[para(837(a,1),5443(a,1,3))].">
      <j1 rule="para" parents="837 5443"/>
    </justification>
  </clause>

  <clause id="5446">
    <literal><![CDATA[
      (a(x,y,z) * (u * (a(x,y,z) \ w))) / w = L(u,a(x,y,z) \ w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(136,a,5275,a(flip),b,160,a(flip))].">
      <j1 rule="hyper" parents="136 5275 160"/>
    </justification>
  </clause>

  <clause id="5447">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) / w = w \ (a(x,y,z) * (w * u))
    ]]></literal>
    <justification jstring="[hyper(133,a,5275,a(flip),b,4415,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 5275 4415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5448">
    <literal><![CDATA[
      L(x,L(y,z,z),a(z,z,y)) * y = a(z,z,y) * (x * L(y,z,z))
    ]]></literal>
    <justification jstring="[para(4951(a,1),5275(a,1,2))].">
      <j1 rule="para" parents="4951 5275"/>
    </justification>
  </clause>

  <clause id="5450">
    <literal><![CDATA[
      a(x,y,z) \ ((u \ w) * u) = (u \ (a(x,y,z) \ w)) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,3921,a(flip),b,5286,a)].">
      <j1 rule="hyper" parents="63 3921 5286"/>
    </justification>
  </clause>

  <clause id="5451">
    <literal><![CDATA[
      (a(x,y,z) * u) \ a(x,y,z) = a(x,y,z) \ (u \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2324,a,b,5326,a)].">
      <j1 rule="hyper" parents="63 2324 5326"/>
    </justification>
  </clause>

  <clause id="5453">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ (u \ a(x,y,z)) = u \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,588,a(flip),b,5342,a),flip(a)].">
      <j1 rule="hyper" parents="63 588 5342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5454">
    <literal><![CDATA[
      (x * y) / (a(z,u,w) * a(z,u,w)) = x * ((a(z,u,w) * a(z,u,w)) \ y)
    ]]></literal>
    <justification jstring="[para(5342(a,1),683(a,2,2))].">
      <j1 rule="para" parents="5342 683"/>
    </justification>
  </clause>

  <clause id="5456">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * (u * w) = u * (w * (a(x,y,z) * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(316,a,32,a(flip),b,5345,a),flip(a)].">
      <j1 rule="hyper" parents="316 32 5345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5457">
    <literal><![CDATA[
      (T(a(x,y,z) * a(u,w,v5),v6) * v7) * T(v8,v7 * (a(u,w,v5) * a(x,y,z))) = K(a(x,y,z) * a(u,w,v5),v6) * (v8 * ((a(x,y,z) * a(u,w,v5)) * v7))
    ]]></literal>
    <justification jstring="[para(5349(a,1),3181(a,1,2,2))].">
      <j1 rule="para" parents="5349 3181"/>
    </justification>
  </clause>

  <clause id="5458">
    <literal><![CDATA[
      (x * x) \ (a(y,z,u) * w) = a(y,z,u) * ((x * x) \ w)
    ]]></literal>
    <justification jstring="[para(824(a,1),5370(a,1,2)),flip(a)].">
      <j1 rule="para" parents="824 5370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5459">
    <literal><![CDATA[
      x * (a(y,z,u) * ((x * x) \ w)) = x \ L(a(y,z,u) * w,x,x)
    ]]></literal>
    <justification jstring="[para(5458(a,1),1118(a,1,2))].">
      <j1 rule="para" parents="5458 1118"/>
    </justification>
  </clause>

  <clause id="5467">
    <literal><![CDATA[
      a(x,y,z * K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,2330,a,b,5232,a)].">
      <j1 rule="hyper" parents="35 2330 5232"/>
    </justification>
  </clause>

  <clause id="5468">
    <literal><![CDATA[
      a(x,y,z * K(u,w)) = a(x,y,z * K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,5467,a,b,5467,a)].">
      <j1 rule="hyper" parents="316 5467 5467"/>
    </justification>
  </clause>

  <clause id="5469">
    <literal><![CDATA[
      a(x,y,z * u) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(94(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="94 5467"/>
    </justification>
  </clause>

  <clause id="5470">
    <literal><![CDATA[
      a(x,y,(z \ u) * z) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(306(a,1),5467(a,1,3)),flip(a)].">
      <j1 rule="para" parents="306 5467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5472">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * (w * u)) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[para(455(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="455 5467"/>
    </justification>
  </clause>

  <clause id="5473">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * u) = a(x,y,u / (z \ 1))
    ]]></literal>
    <justification jstring="[para(1454(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="1454 5467"/>
    </justification>
  </clause>

  <clause id="5474">
    <literal><![CDATA[
      a(x,y,(z \ 1) * R(z,u,w)) = a(x,y,z \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(981(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="981 5467"/>
    </justification>
  </clause>

  <clause id="5475">
    <literal><![CDATA[
      a(x,y,(z * u) / z) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(2722(a,2),5467(a,1,3))].">
      <j1 rule="para" parents="2722 5467"/>
    </justification>
  </clause>

  <clause id="5476">
    <literal><![CDATA[
      a(x,y,T(z,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2733(a,1),5467(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2733 5467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5477">
    <literal><![CDATA[
      a(x,y,z / u) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(2732(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="2732 5467"/>
    </justification>
  </clause>

  <clause id="5478">
    <literal><![CDATA[
      a(x,y,z \ (u * z)) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(2825(a,2),5467(a,1,3))].">
      <j1 rule="para" parents="2825 5467"/>
    </justification>
  </clause>

  <clause id="5479">
    <literal><![CDATA[
      a(x,y,(z \ u) \ u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2819(a,2),5467(a,1,3))].">
      <j1 rule="para" parents="2819 5467"/>
    </justification>
  </clause>

  <clause id="5480">
    <literal><![CDATA[
      a(x,y,z * ((u * w) / u)) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(3148(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="3148 5467"/>
    </justification>
  </clause>

  <clause id="5481">
    <literal><![CDATA[
      a(x,y,z * (u / w)) = a(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[para(3151(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="3151 5467"/>
    </justification>
  </clause>

  <clause id="5482">
    <literal><![CDATA[
      a(x,y,z * T(u,w)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(3268(a,1),5467(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3268 5467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5483">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ w)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(3272(a,1),5467(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3272 5467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5484">
    <literal><![CDATA[
      a(x,y,K(z,u) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(3631(a,1),5467(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3631 5467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5485">
    <literal><![CDATA[
      a(x,y,T(z,u) * w) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(3638(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="3638 5467"/>
    </justification>
  </clause>

  <clause id="5487">
    <literal><![CDATA[
      a(x,y,z \ T(u,w)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(3846(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="3846 5467"/>
    </justification>
  </clause>

  <clause id="5488">
    <literal><![CDATA[
      a(x,y,z * (u * K(w,v5))) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(3763(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="3763 5467"/>
    </justification>
  </clause>

  <clause id="5489">
    <literal><![CDATA[
      a(x,y,z \ (u * K(w,v5))) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(3781(a,2),5467(a,1,3))].">
      <j1 rule="para" parents="3781 5467"/>
    </justification>
  </clause>

  <clause id="5490">
    <literal><![CDATA[
      a(x,y,z \ (u * w)) = a(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[para(3922(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="3922 5467"/>
    </justification>
  </clause>

  <clause id="5491">
    <literal><![CDATA[
      a(x,y,z * (u * w)) = a(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[para(3933(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="3933 5467"/>
    </justification>
  </clause>

  <clause id="5492">
    <literal><![CDATA[
      a(x,y,T(z,u) \ w) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(3882(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="3882 5467"/>
    </justification>
  </clause>

  <clause id="5493">
    <literal><![CDATA[
      a(x,y,z \ ((u \ w) \ w)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(3896(a,2),5467(a,1,3))].">
      <j1 rule="para" parents="3896 5467"/>
    </justification>
  </clause>

  <clause id="5494">
    <literal><![CDATA[
      a(x,y,z \ (u \ T(w,v5))) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(3912(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="3912 5467"/>
    </justification>
  </clause>

  <clause id="5495">
    <literal><![CDATA[
      a(x,y,z \ (u * T(w,v5))) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(3913(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="3913 5467"/>
    </justification>
  </clause>

  <clause id="5496">
    <literal><![CDATA[
      a(x,y,z \ (K(u,w) * v5)) = a(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(3914(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="3914 5467"/>
    </justification>
  </clause>

  <clause id="5497">
    <literal><![CDATA[
      a(x,y,z \ (u / w)) = a(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(3917(a,1),5467(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3917 5467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5500">
    <literal><![CDATA[
      a(x,y,z * (K(u,w) * v5)) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(3941(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="3941 5467"/>
    </justification>
  </clause>

  <clause id="5501">
    <literal><![CDATA[
      a(x,y,z * (u * T(w,v5))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(3942(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="3942 5467"/>
    </justification>
  </clause>

  <clause id="5502">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * K(v5,v6)))) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(3932(a,2),5467(a,1,3))].">
      <j1 rule="para" parents="3932 5467"/>
    </justification>
  </clause>

  <clause id="5503">
    <literal><![CDATA[
      a(x,y,L(T(z,u),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(4449(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="4449 5467"/>
    </justification>
  </clause>

  <clause id="5504">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((u * w) * z)) = a(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[para(3953(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="3953 5467"/>
    </justification>
  </clause>

  <clause id="5505">
    <literal><![CDATA[
      a(x,y,z * (u * (w / v5))) = a(x,y,z * (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(4028(a,1),5467(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4028 5467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5506">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * T(v5,v6)))) = a(x,y,z \ (u \ (w * v5)))
    ]]></literal>
    <justification jstring="[para(4033(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="4033 5467"/>
    </justification>
  </clause>

  <clause id="5507">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * (v5 / w)))) = a(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(4038(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="4038 5467"/>
    </justification>
  </clause>

  <clause id="5509">
    <literal><![CDATA[
      a(x,y,z \ (u * (K(w,v5) * v6))) = a(x,y,z \ (u * v6))
    ]]></literal>
    <justification jstring="[para(4046(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="4046 5467"/>
    </justification>
  </clause>

  <clause id="5510">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * T(v5,v6)))) = a(x,y,z \ (u * (w * v5)))
    ]]></literal>
    <justification jstring="[para(4049(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="4049 5467"/>
    </justification>
  </clause>

  <clause id="5511">
    <literal><![CDATA[
      a(x,y,((z \ u) * z) * w) = a(x,y,u * w)
    ]]></literal>
    <justification jstring="[para(4506(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="4506 5467"/>
    </justification>
  </clause>

  <clause id="5513">
    <literal><![CDATA[
      a(x,y,z * L(T(u,w),v5,v6)) = a(x,y,z * L(u,v5,v6))
    ]]></literal>
    <justification jstring="[para(4453(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="4453 5467"/>
    </justification>
  </clause>

  <clause id="5514">
    <literal><![CDATA[
      a(x,y,L(z * K(u,w),v5,v6)) = a(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(4837(a,2),5467(a,1,3))].">
      <j1 rule="para" parents="4837 5467"/>
    </justification>
  </clause>

  <clause id="5515">
    <literal><![CDATA[
      a(x,y,L(z / u,w,v5)) = a(x,y,L(u \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(4844(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="4844 5467"/>
    </justification>
  </clause>

  <clause id="5516">
    <literal><![CDATA[
      a(x,y,L(z * T(u,w),v5,v6)) = a(x,y,L(z * u,v5,v6))
    ]]></literal>
    <justification jstring="[para(4847(a,1),5467(a,1,3))].">
      <j1 rule="para" parents="4847 5467"/>
    </justification>
  </clause>

  <clause id="5517">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 * K(v6,v7))))) = a(x,y,z \ (u * (w * v5)))
    ]]></literal>
    <justification jstring="[para(4226(a,2),5467(a,1,3))].">
      <j1 rule="para" parents="4226 5467"/>
    </justification>
  </clause>

  <clause id="5518">
    <literal><![CDATA[
      T(a(x,y,z),u) = a(x,y,T(z,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,2286,a,b,5476,a)].">
      <j1 rule="hyper" parents="316 2286 5476"/>
    </justification>
  </clause>

  <clause id="5520">
    <literal><![CDATA[
      a(T(x,y),z,T(u,w)) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,1810,a(flip),b,5476,a),flip(a)].">
      <j1 rule="hyper" parents="316 1810 5476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5522">
    <literal><![CDATA[
      (L(x,y,z) * (y * z)) \ (x * (y * z)) = a(z,T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3298,a,b,5476,a)].">
      <j1 rule="hyper" parents="63 3298 5476"/>
    </justification>
  </clause>

  <clause id="5523">
    <literal><![CDATA[
      a(x,y,z) = ((x * y) * T(z,y)) / (x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,2337,a,b,5476,a),flip(a)].">
      <j1 rule="hyper" parents="63 2337 5476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5524">
    <literal><![CDATA[
      (x * (y * z)) * a(x,z,y) = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,5476,a(flip),b,244,a)].">
      <j1 rule="hyper" parents="139 5476 244"/>
    </justification>
  </clause>

  <clause id="5525">
    <literal><![CDATA[
      a(x,y,z \ (z * u)) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(2278(a,1),5476(a,1,3))].">
      <j1 rule="para" parents="2278 5476"/>
    </justification>
  </clause>

  <clause id="5526">
    <literal><![CDATA[
      a(x,y,L(z,u,K(w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2279(a,1),5476(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2279 5476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5527">
    <literal><![CDATA[
      a(x,y,z * K(u,z)) = a(x,y,L(z,u,z))
    ]]></literal>
    <justification jstring="[para(2747(a,1),5476(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2747 5476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5528">
    <literal><![CDATA[
      a(x,y,(z * u) * K(w,v5)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5467,a,b,5469,a)].">
      <j1 rule="hyper" parents="316 5467 5469"/>
    </justification>
  </clause>

  <clause id="5529">
    <literal><![CDATA[
      a(x,y,z * (u \ 1)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2651,a,b,5469,a)].">
      <j1 rule="hyper" parents="316 2651 5469"/>
    </justification>
  </clause>

  <clause id="5530">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * w))) = a(x,y,(w * w) * (z \ u))
    ]]></literal>
    <justification jstring="[para(388(a,2),5469(a,1,3))].">
      <j1 rule="para" parents="388 5469"/>
    </justification>
  </clause>

  <clause id="5531">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),v5,v6) * v7) = a(x,y,v7 * L(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(156(a,1),5469(a,1,3))].">
      <j1 rule="para" parents="156 5469"/>
    </justification>
  </clause>

  <clause id="5532">
    <literal><![CDATA[
      a(x,y,(z \ 1) * L(z,u,w)) = a(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(969(a,1),5469(a,1,3)),flip(a)].">
      <j1 rule="para" parents="969 5469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5533">
    <literal><![CDATA[
      a(x,y,(z * u) * L(L(z,w,v5),v6,v7)) = a(x,y,z * (L(L(z,w,v5),v6,v7) * u))
    ]]></literal>
    <justification jstring="[para(1844(a,1),5469(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1844 5469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5534">
    <literal><![CDATA[
      a(x,y,a(z,u,z) * ((w * v5) * v6)) = a(x,y,v6 * (w * (a(z,u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(5403(a,1),5469(a,1,3))].">
      <j1 rule="para" parents="5403 5469"/>
    </justification>
  </clause>

  <clause id="5535">
    <literal><![CDATA[
      a(x,y,L(z * u,w,v5)) = a(x,y,L(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(1360(a,1),5470(a,1,3))].">
      <j1 rule="para" parents="1360 5470"/>
    </justification>
  </clause>

  <clause id="5536">
    <literal><![CDATA[
      a(x,y,T(z / u,w)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5476,a,b,5477,a)].">
      <j1 rule="hyper" parents="63 5476 5477"/>
    </justification>
  </clause>

  <clause id="5539">
    <literal><![CDATA[
      a(x,y,(z / u) * L(z / u,w \ 1,w)) = a(x,y,a(w,w \ 1,u \ z))
    ]]></literal>
    <justification jstring="[para(5477(a,1),2659(a,2,3))].">
      <j1 rule="para" parents="5477 2659"/>
    </justification>
  </clause>

  <clause id="5540">
    <literal><![CDATA[
      a(x,y,K(z,u) * (w * v5)) = a(x,y,v5 * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,5484,a),flip(a)].">
      <j1 rule="hyper" parents="316 5469 5484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5541">
    <literal><![CDATA[
      a(x,y,(K(z,u) * w) * v5) = a(x,y,w * v5)
    ]]></literal>
    <justification jstring="[para(406(a,2),5484(a,1,3))].">
      <j1 rule="para" parents="406 5484"/>
    </justification>
  </clause>

  <clause id="5542">
    <literal><![CDATA[
      a(x,y,(z * u) * w) = a(x,y,(u * z) * w)
    ]]></literal>
    <justification jstring="[para(2759(a,1),5484(a,1,3))].">
      <j1 rule="para" parents="2759 5484"/>
    </justification>
  </clause>

  <clause id="5543">
    <literal><![CDATA[
      a(x,y,(z / u) * w) = a(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(2774(a,1),5484(a,1,3))].">
      <j1 rule="para" parents="2774 5484"/>
    </justification>
  </clause>

  <clause id="5545">
    <literal><![CDATA[
      a(x,y,(T(z,u) \ w) * v5) = a(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[para(2902(a,1),5484(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2902 5484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5546">
    <literal><![CDATA[
      a(x,y,(z / u) \ w) = a(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(3143(a,1),5484(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3143 5484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5547">
    <literal><![CDATA[
      a(x,y,((z / u) * w) * v5) = a(x,y,((u \ z) * w) * v5)
    ]]></literal>
    <justification jstring="[para(2777(a,1),5484(a,1,3))].">
      <j1 rule="para" parents="2777 5484"/>
    </justification>
  </clause>

  <clause id="5548">
    <literal><![CDATA[
      a(x,y,((T(z,u) \ w) * v5) * v6) = a(x,y,((z \ w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(2907(a,1),5484(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2907 5484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5549">
    <literal><![CDATA[
      a(x,y,((z / u) \ w) * v5) = a(x,y,((u \ z) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(3216(a,1),5484(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3216 5484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5551">
    <literal><![CDATA[
      a(x,y,(((z / u) \ w) * v5) * v6) = a(x,y,(((u \ z) \ w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(3224(a,1),5484(a,1,3))].">
      <j1 rule="para" parents="3224 5484"/>
    </justification>
  </clause>

  <clause id="5552">
    <literal><![CDATA[
      a(x,y,(L(T(z,u),w,v5) * v6) * v7) = a(x,y,(L(z,w,v5) * v6) * v7)
    ]]></literal>
    <justification jstring="[para(3415(a,1),5484(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3415 5484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5553">
    <literal><![CDATA[
      a(x,y,(z * T(u,w)) * v5) = a(x,y,(z * u) * v5)
    ]]></literal>
    <justification jstring="[para(4166(a,1),5484(a,1,3))].">
      <j1 rule="para" parents="4166 5484"/>
    </justification>
  </clause>

  <clause id="5554">
    <literal><![CDATA[
      a(x,y,L(K(z,u) * w,v5,v6)) = a(x,y,L(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(4850(a,2),5484(a,1,3))].">
      <j1 rule="para" parents="4850 5484"/>
    </justification>
  </clause>

  <clause id="5555">
    <literal><![CDATA[
      a(x,y,(L(T(z,u),w,v5) \ v6) * v7) = a(x,y,(L(z,w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[para(4450(a,1),5484(a,1,3))].">
      <j1 rule="para" parents="4450 5484"/>
    </justification>
  </clause>

  <clause id="5556">
    <literal><![CDATA[
      a(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(5518(a,1),193(a,1)),flip(b)].">
      <j1 rule="para" parents="5518 193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5557">
    <literal><![CDATA[
      a(x,y,L(z,u,w * v5)) = a(x,y,L(z,u,v5 * w))
    ]]></literal>
    <justification jstring="[para(1673(a,1),5526(a,1,3))].">
      <j1 rule="para" parents="1673 5526"/>
    </justification>
  </clause>

  <clause id="5558">
    <literal><![CDATA[
      a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(T(x,w),y,z) = u
    ]]></literal>
    <justification jstring="[para(5520(a,1),5556(a,1))].">
      <j1 rule="para" parents="5520 5556"/>
    </justification>
  </clause>

  <clause id="5560">
    <literal><![CDATA[
      a(x,y,z * L(u / w,v5,v6)) = a(x,y,z * L(w \ u,v5,v6))
    ]]></literal>
    <justification jstring="[para(261(a,1),5482(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="261 5482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5562">
    <literal><![CDATA[
      a(x,y,L(z / u,w,v5) * v6) = a(x,y,L(u \ z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(261(a,1),5485(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="261 5485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5564">
    <literal><![CDATA[
      a(x,y,(z \ 1) * u) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,5529,a)].">
      <j1 rule="hyper" parents="63 5469 5529"/>
    </justification>
  </clause>

  <clause id="5565">
    <literal><![CDATA[
      x \ R(x,y * (z \ 1),y * z) = a(x,y * (z \ 1),z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2385,a(flip),b,5529,a)].">
      <j1 rule="hyper" parents="63 2385 5529"/>
    </justification>
  </clause>

  <clause id="5566">
    <literal><![CDATA[
      a(x,y,z \ L(z,u,w)) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(969(a,1),5529(a,1,3))].">
      <j1 rule="para" parents="969 5529"/>
    </justification>
  </clause>

  <clause id="5567">
    <literal><![CDATA[
      a(x,y,z \ R(z,u,w)) = a(x,y,z * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(978(a,1),5529(a,1,3))].">
      <j1 rule="para" parents="978 5529"/>
    </justification>
  </clause>

  <clause id="5568">
    <literal><![CDATA[
      a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(x,y,(z \ (u \ w)) * ((u * z) \ w))
    ]]></literal>
    <justification jstring="[para(1800(a,1),5529(a,1,3))].">
      <j1 rule="para" parents="1800 5529"/>
    </justification>
  </clause>

  <clause id="5569">
    <literal><![CDATA[
      a(x,y,z \ (u * (z * z))) = a(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(580(a,1),5536(a,1,3))].">
      <j1 rule="para" parents="580 5536"/>
    </justification>
  </clause>

  <clause id="5570">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((z * w) * u)) = a(x,y,R(w,z,u))
    ]]></literal>
    <justification jstring="[para(734(a,2),5536(a,1,3)),flip(a)].">
      <j1 rule="para" parents="734 5536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5571">
    <literal><![CDATA[
      R(x,(y \ 1) * z,(y \ 1) * z) = x * a(x,(y \ 1) * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,5564,a(flip),b,2380,a),flip(a)].">
      <j1 rule="hyper" parents="139 5564 2380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5572">
    <literal><![CDATA[
      a(x,y,(1 / z) * u) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(83(a,1),5564(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="83 5564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5573">
    <literal><![CDATA[
      a(x,y,z * R(z,u,u)) = a(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(2379(a,1),5572(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2379 5572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5574">
    <literal><![CDATA[
      a(x,y,L(z,u,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5467,a(flip),b,5527,a),flip(a)].">
      <j1 rule="hyper" parents="63 5467 5527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5576">
    <literal><![CDATA[
      a(x,y,R(z,u,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(4636(a,1),5574(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4636 5574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5577">
    <literal><![CDATA[
      a(x,y,R(z \ (u \ z),w,u)) = a(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[para(4783(a,1),5576(a,1,3))].">
      <j1 rule="para" parents="4783 5576"/>
    </justification>
  </clause>

  <clause id="5578">
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * K(v5,v6)) = a(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[para(3922(a,1),5468(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3922 5468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5580">
    <literal><![CDATA[
      a(x,y,z * (u / (w * (v5 * v5)))) = a(x,y,z * (w \ (u / (v5 * v5))))
    ]]></literal>
    <justification jstring="[para(393(a,1),5481(a,1,3,2))].">
      <j1 rule="para" parents="393 5481"/>
    </justification>
  </clause>

  <clause id="5581">
    <literal><![CDATA[
      a(x,y,z * ((u * u) \ (w \ v5))) = a(x,y,z * (w \ (v5 / (u * u))))
    ]]></literal>
    <justification jstring="[para(675(a,1),5481(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="675 5481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5583">
    <literal><![CDATA[
      a(x,y,z * R(u * K(w,u),w,v5)) = a(x,y,z * ((w * v5) \ ((w * u) * v5)))
    ]]></literal>
    <justification jstring="[para(2746(a,2),5481(a,1,3,2))].">
      <j1 rule="para" parents="2746 5481"/>
    </justification>
  </clause>

  <clause id="5584">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ w)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,5483,a),flip(a)].">
      <j1 rule="hyper" parents="316 5469 5483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5585">
    <literal><![CDATA[
      a(x,y,z * (u * K(w,v5))) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,5488,a),flip(a)].">
      <j1 rule="hyper" parents="316 5469 5488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5586">
    <literal><![CDATA[
      a(x,y,(z * K(u,w)) * v5) = a(x,y,v5 * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,5488,a)].">
      <j1 rule="hyper" parents="63 5469 5488"/>
    </justification>
  </clause>

  <clause id="5587">
    <literal><![CDATA[
      a(x,y,z * (u * ((w \ v5) \ v5))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(3272(a,1),5488(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3272 5488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5588">
    <literal><![CDATA[
      a(x,y,z * (u \ T(w,v5))) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[para(3846(a,1),5488(a,1,3,2))].">
      <j1 rule="para" parents="3846 5488"/>
    </justification>
  </clause>

  <clause id="5589">
    <literal><![CDATA[
      a(x,y,z * (u * (w * v5))) = a(x,y,z * (u * (v5 * w)))
    ]]></literal>
    <justification jstring="[para(3933(a,1),5488(a,1,3,2))].">
      <j1 rule="para" parents="3933 5488"/>
    </justification>
  </clause>

  <clause id="5590">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * T(v5,v6)))) = a(x,y,z * (u \ (w * v5)))
    ]]></literal>
    <justification jstring="[para(3913(a,1),5488(a,1,3,2))].">
      <j1 rule="para" parents="3913 5488"/>
    </justification>
  </clause>

  <clause id="5591">
    <literal><![CDATA[
      a(x,y,z * (u \ (w / v5))) = a(x,y,z * (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(3917(a,1),5488(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3917 5488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5592">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ K(v5,v6)))) = a(x,y,z * (u * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(3940(a,1),5488(a,1,3,2))].">
      <j1 rule="para" parents="3940 5488"/>
    </justification>
  </clause>

  <clause id="5593">
    <literal><![CDATA[
      a(x,y,z * (u * (K(w,v5) * v6))) = a(x,y,z * (u * v6))
    ]]></literal>
    <justification jstring="[para(3941(a,1),5488(a,1,3,2))].">
      <j1 rule="para" parents="3941 5488"/>
    </justification>
  </clause>

  <clause id="5594">
    <literal><![CDATA[
      a(x,y,z * (u * (w * T(v5,v6)))) = a(x,y,z * (u * (w * v5)))
    ]]></literal>
    <justification jstring="[para(3942(a,1),5488(a,1,3,2))].">
      <j1 rule="para" parents="3942 5488"/>
    </justification>
  </clause>

  <clause id="5595">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ ((w * v5) * u))) = a(x,y,z * L(v5,w,u))
    ]]></literal>
    <justification jstring="[para(3953(a,1),5488(a,1,3,2))].">
      <j1 rule="para" parents="3953 5488"/>
    </justification>
  </clause>

  <clause id="5596">
    <literal><![CDATA[
      a(x,y,z * R(u * K(w,v5),v6,v7)) = a(x,y,z * R(u,v6,v7))
    ]]></literal>
    <justification jstring="[para(4604(a,2),5488(a,1,3,2))].">
      <j1 rule="para" parents="4604 5488"/>
    </justification>
  </clause>

  <clause id="5597">
    <literal><![CDATA[
      a(x,y,z * L(u * K(w,v5),v6,v7)) = a(x,y,z * L(u,v6,v7))
    ]]></literal>
    <justification jstring="[para(4837(a,2),5488(a,1,3,2))].">
      <j1 rule="para" parents="4837 5488"/>
    </justification>
  </clause>

  <clause id="5598">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,v5) * (v5 * w))) = a(x,y,z \ (v5 * (w * u)))
    ]]></literal>
    <justification jstring="[para(455(a,1),5489(a,1,3,2))].">
      <j1 rule="para" parents="455 5489"/>
    </justification>
  </clause>

  <clause id="5599">
    <literal><![CDATA[
      a(x,y,z \ (u * (w / v5))) = a(x,y,z \ (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(3151(a,1),5489(a,1,3,2))].">
      <j1 rule="para" parents="3151 5489"/>
    </justification>
  </clause>

  <clause id="5600">
    <literal><![CDATA[
      a(x,y,z \ (T(u,w) * v5)) = a(x,y,z \ (u * v5))
    ]]></literal>
    <justification jstring="[para(3638(a,1),5489(a,1,3,2))].">
      <j1 rule="para" parents="3638 5489"/>
    </justification>
  </clause>

  <clause id="5601">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * K(v5,v6)))) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(3781(a,2),5489(a,1,3,2))].">
      <j1 rule="para" parents="3781 5489"/>
    </justification>
  </clause>

  <clause id="5602">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * v5))) = a(x,y,z \ (u \ (v5 * w)))
    ]]></literal>
    <justification jstring="[para(3922(a,1),5489(a,1,3,2))].">
      <j1 rule="para" parents="3922 5489"/>
    </justification>
  </clause>

  <clause id="5603">
    <literal><![CDATA[
      a(x,y,z \ (T(u,w) \ v5)) = a(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(3882(a,1),5489(a,1,3,2))].">
      <j1 rule="para" parents="3882 5489"/>
    </justification>
  </clause>

  <clause id="5604">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ T(v5,v6)))) = a(x,y,z \ (u \ (w \ v5)))
    ]]></literal>
    <justification jstring="[para(3912(a,1),5489(a,1,3,2))].">
      <j1 rule="para" parents="3912 5489"/>
    </justification>
  </clause>

  <clause id="5605">
    <literal><![CDATA[
      a(x,y,z \ (u \ (K(w,v5) * v6))) = a(x,y,z \ (u \ v6))
    ]]></literal>
    <justification jstring="[para(3914(a,1),5489(a,1,3,2))].">
      <j1 rule="para" parents="3914 5489"/>
    </justification>
  </clause>

  <clause id="5606">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w / v5))) = a(x,y,z \ (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(3917(a,1),5489(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3917 5489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5607">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w \ v5) * w))) = a(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(3921(a,1),5489(a,1,3,2))].">
      <j1 rule="para" parents="3921 5489"/>
    </justification>
  </clause>

  <clause id="5608">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w \ v5) * w))) = a(x,y,z \ (u * v5))
    ]]></literal>
    <justification jstring="[para(3934(a,1),5489(a,1,3,2))].">
      <j1 rule="para" parents="3934 5489"/>
    </justification>
  </clause>

  <clause id="5609">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 / v6)))) = a(x,y,z \ (u * (w * (v6 \ v5))))
    ]]></literal>
    <justification jstring="[para(4028(a,1),5489(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="4028 5489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5610">
    <literal><![CDATA[
      a(x,y,(z * u) / w) = a(x,y,w \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5477,a,b,5490,a)].">
      <j1 rule="hyper" parents="316 5477 5490"/>
    </justification>
  </clause>

  <clause id="5611">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) * (w * v5))) = a(x,y,z \ (w * (v5 * (u * u))))
    ]]></literal>
    <justification jstring="[para(32(a,1),5490(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="32 5490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5612">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,w)) = a(x,y,(w * z) \ (u * w))
    ]]></literal>
    <justification jstring="[para(102(a,2),5490(a,1,3))].">
      <j1 rule="para" parents="102 5490"/>
    </justification>
  </clause>

  <clause id="5614">
    <literal><![CDATA[
      a(x,y,(z * z) \ (u * z)) = a(x,y,L(z \ u,z,z))
    ]]></literal>
    <justification jstring="[para(820(a,1),5490(a,1,3)),flip(a)].">
      <j1 rule="para" parents="820 5490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5615">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * (1 / u))) = a(x,y,z \ L(w,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(890(a,1),5490(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="890 5490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5617">
    <literal><![CDATA[
      a(x,y,z \ (K(u,w) * (R(v5,v6,v7) * v8))) = a(x,y,z \ (v8 * R(K(u,w) * v5,v6,v7)))
    ]]></literal>
    <justification jstring="[para(1029(a,1),5490(a,1,3,2))].">
      <j1 rule="para" parents="1029 5490"/>
    </justification>
  </clause>

  <clause id="5619">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) * ((u * w) \ w))) = a(x,y,z \ ((w / (u \ 1)) / w))
    ]]></literal>
    <justification jstring="[para(3302(a,1),5490(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3302 5490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5622">
    <literal><![CDATA[
      a(x,y,z \ (K(u,w) * (L(v5,v6,v7) * v8))) = a(x,y,z \ (v8 * L(K(u,w) * v5,v6,v7)))
    ]]></literal>
    <justification jstring="[para(4856(a,1),5490(a,1,3,2))].">
      <j1 rule="para" parents="4856 5490"/>
    </justification>
  </clause>

  <clause id="5623">
    <literal><![CDATA[
      a(x,y,(z * u) * w) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,5491,a)].">
      <j1 rule="hyper" parents="316 5469 5491"/>
    </justification>
  </clause>

  <clause id="5624">
    <literal><![CDATA[
      a(x,y,(K(z,u) * w) \ v5) = a(x,y,w \ v5)
    ]]></literal>
    <justification jstring="[para(477(a,1),5496(a,1,3)),flip(a)].">
      <j1 rule="para" parents="477 5496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5626">
    <literal><![CDATA[
      a(x,y,(z * u) \ w) = a(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[para(2765(a,1),5496(a,1,3))].">
      <j1 rule="para" parents="2765 5496"/>
    </justification>
  </clause>

  <clause id="5627">
    <literal><![CDATA[
      a(x,y,z \ ((u / w) * v5)) = a(x,y,z \ ((w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(2774(a,1),5496(a,1,3,2))].">
      <j1 rule="para" parents="2774 5496"/>
    </justification>
  </clause>

  <clause id="5628">
    <literal><![CDATA[
      a(x,y,((z \ u) * z) \ w) = a(x,y,u \ w)
    ]]></literal>
    <justification jstring="[para(2785(a,1),5496(a,1,3))].">
      <j1 rule="para" parents="2785 5496"/>
    </justification>
  </clause>

  <clause id="5629">
    <literal><![CDATA[
      a(x,y,z \ ((u / w) \ v5)) = a(x,y,z \ ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(3143(a,1),5496(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3143 5496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5630">
    <literal><![CDATA[
      a(x,y,z \ (((u / w) * v5) * v6)) = a(x,y,z \ (((w \ u) * v5) * v6))
    ]]></literal>
    <justification jstring="[para(2777(a,1),5496(a,1,3,2))].">
      <j1 rule="para" parents="2777 5496"/>
    </justification>
  </clause>

  <clause id="5631">
    <literal><![CDATA[
      a(x,y,((z / u) * w) \ v5) = a(x,y,((u \ z) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(3176(a,1),5496(a,1,3))].">
      <j1 rule="para" parents="3176 5496"/>
    </justification>
  </clause>

  <clause id="5632">
    <literal><![CDATA[
      a(x,y,((T(z,u) * w) * v5) \ v6) = a(x,y,((z * w) * v5) \ v6)
    ]]></literal>
    <justification jstring="[para(3183(a,1),5496(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3183 5496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5633">
    <literal><![CDATA[
      a(x,y,z \ (((u / w) \ v5) * v6)) = a(x,y,z \ (((w \ u) \ v5) * v6))
    ]]></literal>
    <justification jstring="[para(3216(a,1),5496(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3216 5496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5635">
    <literal><![CDATA[
      a(x,y,z \ (L(T(u,w),v5,v6) * v7)) = a(x,y,z \ (L(u,v5,v6) * v7))
    ]]></literal>
    <justification jstring="[para(3020(a,1),5496(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3020 5496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5636">
    <literal><![CDATA[
      a(x,y,(z * K(u,w)) \ v5) = a(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(4150(a,1),5496(a,1,3))].">
      <j1 rule="para" parents="4150 5496"/>
    </justification>
  </clause>

  <clause id="5637">
    <literal><![CDATA[
      a(x,y,z \ (u / (w / (v5 * v5)))) = a(x,y,z \ (w \ (u * (v5 * v5))))
    ]]></literal>
    <justification jstring="[para(676(a,1),5497(a,1,3,2))].">
      <j1 rule="para" parents="676 5497"/>
    </justification>
  </clause>

  <clause id="5638">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) \ (w * v5))) = a(x,y,z \ (w * (v5 / (u * u))))
    ]]></literal>
    <justification jstring="[para(683(a,1),5497(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="683 5497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5639">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ (w * (v5 * (u \ 1))))) = a(x,y,z \ ((w * (v5 * u)) / u))
    ]]></literal>
    <justification jstring="[para(964(a,1),5497(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="964 5497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5640">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) = a(x,y,u \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(1447(a,2),5497(a,1,3))].">
      <j1 rule="para" parents="1447 5497"/>
    </justification>
  </clause>

  <clause id="5641">
    <literal><![CDATA[
      a(x,y,z \ ((u \ w) * (L(u \ w,v5,v6) \ u))) = a(x,y,z \ (L(u \ w,v5,v6) \ w))
    ]]></literal>
    <justification jstring="[para(4391(a,2),5497(a,1,3,2))].">
      <j1 rule="para" parents="4391 5497"/>
    </justification>
  </clause>

  <clause id="5642">
    <literal><![CDATA[
      a(x,y,z * ((u / w) * v5)) = a(x,y,z * ((w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(2774(a,1),5500(a,1,3,2))].">
      <j1 rule="para" parents="2774 5500"/>
    </justification>
  </clause>

  <clause id="5643">
    <literal><![CDATA[
      a(x,y,z * ((u / w) \ v5)) = a(x,y,z * ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(3143(a,1),5500(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3143 5500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5644">
    <literal><![CDATA[
      a(x,y,z * ((u * T(w,v5)) * v6)) = a(x,y,z * ((u * w) * v6))
    ]]></literal>
    <justification jstring="[para(4166(a,1),5500(a,1,3,2))].">
      <j1 rule="para" parents="4166 5500"/>
    </justification>
  </clause>

  <clause id="5645">
    <literal><![CDATA[
      a(x,y,L(L(z / u,w,v5),v6,v7)) = a(x,y,L(L(u \ z,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(261(a,1),5503(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="261 5503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5646">
    <literal><![CDATA[
      a(x,y,L((z * z) \ (u * z),w,v5)) = a(x,y,L(u * (z \ 1),w,v5))
    ]]></literal>
    <justification jstring="[para(577(a,1),5503(a,1,3,1))].">
      <j1 rule="para" parents="577 5503"/>
    </justification>
  </clause>

  <clause id="5647">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * (w * u)) * v5) = a(x,y,(w * (u * z)) * v5)
    ]]></literal>
    <justification jstring="[para(18(a,2),5511(a,1,3,1,1))].">
      <j1 rule="para" parents="18 5511"/>
    </justification>
  </clause>

  <clause id="5650">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) * u) * w) = a(x,y,(u / (z \ 1)) * w)
    ]]></literal>
    <justification jstring="[para(1447(a,2),5511(a,1,3,1,1))].">
      <j1 rule="para" parents="1447 5511"/>
    </justification>
  </clause>

  <clause id="5651">
    <literal><![CDATA[
      a(x,y,z * (u * T(w,v5))) = a(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[para(3942(a,1),5528(a,1,3))].">
      <j1 rule="para" parents="3942 5528"/>
    </justification>
  </clause>

  <clause id="5652">
    <literal><![CDATA[
      a(x,y,z * L(u \ K(w,v5),v6,v7)) = a(x,y,L(u \ 1,v6,v7) * z)
    ]]></literal>
    <justification jstring="[para(4867(a,1),5528(a,1,3))].">
      <j1 rule="para" parents="4867 5528"/>
    </justification>
  </clause>

  <clause id="5653">
    <literal><![CDATA[
      a(x,y,R(T(z,u),w,v5) * v6) = a(x,y,v6 * R(z,w,v5))
    ]]></literal>
    <justification jstring="[para(2813(a,1),5540(a,1,3))].">
      <j1 rule="para" parents="2813 5540"/>
    </justification>
  </clause>

  <clause id="5654">
    <literal><![CDATA[
      a(x,y,L(z * u,w,v5) * v6) = a(x,y,v6 * L(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(4878(a,1),5540(a,1,3))].">
      <j1 rule="para" parents="4878 5540"/>
    </justification>
  </clause>

  <clause id="5655">
    <literal><![CDATA[
      a(x,y,(((z / u) * w) * v5) * v6) = a(x,y,(((u \ z) * w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(2777(a,1),5541(a,1,3,1))].">
      <j1 rule="para" parents="2777 5541"/>
    </justification>
  </clause>

  <clause id="5656">
    <literal><![CDATA[
      a(x,y,(z * K(u,w)) * v5) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(3622(a,1),5541(a,1,3,1))].">
      <j1 rule="para" parents="3622 5541"/>
    </justification>
  </clause>

  <clause id="5657">
    <literal><![CDATA[
      a(x,y,(z / u) * L(u \ z,w \ 1,w)) = a(x,y,a(w,w \ 1,u \ z))
    ]]></literal>
    <justification jstring="[hyper(316,a,2659,a(flip),b,5543,a),flip(a)].">
      <j1 rule="hyper" parents="316 2659 5543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5658">
    <literal><![CDATA[
      a(x,y,(z / (u * (w * w))) * v5) = a(x,y,(u \ (z / (w * w))) * v5)
    ]]></literal>
    <justification jstring="[para(393(a,1),5543(a,1,3,1))].">
      <j1 rule="para" parents="393 5543"/>
    </justification>
  </clause>

  <clause id="5660">
    <literal><![CDATA[
      a(x,y,(z / (u / (w * w))) * v5) = a(x,y,(u \ (z * (w * w))) * v5)
    ]]></literal>
    <justification jstring="[para(676(a,1),5543(a,1,3,1))].">
      <j1 rule="para" parents="676 5543"/>
    </justification>
  </clause>

  <clause id="5662">
    <literal><![CDATA[
      a(x,y,(z \ L(u,z,z)) * w) = a(x,y,(u / R(z,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(4657(a,1),5543(a,2,3,1)),flip(a)].">
      <j1 rule="para" parents="4657 5543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5663">
    <literal><![CDATA[
      a(x,y,(z \ K(u,w)) * v5) = a(x,y,v5 * (z \ 1))
    ]]></literal>
    <justification jstring="[para(3828(a,1),5585(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3828 5585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5664">
    <literal><![CDATA[
      a(x,y,z * (u \ T(w,v5))) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[para(3846(a,1),5585(a,1,3,2))].">
      <j1 rule="para" parents="3846 5585"/>
    </justification>
  </clause>

  <clause id="5665">
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * v5) = a(x,y,v5 * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[para(3922(a,1),5585(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3922 5585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5666">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * v5) = a(x,y,v5 * (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(3933(a,1),5585(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3933 5585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5667">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ ((w * v5) * u))) = a(x,y,L(v5,w,u) * z)
    ]]></literal>
    <justification jstring="[para(3953(a,1),5585(a,1,3,2))].">
      <j1 rule="para" parents="3953 5585"/>
    </justification>
  </clause>

  <clause id="5668">
    <literal><![CDATA[
      a(x,y,z * (u * (w * (v5 * K(v6,v7))))) = a(x,y,(u * (w * v5)) * z)
    ]]></literal>
    <justification jstring="[para(4445(a,1),5585(a,1,3,2))].">
      <j1 rule="para" parents="4445 5585"/>
    </justification>
  </clause>

  <clause id="5669">
    <literal><![CDATA[
      a(x,y,z * (u * L(T(w,v5),v6,v7))) = a(x,y,(u * L(w,v6,v7)) * z)
    ]]></literal>
    <justification jstring="[para(4453(a,1),5585(a,1,3,2))].">
      <j1 rule="para" parents="4453 5585"/>
    </justification>
  </clause>

  <clause id="5670">
    <literal><![CDATA[
      a(x,y,(z \ ((u \ w) * u)) * v5) = a(x,y,v5 * (z \ w))
    ]]></literal>
    <justification jstring="[para(3921(a,1),5586(a,1,3,1))].">
      <j1 rule="para" parents="3921 5586"/>
    </justification>
  </clause>

  <clause id="5671">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,w) \ (u * w)) = a(x,y,w * z)
    ]]></literal>
    <justification jstring="[para(449(a,1),5610(a,1,3)),flip(a)].">
      <j1 rule="para" parents="449 5610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5674">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * (u * w)) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[para(100(a,1),5623(a,1,3)),flip(a)].">
      <j1 rule="para" parents="100 5623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5676">
    <literal><![CDATA[
      a(x,y,(z * u) * L(z,w,v5)) = a(x,y,z * (u * L(z,w,v5)))
    ]]></literal>
    <justification jstring="[para(4398(a,1),5623(a,2,3))].">
      <j1 rule="para" parents="4398 5623"/>
    </justification>
  </clause>

  <clause id="5677">
    <literal><![CDATA[
      a(x,y,(z * T(u,w)) \ v5) = a(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(3128(a,1),5624(a,1,3,1))].">
      <j1 rule="para" parents="3128 5624"/>
    </justification>
  </clause>

  <clause id="5679">
    <literal><![CDATA[
      a(x,y,z / (u * w)) = a(x,y,(w * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5477,a,b,5626,a)].">
      <j1 rule="hyper" parents="316 5477 5626"/>
    </justification>
  </clause>

  <clause id="5682">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (u * z)) \ w) = a(x,y,R(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(565(a,1),5626(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="565 5626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5683">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (u / z)) \ w) = a(x,y,(u / (z * z)) \ w)
    ]]></literal>
    <justification jstring="[para(566(a,1),5626(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="566 5626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5684">
    <literal><![CDATA[
      a(x,y,(z * (u / w)) \ v5) = a(x,y,(z * (w \ u)) \ v5)
    ]]></literal>
    <justification jstring="[para(3151(a,1),5636(a,1,3,1))].">
      <j1 rule="para" parents="3151 5636"/>
    </justification>
  </clause>

  <clause id="5685">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) \ v5) = a(x,y,(z * (w * u)) \ v5)
    ]]></literal>
    <justification jstring="[para(3933(a,1),5636(a,1,3,1))].">
      <j1 rule="para" parents="3933 5636"/>
    </justification>
  </clause>

  <clause id="5686">
    <literal><![CDATA[
      a(x,y,(z * (u \ K(w,v5))) \ v6) = a(x,y,(z * (u \ 1)) \ v6)
    ]]></literal>
    <justification jstring="[para(3940(a,1),5636(a,1,3,1))].">
      <j1 rule="para" parents="3940 5636"/>
    </justification>
  </clause>

  <clause id="5687">
    <literal><![CDATA[
      a(x,y,(z * (K(u,w) * v5)) \ v6) = a(x,y,(z * v5) \ v6)
    ]]></literal>
    <justification jstring="[para(3941(a,1),5636(a,1,3,1))].">
      <j1 rule="para" parents="3941 5636"/>
    </justification>
  </clause>

  <clause id="5688">
    <literal><![CDATA[
      a(x,y,(z * L(T(u,w),v5,v6)) \ v7) = a(x,y,(z * L(u,v5,v6)) \ v7)
    ]]></literal>
    <justification jstring="[para(4453(a,1),5636(a,1,3,1))].">
      <j1 rule="para" parents="4453 5636"/>
    </justification>
  </clause>

  <clause id="5689">
    <literal><![CDATA[
      a(x,y,(z * (u / w)) * v5) = a(x,y,(z * (w \ u)) * v5)
    ]]></literal>
    <justification jstring="[para(3151(a,1),5656(a,1,3,1))].">
      <j1 rule="para" parents="3151 5656"/>
    </justification>
  </clause>

  <clause id="5690">
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * v5) = a(x,y,(z \ (w * u)) * v5)
    ]]></literal>
    <justification jstring="[para(3922(a,1),5656(a,1,3,1))].">
      <j1 rule="para" parents="3922 5656"/>
    </justification>
  </clause>

  <clause id="5691">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * v5) = a(x,y,(z * (w * u)) * v5)
    ]]></literal>
    <justification jstring="[para(3933(a,1),5656(a,1,3,1))].">
      <j1 rule="para" parents="3933 5656"/>
    </justification>
  </clause>

  <clause id="5692">
    <literal><![CDATA[
      a(x,y,(z \ (u * T(w,v5))) * v6) = a(x,y,(z \ (u * w)) * v6)
    ]]></literal>
    <justification jstring="[para(3913(a,1),5656(a,1,3,1))].">
      <j1 rule="para" parents="3913 5656"/>
    </justification>
  </clause>

  <clause id="5693">
    <literal><![CDATA[
      a(x,y,(z \ (K(u,w) * v5)) * v6) = a(x,y,(z \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(3914(a,1),5656(a,1,3,1))].">
      <j1 rule="para" parents="3914 5656"/>
    </justification>
  </clause>

  <clause id="5694">
    <literal><![CDATA[
      a(x,y,(z \ (u / w)) * v5) = a(x,y,(z \ (w \ u)) * v5)
    ]]></literal>
    <justification jstring="[para(3917(a,1),5656(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="3917 5656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5695">
    <literal><![CDATA[
      a(x,y,(z * (K(u,w) * v5)) * v6) = a(x,y,(z * v5) * v6)
    ]]></literal>
    <justification jstring="[para(3941(a,1),5656(a,1,3,1))].">
      <j1 rule="para" parents="3941 5656"/>
    </justification>
  </clause>

  <clause id="5696">
    <literal><![CDATA[
      a(x,y,(z * (u * T(w,v5))) * v6) = a(x,y,(z * (u * w)) * v6)
    ]]></literal>
    <justification jstring="[para(3942(a,1),5656(a,1,3,1))].">
      <j1 rule="para" parents="3942 5656"/>
    </justification>
  </clause>

  <clause id="5697">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((w * u) * z)) = a(x,y,R(w,u,z))
    ]]></literal>
    <justification jstring="[para(20(a,2),5679(a,1,3)),flip(a)].">
      <j1 rule="para" parents="20 5679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5698">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * u) = a(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,5477,a(flip),b,5473,a),flip(a)].">
      <j1 rule="hyper" parents="316 5477 5473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5700">
    <literal><![CDATA[
      T(x,y \ 1) / (y * (x * (y \ 1))) = a(y,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(71(a,1),5523(a,2,1)),flip(a)].">
      <j1 rule="para" parents="71 5523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5701">
    <literal><![CDATA[
      (((a(x,y,z) * a(u,w,v5)) * v6) * T(v7,v6)) / ((v7 * v6) * (a(u,w,v5) * a(x,y,z))) = a(a(x,y,z) * a(u,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(5349(a,1),5523(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5349 5523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5702">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ ((w * u) * T(z,u))) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(5523(a,2),5679(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5523 5679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5704">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w \ v5) * (w * w)))) = a(x,y,z \ (u \ (v5 / (w \ 1))))
    ]]></literal>
    <justification jstring="[para(613(a,1),5494(a,1,3,2,2))].">
      <j1 rule="para" parents="613 5494"/>
    </justification>
  </clause>

  <clause id="5705">
    <literal><![CDATA[
      a(x,y,z * (u * L(w / v5,v6,v7))) = a(x,y,z * (u * L(v5 \ w,v6,v7)))
    ]]></literal>
    <justification jstring="[para(261(a,1),5501(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="261 5501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5707">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) * K(v5,v6),v7,v8)) = a(x,y,L(L(z,v7,v8),u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),5514(a,2,3))].">
      <j1 rule="para" parents="30 5514"/>
    </justification>
  </clause>

  <clause id="5708">
    <literal><![CDATA[
      a(x,y,L(z \ T(u,w),v5,v6)) = a(x,y,L(z \ u,v5,v6))
    ]]></literal>
    <justification jstring="[para(3846(a,1),5514(a,1,3,1))].">
      <j1 rule="para" parents="3846 5514"/>
    </justification>
  </clause>

  <clause id="5709">
    <literal><![CDATA[
      a(x,y,L(z * (u * w),v5,v6)) = a(x,y,L(z * (w * u),v5,v6))
    ]]></literal>
    <justification jstring="[para(3933(a,1),5514(a,1,3,1))].">
      <j1 rule="para" parents="3933 5514"/>
    </justification>
  </clause>

  <clause id="5710">
    <literal><![CDATA[
      a(x,y,L(z \ (u / w),v5,v6)) = a(x,y,L(z \ (w \ u),v5,v6))
    ]]></literal>
    <justification jstring="[para(3917(a,1),5514(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="3917 5514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5711">
    <literal><![CDATA[
      a(x,y,L(z * ((u \ w) * u),v5,v6)) = a(x,y,L(z * w,v5,v6))
    ]]></literal>
    <justification jstring="[para(3934(a,1),5514(a,1,3,1))].">
      <j1 rule="para" parents="3934 5514"/>
    </justification>
  </clause>

  <clause id="5712">
    <literal><![CDATA[
      a(x,y,L(z * (u * (w / v5)),v6,v7)) = a(x,y,L(z * (u * (v5 \ w)),v6,v7))
    ]]></literal>
    <justification jstring="[para(4028(a,1),5514(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4028 5514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5713">
    <literal><![CDATA[
      a(x,y,L(z * (u * (w * K(v5,v6))),v7,v8)) = a(x,y,L(z * (u * w),v7,v8))
    ]]></literal>
    <justification jstring="[para(4445(a,1),5514(a,1,3,1))].">
      <j1 rule="para" parents="4445 5514"/>
    </justification>
  </clause>

  <clause id="5715">
    <literal><![CDATA[
      a(x,y,(((z * z) \ (u * z)) \ w) * v5) = a(x,y,((u * (z \ 1)) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(577(a,1),5545(a,1,3,1,1))].">
      <j1 rule="para" parents="577 5545"/>
    </justification>
  </clause>

  <clause id="5716">
    <literal><![CDATA[
      a(x,y,L(K(z,u) * L(w,v5,v6),v7,v8)) = a(x,y,L(L(w,v7,v8),v5,v6))
    ]]></literal>
    <justification jstring="[para(30(a,1),5554(a,2,3))].">
      <j1 rule="para" parents="30 5554"/>
    </justification>
  </clause>

  <clause id="5717">
    <literal><![CDATA[
      a(x,y,L((z / u) * w,v5,v6)) = a(x,y,L((u \ z) * w,v5,v6))
    ]]></literal>
    <justification jstring="[para(2774(a,1),5554(a,1,3,1))].">
      <j1 rule="para" parents="2774 5554"/>
    </justification>
  </clause>

  <clause id="5718">
    <literal><![CDATA[
      a(x,y,L((z / u) \ w,v5,v6)) = a(x,y,L((u \ z) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(3143(a,1),5554(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="3143 5554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5720">
    <literal><![CDATA[
      a(x,y,x * L(x,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,5145,a(flip),b,5566,a),flip(a)].">
      <j1 rule="hyper" parents="63 5145 5566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5721">
    <literal><![CDATA[
      x * a(x,y \ L(y,z,u),y * L(y,z,u)) = R(x,y \ L(y,z,u),y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,5566,a(flip),b,2386,a)].">
      <j1 rule="hyper" parents="139 5566 2386"/>
    </justification>
  </clause>

  <clause id="5722">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(z \ u,z,z \ 1)) = a(x,y,(z \ u) \ ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(887(a,1),5566(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="887 5566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5723">
    <literal><![CDATA[
      a(x,x \ 1,y * L(y,z,u)) \ (y \ L(y,z,u)) = L(y \ L(y,z,u),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(5566(a,1),1384(a,1,1))].">
      <j1 rule="para" parents="5566 1384"/>
    </justification>
  </clause>

  <clause id="5724">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * L(L(z,u,w),v5,v6)) = a(x,y,L(z \ L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(2136(a,1),5566(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2136 5566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5725">
    <literal><![CDATA[
      a(x,x,y * L(y,z,u)) \ (y \ L(y,z,u)) = L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(5566(a,1),4950(a,1,1))].">
      <j1 rule="para" parents="5566 4950"/>
    </justification>
  </clause>

  <clause id="5726">
    <literal><![CDATA[
      a(x,y,(z \ u) \ L(z \ u,w,v5)) = a(x,y,(u / z) * L(u / z,w,v5))
    ]]></literal>
    <justification jstring="[para(5190(a,1),5566(a,1,3))].">
      <j1 rule="para" parents="5190 5566"/>
    </justification>
  </clause>

  <clause id="5727">
    <literal><![CDATA[
      a(x * y,z,x * (y * (x * y))) = 1
    ]]></literal>
    <justification jstring="[para(100(a,1),5720(a,1,3))].">
      <j1 rule="para" parents="100 5720"/>
    </justification>
  </clause>

  <clause id="5728">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * w) \ (v5 * w)))) = a(x,y,z * (u \ (v5 * (w \ 1))))
    ]]></literal>
    <justification jstring="[para(577(a,1),5588(a,1,3,2,2))].">
      <j1 rule="para" parents="577 5588"/>
    </justification>
  </clause>

  <clause id="5729">
    <literal><![CDATA[
      a(x,y,z \ (L(u / w,v5,v6) * v7)) = a(x,y,z \ (L(w \ u,v5,v6) * v7))
    ]]></literal>
    <justification jstring="[para(261(a,1),5600(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="261 5600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5730">
    <literal><![CDATA[
      a(x,y,z \ (L(u / w,v5,v6) \ v7)) = a(x,y,z \ (L(w \ u,v5,v6) \ v7))
    ]]></literal>
    <justification jstring="[para(261(a,1),5603(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="261 5603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5731">
    <literal><![CDATA[
      a(x,y,z * (u * R(T(w,v5),v6,v7))) = a(x,y,(u * R(w,v6,v7)) * z)
    ]]></literal>
    <justification jstring="[para(27(a,2),5651(a,1,3,2,2))].">
      <j1 rule="para" parents="27 5651"/>
    </justification>
  </clause>

  <clause id="5732">
    <literal><![CDATA[
      a(x,y,((z \ u) * (w * w)) * v5) = a(x,y,v5 * (z \ ((w * w) * u)))
    ]]></literal>
    <justification jstring="[para(822(a,1),5651(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="822 5651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5733">
    <literal><![CDATA[
      a(x,y,(z \ K(u,w)) * v5) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,5529,a(flip),b,5663,a),flip(a)].">
      <j1 rule="hyper" parents="316 5529 5663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5734">
    <literal><![CDATA[
      a(x,y,(z \ R(K(u,w) * v5,v6,v7)) * v8) = a(x,y,v8 * (z \ (R(v5,v6,v7) * K(u,w))))
    ]]></literal>
    <justification jstring="[para(1031(a,1),5664(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="1031 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5737">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((z * w) * u)) = a(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5626,a,b,5504,a)].">
      <j1 rule="hyper" parents="63 5626 5504"/>
    </justification>
  </clause>

  <clause id="5738">
    <literal><![CDATA[
      a(x,y,L((z * z) \ (u * z),w,v5)) = a(x,y,L(L(z \ u,w,v5),z,z))
    ]]></literal>
    <justification jstring="[para(1539(a,1),5504(a,1,3))].">
      <j1 rule="para" parents="1539 5504"/>
    </justification>
  </clause>

  <clause id="5741">
    <literal><![CDATA[
      a(x,y,L(L(z,u,u \ 1),a(u \ 1,u,z),w) \ (z * w)) = a(x,y,w * a(u \ 1,u,z))
    ]]></literal>
    <justification jstring="[para(2406(a,1),5671(a,1,3,1,1))].">
      <j1 rule="para" parents="2406 5671"/>
    </justification>
  </clause>

  <clause id="5742">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ v5,L(z,u,w),1 / L(z,v6,v7)) \ (v5 * (1 / L(z,v6,v7)))) = a(x,y,L(z,v6,v7) \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(4916(a,1),5671(a,2,3))].">
      <j1 rule="para" parents="4916 5671"/>
    </justification>
  </clause>

  <clause id="5743">
    <literal><![CDATA[
      a(x,y,L(z,u,w \ 1) * (u * (w \ 1))) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5564,a(flip),b,5674,a),flip(a)].">
      <j1 rule="hyper" parents="316 5564 5674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5744">
    <literal><![CDATA[
      T(x,y \ 1) / (L(y,z,u) * (x * (L(y,z,u) \ 1))) = a(L(y,z,u),L(y,z,u) \ 1,x)
    ]]></literal>
    <justification jstring="[para(4471(a,1),5700(a,1,1))].">
      <j1 rule="para" parents="4471 5700"/>
    </justification>
  </clause>

  <clause id="5746">
    <literal><![CDATA[
      a(x,y,R(z,u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5570,a(flip),b,5737,a)].">
      <j1 rule="hyper" parents="63 5570 5737"/>
    </justification>
  </clause>

  <clause id="5751">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((w * u) * z)) = a(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5697,a,b,5746,a)].">
      <j1 rule="hyper" parents="63 5697 5746"/>
    </justification>
  </clause>

  <clause id="5752">
    <literal><![CDATA[
      a(x,y,L(z \ (u \ z),w,u)) = a(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5577,a(flip),b,5746,a),flip(a)].">
      <j1 rule="hyper" parents="63 5577 5746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5753">
    <literal><![CDATA[
      a(x,y,R(L(z,u,w),v5,v6)) = a(x,y,L(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),5746(a,2,3))].">
      <j1 rule="para" parents="30 5746"/>
    </justification>
  </clause>

  <clause id="5754">
    <literal><![CDATA[
      a(x,y,L(z,u,w * w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(497(a,1),5746(a,1,3)),flip(a)].">
      <j1 rule="para" parents="497 5746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5755">
    <literal><![CDATA[
      a(x,y,L(z,u,w \ 1)) = a(x,y,R(z,u,w))
    ]]></literal>
    <justification jstring="[para(1033(a,1),5746(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1033 5746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5756">
    <literal><![CDATA[
      a(x,y,L(z,u,w * (v5 * v5))) = a(x,y,R(z,u,w))
    ]]></literal>
    <justification jstring="[para(1701(a,1),5746(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1701 5746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5757">
    <literal><![CDATA[
      a(x,y,L(z,u,(w * w) \ v5)) = a(x,y,R(z,u,v5))
    ]]></literal>
    <justification jstring="[para(4712(a,1),5746(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4712 5746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5760">
    <literal><![CDATA[
      a(x,y,((z * z) * u) \ w) = a(x,y,u \ ((z * z) \ w))
    ]]></literal>
    <justification jstring="[para(298(a,1),5754(a,1,3))].">
      <j1 rule="para" parents="298 5754"/>
    </justification>
  </clause>

  <clause id="5761">
    <literal><![CDATA[
      a(x,y,L(z,u,w \ 1)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5746,a(flip),b,5755,a),flip(a)].">
      <j1 rule="hyper" parents="316 5746 5755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5762">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w \ 1),v5,v6)) = a(x,y,L(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),5761(a,1,3))].">
      <j1 rule="para" parents="30 5761"/>
    </justification>
  </clause>

  <clause id="5763">
    <literal><![CDATA[
      a(x,y,L(z,u,w * (v5 * v5))) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5746,a(flip),b,5756,a),flip(a)].">
      <j1 rule="hyper" parents="316 5746 5756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5764">
    <literal><![CDATA[
      a(x,y,L(z,u,(w * w) \ v5)) = a(x,y,L(z,u,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,5746,a(flip),b,5757,a),flip(a)].">
      <j1 rule="hyper" parents="316 5746 5757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5765">
    <literal><![CDATA[
      a(x,y,L(z,u,w * (v5 * (v6 * v6)))) = a(x,y,L(z,u,w * v5))
    ]]></literal>
    <justification jstring="[para(32(a,1),5763(a,1,3,3))].">
      <j1 rule="para" parents="32 5763"/>
    </justification>
  </clause>

  <clause id="5766">
    <literal><![CDATA[
      a(x,y,L(z,u,L(w * (v5 * v5),v6,v7))) = a(x,y,L(z,u,L(w,v6,v7)))
    ]]></literal>
    <justification jstring="[para(1058(a,2),5763(a,1,3,3))].">
      <j1 rule="para" parents="1058 5763"/>
    </justification>
  </clause>

  <clause id="5767">
    <literal><![CDATA[
      a(x,y,L(z,u,(w \ 1) \ v5)) = a(x,y,L(z,u,w \ v5))
    ]]></literal>
    <justification jstring="[para(1653(a,1),5763(a,1,3))].">
      <j1 rule="para" parents="1653 5763"/>
    </justification>
  </clause>

  <clause id="5768">
    <literal><![CDATA[
      a(x,y,L(z,u,(w \ 1) * v5)) = a(x,y,L(z,u,v5 * w))
    ]]></literal>
    <justification jstring="[para(1678(a,1),5764(a,1,3))].">
      <j1 rule="para" parents="1678 5764"/>
    </justification>
  </clause>

  <clause id="5771">
    <literal><![CDATA[
      a(x,y,(z * u) \ u) = a(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[para(298(a,1),5752(a,1,3))].">
      <j1 rule="para" parents="298 5752"/>
    </justification>
  </clause>

  <clause id="5772">
    <literal><![CDATA[
      a(x,y,(z * u) \ z) = a(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5626,a,b,5771,a)].">
      <j1 rule="hyper" parents="63 5626 5771"/>
    </justification>
  </clause>

  <clause id="5773">
    <literal><![CDATA[
      a(x,y,z \ (u * (T(w,v5) * v6))) = a(x,y,z \ (u * (w * v6)))
    ]]></literal>
    <justification jstring="[para(3638(a,1),5502(a,1,3,2,2))].">
      <j1 rule="para" parents="3638 5502"/>
    </justification>
  </clause>

  <clause id="5774">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ T(v5,v6)))) = a(x,y,z \ (u * (w \ v5)))
    ]]></literal>
    <justification jstring="[para(3846(a,1),5502(a,1,3,2,2))].">
      <j1 rule="para" parents="3846 5502"/>
    </justification>
  </clause>

  <clause id="5775">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ (v5 \ T(v6,v7))))) = a(x,y,z \ (u * (w \ (v5 \ v6))))
    ]]></literal>
    <justification jstring="[para(3912(a,1),5502(a,1,3,2,2))].">
      <j1 rule="para" parents="3912 5502"/>
    </justification>
  </clause>

  <clause id="5776">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ (v5 / v6)))) = a(x,y,z \ (u * (w \ (v6 \ v5))))
    ]]></literal>
    <justification jstring="[para(3917(a,1),5502(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="3917 5502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5777">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 * (v6 / v7))))) = a(x,y,z \ (u * (w * (v5 * (v7 \ v6)))))
    ]]></literal>
    <justification jstring="[para(4028(a,1),5502(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="4028 5502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5779">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w \ 1) * ((v5 * (v6 * w)) / w)))) = a(x,y,z \ (u \ (v5 * (v6 * (w \ 1)))))
    ]]></literal>
    <justification jstring="[para(964(a,1),5507(a,1,3,2,2,2))].">
      <j1 rule="para" parents="964 5507"/>
    </justification>
  </clause>

  <clause id="5780">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w / v5) * v6))) = a(x,y,z \ (u * ((v5 \ w) * v6)))
    ]]></literal>
    <justification jstring="[para(2774(a,1),5509(a,1,3,2,2))].">
      <j1 rule="para" parents="2774 5509"/>
    </justification>
  </clause>

  <clause id="5781">
    <literal><![CDATA[
      a(x,y,T(z,u) * L(T(w,v5),v6,v7)) = a(x,y,z * L(w,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(316,a,5485,a(flip),b,5513,a),flip(a)].">
      <j1 rule="hyper" parents="316 5485 5513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5782">
    <literal><![CDATA[
      a(x,y,L(z * L(u / w,v5,v6),v7,v8)) = a(x,y,L(z * L(w \ u,v5,v6),v7,v8))
    ]]></literal>
    <justification jstring="[para(261(a,1),5516(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="261 5516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5784">
    <literal><![CDATA[
      a(x,y,z) = (L(z,y,x) * (y * x)) \ (z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(316,a,3465,a(flip),b,5522,a)].">
      <j1 rule="hyper" parents="316 3465 5522"/>
    </justification>
  </clause>

  <clause id="5785">
    <literal><![CDATA[
      (L(L(x,y,z),u,x) * (u * x)) \ (x * (u * L(x,y,z))) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(4398(a,1),5784(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4398 5784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5786">
    <literal><![CDATA[
      L(x,y,(L(z,u,w) * (w * u)) \ (z * (u * w))) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(5784(a,2),4197(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5784 4197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5788">
    <literal><![CDATA[
      a(x,y,(z * z) * (z \ u)) = a(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5569,a(flip),b,5530,a),flip(a)].">
      <j1 rule="hyper" parents="63 5569 5530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5791">
    <literal><![CDATA[
      a(x,y,((z / (u * (w * w))) * v5) * v6) = a(x,y,((u \ (z / (w * w))) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(393(a,1),5547(a,1,3,1,1))].">
      <j1 rule="para" parents="393 5547"/>
    </justification>
  </clause>

  <clause id="5792">
    <literal><![CDATA[
      a(x,y,(((z * z) \ (u \ w)) * v5) * v6) = a(x,y,((u \ (w / (z * z))) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(675(a,1),5547(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="675 5547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5793">
    <literal><![CDATA[
      a(x,y,(((z \ 1) / (u \ K(w,v5))) \ v6) * v7) = a(x,y,(((u \ 1) \ (z \ K(v5,w))) \ v6) * v7)
    ]]></literal>
    <justification jstring="[para(4010(a,1),5549(a,1,3,1,1))].">
      <j1 rule="para" parents="4010 5549"/>
    </justification>
  </clause>

  <clause id="5795">
    <literal><![CDATA[
      a(x,y,((z * u) * w) * v5) = a(x,y,v5 * (w * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5623,a,b,5589,a)].">
      <j1 rule="hyper" parents="316 5623 5589"/>
    </justification>
  </clause>

  <clause id="5796">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * v5)) = a(x,y,z * (v5 * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5491,a,b,5589,a)].">
      <j1 rule="hyper" parents="316 5491 5589"/>
    </justification>
  </clause>

  <clause id="5797">
    <literal><![CDATA[
      a(x,y,z * ((u \ L(u,w,v5)) * (v6 * u))) = a(x,y,z * (u * (v6 * (u \ L(u,w,v5)))))
    ]]></literal>
    <justification jstring="[para(5112(a,1),5589(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5112 5589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5798">
    <literal><![CDATA[
      a(x,y,z * (u \ (u \ 1))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2648,a(flip),b,5591,a),flip(a)].">
      <j1 rule="hyper" parents="63 2648 5591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5800">
    <literal><![CDATA[
      a(x,y,z / (u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(434(a,1),5798(a,1,3))].">
      <j1 rule="para" parents="434 5798"/>
    </justification>
  </clause>

  <clause id="5801">
    <literal><![CDATA[
      a(x,y,(z * u) / (w * w)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,5800,a),flip(a)].">
      <j1 rule="hyper" parents="316 5469 5800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5802">
    <literal><![CDATA[
      a(x,y,(z * z) \ u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5679,a(flip),b,5800,a)].">
      <j1 rule="hyper" parents="63 5679 5800"/>
    </justification>
  </clause>

  <clause id="5803">
    <literal><![CDATA[
      a(x,y,(z * z) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5475,a(flip),b,5800,a),flip(a)].">
      <j1 rule="hyper" parents="63 5475 5800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5804">
    <literal><![CDATA[
      a(x,y,z * (u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5800(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11 5800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5805">
    <literal><![CDATA[
      a(x,y,z \ (u \ 1)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(588(a,1),5800(a,1,3))].">
      <j1 rule="para" parents="588 5800"/>
    </justification>
  </clause>

  <clause id="5806">
    <literal><![CDATA[
      a(x,y,L(z / (u * u),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(1112(a,2),5800(a,1,3))].">
      <j1 rule="para" parents="1112 5800"/>
    </justification>
  </clause>

  <clause id="5808">
    <literal><![CDATA[
      a(x,y,(z * u) * u) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5751,a(flip),b,5802,a),flip(a)].">
      <j1 rule="hyper" parents="63 5751 5802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5809">
    <literal><![CDATA[
      a(x,y,(z * u) * z) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5737,a(flip),b,5802,a),flip(a)].">
      <j1 rule="hyper" parents="63 5737 5802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5810">
    <literal><![CDATA[
      a(x,y,z * (z * u)) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(18(a,2),5802(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18 5802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5811">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,z)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(102(a,2),5802(a,1,3))].">
      <j1 rule="para" parents="102 5802"/>
    </justification>
  </clause>

  <clause id="5813">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * w))) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5530,a,b,5803,a)].">
      <j1 rule="hyper" parents="63 5530 5803"/>
    </justification>
  </clause>

  <clause id="5814">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5788,a(flip),b,5803,a)].">
      <j1 rule="hyper" parents="63 5788 5803"/>
    </justification>
  </clause>

  <clause id="5815">
    <literal><![CDATA[
      a(x,y,L((z * z) * u,w,v5)) = a(x,y,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(1115(a,2),5803(a,1,3))].">
      <j1 rule="para" parents="1115 5803"/>
    </justification>
  </clause>

  <clause id="5816">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * (w * u))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5589,a,b,5804,a)].">
      <j1 rule="hyper" parents="63 5589 5804"/>
    </justification>
  </clause>

  <clause id="5817">
    <literal><![CDATA[
      a(x,y,L(z * (u * u),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(1058(a,2),5804(a,1,3))].">
      <j1 rule="para" parents="1058 5804"/>
    </justification>
  </clause>

  <clause id="5818">
    <literal><![CDATA[
      a(x,y,z \ L(u \ 1,w,v5)) = a(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(1108(a,1),5804(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1108 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5819">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,v5) \ u)) = a(x,y,z \ (u \ L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(1894(a,1),5805(a,1,3,2))].">
      <j1 rule="para" parents="1894 5805"/>
    </justification>
  </clause>

  <clause id="5821">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5698,a,b,5814,a)].">
      <j1 rule="hyper" parents="63 5698 5814"/>
    </justification>
  </clause>

  <clause id="5823">
    <literal><![CDATA[
      x \ R(x,(y \ 1) \ z,(y \ 1) \ z) = a(x,(y \ 1) \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2380,a,b,5814,a)].">
      <j1 rule="hyper" parents="63 2380 5814"/>
    </justification>
  </clause>

  <clause id="5825">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * (w * u)) = a(x,y,L(z,u * w,u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5491,a,b,5808,a)].">
      <j1 rule="hyper" parents="63 5491 5808"/>
    </justification>
  </clause>

  <clause id="5826">
    <literal><![CDATA[
      a(x,y,z * (u * z)) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,5808,a)].">
      <j1 rule="hyper" parents="63 5469 5808"/>
    </justification>
  </clause>

  <clause id="5828">
    <literal><![CDATA[
      a(x,y,L(z * (z * u),w,v5)) = a(x,y,L(L(u,w,v5),z,z))
    ]]></literal>
    <justification jstring="[para(1367(a,2),5810(a,1,3))].">
      <j1 rule="para" parents="1367 5810"/>
    </justification>
  </clause>

  <clause id="5830">
    <literal><![CDATA[
      a(x,y,z * (u / (w * w))) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(683(a,1),5801(a,1,3))].">
      <j1 rule="para" parents="683 5801"/>
    </justification>
  </clause>

  <clause id="5833">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) * w)) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,5813,a)].">
      <j1 rule="hyper" parents="63 5490 5813"/>
    </justification>
  </clause>

  <clause id="5834">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ (v5 \ 1)))) = a(x,y,z \ (u \ (w \ v5)))
    ]]></literal>
    <justification jstring="[para(591(a,1),5813(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="591 5813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5835">
    <literal><![CDATA[
      a(x,y,z * ((u * u) \ w)) = a(x,y,w * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5481,a(flip),b,5830,a)].">
      <j1 rule="hyper" parents="63 5481 5830"/>
    </justification>
  </clause>

  <clause id="5836">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ 1))) = a(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[para(562(a,1),5830(a,1,3,2))].">
      <j1 rule="para" parents="562 5830"/>
    </justification>
  </clause>

  <clause id="5837">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ 1))) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[para(588(a,1),5830(a,1,3,2))].">
      <j1 rule="para" parents="588 5830"/>
    </justification>
  </clause>

  <clause id="5838">
    <literal><![CDATA[
      a(x,y,z * (u * (w / (v5 * v5)))) = a(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[para(683(a,1),5830(a,1,3,2))].">
      <j1 rule="para" parents="683 5830"/>
    </justification>
  </clause>

  <clause id="5839">
    <literal><![CDATA[
      a(x,y,z * L(u \ 1,w,v5)) = a(x,y,L(u,w,v5) * z)
    ]]></literal>
    <justification jstring="[para(1110(a,1),5830(a,1,3,2))].">
      <j1 rule="para" parents="1110 5830"/>
    </justification>
  </clause>

  <clause id="5841">
    <literal><![CDATA[
      a(x,y,z \ (u * u)) = a(x,y,z \ (w * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5813,a(flip),b,5833,a)].">
      <j1 rule="hyper" parents="63 5813 5833"/>
    </justification>
  </clause>

  <clause id="5842">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) \ w)) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(10(a,1),5833(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 5833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5843">
    <literal><![CDATA[
      a(x,y,z \ (u * (u * w))) = a(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[para(100(a,1),5833(a,1,3,2))].">
      <j1 rule="para" parents="100 5833"/>
    </justification>
  </clause>

  <clause id="5844">
    <literal><![CDATA[
      a(x,y,R(z,z,u) * u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(1164(a,1),5833(a,1,3))].">
      <j1 rule="para" parents="1164 5833"/>
    </justification>
  </clause>

  <clause id="5849">
    <literal><![CDATA[
      a(x,y,z * ((u * u) \ w)) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,5835,a),flip(a)].">
      <j1 rule="hyper" parents="316 5469 5835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5851">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) * w) = a(x,y,u * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,5835,a)].">
      <j1 rule="hyper" parents="63 5469 5835"/>
    </justification>
  </clause>

  <clause id="5852">
    <literal><![CDATA[
      a(x,y,(z * (z * u)) * w) = a(x,y,w * L(u,z,z))
    ]]></literal>
    <justification jstring="[para(18(a,2),5835(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="18 5835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5854">
    <literal><![CDATA[
      a(x,y,z * L((u * u) \ w,v5,v6)) = a(x,y,L(w,v5,v6) * z)
    ]]></literal>
    <justification jstring="[para(1120(a,2),5835(a,1,3,2))].">
      <j1 rule="para" parents="1120 5835"/>
    </justification>
  </clause>

  <clause id="5855">
    <literal><![CDATA[
      a(x,y,R(z,z,u) \ u) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(4655(a,2),5835(a,1,3))].">
      <j1 rule="para" parents="4655 5835"/>
    </justification>
  </clause>

  <clause id="5856">
    <literal><![CDATA[
      a(x,y,R(z,z,u * w) \ (w * u)) = a(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,5855,a)].">
      <j1 rule="hyper" parents="63 5490 5855"/>
    </justification>
  </clause>

  <clause id="5857">
    <literal><![CDATA[
      a(x,y,z \ (u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5525,a(flip),b,5841,a),flip(a)].">
      <j1 rule="hyper" parents="316 5525 5841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5860">
    <literal><![CDATA[
      a(x,y,L(z,u,u * z)) = a(x,y,(u * z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5504,a(flip),b,5857,a)].">
      <j1 rule="hyper" parents="63 5504 5857"/>
    </justification>
  </clause>

  <clause id="5861">
    <literal><![CDATA[
      a(x,y,(z / u) * (u * z)) = a(x,y,a(u \ z,u,z))
    ]]></literal>
    <justification jstring="[para(2400(a,1),5857(a,1,3))].">
      <j1 rule="para" parents="2400 5857"/>
    </justification>
  </clause>

  <clause id="5866">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) * w) = a(x,y,w * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,5849,a)].">
      <j1 rule="hyper" parents="63 5469 5849"/>
    </justification>
  </clause>

  <clause id="5867">
    <literal><![CDATA[
      a(x,y,z * L(u \ w,u,u)) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(102(a,2),5849(a,1,3,2))].">
      <j1 rule="para" parents="102 5849"/>
    </justification>
  </clause>

  <clause id="5868">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * (w \ u))) = a(x,y,z * a(u,w,w \ u))
    ]]></literal>
    <justification jstring="[para(90(a,1),5849(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="90 5849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5870">
    <literal><![CDATA[
      a(x,y,((z * z) * u) * w) = a(x,y,u * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),5851(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="9 5851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5872">
    <literal><![CDATA[
      a(x,y,z * ((u * u) * w)) = a(x,y,w * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5866(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="9 5866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5874">
    <literal><![CDATA[
      a(x,y,(z * (u * u)) * w) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5542,a,b,5870,a)].">
      <j1 rule="hyper" parents="63 5542 5870"/>
    </justification>
  </clause>

  <clause id="5875">
    <literal><![CDATA[
      a(x,y,z * (u * (w * w))) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5623,a(flip),b,5870,a)].">
      <j1 rule="hyper" parents="63 5623 5870"/>
    </justification>
  </clause>

  <clause id="5878">
    <literal><![CDATA[
      a(x,y,(z * (u * (w * w))) * v5) = a(x,y,(z * u) * v5)
    ]]></literal>
    <justification jstring="[para(32(a,1),5874(a,1,3,1))].">
      <j1 rule="para" parents="32 5874"/>
    </justification>
  </clause>

  <clause id="5879">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * w) = a(x,y,((u * z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(587(a,1),5874(a,1,3,1))].">
      <j1 rule="para" parents="587 5874"/>
    </justification>
  </clause>

  <clause id="5880">
    <literal><![CDATA[
      a(x,y,(z \ (u \ (w \ 1))) * v5) = a(x,y,(z \ (u \ w)) * v5)
    ]]></literal>
    <justification jstring="[para(591(a,1),5874(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="591 5874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5883">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * w)) = a(x,y,R(u,w,w) * z)
    ]]></literal>
    <justification jstring="[para(109(a,1),5875(a,1,3,2))].">
      <j1 rule="para" parents="109 5875"/>
    </justification>
  </clause>

  <clause id="5884">
    <literal><![CDATA[
      a(x,y,(z \ (u \ 1)) * w) = a(x,y,w * (z \ u))
    ]]></literal>
    <justification jstring="[para(584(a,1),5875(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="584 5875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5887">
    <literal><![CDATA[
      a(x,y,L(z,u,u * z)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5809,a(flip),b,5860,a),flip(a)].">
      <j1 rule="hyper" parents="316 5809 5860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5888">
    <literal><![CDATA[
      a(x,y,L(z * (u \ 1),w,v5)) = a(x,y,L(z * u,w,v5))
    ]]></literal>
    <justification jstring="[para(562(a,1),5806(a,1,3,1))].">
      <j1 rule="para" parents="562 5806"/>
    </justification>
  </clause>

  <clause id="5889">
    <literal><![CDATA[
      a(x,y,L(z \ (u \ 1),w,v5)) = a(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(588(a,1),5806(a,1,3,1))].">
      <j1 rule="para" parents="588 5806"/>
    </justification>
  </clause>

  <clause id="5890">
    <literal><![CDATA[
      a(x,y,L(z \ (u / (w * w)),v5,v6)) = a(x,y,L(z \ u,v5,v6))
    ]]></literal>
    <justification jstring="[para(675(a,1),5806(a,1,3,1))].">
      <j1 rule="para" parents="675 5806"/>
    </justification>
  </clause>

  <clause id="5891">
    <literal><![CDATA[
      a(x,y,L(L(z \ 1,u,w),v5,v6)) = a(x,y,L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(1110(a,1),5806(a,1,3,1))].">
      <j1 rule="para" parents="1110 5806"/>
    </justification>
  </clause>

  <clause id="5892">
    <literal><![CDATA[
      a(x,y,L(z \ R(z,u,w),v5,v6)) = a(x,y,L(z * R(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(4484(a,1),5806(a,1,3,1))].">
      <j1 rule="para" parents="4484 5806"/>
    </justification>
  </clause>

  <clause id="5893">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,w),v5,v6)) = a(x,y,L(z * L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(5137(a,1),5815(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5137 5815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5895">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ 1))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,5836,a),flip(a)].">
      <j1 rule="hyper" parents="316 5469 5836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5896">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) * w) = a(x,y,w * (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5587,a(flip),b,5836,a),flip(a)].">
      <j1 rule="hyper" parents="63 5587 5836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5901">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) * w) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5623,a,b,5895,a)].">
      <j1 rule="hyper" parents="63 5623 5895"/>
    </justification>
  </clause>

  <clause id="5902">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) * w)) = a(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5491,a,b,5895,a)].">
      <j1 rule="hyper" parents="63 5491 5895"/>
    </justification>
  </clause>

  <clause id="5903">
    <literal><![CDATA[
      a(x,y,z * (L(u,w,v5) \ u)) = a(x,y,z * (u * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(1002(a,1),5895(a,1,3,2))].">
      <j1 rule="para" parents="1002 5895"/>
    </justification>
  </clause>

  <clause id="5904">
    <literal><![CDATA[
      a(x,y,z * (u * (L(u,w,v5) \ u))) = a(x,y,L(u,w,v5) * z)
    ]]></literal>
    <justification jstring="[para(5081(a,1),5896(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5081 5896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5906">
    <literal><![CDATA[
      a(x,y,((1 / z) * u) * w) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5547,a,b,5901,a)].">
      <j1 rule="hyper" parents="63 5547 5901"/>
    </justification>
  </clause>

  <clause id="5907">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) * w)) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5491,a,b,5902,a),flip(a)].">
      <j1 rule="hyper" parents="316 5491 5902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5909">
    <literal><![CDATA[
      a(x,y,(z \ u) * (z * u)) = a(x,y,a(z \ u,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5543,a(flip),b,5861,a)].">
      <j1 rule="hyper" parents="63 5543 5861"/>
    </justification>
  </clause>

  <clause id="5911">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * w) = a(x,y,w * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,5879,a),flip(a)].">
      <j1 rule="hyper" parents="316 5469 5879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5912">
    <literal><![CDATA[
      a(x,y,L((z * u) \ z,w,v5) \ ((z * u) \ z)) = a(x,y,L(u,u,z) * L((z * u) \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,2652,a,b,5879,a)].">
      <j1 rule="hyper" parents="316 2652 5879"/>
    </justification>
  </clause>

  <clause id="5914">
    <literal><![CDATA[
      a(x,y,z * L(u,u,w)) = a(x,y,z * ((w * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,5911,a)].">
      <j1 rule="hyper" parents="63 5469 5911"/>
    </justification>
  </clause>

  <clause id="5915">
    <literal><![CDATA[
      a(x,y,z * ((K(u,w) * v5) * v6)) = a(x,y,z * (v6 * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5491,a,b,5593,a)].">
      <j1 rule="hyper" parents="63 5491 5593"/>
    </justification>
  </clause>

  <clause id="5916">
    <literal><![CDATA[
      a(x,y,z * (u * L(K(w,v5) * v6,v7,v8))) = a(x,y,z * (u * L(v6,v7,v8)))
    ]]></literal>
    <justification jstring="[para(4850(a,2),5593(a,1,3,2,2))].">
      <j1 rule="para" parents="4850 5593"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      a(x,y,z \ (u * T(w / v5,v6))) = a(x,y,z \ (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5495,a,b,5599,a)].">
      <j1 rule="hyper" parents="63 5495 5599"/>
    </justification>
  </clause>

  <clause id="5918">
    <literal><![CDATA[
      a(x,y,z \ (u * (R(w,v5,v5) \ (v5 \ 1)))) = a(x,y,z \ (u * (v5 / ((w * v5) * v5))))
    ]]></literal>
    <justification jstring="[para(593(a,1),5599(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="593 5599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5919">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * (v5 * v6)))) = a(x,y,z \ (u \ (w * (v6 * v5))))
    ]]></literal>
    <justification jstring="[para(3933(a,1),5601(a,1,3,2,2))].">
      <j1 rule="para" parents="3933 5601"/>
    </justification>
  </clause>

  <clause id="5920">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ (v5 / v6)))) = a(x,y,z \ (u \ (w \ (v6 \ v5))))
    ]]></literal>
    <justification jstring="[para(3917(a,1),5601(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="3917 5601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5921">
    <literal><![CDATA[
      a(x,y,z \ (u \ (((w \ v5) * w) * v6))) = a(x,y,z \ (u \ (v5 * v6)))
    ]]></literal>
    <justification jstring="[para(4506(a,1),5601(a,1,3,2,2))].">
      <j1 rule="para" parents="4506 5601"/>
    </justification>
  </clause>

  <clause id="5922">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w * (v5 * v5)) * v6))) = a(x,y,z \ (u \ ((v6 * w) * (v5 * v5))))
    ]]></literal>
    <justification jstring="[para(32(a,2),5602(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="32 5602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5923">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w * w) * v5))) = a(x,y,(z \ (u \ v5)) * (w * w))
    ]]></literal>
    <justification jstring="[para(637(a,1),5602(a,1,3)),flip(a)].">
      <j1 rule="para" parents="637 5602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5924">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w / v5) * v6))) = a(x,y,z \ (u \ ((v5 \ w) * v6)))
    ]]></literal>
    <justification jstring="[para(2774(a,1),5605(a,1,3,2,2))].">
      <j1 rule="para" parents="2774 5605"/>
    </justification>
  </clause>

  <clause id="5925">
    <literal><![CDATA[
      a(x,y,z \ ((T(u,w) \ v5) \ v6)) = a(x,y,z \ ((u \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(2906(a,1),5605(a,1,3,2))].">
      <j1 rule="para" parents="2906 5605"/>
    </justification>
  </clause>

  <clause id="5926">
    <literal><![CDATA[
      a(x,y,z \ (((u / w) \ v5) \ v6)) = a(x,y,z \ (((w \ u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(3217(a,1),5605(a,1,3,2))].">
      <j1 rule="para" parents="3217 5605"/>
    </justification>
  </clause>

  <clause id="5927">
    <literal><![CDATA[
      a(x,y,z \ (((u \ w) * u) * v5)) = a(x,y,z \ (v5 * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,5608,a)].">
      <j1 rule="hyper" parents="63 5490 5608"/>
    </justification>
  </clause>

  <clause id="5929">
    <literal><![CDATA[
      a(x,y,z \ ((u / (w * (v5 * v5))) \ v6)) = a(x,y,z \ ((w \ (u / (v5 * v5))) \ v6))
    ]]></literal>
    <justification jstring="[para(393(a,1),5629(a,1,3,2,1))].">
      <j1 rule="para" parents="393 5629"/>
    </justification>
  </clause>

  <clause id="5933">
    <literal><![CDATA[
      a(x,y,((z \ u) * w) \ v5) = a(x,y,(w * (u / z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5626,a,b,5631,a),flip(a)].">
      <j1 rule="hyper" parents="63 5626 5631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5934">
    <literal><![CDATA[
      a(x,y,(((z / (u * u)) / w) * (u * u)) \ v5) = a(x,y,(w \ z) \ v5)
    ]]></literal>
    <justification jstring="[para(586(a,1),5631(a,2,3,1))].">
      <j1 rule="para" parents="586 5631"/>
    </justification>
  </clause>

  <clause id="5935">
    <literal><![CDATA[
      a(x,y,(((z * z) \ (u * w)) * v5) \ v6) = a(x,y,((u * (w / (z * z))) * v5) \ v6)
    ]]></literal>
    <justification jstring="[para(683(a,1),5631(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="683 5631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5936">
    <literal><![CDATA[
      a(x,y,((1 / z) * u) \ (z \ u)) = a(x,y,(z \ u) * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2662,a,b,5642,a)].">
      <j1 rule="hyper" parents="63 2662 5642"/>
    </justification>
  </clause>

  <clause id="5937">
    <literal><![CDATA[
      a(x,y,z * (((u / (w * w)) \ 1) \ v5)) = a(x,y,z * (((w * w) / u) \ v5))
    ]]></literal>
    <justification jstring="[para(441(a,1),5643(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="441 5643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5940">
    <literal><![CDATA[
      a(x,y,(z \ L(K(u,w) * v5,v6,v7)) * v8) = a(x,y,v8 * (z \ (L(v5,v6,v7) * K(u,w))))
    ]]></literal>
    <justification jstring="[para(4850(a,2),5665(a,1,3,1,2))].">
      <j1 rule="para" parents="4850 5665"/>
    </justification>
  </clause>

  <clause id="5941">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * v5) = a(x,y,v5 * ((w * u) * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5491,a,b,5666,a),flip(a)].">
      <j1 rule="hyper" parents="316 5491 5666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5942">
    <literal><![CDATA[
      a(x,y,z * (u * (w * u))) = a(x,y,z * L(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5852,a(flip),b,5666,a),flip(a)].">
      <j1 rule="hyper" parents="63 5852 5666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5945">
    <literal><![CDATA[
      a(x,y,(z * (K(u,w) * v5)) \ v6) = a(x,y,(v5 * z) \ v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,5626,a,b,5687,a),flip(a)].">
      <j1 rule="hyper" parents="316 5626 5687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5946">
    <literal><![CDATA[
      a(x,y,(z * (T(u,w) * v5)) \ v6) = a(x,y,(z * (u * v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(2800(a,1),5687(a,1,3,1,2))].">
      <j1 rule="para" parents="2800 5687"/>
    </justification>
  </clause>

  <clause id="5947">
    <literal><![CDATA[
      a(x,y,(z * (T(u,w) \ v5)) \ v6) = a(x,y,(z * (u \ v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(2859(a,1),5687(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="2859 5687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5948">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) * v5) = a(x,y,((u * z) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(2765(a,1),5693(a,1,3,1))].">
      <j1 rule="para" parents="2765 5693"/>
    </justification>
  </clause>

  <clause id="5949">
    <literal><![CDATA[
      a(x,y,(z \ (u / (w / (v5 * v5)))) * v6) = a(x,y,(z \ (w \ (u * (v5 * v5)))) * v6)
    ]]></literal>
    <justification jstring="[para(676(a,1),5694(a,1,3,1,2))].">
      <j1 rule="para" parents="676 5694"/>
    </justification>
  </clause>

  <clause id="5950">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * w) = a(x,y,(u \ ((z \ 1) \ u)) * w)
    ]]></literal>
    <justification jstring="[para(1447(a,2),5694(a,1,3,1))].">
      <j1 rule="para" parents="1447 5694"/>
    </justification>
  </clause>

  <clause id="5951">
    <literal><![CDATA[
      a(x,y,L(z \ ((u \ w) * (u * u)),v5,v6)) = a(x,y,L(z \ (w / (u \ 1)),v5,v6))
    ]]></literal>
    <justification jstring="[para(613(a,1),5708(a,1,3,1,2))].">
      <j1 rule="para" parents="613 5708"/>
    </justification>
  </clause>

  <clause id="5952">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),v5,v6)) = a(x,y,L(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5746,a(flip),b,5753,a)].">
      <j1 rule="hyper" parents="63 5746 5753"/>
    </justification>
  </clause>

  <clause id="5953">
    <literal><![CDATA[
      a(x,y,L(R(z,u,w),v5,v6)) = a(x,y,L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(29(a,1),5753(a,1,3))].">
      <j1 rule="para" parents="29 5753"/>
    </justification>
  </clause>

  <clause id="5954">
    <literal><![CDATA[
      a(x,y,((z * z) * u) \ w) = a(x,y,u \ w)
    ]]></literal>
    <justification jstring="[hyper(316,a,5842,a(flip),b,5760,a),flip(a)].">
      <j1 rule="hyper" parents="316 5842 5760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5957">
    <literal><![CDATA[
      a(x,y,((z * z) * u) \ w) = a(x,y,w / u)
    ]]></literal>
    <justification jstring="[hyper(316,a,5477,a,b,5954,a),flip(a)].">
      <j1 rule="hyper" parents="316 5477 5954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5958">
    <literal><![CDATA[
      a(x,y,(z * (u * u)) \ w) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5626,a,b,5954,a)].">
      <j1 rule="hyper" parents="63 5626 5954"/>
    </justification>
  </clause>

  <clause id="5960">
    <literal><![CDATA[
      a(x,y,(z * (z * u)) \ w) = a(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(100(a,1),5954(a,1,3,1))].">
      <j1 rule="para" parents="100 5954"/>
    </justification>
  </clause>

  <clause id="5962">
    <literal><![CDATA[
      a(x,y,(z / (u * u)) \ w) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(12(a,1),5958(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="12 5958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5963">
    <literal><![CDATA[
      a(x,y,(z * (u * (w * w))) \ v5) = a(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(32(a,1),5958(a,1,3,1))].">
      <j1 rule="para" parents="32 5958"/>
    </justification>
  </clause>

  <clause id="5970">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) \ w) = a(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[para(562(a,1),5962(a,1,3,1))].">
      <j1 rule="para" parents="562 5962"/>
    </justification>
  </clause>

  <clause id="5971">
    <literal><![CDATA[
      a(x,y,(z * (u / (w * w))) \ v5) = a(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(683(a,1),5962(a,1,3,1))].">
      <j1 rule="para" parents="683 5962"/>
    </justification>
  </clause>

  <clause id="5972">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) \ v5) = a(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(1110(a,1),5962(a,1,3,1))].">
      <j1 rule="para" parents="1110 5962"/>
    </justification>
  </clause>

  <clause id="5976">
    <literal><![CDATA[
      a(x,y,(z * (u * z)) \ w) = a(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5685,a,b,5960,a)].">
      <j1 rule="hyper" parents="63 5685 5960"/>
    </justification>
  </clause>

  <clause id="5979">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * (v5 \ (v6 \ 1))) = a(x,y,(v5 \ v6) * ((w * u) * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5837,a,b,5796,a)].">
      <j1 rule="hyper" parents="316 5837 5796"/>
    </justification>
  </clause>

  <clause id="5980">
    <literal><![CDATA[
      a(x,y,z * (((u * w) / (v5 * v5)) * v6)) = a(x,y,z * (v6 * ((w / (v5 * v5)) * u)))
    ]]></literal>
    <justification jstring="[para(683(a,2),5796(a,1,3,2,1))].">
      <j1 rule="para" parents="683 5796"/>
    </justification>
  </clause>

  <clause id="5981">
    <literal><![CDATA[
      a(x,y,z * (u * ((w \ 1) * R(v5,w \ 1,w)))) = a(x,y,z * (R(v5 * (1 / w),w,w) * u))
    ]]></literal>
    <justification jstring="[para(2573(a,1),5796(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="2573 5796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5984">
    <literal><![CDATA[
      a(x,y,z * ((u / (w * w)) * v5)) = a(x,y,(v5 * u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5491,a,b,5838,a)].">
      <j1 rule="hyper" parents="63 5491 5838"/>
    </justification>
  </clause>

  <clause id="5985">
    <literal><![CDATA[
      a(x,y,z * (u * ((w * w) \ v5))) = a(x,y,(u * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5505,a(flip),b,5838,a)].">
      <j1 rule="hyper" parents="63 5505 5838"/>
    </justification>
  </clause>

  <clause id="5986">
    <literal><![CDATA[
      a(x,y,(z * (u \ (w * w))) * v5) = a(x,y,v5 * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(428(a,1),5838(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="428 5838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5987">
    <literal><![CDATA[
      a(x,y,z * (u * (w * (v5 \ 1)))) = a(x,y,(u * (w * v5)) * z)
    ]]></literal>
    <justification jstring="[para(562(a,1),5838(a,1,3,2,2))].">
      <j1 rule="para" parents="562 5838"/>
    </justification>
  </clause>

  <clause id="5989">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) * v5) = a(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,5839,a)].">
      <j1 rule="hyper" parents="63 5469 5839"/>
    </justification>
  </clause>

  <clause id="5996">
    <literal><![CDATA[
      a(x,y,z * ((u * (w * w)) * v5)) = a(x,y,(v5 * u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5623,a(flip),b,5878,a)].">
      <j1 rule="hyper" parents="63 5623 5878"/>
    </justification>
  </clause>

  <clause id="5997">
    <literal><![CDATA[
      a(x,y,(z * L(u * (w * w),v5,v6)) * v7) = a(x,y,(z * L(u,v5,v6)) * v7)
    ]]></literal>
    <justification jstring="[para(1058(a,2),5878(a,1,3,1,2))].">
      <j1 rule="para" parents="1058 5878"/>
    </justification>
  </clause>

  <clause id="5999">
    <literal><![CDATA[
      a(x,y,L(z * (u \ 1),w,v5)) = a(x,y,L(u * z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,5535,a,b,5888,a),flip(a)].">
      <j1 rule="hyper" parents="316 5535 5888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6000">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ z,v5,v6)) = a(x,y,L(z * L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(1002(a,1),5888(a,1,3,1))].">
      <j1 rule="para" parents="1002 5888"/>
    </justification>
  </clause>

  <clause id="6001">
    <literal><![CDATA[
      a(x,y,L((L(z \ 1,u,w) * ((z \ 1) \ v5)) * z,v6,v7)) = a(x,y,L(v5 * L(z \ 1,u,w),v6,v7))
    ]]></literal>
    <justification jstring="[para(4380(a,1),5888(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4380 5888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6002">
    <literal><![CDATA[
      a(x,y,z * (((u * w) * v5) * v6)) = a(x,y,z * (v6 * ((w * u) * v5)))
    ]]></literal>
    <justification jstring="[para(2759(a,1),5915(a,1,3,2,1))].">
      <j1 rule="para" parents="2759 5915"/>
    </justification>
  </clause>

  <clause id="6003">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * v5)) = a(x,y,z \ (v5 * (w * u)))
    ]]></literal>
    <justification jstring="[para(9(a,1),5927(a,1,3,2,1,1))].">
      <j1 rule="para" parents="9 5927"/>
    </justification>
  </clause>

  <clause id="6004">
    <literal><![CDATA[
      a(x,y,z * (((u * u) * w) * v5)) = a(x,y,(v5 * w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5878,a(flip),b,5941,a),flip(a)].">
      <j1 rule="hyper" parents="63 5878 5941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6007">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) * v5) = a(x,y,v5 * ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,5948,a),flip(a)].">
      <j1 rule="hyper" parents="316 5469 5948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6011">
    <literal><![CDATA[
      a(x,y,((z * (u * u)) * w) \ v5) = a(x,y,(w * z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5626,a,b,5963,a)].">
      <j1 rule="hyper" parents="63 5626 5963"/>
    </justification>
  </clause>

  <clause id="6014">
    <literal><![CDATA[
      a(x,y,(((z * z) \ u) * w) \ v5) = a(x,y,(w * u) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5933,a,b,5971,a)].">
      <j1 rule="hyper" parents="63 5933 5971"/>
    </justification>
  </clause>

  <clause id="6016">
    <literal><![CDATA[
      a(x,y,(z * L(u \ 1,w,v5)) \ v6) = a(x,y,(z * L(u,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(1110(a,1),5971(a,1,3,1,2))].">
      <j1 rule="para" parents="1110 5971"/>
    </justification>
  </clause>

  <clause id="6017">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) * L(L(z \ 1,u,w),v5,v6)) = a(x,y,L(z,u,w) \ L(L(z \ 1,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5566,a(flip),b,5972,a)].">
      <j1 rule="hyper" parents="63 5566 5972"/>
    </justification>
  </clause>

  <clause id="6018">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ L(L(z \ 1,u,w),v5,v5 \ 1)) = a(x,y,a(v5 \ 1,v5,L(z \ 1,u,w)) \ 1)
    ]]></literal>
    <justification jstring="[para(5087(a,2),5972(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5087 5972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6019">
    <literal><![CDATA[
      a(x,y,z * (((u * w) / (v5 * v5)) * v6)) = a(x,y,(v6 * (w * u)) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5691,a,b,5984,a),flip(a)].">
      <j1 rule="hyper" parents="316 5691 5984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6020">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w \ 1)) * v5)) = a(x,y,(v5 * (u \ w)) * z)
    ]]></literal>
    <justification jstring="[para(588(a,1),5984(a,1,3,2,1))].">
      <j1 rule="para" parents="588 5984"/>
    </justification>
  </clause>

  <clause id="6022">
    <literal><![CDATA[
      a(x,y,z * (u * ((w * w) \ v5))) = a(x,y,z * (u * v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,5985,a),flip(a)].">
      <j1 rule="hyper" parents="316 5469 5985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6027">
    <literal><![CDATA[
      a(x,y,L((z \ 1) * u,w,v5)) = a(x,y,L(z * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5535,a,b,5999,a)].">
      <j1 rule="hyper" parents="63 5535 5999"/>
    </justification>
  </clause>

  <clause id="6028">
    <literal><![CDATA[
      a(x,y,(z * u) \ (u * (w * z))) = a(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5737,a(flip),b,6003,a),flip(a)].">
      <j1 rule="hyper" parents="63 5737 6003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6029">
    <literal><![CDATA[
      a(x,y,z \ (u * (R(w,v5,v5) * T(v5,v5 \ 1)))) = a(x,y,z \ (R(v5 * w,v5 \ 1,v5) * u))
    ]]></literal>
    <justification jstring="[para(3039(a,1),6003(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="3039 6003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6030">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * K(v5 \ 1,w * v5)) * v5))) = a(x,y,z \ (L(w / (v5 \ 1),v5 \ 1,v5) * u))
    ]]></literal>
    <justification jstring="[para(4908(a,1),6003(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="4908 6003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6032">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ v5)) = a(x,y,z * ((w * u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,6007,a)].">
      <j1 rule="hyper" parents="63 5469 6007"/>
    </justification>
  </clause>

  <clause id="6034">
    <literal><![CDATA[
      a(x,y,(z * u) \ (z * (w * (u * (v5 * v5))))) = a(x,y,L(w,u * (v5 * v5),z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6028,a(flip),b,6011,a),flip(a)].">
      <j1 rule="hyper" parents="63 6028 6011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6035">
    <literal><![CDATA[
      a(x,y,(((z * z) \ u) * w) * v5) = a(x,y,v5 * (w * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5623,a,b,6022,a)].">
      <j1 rule="hyper" parents="63 5623 6022"/>
    </justification>
  </clause>

  <clause id="6037">
    <literal><![CDATA[
      a(x,y,z * L(u,u,w)) = a(x,y,z * ((u * w) \ w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5914,a,b,6032,a)].">
      <j1 rule="hyper" parents="316 5914 6032"/>
    </justification>
  </clause>

  <clause id="6041">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) * u) * w) = a(x,y,((z \ 1) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,5543,a(flip),b,5650,a),flip(a)].">
      <j1 rule="hyper" parents="316 5543 5650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6042">
    <literal><![CDATA[
      a(x,y,L(L(L(z \ u,w,v5),v6,v7),z,z)) = a(x,y,L(L(z * u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(1356(a,1),5828(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1356 5828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6044">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * L(v5 / v6,v7,v8)))) = a(x,y,z \ (u \ (w * L(v6 \ v5,v7,v8))))
    ]]></literal>
    <justification jstring="[para(261(a,1),5506(a,1,3,2,2,2)),flip(a)].">
      <j1 rule="para" parents="261 5506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6048">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * ((v5 * v5) \ (v6 * (v7 * v5)))))) = a(x,y,z \ (u * (w * (v6 * (v7 * (v5 \ 1))))))
    ]]></literal>
    <justification jstring="[para(1055(a,1),5510(a,1,3,2,2,2))].">
      <j1 rule="para" parents="1055 5510"/>
    </justification>
  </clause>

  <clause id="6049">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * (v5 / v6)))) = a(x,y,z * (u \ (w * (v6 \ v5))))
    ]]></literal>
    <justification jstring="[para(116(a,1),5590(a,1,3,2,2,2)),flip(a)].">
      <j1 rule="para" parents="116 5590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6050">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ K(v5,v6)))) = a(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5836,a(flip),b,5592,a),flip(a)].">
      <j1 rule="hyper" parents="316 5836 5592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6051">
    <literal><![CDATA[
      a(x,y,z * (u * (w * T(v5,v6)))) = a(x,y,((w * v5) * u) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5623,a,b,5594,a),flip(a)].">
      <j1 rule="hyper" parents="316 5623 5594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6052">
    <literal><![CDATA[
      a(x,y,z * L(u \ (K(w,v5) * v6),v7,v8)) = a(x,y,z * L(u \ v6,v7,v8))
    ]]></literal>
    <justification jstring="[para(3914(a,1),5597(a,1,3,2,1))].">
      <j1 rule="para" parents="3914 5597"/>
    </justification>
  </clause>

  <clause id="6054">
    <literal><![CDATA[
      a(x,y,((T(z,u) * w) * v5) \ ((z * w) * R(v5,z,w))) = a(x,y,a(v5,z,w))
    ]]></literal>
    <justification jstring="[para(3417(a,2),5632(a,2,3))].">
      <j1 rule="para" parents="3417 5632"/>
    </justification>
  </clause>

  <clause id="6055">
    <literal><![CDATA[
      a(x,y,z * ((u * T(w,v5)) * v6)) = a(x,y,(v6 * (u * w)) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5623,a,b,5644,a),flip(a)].">
      <j1 rule="hyper" parents="316 5623 5644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6056">
    <literal><![CDATA[
      a(x,y,z * ((u * (w / v5)) * v6)) = a(x,y,z * ((u * (v5 \ w)) * v6))
    ]]></literal>
    <justification jstring="[para(116(a,1),5644(a,1,3,2,1,2)),flip(a)].">
      <j1 rule="para" parents="116 5644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6057">
    <literal><![CDATA[
      a(x,y,(R(z,z,u) \ u) * w) = a(x,y,(z \ L(u,z,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,5543,a(flip),b,5662,a)].">
      <j1 rule="hyper" parents="316 5543 5662"/>
    </justification>
  </clause>

  <clause id="6058">
    <literal><![CDATA[
      a(x,y,(z \ (1 / u)) * (w * ((u * z) \ K(u,u \ 1)))) = a(x,y,((z \ (1 / u)) * w) * L(z \ (1 / u),z,u))
    ]]></literal>
    <justification jstring="[para(1090(a,1),5676(a,2,3,2,2)),flip(a)].">
      <j1 rule="para" parents="1090 5676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6059">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (u / z)) \ w) = a(x,y,u \ w)
    ]]></literal>
    <justification jstring="[hyper(316,a,5962,a(flip),b,5683,a),flip(a)].">
      <j1 rule="hyper" parents="316 5962 5683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6063">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (z \ u)) \ w) = a(x,y,u \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5684,a(flip),b,6059,a)].">
      <j1 rule="hyper" parents="63 5684 6059"/>
    </justification>
  </clause>

  <clause id="6064">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) \ w) = a(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[para(9(a,1),6063(a,1,3,1,2))].">
      <j1 rule="para" parents="9 6063"/>
    </justification>
  </clause>

  <clause id="6065">
    <literal><![CDATA[
      a(x,y,(z * (u * z)) \ w) = a(x,y,R(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5682,a(flip),b,6064,a),flip(a)].">
      <j1 rule="hyper" parents="63 5682 6064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6066">
    <literal><![CDATA[
      a(x,y,R(z,u,u) \ w) = a(x,y,L(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5976,a(flip),b,6065,a),flip(a)].">
      <j1 rule="hyper" parents="63 5976 6065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6067">
    <literal><![CDATA[
      a(x,y,z \ ((u * z) \ z)) = a(x,y,R(u,z,z) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5772,a(flip),b,6065,a)].">
      <j1 rule="hyper" parents="63 5772 6065"/>
    </justification>
  </clause>

  <clause id="6068">
    <literal><![CDATA[
      a(x,y,(z * (u \ K(w,v5))) \ v6) = a(x,y,(z * u) \ v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,5970,a(flip),b,5686,a),flip(a)].">
      <j1 rule="hyper" parents="316 5970 5686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6069">
    <literal><![CDATA[
      a(x,y,(z \ (u * (w / v5))) * v6) = a(x,y,(z \ (u * (v5 \ w))) * v6)
    ]]></literal>
    <justification jstring="[para(116(a,1),5692(a,1,3,1,2,2)),flip(a)].">
      <j1 rule="para" parents="116 5692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6070">
    <literal><![CDATA[
      a(x,y,(z * ((u * (w \ 1)) * w)) * v5) = a(x,y,(z * R(u,w \ 1,w)) * v5)
    ]]></literal>
    <justification jstring="[para(1041(a,1),5696(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="1041 5696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6071">
    <literal><![CDATA[
      a(x,y,L((z * u) * (w * w),v5,v6)) = a(x,y,L(z * ((w * w) * u),v5,v6))
    ]]></literal>
    <justification jstring="[para(32(a,2),5709(a,1,3,1))].">
      <j1 rule="para" parents="32 5709"/>
    </justification>
  </clause>

  <clause id="6073">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),z \ v5,z \ v5)) = a(x,y,L((z \ v5) * v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5828,a(flip),b,5711,a)].">
      <j1 rule="hyper" parents="63 5828 5711"/>
    </justification>
  </clause>

  <clause id="6074">
    <literal><![CDATA[
      a(x,y,L(z,u,w * ((v5 * v5) \ v6))) = a(x,y,L(z,u,w * v6))
    ]]></literal>
    <justification jstring="[para(2782(a,1),5765(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2782 5765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6075">
    <literal><![CDATA[
      a(x,y,z \ ((T(u,w) * v5) * v6)) = a(x,y,z \ (v6 * (u * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,5773,a)].">
      <j1 rule="hyper" parents="63 5490 5773"/>
    </justification>
  </clause>

  <clause id="6076">
    <literal><![CDATA[
      a(x,y,z \ ((u \ T(w,v5)) * v6)) = a(x,y,z \ (v6 * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,5774,a)].">
      <j1 rule="hyper" parents="63 5490 5774"/>
    </justification>
  </clause>

  <clause id="6077">
    <literal><![CDATA[
      a(x,y,T(z,u) * L(T(z,w),v5,v6)) = a(x,y,L(z,v5,v6) \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2652,a,b,5781,a),flip(a)].">
      <j1 rule="hyper" parents="316 2652 5781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6078">
    <literal><![CDATA[
      a(x,y,L((z * z) * u,w,v5) * v6) = a(x,y,v6 * L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(9(a,1),5854(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="9 5854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6081">
    <literal><![CDATA[
      a(x,y,L(z \ (L(u,w,v5) \ (L(u,w,v5) \ u)),v6,v7)) = a(x,y,L(z \ u,v6,v7))
    ]]></literal>
    <justification jstring="[para(1522(a,1),5890(a,1,3,1,2))].">
      <j1 rule="para" parents="1522 5890"/>
    </justification>
  </clause>

  <clause id="6086">
    <literal><![CDATA[
      a(x,y,(z * (u \ (w * w))) * v5) = a(x,y,(z * u) * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,5836,a(flip),b,5986,a),flip(a)].">
      <j1 rule="hyper" parents="316 5836 5986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6088">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w * w)) * v5)) = a(x,y,(v5 * u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5623,a(flip),b,6086,a)].">
      <j1 rule="hyper" parents="63 5623 6086"/>
    </justification>
  </clause>

  <clause id="6089">
    <literal><![CDATA[
      a(x,y,(z * (u \ L(u,w,v5))) * v6) = a(x,y,(z * (u * L(u,w,v5))) * v6)
    ]]></literal>
    <justification jstring="[para(1503(a,1),6086(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="1503 6086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6091">
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) * w) * v5)) = a(x,y,(v5 * (w * u)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5796,a,b,5987,a)].">
      <j1 rule="hyper" parents="63 5796 5987"/>
    </justification>
  </clause>

  <clause id="6092">
    <literal><![CDATA[
      a(x,y,(((z \ 1) * u) * w) * v5) = a(x,y,(w * (u * z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5795,a,b,5987,a)].">
      <j1 rule="hyper" parents="63 5795 5987"/>
    </justification>
  </clause>

  <clause id="6093">
    <literal><![CDATA[
      a(x,y,(z * ((u \ 1) * w)) * v5) = a(x,y,(z * (w * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5666,a,b,5987,a)].">
      <j1 rule="hyper" parents="63 5666 5987"/>
    </justification>
  </clause>

  <clause id="6102">
    <literal><![CDATA[
      a(x,y,z \ ((u \ ((w \ v5) * (w * w))) * v6)) = a(x,y,z \ (v6 * (u \ (v5 / (w \ 1)))))
    ]]></literal>
    <justification jstring="[para(613(a,1),6076(a,1,3,2,1,2))].">
      <j1 rule="para" parents="613 6076"/>
    </justification>
  </clause>

  <clause id="6103">
    <literal><![CDATA[
      a(x,y,T(z,u) * L(T(z,w),v5,v5 \ 1)) = a(x,y,a(v5 \ 1,v5,z))
    ]]></literal>
    <justification jstring="[para(2408(a,1),6077(a,2,3))].">
      <j1 rule="para" parents="2408 6077"/>
    </justification>
  </clause>

  <clause id="6104">
    <literal><![CDATA[
      a(x,y,z * L(u * (w * w),v5,v6)) = a(x,y,z * L(u,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5654,a(flip),b,6078,a)].">
      <j1 rule="hyper" parents="63 5654 6078"/>
    </justification>
  </clause>

  <clause id="6106">
    <literal><![CDATA[
      a(x,y,((L((z \ 1) * u,w,v5) \ ((z \ 1) * u)) * (u * z)) * v6) = a(x,y,L((z \ 1) * u,w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5904,a(flip),b,6091,a),flip(a)].">
      <j1 rule="hyper" parents="63 5904 6091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6107">
    <literal><![CDATA[
      a(x,y,(z * ((u \ 1) * w)) * v5) = a(x,y,(z * (u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,5691,a,b,6093,a),flip(a)].">
      <j1 rule="hyper" parents="316 5691 6093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6109">
    <literal><![CDATA[
      a(x,y,(z * ((L(u,w,v5) \ u) * v6)) * v7) = a(x,y,(z * ((u \ L(u,w,v5)) * v6)) * v7)
    ]]></literal>
    <justification jstring="[para(1894(a,1),6107(a,1,3,1,2,1))].">
      <j1 rule="para" parents="1894 6107"/>
    </justification>
  </clause>

  <clause id="6110">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) = R(z,u,w) * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(20(a,2),5234(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 5234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6111">
    <literal><![CDATA[
      a(x,y,x) \ R(a(x,y,x) * z,u,w) = R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,6110,a,b,2290,a)].">
      <j1 rule="hyper" parents="133 6110 2290"/>
    </justification>
  </clause>

  <clause id="6112">
    <literal><![CDATA[
      R(x * a(y,z,y),u,w) = R(x,u,w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(2290(a,1),6110(a,1,1))].">
      <j1 rule="para" parents="2290 6110"/>
    </justification>
  </clause>

  <clause id="6113">
    <literal><![CDATA[
      R(a(x,y,x) \ z,u,w) = a(x,y,x) \ R(z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),6111(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 6111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6114">
    <literal><![CDATA[
      R(x * a(y,z,y),u,w) * v5 = a(y,z,y) * (R(x,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(6112(a,2),4538(a,1,1))].">
      <j1 rule="para" parents="6112 4538"/>
    </justification>
  </clause>

  <clause id="6115">
    <literal><![CDATA[
      R(a(x,y,x) \ z,u,w) \ v5 = (R(z,u,w) \ v5) * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(6113(a,2),5425(a,1,1))].">
      <j1 rule="para" parents="6113 5425"/>
    </justification>
  </clause>

  <clause id="6116">
    <literal><![CDATA[
      a(x,y,x) * (R(y,z,u) * x) = T(x * R(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5233,a(flip),b,6114,a),flip(a)].">
      <j1 rule="hyper" parents="63 5233 6114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6117">
    <literal><![CDATA[
      a(x,R(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,4948,a,b,6116,a)].">
      <j1 rule="hyper" parents="35 4948 6116"/>
    </justification>
  </clause>

  <clause id="6118">
    <literal><![CDATA[
      T(x * K(y,x),x * y) = L(x,a(z,u,w) * y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5242,a(flip),b,5281,a)].">
      <j1 rule="hyper" parents="63 5242 5281"/>
    </justification>
  </clause>

  <clause id="6120">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,x) = L(x,w,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2747,a(flip),b,6118,a),flip(a)].">
      <j1 rule="hyper" parents="63 2747 6118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6121">
    <literal><![CDATA[
      L(x,a(y,z,u) \ w,x) = L(x,w,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),6120(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 6120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6122">
    <literal><![CDATA[
      T(x * (K(y,x) * a(z,u,w)),y * x) = L(x,y,x) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(3075(a,1),5335(a,1,1))].">
      <j1 rule="para" parents="3075 5335"/>
    </justification>
  </clause>

  <clause id="6123">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),a(x,y,z)) = (1 / a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(316,a,5053,a,b,5380,a),flip(a)].">
      <j1 rule="hyper" parents="316 5053 5380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6124">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),a(x,y,z)) = (a(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(316,a,5006,a,b,5380,a),flip(a)].">
      <j1 rule="hyper" parents="316 5006 5380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6126">
    <literal><![CDATA[
      a(x,y,x) * ((z * u) \ (z * (u * w))) = L(w * a(x,y,x),u,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5423,a(flip),b,5408,a)].">
      <j1 rule="hyper" parents="63 5423 5408"/>
    </justification>
  </clause>

  <clause id="6127">
    <literal><![CDATA[
      x * (((x * x) \ y) * a(z,u,w)) = x \ L(a(z,u,w) * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2293,a(flip),b,5459,a)].">
      <j1 rule="hyper" parents="63 2293 5459"/>
    </justification>
  </clause>

  <clause id="6128">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ ((u * v5) * w))) = a(x,y,z * L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6032,a,b,5595,a)].">
      <j1 rule="hyper" parents="63 6032 5595"/>
    </justification>
  </clause>

  <clause id="6129">
    <literal><![CDATA[
      a(x,y,z \ (L(u \ (1 / u),w * v5,v6) * (v6 * (w * v5)))) = a(x,y,z \ (v6 * (w * (v5 * (u \ (1 / u))))))
    ]]></literal>
    <justification jstring="[para(505(a,1),5598(a,2,3,2,2))].">
      <j1 rule="para" parents="505 5598"/>
    </justification>
  </clause>

  <clause id="6130">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * (u \ 1))) = a(x,y,z \ L(w,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,5599,a(flip),b,5615,a)].">
      <j1 rule="hyper" parents="63 5599 5615"/>
    </justification>
  </clause>

  <clause id="6131">
    <literal><![CDATA[
      a(x,y,((z * u) * z) * w) = a(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5835,a(flip),b,5667,a)].">
      <j1 rule="hyper" parents="63 5835 5667"/>
    </justification>
  </clause>

  <clause id="6132">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ ((w * u) * z)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5495,a(flip),b,5702,a)].">
      <j1 rule="hyper" parents="63 5495 5702"/>
    </justification>
  </clause>

  <clause id="6134">
    <literal><![CDATA[
      a(x,y,((z * ((u * w) / u)) * u) \ ((T(u,w) * w) * z)) = a(x,y,a(u,(u * w) / u,z))
    ]]></literal>
    <justification jstring="[para(2891(a,2),6132(a,1,3,2,1))].">
      <j1 rule="para" parents="2891 6132"/>
    </justification>
  </clause>

  <clause id="6135">
    <literal><![CDATA[
      a(x,y,((z * u) * (w \ K(u,w \ 1))) \ ((u * (w \ 1)) * z)) = a(x,y,a(w \ K(u,w \ 1),u,z))
    ]]></literal>
    <justification jstring="[para(3056(a,1),6132(a,1,3,2,1))].">
      <j1 rule="para" parents="3056 6132"/>
    </justification>
  </clause>

  <clause id="6136">
    <literal><![CDATA[
      a(x,y,(z * u) * L(w,z,u \ 1)) = a(x,y,u * (z * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5836,a(flip),b,5743,a)].">
      <j1 rule="hyper" parents="63 5836 5743"/>
    </justification>
  </clause>

  <clause id="6139">
    <literal><![CDATA[
      L(x * a(y,z,y),u,w) = a(y,z,y) * L(x,u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),6126(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 6126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6140">
    <literal><![CDATA[
      L(x * a(y,z,y),u,w) = L(x,u,w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2298,a,b,6139,a),flip(a)].">
      <j1 rule="hyper" parents="316 2298 6139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6141">
    <literal><![CDATA[
      L(a(x,y,x) * z,u,w) = a(x,y,x) * L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2314,a,b,6139,a)].">
      <j1 rule="hyper" parents="63 2314 6139"/>
    </justification>
  </clause>

  <clause id="6142">
    <literal><![CDATA[
      a(x,y,x) \ L(a(x,y,x) * z,u,w) = L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,2314,a,b,6139,a(flip))].">
      <j1 rule="hyper" parents="133 2314 6139"/>
    </justification>
  </clause>

  <clause id="6143">
    <literal><![CDATA[
      a(x,y,x) * L(a(x,y,x) \ z,u,w) = L(z,u,w)
    ]]></literal>
    <justification jstring="[para(2274(a,1),6139(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2274 6139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6144">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) = a(x,y,x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(35,a,1369,a(flip),b,6140,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 1369 6140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6145">
    <literal><![CDATA[
      L(x,y,z) * a(x,u,x) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(4528(a,1),6140(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4528 6140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6146">
    <literal><![CDATA[
      (x \ L(y,z,u)) * a(y,w,y) = x \ L(R(y,w,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,6145,a(flip),b,5390,a),flip(a)].">
      <j1 rule="hyper" parents="133 6145 5390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6148">
    <literal><![CDATA[
      x * L(a(x,y,x) \ z,u,w) = L(x,y,x) * L(z,u,w)
    ]]></literal>
    <justification jstring="[para(6143(a,1),4945(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6143 4945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6149">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) \ v5 = (L(z,u,w) \ v5) * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(6144(a,2),5425(a,1,1))].">
      <j1 rule="para" parents="6144 5425"/>
    </justification>
  </clause>

  <clause id="6150">
    <literal><![CDATA[
      R(x,y,x) \ L(R(x,y,x),z,u) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5432,a(flip),b,6146,a),flip(a)].">
      <j1 rule="hyper" parents="63 5432 6146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6151">
    <literal><![CDATA[
      R(x \ L(x,y,z),u,x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2158,a(flip),b,6150,a)].">
      <j1 rule="hyper" parents="63 2158 6150"/>
    </justification>
  </clause>

  <clause id="6152">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * y = (y \ L(y,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(138,a,6151,a(flip),b,5103,a),flip(a)].">
      <j1 rule="hyper" parents="138 6151 5103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6153">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) * x = (x \ L(x,y,z)) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(138,a,6151,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="138 6151 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6154">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (u * x) = ((x \ L(x,y,z)) \ u) * x
    ]]></literal>
    <justification jstring="[para(6151(a,1),492(a,1,1))].">
      <j1 rule="para" parents="6151 492"/>
    </justification>
  </clause>

  <clause id="6155">
    <literal><![CDATA[
      (x \ 1) * T((x \ L(x,y,z)) * (u * x),x \ 1) = R(u * (x \ L(x,y,z)),x,x)
    ]]></literal>
    <justification jstring="[para(6152(a,1),572(a,1,2,1))].">
      <j1 rule="para" parents="6152 572"/>
    </justification>
  </clause>

  <clause id="6156">
    <literal><![CDATA[
      L(x,y,x \ L(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(463,a,6153,a)].">
      <j1 rule="hyper" parents="463 6153"/>
    </justification>
  </clause>

  <clause id="6157">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((L(x \ L(x,y,z),u,w) \ 1) * x) = (L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z))) * x
    ]]></literal>
    <justification jstring="[para(1002(a,1),6153(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1002 6153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6158">
    <literal><![CDATA[
      L(x,y,R(x,z,u) \ L(R(x,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,29,a,b,6156,a(flip))].">
      <j1 rule="hyper" parents="42 29 6156"/>
    </justification>
  </clause>

  <clause id="6159">
    <literal><![CDATA[
      L(L(x,y,z),u,x \ L(x,w,v5)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(6156(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6156 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6161">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x \ L(x,w,v5)) = x \ L(L(x,y,z),u,x \ L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(6156(a,1),2138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6156 2138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6162">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) * a(x,x \ L(x,y,z),u) = (x \ L(x,y,z)) * (u * R(x,x \ L(x,y,z),u))
    ]]></literal>
    <justification jstring="[para(6156(a,1),3474(a,1,2,1))].">
      <j1 rule="para" parents="6156 3474"/>
    </justification>
  </clause>

  <clause id="6163">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (u * L(x,w,v5)) = ((x \ L(x,y,z)) \ u) * L(x,w,v5)
    ]]></literal>
    <justification jstring="[para(6159(a,1),456(a,1,2,2))].">
      <j1 rule="para" parents="6159 456"/>
    </justification>
  </clause>

  <clause id="6169">
    <literal><![CDATA[
      (L(x * y,z,u) \ (x * y)) \ (y * x) = L((x * y) * K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4837,a,b,3955,a),flip(a)].">
      <j1 rule="hyper" parents="316 4837 3955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6170">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * K(y \ 1,x) = K(z,K(x,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(139,a,4184,a(flip),b,4195,a)].">
      <j1 rule="hyper" parents="139 4184 4195"/>
    </justification>
  </clause>

  <clause id="6171">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * K((z \ y) \ 1,x) = K(z,K(x,(z \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(3028(a,1),6170(a,1,1,2))].">
      <j1 rule="para" parents="3028 6170"/>
    </justification>
  </clause>

  <clause id="6172">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (K(v5,v6) * v7)))) = a(x,y,z \ ((w * v7) * u))
    ]]></literal>
    <justification jstring="[para(4227(a,1),5578(a,1,3))].">
      <j1 rule="para" parents="4227 5578"/>
    </justification>
  </clause>

  <clause id="6173">
    <literal><![CDATA[
      (x * ((y \ z) * y)) / (u * ((y \ z) * y)) = (x * z) / (u * z)
    ]]></literal>
    <justification jstring="[para(307(a,1),4230(a,1,2,2))].">
      <j1 rule="para" parents="307 4230"/>
    </justification>
  </clause>

  <clause id="6174">
    <literal><![CDATA[
      (x * y) / (L(x,z,z \ y) * y) = a(z \ y,z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4932,a,b,6173,a),flip(a)].">
      <j1 rule="hyper" parents="63 4932 6173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6175">
    <literal><![CDATA[
      T(K(x,y),z) * T(T(y,x),u) = T(y,K(x,z)) * K(T(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4088,a(flip),b,4240,a),flip(a)].">
      <j1 rule="hyper" parents="63 4088 4240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6176">
    <literal><![CDATA[
      T(K(x,y),z) * T(y,x) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,3832,a,b,6175,a(flip))].">
      <j1 rule="hyper" parents="35 3832 6175"/>
    </justification>
  </clause>

  <clause id="6177">
    <literal><![CDATA[
      K(x,T(y,z)) * T(y,x) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(3865(a,2),6176(a,1,1))].">
      <j1 rule="para" parents="3865 6176"/>
    </justification>
  </clause>

  <clause id="6179">
    <literal><![CDATA[
      K(x,T(y,z)) * T(y,x) = T(y,K(x,x * z))
    ]]></literal>
    <justification jstring="[para(3863(a,1),6176(a,1,1))].">
      <j1 rule="para" parents="3863 6176"/>
    </justification>
  </clause>

  <clause id="6181">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6177,a(flip),b,6179,a),flip(a)].">
      <j1 rule="hyper" parents="63 6177 6179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6182">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,4106,a,b,6181,a),flip(a)].">
      <j1 rule="hyper" parents="316 4106 6181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6183">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),6181(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 6181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6184">
    <literal><![CDATA[
      T(x,K(y * z,y)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(4120,a,6182,a)].">
      <j1 rule="hyper" parents="4120 6182"/>
    </justification>
  </clause>

  <clause id="6186">
    <literal><![CDATA[
      T(x * (y \ z),K(y,z)) = (y \ z) * T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4170,a(flip),b,6183,a),flip(a)].">
      <j1 rule="hyper" parents="63 4170 6183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6187">
    <literal><![CDATA[
      T(x * K(y,y \ z),K(y,z)) = K(y,y \ z) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,4115,a(flip),b,6183,a),flip(a)].">
      <j1 rule="hyper" parents="63 4115 6183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6195">
    <literal><![CDATA[
      T(x * ((y * z) \ y),K(y * z,y)) = L(z \ 1,z,y) * T(x,y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,360,a,b,6186,a),flip(a)].">
      <j1 rule="hyper" parents="316 360 6186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6196">
    <literal><![CDATA[
      K(x,x \ y) * (z \ (x \ y)) = T(z \ (y / x),K(x,y))
    ]]></literal>
    <justification jstring="[para(3919(a,1),6187(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3919 6187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6200">
    <literal><![CDATA[
      K(x,x \ L(y,z,u)) * (w \ (x \ L(y,z,u))) = T(w \ (L(y,z,u) / x),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,4320,a(flip),b,6196,a),flip(a)].">
      <j1 rule="hyper" parents="316 4320 6196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6201">
    <literal><![CDATA[
      (L(x \ ((x * (y * x)) / x),z,u) * x) * ((x \ ((x * (y * x)) / x)) \ ((x * (y * x)) / x)) = (x * L(a(x,y,x) \ y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(4946(a,2),4339(a,2,1,2,1))].">
      <j1 rule="para" parents="4946 4339"/>
    </justification>
  </clause>

  <clause id="6202">
    <literal><![CDATA[
      (x * x) \ (((x * x) / y) * L(y,z,u)) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,5017,a(flip),b,4384,a),flip(a)].">
      <j1 rule="hyper" parents="316 5017 4384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6205">
    <literal><![CDATA[
      (x / L(y * K(z,u),w,v5)) * y = y * (L(y,w,v5) \ (x * K(u,z)))
    ]]></literal>
    <justification jstring="[para(4837(a,2),4399(a,1,1,2))].">
      <j1 rule="para" parents="4837 4399"/>
    </justification>
  </clause>

  <clause id="6206">
    <literal><![CDATA[
      L(x,y,x \ 1) * ((x \ 1) * y) = x * (y * T(x \ 1,x \ y))
    ]]></literal>
    <justification jstring="[para(3491(a,1),4448(a,2,2))].">
      <j1 rule="para" parents="3491 4448"/>
    </justification>
  </clause>

  <clause id="6207">
    <literal><![CDATA[
      (x \ 1) * (y * T(x,x \ y)) = x * (y * T(x \ 1,x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3492,a(flip),b,6206,a)].">
      <j1 rule="hyper" parents="63 3492 6206"/>
    </justification>
  </clause>

  <clause id="6208">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ w)) = T(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(114(a,1),4498(a,1,2)),flip(a)].">
      <j1 rule="para" parents="114 4498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6209">
    <literal><![CDATA[
      x / T(x,y * ((z \ u) * w)) = K(y * ((u \ z) \ w),x)
    ]]></literal>
    <justification jstring="[hyper(209,a,6208,a(flip),b,2928,a(flip))].">
      <j1 rule="hyper" parents="209 6208 2928"/>
    </justification>
  </clause>

  <clause id="6210">
    <literal><![CDATA[
      K(x * ((y \ z) \ u),w) = K(x * ((z \ y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(2943,a,6209,a),flip(a)].">
      <j1 rule="hyper" parents="2943 6209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6211">
    <literal><![CDATA[
      x / L(T(K(y,z),u),w,v5) = x * L(T(K(z,y),u),w,v5)
    ]]></literal>
    <justification jstring="[para(3191(a,1),4519(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3191 4519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6213">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(T(K(z,y),u),u,x) = x * u
    ]]></literal>
    <justification jstring="[hyper(63,a,448,a(flip),b,6211,a),flip(a)].">
      <j1 rule="hyper" parents="63 448 6211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6214">
    <literal><![CDATA[
      ((x * (K(y,z) * u)) * R(L(T(K(z,y),u),u,x),w,v5)) / (x * (K(y,z) * u)) = R((x * u) / (x * (K(y,z) * u)),w,v5)
    ]]></literal>
    <justification jstring="[para(6213(a,1),756(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6213 756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6215">
    <literal><![CDATA[
      R((x * y) / (x * (K(z,u) * y)),x * (K(z,u) * y),L(T(K(u,z),y),y,x)) = (x * (y * T(K(u,z),y))) / (x * y)
    ]]></literal>
    <justification jstring="[para(6213(a,1),515(a,2,2))].">
      <j1 rule="para" parents="6213 515"/>
    </justification>
  </clause>

  <clause id="6216">
    <literal><![CDATA[
      a(x \ (x * ((y * y) \ ((y * y) * z))),u,w) = a(L(z,y * y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3379,a(flip),b,4571,a),flip(a)].">
      <j1 rule="hyper" parents="63 3379 4571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6218">
    <literal><![CDATA[
      a(x,y,L(z,u,w * (v5 * ((v6 * v6) \ v7)))) = a(x,y,L(z,u,w * (v5 * v7)))
    ]]></literal>
    <justification jstring="[para(4602(a,1),6074(a,1,3))].">
      <j1 rule="para" parents="4602 6074"/>
    </justification>
  </clause>

  <clause id="6219">
    <literal><![CDATA[
      R(x,y,z * ((u * (w * w)) \ v5)) = R(x,y,z * (u \ (v5 / (w * w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,4683,a(flip),b,4742,a)].">
      <j1 rule="hyper" parents="63 4683 4742"/>
    </justification>
  </clause>

  <clause id="6220">
    <literal><![CDATA[
      R(x,y,z * ((u * u) \ (w \ v5))) = R(x,y,z * (w \ ((u * u) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,4745,a(flip),b,4743,a),flip(a)].">
      <j1 rule="hyper" parents="316 4745 4743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6221">
    <literal><![CDATA[
      R(x,y,z \ ((u / (w * w)) \ v5)) = R(x,y,z \ (u \ (v5 * (w * w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,4695,a(flip),b,4758,a)].">
      <j1 rule="hyper" parents="63 4695 4758"/>
    </justification>
  </clause>

  <clause id="6222">
    <literal><![CDATA[
      ((x * (y \ x)) / ((x / y) * y)) \ y = y * (((x / y) * y) \ y)
    ]]></literal>
    <justification jstring="[para(116(a,1),4782(a,1,1,1,2))].">
      <j1 rule="para" parents="116 4782"/>
    </justification>
  </clause>

  <clause id="6223">
    <literal><![CDATA[
      ((x * (y \ x)) / x) \ y = y * (((x / y) * y) \ y)
    ]]></literal>
    <justification jstring="[para(12(a,1),6222(a,1,1,2))].">
      <j1 rule="para" parents="12 6222"/>
    </justification>
  </clause>

  <clause id="6224">
    <literal><![CDATA[
      ((x * (y \ x)) / x) \ y = y * (x \ y)
    ]]></literal>
    <justification jstring="[para(12(a,1),6223(a,2,2,1))].">
      <j1 rule="para" parents="12 6223"/>
    </justification>
  </clause>

  <clause id="6225">
    <literal><![CDATA[
      a(x * ((y \ (y * (z \ y))) \ z),u,w) = a(x * (z * (y \ z)),u,w)
    ]]></literal>
    <justification jstring="[para(6224(a,1),4180(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6224 4180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6226">
    <literal><![CDATA[
      (K(x,y) * z) * L((K(x,y) * z) \ u,w,v5) = z * L(z \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,602,a(flip),b,4853,a),flip(a)].">
      <j1 rule="hyper" parents="316 602 4853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6227">
    <literal><![CDATA[
      (T(x,y) \ z) \ L(T(x,y) \ z,x,u) = (((u * x) \ (u * z)) \ (x \ z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,5084,a,b,4869,a),flip(a)].">
      <j1 rule="hyper" parents="316 5084 4869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6228">
    <literal><![CDATA[
      ((x \ y) \ z) \ L(T(y / x,x) \ u,w,v5) = ((y / x) \ z) \ L((y / x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(116(a,1),4869(a,1,1,1))].">
      <j1 rule="para" parents="116 4869"/>
    </justification>
  </clause>

  <clause id="6229">
    <literal><![CDATA[
      (((x * x) \ x) \ y) \ L(T(x \ 1,x * x) \ z,u,w) = ((x \ 1) \ y) \ L((x \ 1) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(283(a,1),4869(a,1,1,1))].">
      <j1 rule="para" parents="283 4869"/>
    </justification>
  </clause>

  <clause id="6230">
    <literal><![CDATA[
      x * (y * L(y \ z,x,y)) = y * (x * ((y * x) \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,100,a(flip),b,4882,a),flip(a)].">
      <j1 rule="hyper" parents="63 100 4882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6232">
    <literal><![CDATA[
      x * (y * L(y \ (x \ z),x,y)) = y * (x * ((y * x) \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),6230(a,2,2,2,2))].">
      <j1 rule="para" parents="10 6230"/>
    </justification>
  </clause>

  <clause id="6233">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) = x * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(34,a,3290,a(flip),b,6232,a(flip))].">
      <j1 rule="hyper" parents="34 3290 6232"/>
    </justification>
  </clause>

  <clause id="6234">
    <literal><![CDATA[
      K(x,y) * ((x * y) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(3047,a,6233,a)].">
      <j1 rule="hyper" parents="3047 6233"/>
    </justification>
  </clause>

  <clause id="6235">
    <literal><![CDATA[
      K(x,y) \ ((y * x) \ z) = (x * y) \ z
    ]]></literal>
    <justification jstring="[hyper(34,a,2901,a,b,6233,a)].">
      <j1 rule="hyper" parents="34 2901 6233"/>
    </justification>
  </clause>

  <clause id="6236">
    <literal><![CDATA[
      (x * y) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(34,a,2912,a(flip),b,6233,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 2912 6233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6237">
    <literal><![CDATA[
      L(x,y,z * ((u * z) \ w)) = L(x,y,z * ((z * u) \ w))
    ]]></literal>
    <justification jstring="[para(6233(a,1),1662(a,1,3))].">
      <j1 rule="para" parents="6233 1662"/>
    </justification>
  </clause>

  <clause id="6238">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ (y \ (x * y)) = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(6233(a,1),1757(a,1,1))].">
      <j1 rule="para" parents="6233 1757"/>
    </justification>
  </clause>

  <clause id="6239">
    <literal><![CDATA[
      (x * ((y * x) \ z)) \ T(x,y) = (x * ((x * y) \ z)) \ x
    ]]></literal>
    <justification jstring="[para(6233(a,1),2877(a,1,1))].">
      <j1 rule="para" parents="6233 2877"/>
    </justification>
  </clause>

  <clause id="6240">
    <literal><![CDATA[
      T(x,x * ((y * x) \ z)) = T(x,x * ((x * y) \ z))
    ]]></literal>
    <justification jstring="[para(6233(a,1),4002(a,1,2))].">
      <j1 rule="para" parents="6233 4002"/>
    </justification>
  </clause>

  <clause id="6241">
    <literal><![CDATA[
      R(x,y,z * ((u * z) \ w)) = R(x,y,z * ((z * u) \ w))
    ]]></literal>
    <justification jstring="[para(6233(a,1),4686(a,1,3))].">
      <j1 rule="para" parents="6233 4686"/>
    </justification>
  </clause>

  <clause id="6246">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,161,a(flip),b,6234,a(flip))].">
      <j1 rule="hyper" parents="139 161 6234"/>
    </justification>
  </clause>

  <clause id="6247">
    <literal><![CDATA[
      K(x,y) * (((x * y) \ z) * u) = ((y * x) \ z) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,6234,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 6234 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6248">
    <literal><![CDATA[
      K(x,x \ y) * (y \ z) = ((x \ y) * x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),6234(a,1,2,1))].">
      <j1 rule="para" parents="10 6234"/>
    </justification>
  </clause>

  <clause id="6249">
    <literal><![CDATA[
      ((x * y) \ z) \ K(y,x) = ((y * x) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(6234(a,1),357(a,1,1))].">
      <j1 rule="para" parents="6234 357"/>
    </justification>
  </clause>

  <clause id="6250">
    <literal><![CDATA[
      T((x * y) \ z,K(y,x)) = ((y * x) \ z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6234(a,1),471(a,1,1))].">
      <j1 rule="para" parents="6234 471"/>
    </justification>
  </clause>

  <clause id="6251">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ v5)) = L(x,y,z * ((w * u) \ v5))
    ]]></literal>
    <justification jstring="[para(6234(a,1),1684(a,1,3,2))].">
      <j1 rule="para" parents="6234 1684"/>
    </justification>
  </clause>

  <clause id="6252">
    <literal><![CDATA[
      L(x,y,((z * u) \ w) \ v5) = L(x,y,((u * z) \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(6234(a,1),4172(a,1,3,1))].">
      <j1 rule="para" parents="6234 4172"/>
    </justification>
  </clause>

  <clause id="6254">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) \ v5) = a(x,y,((u * z) \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(6234(a,1),5624(a,1,3,1))].">
      <j1 rule="para" parents="6234 5624"/>
    </justification>
  </clause>

  <clause id="6255">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,v5,v6)) = a(x,y,L((u * z) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(6234(a,1),5554(a,1,3,1))].">
      <j1 rule="para" parents="6234 5554"/>
    </justification>
  </clause>

  <clause id="6257">
    <literal><![CDATA[
      a(x,y,(((z * u) \ w) * v5) \ v6) = a(x,y,(v5 * ((u * z) \ w)) \ v6)
    ]]></literal>
    <justification jstring="[para(6234(a,1),5945(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="6234 5945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6258">
    <literal><![CDATA[
      (x * y) * (y \ L(T(y,x),z,u)) = (y * x) * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,4350,a(flip),b,6236,a)].">
      <j1 rule="hyper" parents="139 4350 6236"/>
    </justification>
  </clause>

  <clause id="6259">
    <literal><![CDATA[
      (x * y) * (T(x,y) \ z) = (y * x) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,3002,a(flip),b,6236,a)].">
      <j1 rule="hyper" parents="139 3002 6236"/>
    </justification>
  </clause>

  <clause id="6260">
    <literal><![CDATA[
      (x * y) * (T(y,x) * z) = (y * x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,2946,a(flip),b,6236,a),flip(a)].">
      <j1 rule="hyper" parents="139 2946 6236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6261">
    <literal><![CDATA[
      x * (K(y \ x,y) * z) = ((y \ x) * y) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,6236,a(flip),b,165,a(flip))].">
      <j1 rule="hyper" parents="139 6236 165"/>
    </justification>
  </clause>

  <clause id="6263">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((y * x) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,3602,a,b,6249,a)].">
      <j1 rule="hyper" parents="63 3602 6249"/>
    </justification>
  </clause>

  <clause id="6264">
    <literal><![CDATA[
      (x * y) * (x \ K(y,x)) = (y * x) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2985,a(flip),b,6259,a)].">
      <j1 rule="hyper" parents="63 2985 6259"/>
    </justification>
  </clause>

  <clause id="6265">
    <literal><![CDATA[
      ((x \ y) * x) * ((x \ y) * z) = y * (T(x \ y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(631,a,6260,a),flip(a)].">
      <j1 rule="hyper" parents="631 6260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6266">
    <literal><![CDATA[
      ((x \ y) * x) * x = y * (y / (y / x))
    ]]></literal>
    <justification jstring="[para(3095(a,2),6261(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3095 6261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6267">
    <literal><![CDATA[
      x * L(K(y \ x,y) * z,u,w) = ((y \ x) * y) * L(z,u,w)
    ]]></literal>
    <justification jstring="[para(4850(a,2),6261(a,1,2))].">
      <j1 rule="para" parents="4850 6261"/>
    </justification>
  </clause>

  <clause id="6268">
    <literal><![CDATA[
      R(x,(x / y) \ x,x / y) * x = (((y \ x) * y) * y) * (x / y)
    ]]></literal>
    <justification jstring="[para(6266(a,2),4479(a,2,1))].">
      <j1 rule="para" parents="6266 4479"/>
    </justification>
  </clause>

  <clause id="6269">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) * x = x * T(((y * x) \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(6263(a,1),250(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6263 250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6270">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ (((v5 * v6) \ v6) \ 1)))) = a(x,y,z \ (u * (w \ (((v6 * v5) \ v6) \ 1))))
    ]]></literal>
    <justification jstring="[para(6263(a,1),5774(a,1,3,2,2,2))].">
      <j1 rule="para" parents="6263 5774"/>
    </justification>
  </clause>

  <clause id="6271">
    <literal><![CDATA[
      (x * y) * (x \ K(y,x)) = R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,565,a(flip),b,6264,a),flip(a)].">
      <j1 rule="hyper" parents="316 565 6264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6272">
    <literal><![CDATA[
      ((x \ K(y,x)) * (L(x \ K(y,x),z,u) \ (x * y))) * L(x \ K(y,x),z,u) = R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4393,a,b,6271,a)].">
      <j1 rule="hyper" parents="63 4393 6271"/>
    </justification>
  </clause>

  <clause id="6273">
    <literal><![CDATA[
      T(x,x * ((x * y) \ z)) = T(x,R(y,x,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3724,a(flip),b,6240,a),flip(a)].">
      <j1 rule="hyper" parents="63 3724 6240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6274">
    <literal><![CDATA[
      R(x,y,((z * u) \ w) * v5) = R(x,y,((u * z) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(6247(a,1),4685(a,1,3))].">
      <j1 rule="para" parents="6247 4685"/>
    </justification>
  </clause>

  <clause id="6275">
    <literal><![CDATA[
      R(x,y,((z * u) \ w) * v5) = R(x,y,v5 * ((u * z) \ w))
    ]]></literal>
    <justification jstring="[para(6247(a,1),4725(a,1,3))].">
      <j1 rule="para" parents="6247 4725"/>
    </justification>
  </clause>

  <clause id="6276">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,y) = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(22(a,2),6238(a,1,2))].">
      <j1 rule="para" parents="22 6238"/>
    </justification>
  </clause>

  <clause id="6277">
    <literal><![CDATA[
      (x * ((x * y) \ y)) \ x = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6276,a(flip),b,6239,a),flip(a)].">
      <j1 rule="hyper" parents="63 6276 6239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6278">
    <literal><![CDATA[
      T((x * (x * ((x * y) \ y))) / x,1 / ((x * y) \ y)) = ((x * ((x * y) \ y)) \ x) \ T(x,x * ((x * y) \ y))
    ]]></literal>
    <justification jstring="[para(6277(a,1),1241(a,1,2))].">
      <j1 rule="para" parents="6277 1241"/>
    </justification>
  </clause>

  <clause id="6279">
    <literal><![CDATA[
      L(x,y,((z * u) \ (u * (w * z))) \ v5) = L(x,y,L(T(w,z),z,u) \ v5)
    ]]></literal>
    <justification jstring="[para(247(a,1),6252(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="247 6252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6280">
    <literal><![CDATA[
      a(x,y,(z / (u * w)) \ v5) = a(x,y,((w * u) \ z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,5546,a,b,6254,a)].">
      <j1 rule="hyper" parents="316 5546 6254"/>
    </justification>
  </clause>

  <clause id="6281">
    <literal><![CDATA[
      a(x,y,(((z * (u * u)) * w) \ v5) \ v6) = a(x,y,(((w * z) * (u * u)) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[para(32(a,2),6254(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="32 6254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6283">
    <literal><![CDATA[
      R(x,y,(T(z / (u \ 1),u) \ w) * v5) = R(x,y,(((u * u) * (u \ z)) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(613(a,2),6274(a,1,3,1,1))].">
      <j1 rule="para" parents="613 6274"/>
    </justification>
  </clause>

  <clause id="6284">
    <literal><![CDATA[
      ((x \ y) * x) * L(((x \ y) * x) \ z,u,w) = y * L((x * (x \ y)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(6234(a,1),6267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6234 6267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6285">
    <literal><![CDATA[
      R(x,y,x / y) * x = (((y \ x) * y) * y) * (x / y)
    ]]></literal>
    <justification jstring="[para(83(a,1),6268(a,1,1,2))].">
      <j1 rule="para" parents="83 6268"/>
    </justification>
  </clause>

  <clause id="6286">
    <literal><![CDATA[
      R(x,y,y \ x) * x = (((y \ x) * y) * y) * (x / y)
    ]]></literal>
    <justification jstring="[para(4061(a,1),6285(a,1,1))].">
      <j1 rule="para" parents="4061 6285"/>
    </justification>
  </clause>

  <clause id="6287">
    <literal><![CDATA[
      (((x \ y) * x) * x) * (y / x) = (y * x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,495,a(flip),b,6286,a),flip(a)].">
      <j1 rule="hyper" parents="63 495 6286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6288">
    <literal><![CDATA[
      a(x,y,L(z,((u \ w) * u) * u,w / u) * ((w * u) * (u \ w))) = a(x,y,(w / u) * ((((u \ w) * u) * u) * z))
    ]]></literal>
    <justification jstring="[para(6287(a,1),5674(a,1,3,2))].">
      <j1 rule="para" parents="6287 5674"/>
    </justification>
  </clause>

  <clause id="6292">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * u = (z * K(x * (y \ z),y)) * u
    ]]></literal>
    <justification jstring="[para(3565(a,1),4925(a,2,1,2))].">
      <j1 rule="para" parents="3565 4925"/>
    </justification>
  </clause>

  <clause id="6293">
    <literal><![CDATA[
      L(x / (y / z),u,w) * (y / z) = (z \ y) * L((z \ y) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,602,a,b,4979,a)].">
      <j1 rule="hyper" parents="63 602 4979"/>
    </justification>
  </clause>

  <clause id="6294">
    <literal><![CDATA[
      ((x \ 1) \ y) * L(((x \ 1) \ y) \ x,z,u) = ((y / (x \ 1)) \ L(y,z,u)) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1876,a(flip),b,4979,a),flip(a)].">
      <j1 rule="hyper" parents="63 1876 4979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6295">
    <literal><![CDATA[
      ((x * x) \ (y \ z)) * L(((x * x) \ (y \ z)) \ u,w,v5) = (y \ (z / (x * x))) * L(((y \ z) / (x * x)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(675(a,1),4979(a,1,1)),flip(a)].">
      <j1 rule="para" parents="675 4979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6296">
    <literal><![CDATA[
      L(x \ ((y \ z) * L((y \ z) \ u,w,v5)),x,y \ z) = ((z / y) * x) \ L((z / y) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(4979(a,1),1599(a,1,1,2))].">
      <j1 rule="para" parents="4979 1599"/>
    </justification>
  </clause>

  <clause id="6297">
    <literal><![CDATA[
      x * (((y * y) \ z) * L(((y * y) \ z) \ (x \ 1),u,w)) = ((x * z) / (y * y)) \ L(x * (z / (y * y)),u,w)
    ]]></literal>
    <justification jstring="[para(4979(a,1),1507(a,1,2))].">
      <j1 rule="para" parents="4979 1507"/>
    </justification>
  </clause>

  <clause id="6298">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) / y) * L(((a(x,x,y) \ 1) / y) \ z,u,w) = L(y \ 1,x,x) * L((y \ (a(x,x,y) \ 1)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(5094(a,1),4979(a,2,1))].">
      <j1 rule="para" parents="5094 4979"/>
    </justification>
  </clause>

  <clause id="6299">
    <literal><![CDATA[
      T(x * L(x \ (x * y),z,u),w) \ (x * L(y,z,u)) = K(w,x * y)
    ]]></literal>
    <justification jstring="[para(4881(a,2),4982(a,1,1))].">
      <j1 rule="para" parents="4881 4982"/>
    </justification>
  </clause>

  <clause id="6300">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * x),u,w) = (y * L(y \ z,u,w)) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,879,a,b,4983,a)].">
      <j1 rule="hyper" parents="63 879 4983"/>
    </justification>
  </clause>

  <clause id="6303">
    <literal><![CDATA[
      (a(x,y,z) \ ((a(x,y,z) \ 1) \ u)) * (a(x,y,z) \ 1) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,2320,a,b,5048,a)].">
      <j1 rule="hyper" parents="63 2320 5048"/>
    </justification>
  </clause>

  <clause id="6304">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ ((a(x,y,z) \ 1) \ u) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,5362,a(flip),b,5048,a)].">
      <j1 rule="hyper" parents="63 5362 5048"/>
    </justification>
  </clause>

  <clause id="6305">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * (a(x,y,z) \ u) = (a(x,y,z) \ 1) \ u
    ]]></literal>
    <justification jstring="[hyper(139,a,5048,a(flip),b,5362,a(flip))].">
      <j1 rule="hyper" parents="139 5048 5362"/>
    </justification>
  </clause>

  <clause id="6308">
    <literal><![CDATA[
      (x \ 1) * (T(y,x \ 1) * (x \ L(x,z,u))) = (x \ L(x,z,u)) * (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,238,a(flip),b,5114,a),flip(a)].">
      <j1 rule="hyper" parents="63 238 5114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6309">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) / u = u \ (L(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[para(604(a,1),5129(a,1,2)),flip(a)].">
      <j1 rule="para" parents="604 5129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6310">
    <literal><![CDATA[
      (x * y) \ (L(z,y,x) * (z \ (x * y))) = ((x * (y * z)) / z) / (x * y)
    ]]></literal>
    <justification jstring="[para(4378(a,1),6309(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4378 6309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6311">
    <literal><![CDATA[
      T(x \ T(x * ((y \ L(y,z,u)) * (y \ L(y,w,v5))),(y \ L(y,z,u)) * (y \ L(y,w,v5))),x * ((y \ L(y,z,u)) * (y \ L(y,w,v5)))) = L(y,z,u) * L(y \ 1,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3650,a,b,5133,a)].">
      <j1 rule="hyper" parents="63 3650 5133"/>
    </justification>
  </clause>

  <clause id="6312">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (x \ L(x,y,z)) = L(x,y,z) * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1893,a,b,5133,a)].">
      <j1 rule="hyper" parents="63 1893 5133"/>
    </justification>
  </clause>

  <clause id="6315">
    <literal><![CDATA[
      (x \ y) * (L(y,z,u) * L(y \ 1,z,u)) = x \ (L(y,z,u) * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(5133(a,1),1888(a,1,2))].">
      <j1 rule="para" parents="5133 1888"/>
    </justification>
  </clause>

  <clause id="6316">
    <literal><![CDATA[
      x * (y * (L(y,z,u) \ (L(y,z,u) \ y))) = x / (L(y,z,u) * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(5133(a,1),1925(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 1925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6319">
    <literal><![CDATA[
      (x * y) * (L(z,u,w) * L(z \ 1,u,w)) = x * (y * (L(z,u,w) * L(z \ 1,u,w)))
    ]]></literal>
    <justification jstring="[para(5133(a,1),2114(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5133 2114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6321">
    <literal><![CDATA[
      a(x,y,z * (u * ((L(w,v5,v6) * L(w \ 1,v5,v6)) \ v7))) = a(x,y,z * (u * v7))
    ]]></literal>
    <justification jstring="[para(5133(a,1),6022(a,1,3,2,2,1))].">
      <j1 rule="para" parents="5133 6022"/>
    </justification>
  </clause>

  <clause id="6323">
    <literal><![CDATA[
      x * (1 / L(x \ L(x,y,z),u,w)) = L(x \ L(x,y,z),u,w) \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,5019,a(flip),b,5168,a),flip(a)].">
      <j1 rule="hyper" parents="316 5019 5168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6324">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ L(u,a(x,y,z),a(x,y,z)) = a(x,y,z) * T(u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,5046,a,b,5251,a(flip))].">
      <j1 rule="hyper" parents="34 5046 5251"/>
    </justification>
  </clause>

  <clause id="6325">
    <literal><![CDATA[
      L(L(x,y,z) \ L(L(x,y,z),x,a(u,w,v5)),L(x,y,z),x * a(u,w,v5)) = a(x,L(x,y,z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,1529,a(flip),b,5385,a),flip(a)].">
      <j1 rule="hyper" parents="316 1529 5385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6327">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 \ T(v6,v7))))) = a(x,y,z \ (u * (w * (v5 \ v6))))
    ]]></literal>
    <justification jstring="[para(3846(a,1),5517(a,1,3,2,2,2))].">
      <j1 rule="para" parents="3846 5517"/>
    </justification>
  </clause>

  <clause id="6328">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 \ (v6 \ T(v7,v8)))))) = a(x,y,z \ (u * (w * (v5 \ (v6 \ v7)))))
    ]]></literal>
    <justification jstring="[para(3912(a,1),5517(a,1,3,2,2,2))].">
      <j1 rule="para" parents="3912 5517"/>
    </justification>
  </clause>

  <clause id="6329">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 \ (v6 / v7))))) = a(x,y,z \ (u * (w * (v5 \ (v7 \ v6)))))
    ]]></literal>
    <justification jstring="[para(3917(a,1),5517(a,1,3,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3917 5517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6330">
    <literal><![CDATA[
      a(x,y,(L((z \ (z \ 1)) \ u,w,v5) \ v6) * v7) = a(x,y,(L(u * (z * z),w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[para(447(a,1),5555(a,1,3,1,1,1))].">
      <j1 rule="para" parents="447 5555"/>
    </justification>
  </clause>

  <clause id="6331">
    <literal><![CDATA[
      x * a(x,(y \ 1) * z,y * z) = R(x,(y \ 1) * z,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4707,a(flip),b,5571,a),flip(a)].">
      <j1 rule="hyper" parents="63 4707 5571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6332">
    <literal><![CDATA[
      a(x,y,z * ((u * (w * w)) \ v5)) = a(x,y,z * (u \ (v5 / (w * w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,5481,a(flip),b,5580,a)].">
      <j1 rule="hyper" parents="63 5481 5580"/>
    </justification>
  </clause>

  <clause id="6333">
    <literal><![CDATA[
      a(x,y,z * ((u * u) \ (w \ v5))) = a(x,y,z * (w \ ((u * u) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5591,a(flip),b,5581,a),flip(a)].">
      <j1 rule="hyper" parents="316 5591 5581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6334">
    <literal><![CDATA[
      a(x,y,z \ ((u * (w * w)) * v5)) = a(x,y,z \ ((w * w) * (v5 * u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5490,a,b,5611,a)].">
      <j1 rule="hyper" parents="316 5490 5611"/>
    </justification>
  </clause>

  <clause id="6336">
    <literal><![CDATA[
      a(x,y,((z * u) * (w / v5)) \ (((v5 \ w) * u) * z)) = a(x,y,a(w / v5,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6132,a(flip),b,5630,a),flip(a)].">
      <j1 rule="hyper" parents="63 6132 5630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6337">
    <literal><![CDATA[
      a(x,y,z \ (u * L(T(w,v5),v6,v7))) = a(x,y,z \ (L(w,v6,v7) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,5635,a)].">
      <j1 rule="hyper" parents="63 5490 5635"/>
    </justification>
  </clause>

  <clause id="6338">
    <literal><![CDATA[
      a(x,y,z \ ((u / (w * w)) \ v5)) = a(x,y,z \ (u \ (v5 * (w * w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,5497,a(flip),b,5637,a)].">
      <j1 rule="hyper" parents="63 5497 5637"/>
    </justification>
  </clause>

  <clause id="6339">
    <literal><![CDATA[
      a(x,y,z \ (u * (w / (v5 * v5)))) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5842,a(flip),b,5638,a),flip(a)].">
      <j1 rule="hyper" parents="63 5842 5638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6341">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * w) \ v5))) = a(x,y,z \ (u * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5599,a(flip),b,6339,a)].">
      <j1 rule="hyper" parents="63 5599 6339"/>
    </justification>
  </clause>

  <clause id="6342">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 \ 1)))) = a(x,y,z \ (u * (w * v5)))
    ]]></literal>
    <justification jstring="[para(562(a,1),6339(a,1,3,2,2))].">
      <j1 rule="para" parents="562 6339"/>
    </justification>
  </clause>

  <clause id="6343">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ (v5 \ 1)))) = a(x,y,z \ (u * (w \ v5)))
    ]]></literal>
    <justification jstring="[para(588(a,1),6339(a,1,3,2,2))].">
      <j1 rule="para" parents="588 6339"/>
    </justification>
  </clause>

  <clause id="6344">
    <literal><![CDATA[
      a(x,y,z \ (u * T(w / (v5 \ 1),v5))) = a(x,y,z \ (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(672(a,1),6339(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="672 6339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6345">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (w * v5)))) = a(x,y,z \ (u * L(v5,w,w)))
    ]]></literal>
    <justification jstring="[para(18(a,2),6341(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="18 6341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6346">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * ((v5 * v5) \ L(v6,w,u)))) = a(x,y,z \ (u * (w * v6)))
    ]]></literal>
    <justification jstring="[para(100(a,1),6341(a,2,3,2))].">
      <j1 rule="para" parents="100 6341"/>
    </justification>
  </clause>

  <clause id="6347">
    <literal><![CDATA[
      a(x,y,z \ (u * L(T(w,v5),v5,v5))) = a(x,y,z \ (u * (v5 * (w * v5))))
    ]]></literal>
    <justification jstring="[para(247(a,1),6341(a,1,3,2,2))].">
      <j1 rule="para" parents="247 6341"/>
    </justification>
  </clause>

  <clause id="6348">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(w,u,u))) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(1118(a,1),6341(a,1,3,2))].">
      <j1 rule="para" parents="1118 6341"/>
    </justification>
  </clause>

  <clause id="6349">
    <literal><![CDATA[
      a(x,y,z \ (R(u,u,w) \ w)) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(4655(a,2),6341(a,1,3,2))].">
      <j1 rule="para" parents="4655 6341"/>
    </justification>
  </clause>

  <clause id="6350">
    <literal><![CDATA[
      a(x,y,R(z,z,R(u,u,w) \ w) \ (u * w)) = a(x,y,(R(u,u,w) \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5855,a(flip),b,6349,a),flip(a)].">
      <j1 rule="hyper" parents="63 5855 6349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6351">
    <literal><![CDATA[
      a(x,y,z \ (R(L(u,w,u),L(u,w,u),v5) \ v5)) = a(x,y,z \ (u * (a(u,w,u) \ v5)))
    ]]></literal>
    <justification jstring="[para(4942(a,2),6349(a,2,3,2))].">
      <j1 rule="para" parents="4942 6349"/>
    </justification>
  </clause>

  <clause id="6352">
    <literal><![CDATA[
      a(x,y,z \ (((u \ 1) * w) * v5)) = a(x,y,z \ (v5 * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6003,a,b,6342,a)].">
      <j1 rule="hyper" parents="63 6003 6342"/>
    </justification>
  </clause>

  <clause id="6353">
    <literal><![CDATA[
      a(x,y,z \ ((u * (w \ 1)) * v5)) = a(x,y,z \ (v5 * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,6342,a)].">
      <j1 rule="hyper" parents="63 5490 6342"/>
    </justification>
  </clause>

  <clause id="6354">
    <literal><![CDATA[
      a(x,y,z \ (u * (L(w,v5,v6) \ w))) = a(x,y,z \ (u * (w * L(w,v5,v6))))
    ]]></literal>
    <justification jstring="[para(1002(a,1),6342(a,1,3,2,2))].">
      <j1 rule="para" parents="1002 6342"/>
    </justification>
  </clause>

  <clause id="6355">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (w \ 1)) * v5)) = a(x,y,z \ (v5 * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,6343,a)].">
      <j1 rule="hyper" parents="63 5490 6343"/>
    </justification>
  </clause>

  <clause id="6356">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w \ 1) * v5))) = a(x,y,z \ (u * (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,6352,a)].">
      <j1 rule="hyper" parents="63 5490 6352"/>
    </justification>
  </clause>

  <clause id="6357">
    <literal><![CDATA[
      a(x,y,z \ (((u \ 1) * (L(1 / u,w,v5) \ 1)) * v6)) = a(x,y,z \ (v6 * (u \ L(u \ 1,w,v5))))
    ]]></literal>
    <justification jstring="[para(899(a,1),6353(a,2,3,2,2))].">
      <j1 rule="para" parents="899 6353"/>
    </justification>
  </clause>

  <clause id="6358">
    <literal><![CDATA[
      a(x,y,z \ (T((u * (w \ 1)) \ ((u * (w \ 1)) / v5),v5) * (u * w))) = a(x,y,z \ ((u * (w \ 1)) / T(v5,v5 \ 1)))
    ]]></literal>
    <justification jstring="[para(2522(a,1),6353(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2522 6353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6359">
    <literal><![CDATA[
      a(x,y,z * L(u \ K(w,v5),v6,v7)) = a(x,y,L(u,v6,v7) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5989,a(flip),b,5652,a),flip(a)].">
      <j1 rule="hyper" parents="316 5989 5652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6360">
    <literal><![CDATA[
      a(x,y,(((1 / z) * u) * w) * v5) = a(x,y,(w * (u * z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,6092,a(flip),b,5655,a),flip(a)].">
      <j1 rule="hyper" parents="316 6092 5655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6361">
    <literal><![CDATA[
      a(x,y,((z * (u * u)) \ w) * v5) = a(x,y,(z \ (w / (u * u))) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5543,a(flip),b,5658,a)].">
      <j1 rule="hyper" parents="63 5543 5658"/>
    </justification>
  </clause>

  <clause id="6363">
    <literal><![CDATA[
      a(x,y,((z / (u * u)) \ w) * v5) = a(x,y,(z \ (w * (u * u))) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5543,a(flip),b,5660,a)].">
      <j1 rule="hyper" parents="63 5543 5660"/>
    </justification>
  </clause>

  <clause id="6365">
    <literal><![CDATA[
      a(x,y,z * (u * (w * (v5 * (v6 * T(v7,v8)))))) = a(x,y,(u * (w * (v5 * (v6 * v7)))) * z)
    ]]></literal>
    <justification jstring="[para(3942(a,1),5668(a,1,3,2,2,2))].">
      <j1 rule="para" parents="3942 5668"/>
    </justification>
  </clause>

  <clause id="6367">
    <literal><![CDATA[
      a(x,y,L(L(z * K(u,w),v5,v6),v7,v8)) = a(x,y,L(L(z,v7,v8),v5,v6))
    ]]></literal>
    <justification jstring="[para(4837(a,2),5707(a,1,3,1))].">
      <j1 rule="para" parents="4837 5707"/>
    </justification>
  </clause>

  <clause id="6368">
    <literal><![CDATA[
      a(x,y,L(L(T(z,u) \ w,v5,v6),v7,v8)) = a(x,y,L(L(z \ w,v7,v8),v5,v6))
    ]]></literal>
    <justification jstring="[para(4854(a,1),5716(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4854 5716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6370">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * w) * v5))) = a(x,y,(u \ v5) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5874,a(flip),b,5732,a),flip(a)].">
      <j1 rule="hyper" parents="63 5874 5732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6372">
    <literal><![CDATA[
      a(x,y,(z \ ((u * u) * w)) * v5) = a(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,6370,a)].">
      <j1 rule="hyper" parents="63 5469 6370"/>
    </justification>
  </clause>

  <clause id="6373">
    <literal><![CDATA[
      a(x,y,(z \ ((u * u) \ w)) * v5) = a(x,y,v5 * (z \ w))
    ]]></literal>
    <justification jstring="[para(10(a,1),6370(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="10 6370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6375">
    <literal><![CDATA[
      a(x,y,(z \ (u \ L(u,w,v5))) * v6) = a(x,y,(z \ (u * L(u,w,v5))) * v6)
    ]]></literal>
    <justification jstring="[para(5137(a,1),6372(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="5137 6372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6377">
    <literal><![CDATA[
      a(x,y,L(z,u,L(w \ 1,v5,v6))) = a(x,y,L(z,u,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(229(a,1),5766(a,1,3,3,1)),flip(a)].">
      <j1 rule="para" parents="229 5766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6378">
    <literal><![CDATA[
      x \ R(x,(y \ 1) \ z,y \ z) = a(x,(y \ 1) \ z,y \ z)
    ]]></literal>
    <justification jstring="[para(4789(a,1),5823(a,1,2))].">
      <j1 rule="para" parents="4789 5823"/>
    </justification>
  </clause>

  <clause id="6379">
    <literal><![CDATA[
      a(x,(y \ 1) \ z,y \ z) * x = R(x,(y \ 1) \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,6378,a)].">
      <j1 rule="hyper" parents="38 2295 6378"/>
    </justification>
  </clause>

  <clause id="6380">
    <literal><![CDATA[
      a(x,y,L(z * R(z,u,u),w,v5)) = a(x,y,L(a(z,u,u),w,v5))
    ]]></literal>
    <justification jstring="[para(2380(a,1),5892(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2380 5892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6381">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,u),w,v5)) = a(x,y,a(u,u,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,4970,a(flip),b,5893,a),flip(a)].">
      <j1 rule="hyper" parents="63 4970 5893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6384">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w * w) * v5))) = a(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,5804,a(flip),b,5923,a),flip(a)].">
      <j1 rule="hyper" parents="316 5804 5923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6387">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * (w * v5)))) = a(x,y,z \ (u \ L(v5,w,w)))
    ]]></literal>
    <justification jstring="[para(100(a,1),6384(a,1,3,2,2))].">
      <j1 rule="para" parents="100 6384"/>
    </justification>
  </clause>

  <clause id="6389">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * (v5 * w)))) = a(x,y,z \ (u \ L(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5919,a,b,6387,a)].">
      <j1 rule="hyper" parents="63 5919 6387"/>
    </justification>
  </clause>

  <clause id="6390">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w * v5) * v5))) = a(x,y,z \ (u \ L(w,v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5602,a,b,6389,a)].">
      <j1 rule="hyper" parents="63 5602 6389"/>
    </justification>
  </clause>

  <clause id="6391">
    <literal><![CDATA[
      a(x,y,z \ (u \ (((w \ v5) * (w * w)) * (v6 * ((w \ v5) * (w * w)))))) = a(x,y,z \ (u \ L(v6,(w \ v5) * (w * w),(w \ 1) \ v5)))
    ]]></literal>
    <justification jstring="[para(1653(a,1),6389(a,2,3,2,2))].">
      <j1 rule="para" parents="1653 6389"/>
    </justification>
  </clause>

  <clause id="6392">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(w \ v5,w,w))) = a(x,y,z \ (u \ (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5921,a(flip),b,6390,a),flip(a)].">
      <j1 rule="hyper" parents="63 5921 6390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6393">
    <literal><![CDATA[
      a(x,y,((z / (u * (w * w))) * (w * w)) \ v5) = a(x,y,(u \ z) \ v5)
    ]]></literal>
    <justification jstring="[para(393(a,1),5934(a,1,3,1,1))].">
      <j1 rule="para" parents="393 5934"/>
    </justification>
  </clause>

  <clause id="6394">
    <literal><![CDATA[
      a(x,y,((1 / z) * u) \ (z \ u)) = a(x,y,(z \ u) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5902,a(flip),b,5936,a),flip(a)].">
      <j1 rule="hyper" parents="316 5902 5936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6395">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) \ (z \ u)) = a(x,y,(z \ u) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5631,a(flip),b,6394,a)].">
      <j1 rule="hyper" parents="63 5631 6394"/>
    </justification>
  </clause>

  <clause id="6396">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,u \ 1),w,v5)) = a(x,y,L(a(u \ 1,u,z),w,v5))
    ]]></literal>
    <justification jstring="[para(2408(a,1),6000(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2408 6000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6398">
    <literal><![CDATA[
      a(x,y,(L(z \ 1,u,w) * v5) \ v6) = a(x,y,(v5 * L(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5626,a,b,6016,a)].">
      <j1 rule="hyper" parents="63 5626 6016"/>
    </justification>
  </clause>

  <clause id="6400">
    <literal><![CDATA[
      a(x,y,T(z,u) * ((1 / w) * (z * w))) = a(x,y,a(w \ 1,w,z))
    ]]></literal>
    <justification jstring="[para(892(a,1),6103(a,1,3,2))].">
      <j1 rule="para" parents="892 6103"/>
    </justification>
  </clause>

  <clause id="6401">
    <literal><![CDATA[
      a(x,y,T(z,u) * ((w \ 1) * (z * w))) = a(x,y,a(w \ 1,w,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5642,a(flip),b,6400,a)].">
      <j1 rule="hyper" parents="63 5642 6400"/>
    </justification>
  </clause>

  <clause id="6402">
    <literal><![CDATA[
      a(x,y,T(z,u) * ((z * w) * w)) = a(x,y,a(w \ 1,w,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5902,a(flip),b,6401,a)].">
      <j1 rule="hyper" parents="63 5902 6401"/>
    </justification>
  </clause>

  <clause id="6403">
    <literal><![CDATA[
      a(x,y,z * ((T(z,u) * w) * w)) = a(x,y,a(w \ 1,w,z))
    ]]></literal>
    <justification jstring="[para(3182(a,1),6402(a,1,3))].">
      <j1 rule="para" parents="3182 6402"/>
    </justification>
  </clause>

  <clause id="6404">
    <literal><![CDATA[
      a(x,y,R(T(z,u),w,w) * z) = a(x,y,a(w \ 1,w,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5883,a(flip),b,6403,a)].">
      <j1 rule="hyper" parents="63 5883 6403"/>
    </justification>
  </clause>

  <clause id="6405">
    <literal><![CDATA[
      a(x,y,a(z \ 1,z,u)) = a(x,y,u * R(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5653,a(flip),b,6404,a),flip(a)].">
      <j1 rule="hyper" parents="63 5653 6404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6406">
    <literal><![CDATA[
      a(x,y,a(z \ 1,z,u)) = a(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5573,a(flip),b,6405,a),flip(a)].">
      <j1 rule="hyper" parents="316 5573 6405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6407">
    <literal><![CDATA[
      (L(x * y,z,u) \ (x * y)) \ (y * x) = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(94(a,1),6169(a,2,1))].">
      <j1 rule="para" parents="94 6169"/>
    </justification>
  </clause>

  <clause id="6408">
    <literal><![CDATA[
      L(x * y,z,u) \ (x * y) = L(y * x,z,u) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(39,a,1379,a,b,6407,a)].">
      <j1 rule="hyper" parents="39 1379 6407"/>
    </justification>
  </clause>

  <clause id="6409">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * K((z \ y) \ 1,x) = K(z,K(x,y \ z))
    ]]></literal>
    <justification jstring="[para(3541(a,1),6171(a,2,2))].">
      <j1 rule="para" parents="3541 6171"/>
    </justification>
  </clause>

  <clause id="6410">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * K((z \ y) \ 1,x) = K(x,K(z,y \ z))
    ]]></literal>
    <justification jstring="[hyper(316,a,4084,a,b,6409,a),flip(a)].">
      <j1 rule="hyper" parents="316 4084 6409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6411">
    <literal><![CDATA[
      K(x,y / z) * K((y \ z) \ 1,x) = K(x,K(y,z \ y))
    ]]></literal>
    <justification jstring="[para(1957(a,1),6410(a,1,1))].">
      <j1 rule="para" parents="1957 6410"/>
    </justification>
  </clause>

  <clause id="6412">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,x) = K(x,K(y,z \ y))
    ]]></literal>
    <justification jstring="[para(3593(a,1),6411(a,1,2))].">
      <j1 rule="para" parents="3593 6411"/>
    </justification>
  </clause>

  <clause id="6413">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4260,a(flip),b,6412,a),flip(a)].">
      <j1 rule="hyper" parents="63 4260 6412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6414">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4103,a,b,6413,a)].">
      <j1 rule="hyper" parents="63 4103 6413"/>
    </justification>
  </clause>

  <clause id="6415">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,4086,a(flip),b,6414,a),flip(a)].">
      <j1 rule="hyper" parents="316 4086 6414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6416">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4092,a,b,6415,a)].">
      <j1 rule="hyper" parents="63 4092 6415"/>
    </justification>
  </clause>

  <clause id="6417">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,4084,a,b,6416,a),flip(a)].">
      <j1 rule="hyper" parents="316 4084 6416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6418">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = K(x,T(y,z \ 1))
    ]]></literal>
    <justification jstring="[para(6417(a,1),4098(a,1,2))].">
      <j1 rule="para" parents="6417 4098"/>
    </justification>
  </clause>

  <clause id="6419">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4098,a(flip),b,6418,a),flip(a)].">
      <j1 rule="hyper" parents="63 4098 6418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6420">
    <literal><![CDATA[
      T(K(x,y),z \ 1) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3865,a(flip),b,6419,a)].">
      <j1 rule="hyper" parents="63 3865 6419"/>
    </justification>
  </clause>

  <clause id="6421">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3053,a(flip),b,6419,a)].">
      <j1 rule="hyper" parents="63 3053 6419"/>
    </justification>
  </clause>

  <clause id="6422">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = T(K(x,y),u \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3664,a(flip),b,6420,a),flip(a)].">
      <j1 rule="hyper" parents="63 3664 6420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6423">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ T(y,u)) = (z \ T(y,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6421(a,1),4216(a,1,1))].">
      <j1 rule="para" parents="6421 4216"/>
    </justification>
  </clause>

  <clause id="6424">
    <literal><![CDATA[
      T(x,T(y,x \ (z \ u))) = x * K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6422(a,2),3900(a,2,2))].">
      <j1 rule="para" parents="6422 3900"/>
    </justification>
  </clause>

  <clause id="6425">
    <literal><![CDATA[
      T(x,T(y,x \ (z \ u))) = T(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(316,a,2815,a,b,6424,a),flip(a)].">
      <j1 rule="hyper" parents="316 2815 6424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6426">
    <literal><![CDATA[
      T(x,T(y,x \ (z \ 1))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(66(a,1),6425(a,2,2,2))].">
      <j1 rule="para" parents="66 6425"/>
    </justification>
  </clause>

  <clause id="6427">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3973,a(flip),b,6426,a)].">
      <j1 rule="hyper" parents="63 3973 6426"/>
    </justification>
  </clause>

  <clause id="6428">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(136,a,3849,a(flip),b,6423,a)].">
      <j1 rule="hyper" parents="136 3849 6423"/>
    </justification>
  </clause>

  <clause id="6429">
    <literal><![CDATA[
      K(x,y) * (z \ T(y,T(x,z))) = z \ y
    ]]></literal>
    <justification jstring="[hyper(138,a,4137,a(flip),b,6428,a)].">
      <j1 rule="hyper" parents="138 4137 6428"/>
    </justification>
  </clause>

  <clause id="6430">
    <literal><![CDATA[
      x \ T(y,T(z,x)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(3006,a,6429,a),flip(a)].">
      <j1 rule="hyper" parents="3006 6429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6431">
    <literal><![CDATA[
      x \ T(T(y,z) / z,T(u,x)) = K(z \ y,u) * (x \ (T(y,z) / z))
    ]]></literal>
    <justification jstring="[para(5288(a,1),6430(a,2,1))].">
      <j1 rule="para" parents="5288 6430"/>
    </justification>
  </clause>

  <clause id="6432">
    <literal><![CDATA[
      a(x,y,z \ ((u * (K(w,v5) * v6)) * v7)) = a(x,y,z \ ((u * v6) * v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,6172,a)].">
      <j1 rule="hyper" parents="63 5490 6172"/>
    </justification>
  </clause>

  <clause id="6433">
    <literal><![CDATA[
      a(x,y,z \ ((u * (T(w,v5) \ v6)) * v7)) = a(x,y,z \ (v7 * (u * (w \ v6))))
    ]]></literal>
    <justification jstring="[para(2859(a,1),6172(a,1,3,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2859 6172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6435">
    <literal><![CDATA[
      (x / L(y * K(z,u),w,v5)) * y = y * ((L(y,w,v5) \ x) * K(u,z))
    ]]></literal>
    <justification jstring="[para(3781(a,1),6205(a,2,2))].">
      <j1 rule="para" parents="3781 6205"/>
    </justification>
  </clause>

  <clause id="6436">
    <literal><![CDATA[
      R(x,y,z * ((u * (w * w)) \ v5)) = R(x,y,z * (u \ ((w * w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,4745,a(flip),b,6219,a),flip(a)].">
      <j1 rule="hyper" parents="316 4745 6219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6437">
    <literal><![CDATA[
      R(x,y,z * (u \ ((w * w) \ v5))) = R(x,y,z * (u \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,4741,a(flip),b,6220,a),flip(a)].">
      <j1 rule="hyper" parents="63 4741 6220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6439">
    <literal><![CDATA[
      R(x,y,(z \ ((u * u) \ w)) * v5) = R(x,y,v5 * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,4676,a,b,6437,a)].">
      <j1 rule="hyper" parents="63 4676 6437"/>
    </justification>
  </clause>

  <clause id="6440">
    <literal><![CDATA[
      R(x,y,z \ ((u / (w * w)) \ v5)) = R(x,y,z \ ((u \ v5) * (w * w)))
    ]]></literal>
    <justification jstring="[para(388(a,1),6221(a,2,3,2))].">
      <j1 rule="para" parents="388 6221"/>
    </justification>
  </clause>

  <clause id="6441">
    <literal><![CDATA[
      a(x * ((y \ z) \ y),u,w) = a(x * (y * (z \ y)),u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),6225(a,1,1,2,1))].">
      <j1 rule="para" parents="9 6225"/>
    </justification>
  </clause>

  <clause id="6443">
    <literal><![CDATA[
      (K(x,y) * z) * L(z \ x,u,w) = z * L(z \ T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(2803(a,1),6226(a,1,2,1))].">
      <j1 rule="para" parents="2803 6226"/>
    </justification>
  </clause>

  <clause id="6444">
    <literal><![CDATA[
      T(x,y) \ (z * L(z \ T(x,y),u,w)) = x \ (z * L(z \ x,u,w))
    ]]></literal>
    <justification jstring="[hyper(133,a,6443,a(flip),b,2857,a)].">
      <j1 rule="hyper" parents="133 6443 2857"/>
    </justification>
  </clause>

  <clause id="6446">
    <literal><![CDATA[
      a(x,y,((((z * z) * (z \ u)) \ w) * v5) \ v6) = a(x,y,(v5 * (T(u / (z \ 1),z) \ w)) \ v6)
    ]]></literal>
    <justification jstring="[para(613(a,2),6257(a,2,3,1,2,1))].">
      <j1 rule="para" parents="613 6257"/>
    </justification>
  </clause>

  <clause id="6447">
    <literal><![CDATA[
      T(x * L(y,z,u),w) \ (x * L(y,z,u)) = K(w,x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),6299(a,1,1,1,2,1))].">
      <j1 rule="para" parents="9 6299"/>
    </justification>
  </clause>

  <clause id="6448">
    <literal><![CDATA[
      K(x,y * L(z,u,w)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(2963,a,6447,a)].">
      <j1 rule="hyper" parents="2963 6447"/>
    </justification>
  </clause>

  <clause id="6449">
    <literal><![CDATA[
      K(x,y * L(y \ z,u,w)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),6448(a,2,2))].">
      <j1 rule="para" parents="10 6448"/>
    </justification>
  </clause>

  <clause id="6450">
    <literal><![CDATA[
      K(x,y * ((z * u) \ w)) = K(x,y * (u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(298(a,1),6448(a,1,2,2))].">
      <j1 rule="para" parents="298 6448"/>
    </justification>
  </clause>

  <clause id="6451">
    <literal><![CDATA[
      K(x,L(y,z,u) * w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(599(a,1),6449(a,1,2))].">
      <j1 rule="para" parents="599 6449"/>
    </justification>
  </clause>

  <clause id="6453">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) * w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(316,a,3578,a(flip),b,6451,a),flip(a)].">
      <j1 rule="hyper" parents="316 3578 6451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6454">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ w)) = K(x,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),6451(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 6451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6456">
    <literal><![CDATA[
      K(x,L(y,z,u) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(1130(a,1),6454(a,1,2))].">
      <j1 rule="para" parents="1130 6454"/>
    </justification>
  </clause>

  <clause id="6457">
    <literal><![CDATA[
      K(x,y / L(z,u,w)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(4400(a,1),6454(a,1,2))].">
      <j1 rule="para" parents="4400 6454"/>
    </justification>
  </clause>

  <clause id="6458">
    <literal><![CDATA[
      ((x * (L(x,y,z) \ u)) * w) * ((x * (L(x,y,z) \ u)) \ K(w,u)) = R(w,x * (L(x,y,z) \ u),x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(6454(a,1),6271(a,1,2,2))].">
      <j1 rule="para" parents="6454 6271"/>
    </justification>
  </clause>

  <clause id="6461">
    <literal><![CDATA[
      K(x,y / L(x,z,u)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3881,a,b,6456,a)].">
      <j1 rule="hyper" parents="63 3881 6456"/>
    </justification>
  </clause>

  <clause id="6462">
    <literal><![CDATA[
      T(x,L(y,z,u) \ w) = K(x,y \ w) * x
    ]]></literal>
    <justification jstring="[hyper(138,a,6456,a(flip),b,2795,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="138 6456 2795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6463">
    <literal><![CDATA[
      (x * (L(y,z,u) \ w)) \ K(x,y \ w) = ((L(y,z,u) \ w) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,6456,a(flip),b,2760,a(flip))].">
      <j1 rule="hyper" parents="133 6456 2760"/>
    </justification>
  </clause>

  <clause id="6465">
    <literal><![CDATA[
      L(K(x,y \ z),u,w) = K(L(y,v5,v6) \ z,x) \ 1
    ]]></literal>
    <justification jstring="[para(6456(a,1),3785(a,1,1))].">
      <j1 rule="para" parents="6456 3785"/>
    </justification>
  </clause>

  <clause id="6467">
    <literal><![CDATA[
      K(x,(y * z) / u) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(521(a,1),6457(a,1,2)),flip(a)].">
      <j1 rule="para" parents="521 6457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6469">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ z) = K(x \ y,(z / y) * x)
    ]]></literal>
    <justification jstring="[para(487(a,1),6461(a,1,2)),flip(a)].">
      <j1 rule="para" parents="487 6461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6470">
    <literal><![CDATA[
      K(x,y / (z / u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1943,a(flip),b,6467,a)].">
      <j1 rule="hyper" parents="63 1943 6467"/>
    </justification>
  </clause>

  <clause id="6471">
    <literal><![CDATA[
      T(x,L(y,z,u) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(316,a,2794,a,b,6462,a),flip(a)].">
      <j1 rule="hyper" parents="316 2794 6462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6472">
    <literal><![CDATA[
      T(L(x,y,z),L(u,w,v5) \ v6) = L(T(x,u \ v6),y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2804,a(flip),b,6462,a),flip(a)].">
      <j1 rule="hyper" parents="316 2804 6462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6475">
    <literal><![CDATA[
      T(x / (L(y,z,u) \ w),y \ w) = (L(y,z,u) \ w) \ x
    ]]></literal>
    <justification jstring="[hyper(377,a,6471,a),flip(a)].">
      <j1 rule="hyper" parents="377 6471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6476">
    <literal><![CDATA[
      T(x,L(L(y,z,u),w,v5) \ v6) = T(x,y \ v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,6471,a(flip),b,6471,a),flip(a)].">
      <j1 rule="hyper" parents="316 6471 6471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6477">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,215,a(flip),b,6471,a),flip(a)].">
      <j1 rule="hyper" parents="316 215 6471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6478">
    <literal><![CDATA[
      T(x,(y * (z * u)) \ ((y * z) * w)) = T(x,u \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3692,a,b,6471,a)].">
      <j1 rule="hyper" parents="63 3692 6471"/>
    </justification>
  </clause>

  <clause id="6479">
    <literal><![CDATA[
      (L(x,y,z) \ u) * T(w,x \ u) = w * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,6471,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 6471 22"/>
    </justification>
  </clause>

  <clause id="6481">
    <literal><![CDATA[
      T(x,y \ (L(y,z,u) * w)) = T(x,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),6471(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 6471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6483">
    <literal><![CDATA[
      x / (L(y,z,u) \ y) = (L(y,z,u) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(377,a,6477,a),flip(a)].">
      <j1 rule="hyper" parents="377 6477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6484">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(137,a,6477,a,b,2927,a)].">
      <j1 rule="hyper" parents="137 6477 2927"/>
    </justification>
  </clause>

  <clause id="6485">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,6477,a,b,4297,a),flip(a)].">
      <j1 rule="hyper" parents="134 6477 4297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6486">
    <literal><![CDATA[
      x / L(L(y,z,u) \ y,w,v5) = L(L(y,z,u) \ y,w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,4307,a(flip),b,6477,a),flip(a)].">
      <j1 rule="hyper" parents="63 4307 6477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6487">
    <literal><![CDATA[
      T(x,y \ (L(z / y,u,w) \ z)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,3725,a(flip),b,6477,a)].">
      <j1 rule="hyper" parents="63 3725 6477"/>
    </justification>
  </clause>

  <clause id="6488">
    <literal><![CDATA[
      (((x / y) * L(y,z,u)) \ x) \ x = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3723,a(flip),b,6477,a)].">
      <j1 rule="hyper" parents="63 3723 6477"/>
    </justification>
  </clause>

  <clause id="6489">
    <literal><![CDATA[
      ((x * L(x \ y,z,u)) \ y) \ y = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3703,a(flip),b,6477,a)].">
      <j1 rule="hyper" parents="63 3703 6477"/>
    </justification>
  </clause>

  <clause id="6491">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,6477,a)].">
      <j1 rule="hyper" parents="55 6477"/>
    </justification>
  </clause>

  <clause id="6492">
    <literal><![CDATA[
      (x * y) / (x * L(y,z,u)) = (x * L(y,z,u)) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(209,a,6477,a(flip),b,3697,a(flip))].">
      <j1 rule="hyper" parents="209 6477 3697"/>
    </justification>
  </clause>

  <clause id="6493">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * v5 = v5 * L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,6477,a(flip),b,4306,a)].">
      <j1 rule="hyper" parents="139 6477 4306"/>
    </justification>
  </clause>

  <clause id="6494">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (u * K((L(x,y,z) \ x) * u,w)) = T(u * (L(x,y,z) \ x),w)
    ]]></literal>
    <justification jstring="[hyper(139,a,6477,a(flip),b,3648,a(flip))].">
      <j1 rule="hyper" parents="139 6477 3648"/>
    </justification>
  </clause>

  <clause id="6496">
    <literal><![CDATA[
      (L(x,y,z) \ x) * u = u * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,6477,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 6477 22"/>
    </justification>
  </clause>

  <clause id="6498">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * w = (u * (L(x,y,z) \ x)) * w
    ]]></literal>
    <justification jstring="[hyper(38,a,915,a(flip),b,6477,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 915 6477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6499">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(6477(a,1),49(a,2))].">
      <j1 rule="para" parents="6477 49"/>
    </justification>
  </clause>

  <clause id="6501">
    <literal><![CDATA[
      (1 / (L(x,y,z) \ x)) * (u * (L(x,y,z) \ x)) = L(u,L(x,y,z) \ x,(L(x,y,z) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(6477(a,1),892(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6477 892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6502">
    <literal><![CDATA[
      R(L(x,y,z) \ x,u,w) * v5 = v5 * R(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(6477(a,1),2842(a,1,2))].">
      <j1 rule="para" parents="6477 2842"/>
    </justification>
  </clause>

  <clause id="6503">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * (w * u) = w * (u * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(6477(a,1),4363(a,1,2))].">
      <j1 rule="para" parents="6477 4363"/>
    </justification>
  </clause>

  <clause id="6504">
    <literal><![CDATA[
      (x * (y * (L(z,u,w) \ z))) / (x * y) = L(L(z,u,w) \ z,y,x)
    ]]></literal>
    <justification jstring="[para(6477(a,1),4365(a,2,2)),flip(a)].">
      <j1 rule="para" parents="6477 4365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6505">
    <literal><![CDATA[
      (L(x \ L(x,y,z),u,w) \ 1) * v5 = v5 * (L(x \ L(x,y,z),u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(6477(a,1),4600(a,1,2))].">
      <j1 rule="para" parents="6477 4600"/>
    </justification>
  </clause>

  <clause id="6506">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3512,a(flip),b,6481,a)].">
      <j1 rule="hyper" parents="63 3512 6481"/>
    </justification>
  </clause>

  <clause id="6507">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[para(1126(a,1),6481(a,1,2))].">
      <j1 rule="para" parents="1126 6481"/>
    </justification>
  </clause>

  <clause id="6508">
    <literal><![CDATA[
      T(x \ (L(y / x,z,u) \ y),w) = x \ (L(y / x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(137,a,6487,a,b,2927,a)].">
      <j1 rule="hyper" parents="137 6487 2927"/>
    </justification>
  </clause>

  <clause id="6509">
    <literal><![CDATA[
      T(x,(y \ z) \ (L(y,u,w) \ z)) = x
    ]]></literal>
    <justification jstring="[para(80(a,1),6487(a,1,2,2,1,1))].">
      <j1 rule="para" parents="80 6487"/>
    </justification>
  </clause>

  <clause id="6510">
    <literal><![CDATA[
      T(x,y * (z \ L(z,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4593,a(flip),b,6506,a)].">
      <j1 rule="hyper" parents="63 4593 6506"/>
    </justification>
  </clause>

  <clause id="6512">
    <literal><![CDATA[
      T(x,L(y,z,u) * w) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),6507(a,1,2,2))].">
      <j1 rule="para" parents="9 6507"/>
    </justification>
  </clause>

  <clause id="6513">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[para(75(a,1),6507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 6507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6514">
    <literal><![CDATA[
      T(x,y * L(z,u,w)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(4329(a,1),6507(a,1,2))].">
      <j1 rule="para" parents="4329 6507"/>
    </justification>
  </clause>

  <clause id="6515">
    <literal><![CDATA[
      x / (L(y,z,u) * (y \ x)) = (L(y,z,u) * (y \ x)) \ x
    ]]></literal>
    <justification jstring="[hyper(209,a,6509,a(flip),b,3703,a(flip))].">
      <j1 rule="hyper" parents="209 6509 3703"/>
    </justification>
  </clause>

  <clause id="6517">
    <literal><![CDATA[
      T(x / (y * (z \ L(z,u,w))),y) = (y * (z \ L(z,u,w))) \ x
    ]]></literal>
    <justification jstring="[hyper(377,a,6510,a),flip(a)].">
      <j1 rule="hyper" parents="377 6510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6520">
    <literal><![CDATA[
      T(x,y \ (z \ L(z,u,w))) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3489,a(flip),b,6510,a)].">
      <j1 rule="hyper" parents="63 3489 6510"/>
    </justification>
  </clause>

  <clause id="6521">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * T(w,x) = w * (x * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(139,a,6510,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 6510 22"/>
    </justification>
  </clause>

  <clause id="6522">
    <literal><![CDATA[
      R(T(x / y,x),L(y,z,u),x / y) = T(x / y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6510(a,1),3532(a,1,1))].">
      <j1 rule="para" parents="6510 3532"/>
    </justification>
  </clause>

  <clause id="6523">
    <literal><![CDATA[
      R(T(x,a(y,z,u) * w),w,L(a(y,z,u),v5,v6)) = L(T(x,w),w,L(a(y,z,u),v5,v6))
    ]]></literal>
    <justification jstring="[para(6512(a,1),2679(a,1,1))].">
      <j1 rule="para" parents="6512 2679"/>
    </justification>
  </clause>

  <clause id="6525">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * L(L(T(w,u),v5,v6),v7,v8) = L(L(w,v5,v6),v7,v8) * (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(6513(a,1),600(a,1,2,1,1))].">
      <j1 rule="para" parents="6513 600"/>
    </justification>
  </clause>

  <clause id="6526">
    <literal><![CDATA[
      K(x * L(y,z,u),w) = T(w,x * y) \ w
    ]]></literal>
    <justification jstring="[para(6514(a,1),2948(a,2,1))].">
      <j1 rule="para" parents="6514 2948"/>
    </justification>
  </clause>

  <clause id="6527">
    <literal><![CDATA[
      L(x,y,z) * T(L(x,y,z) \ x,u) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,6484,a,b,xx)].">
      <j1 rule="hyper" parents="139 6484"/>
    </justification>
  </clause>

  <clause id="6528">
    <literal><![CDATA[
      x * ((L(y,z,u) \ y) * (x \ 1)) = L(L(y,z,u) \ y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(6484(a,1),527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6484 527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6529">
    <literal><![CDATA[
      x * (L(L(y,z,u) \ y,w,v5) * v6) = x * (v6 * L(L(y,z,u) \ y,w,v5))
    ]]></literal>
    <justification jstring="[para(6484(a,1),412(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6484 412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6532">
    <literal><![CDATA[
      (x \ (y * (L(y,z,u) \ x))) * x = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(6527(a,1),963(a,2,1))].">
      <j1 rule="para" parents="6527 963"/>
    </justification>
  </clause>

  <clause id="6533">
    <literal><![CDATA[
      T(x,y \ a(z,u,w)) = T(x,y \ (v5 \ L(v5,v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5260,a,b,6520,a)].">
      <j1 rule="hyper" parents="316 5260 6520"/>
    </justification>
  </clause>

  <clause id="6534">
    <literal><![CDATA[
      K(x * L(y,z,u),w) = K(x * y,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,2948,a,b,6526,a),flip(a)].">
      <j1 rule="hyper" parents="316 2948 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6535">
    <literal><![CDATA[
      K((x * y) * R(z,u,w),v5) = K(x * (y * L(z,v6,v7)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3727,a(flip),b,6534,a),flip(a)].">
      <j1 rule="hyper" parents="63 3727 6534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6536">
    <literal><![CDATA[
      K(x * ((y * z) \ u),w) = K(x * (z \ (y \ u)),w)
    ]]></literal>
    <justification jstring="[para(298(a,1),6534(a,1,1,2))].">
      <j1 rule="para" parents="298 6534"/>
    </justification>
  </clause>

  <clause id="6537">
    <literal><![CDATA[
      K(x * ((y * a(z,u,w)) \ (v5 * a(z,u,w))),v6) = K(x * (y \ v5),v6)
    ]]></literal>
    <justification jstring="[para(2492(a,1),6534(a,1,1,2))].">
      <j1 rule="para" parents="2492 6534"/>
    </justification>
  </clause>

  <clause id="6539">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(x,y,z) \ 1) = R(1 / x,x,L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1006,a(flip),b,6483,a),flip(a)].">
      <j1 rule="hyper" parents="63 1006 6483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6541">
    <literal><![CDATA[
      (x * L(L(y,z,u) \ y,w,v5)) / (L(y,z,u) \ y) = ((L(y,z,u) \ y) \ x) * L(L(y,z,u) \ y,w,v5)
    ]]></literal>
    <justification jstring="[para(6483(a,1),1438(a,2,1))].">
      <j1 rule="para" parents="6483 1438"/>
    </justification>
  </clause>

  <clause id="6542">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x,u,w) = x * (L(x,y,z) \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,1521,a(flip),b,6496,a),flip(a)].">
      <j1 rule="hyper" parents="316 1521 6496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6543">
    <literal><![CDATA[
      ((x * y) * (L(z,u,w) \ z)) / ((L(z,u,w) \ z) * y) = R(x,y,L(z,u,w) \ z)
    ]]></literal>
    <justification jstring="[hyper(209,a,6496,a,b,199,a)].">
      <j1 rule="hyper" parents="209 6496 199"/>
    </justification>
  </clause>

  <clause id="6545">
    <literal><![CDATA[
      K(x,y) * (L(z \ x,u,w) \ (z \ x)) = L(z \ x,u,w) \ (z \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3912,a(flip),b,6496,a),flip(a)].">
      <j1 rule="hyper" parents="63 3912 6496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6546">
    <literal><![CDATA[
      (x * ((L(y,z,u) \ y) * w)) \ (((L(y,z,u) \ y) * x) * w) = a(x,L(y,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[para(6496(a,2),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6496 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6547">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) \ (u * (w * (L(x,y,z) \ x))) = L(T(w,L(x,y,z) \ x),L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(6496(a,2),247(a,1,1))].">
      <j1 rule="para" parents="6496 247"/>
    </justification>
  </clause>

  <clause id="6548">
    <literal><![CDATA[
      (x * y) \ ((x * (L(z,u,w) \ z)) * y) = R(T(L(z,u,w) \ z,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(6496(a,1),560(a,1,2,1))].">
      <j1 rule="para" parents="6496 560"/>
    </justification>
  </clause>

  <clause id="6549">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) \ ((x * w) * (L(y,z,u) \ y)) = L(K(L(y,z,u) \ y,x) * w,x,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(6496(a,1),3299(a,1,2))].">
      <j1 rule="para" parents="6496 3299"/>
    </justification>
  </clause>

  <clause id="6551">
    <literal><![CDATA[
      x \ ((L(x,y,z) \ x) * u) = (x \ u) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(6496(a,2),5152(a,1,2))].">
      <j1 rule="para" parents="6496 5152"/>
    </justification>
  </clause>

  <clause id="6552">
    <literal><![CDATA[
      K(L(x,y,z) \ u,w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[hyper(39,a,3785,a(flip),b,6465,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 3785 6465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6556">
    <literal><![CDATA[
      K(a(x,y,z) \ (u * w),v5) = K(u * (a(x,y,z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(2541(a,1),6552(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2541 6552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6557">
    <literal><![CDATA[
      (x \ y) * K(x \ y,(x \ y) \ z) = T(x \ y,(z / y) * x)
    ]]></literal>
    <justification jstring="[hyper(139,a,6469,a,b,2806,a(flip))].">
      <j1 rule="hyper" parents="139 6469 2806"/>
    </justification>
  </clause>

  <clause id="6559">
    <literal><![CDATA[
      T(x,(y * (z * u)) \ w) = T(x,u \ ((y * z) \ w))
    ]]></literal>
    <justification jstring="[para(10(a,1),6478(a,1,2,2))].">
      <j1 rule="para" parents="10 6478"/>
    </justification>
  </clause>

  <clause id="6561">
    <literal><![CDATA[
      T(x,x \ a(y,z,u)) = (x \ (w \ L(w,v5,v6))) \ (w \ L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,115,a(flip),b,6533,a),flip(a)].">
      <j1 rule="hyper" parents="316 115 6533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6562">
    <literal><![CDATA[
      K(K(x,y) \ ((z * u) \ w),v5) = K(K(y,x) * (u \ (z \ w)),v5)
    ]]></literal>
    <justification jstring="[para(2981(a,2),6536(a,1,1))].">
      <j1 rule="para" parents="2981 6536"/>
    </justification>
  </clause>

  <clause id="6563">
    <literal><![CDATA[
      T(x,(y * z) \ (u \ w)) = T(x,z \ ((u * y) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,3698,a(flip),b,6559,a)].">
      <j1 rule="hyper" parents="63 3698 6559"/>
    </justification>
  </clause>

  <clause id="6564">
    <literal><![CDATA[
      T(x,y \ ((z * u) \ w)) = T(x,y \ (u \ (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3698,a(flip),b,6563,a),flip(a)].">
      <j1 rule="hyper" parents="63 3698 6563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6565">
    <literal><![CDATA[
      x / L(T(y,y \ x),z,u) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(209,a,6472,a(flip),b,115,a(flip))].">
      <j1 rule="hyper" parents="209 6472 115"/>
    </justification>
  </clause>

  <clause id="6566">
    <literal><![CDATA[
      L(T(x,x \ (L(x,y,z) \ u)),y,z) \ u = (L(x,y,z) \ (L(x,y,z) \ u)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(6472(a,1),2899(a,1,1))].">
      <j1 rule="para" parents="6472 2899"/>
    </justification>
  </clause>

  <clause id="6567">
    <literal><![CDATA[
      x / L((y \ x) \ x,z,u) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(115(a,1),6565(a,1,2,1))].">
      <j1 rule="para" parents="115 6565"/>
    </justification>
  </clause>

  <clause id="6568">
    <literal><![CDATA[
      x / L(y \ x,z,u) = L(x / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(614(a,1),6565(a,1,2,1))].">
      <j1 rule="para" parents="614 6565"/>
    </justification>
  </clause>

  <clause id="6569">
    <literal><![CDATA[
      (L(x,y,z) * u) / L(T(x,u),w,v5) = L(x,w,v5) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(6481(a,1),6565(a,1,2,1))].">
      <j1 rule="para" parents="6481 6565"/>
    </justification>
  </clause>

  <clause id="6570">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) = (L(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(204,a,6567,a),flip(a)].">
      <j1 rule="hyper" parents="204 6567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6571">
    <literal><![CDATA[
      L(x / (x / y),z,u) \ x = x / L(y,z,u)
    ]]></literal>
    <justification jstring="[para(208(a,1),6567(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="208 6567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6572">
    <literal><![CDATA[
      x / (x / L(y \ x,z,u)) = L(x / y,z,u)
    ]]></literal>
    <justification jstring="[hyper(209,a,6568,a,b,xx)].">
      <j1 rule="hyper" parents="209 6568"/>
    </justification>
  </clause>

  <clause id="6573">
    <literal><![CDATA[
      (L(x / y,z,u) \ x) \ x = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(204,a,6568,a)].">
      <j1 rule="hyper" parents="204 6568"/>
    </justification>
  </clause>

  <clause id="6574">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,z,u) \ x) = L(y / x,z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,4391,a,b,6568,a)].">
      <j1 rule="hyper" parents="63 4391 6568"/>
    </justification>
  </clause>

  <clause id="6575">
    <literal><![CDATA[
      x / (L(y \ T(x,z),u,w) * K(z,x)) = L(T(x,z) / y,u,w) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3819,a,b,6568,a)].">
      <j1 rule="hyper" parents="63 3819 6568"/>
    </justification>
  </clause>

  <clause id="6576">
    <literal><![CDATA[
      K(x,y) * (L(1 / z,u,w) \ 1) = K(x,y) / L(z \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,6568,a(flip),b,437,a)].">
      <j1 rule="hyper" parents="139 6568 437"/>
    </justification>
  </clause>

  <clause id="6577">
    <literal><![CDATA[
      T(x * (L(y \ x,z,u) \ 1),L(x / y,z,u) \ x) = x * (L(y \ x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(6568(a,1),556(a,1,2))].">
      <j1 rule="para" parents="6568 556"/>
    </justification>
  </clause>

  <clause id="6578">
    <literal><![CDATA[
      L(x / (y \ z),y \ z,y) \ x = x / (z \ (y * x))
    ]]></literal>
    <justification jstring="[para(475(a,1),6568(a,1,2)),flip(a)].">
      <j1 rule="para" parents="475 6568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6579">
    <literal><![CDATA[
      x / ((L(1 / y,z,u) \ 1) \ L(y \ 1,z,u)) = x * (L(y \ 1,z,u) \ (1 / L(y \ 1,z,u)))
    ]]></literal>
    <justification jstring="[para(6568(a,1),741(a,1,2,1))].">
      <j1 rule="para" parents="6568 741"/>
    </justification>
  </clause>

  <clause id="6580">
    <literal><![CDATA[
      ((L(x,y,z) \ 1) * u) * L((x \ 1) \ 1,y,z) = ((1 / L(x,y,z)) * u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(6570(a,2),2566(a,1,2))].">
      <j1 rule="para" parents="6570 2566"/>
    </justification>
  </clause>

  <clause id="6582">
    <literal><![CDATA[
      L(x / (x / y),z,u) = x / (x / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(210,a,6571,a),flip(a)].">
      <j1 rule="hyper" parents="210 6571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6583">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),z,u) = 1 / (1 / L(T(y,x),z,u))
    ]]></literal>
    <justification jstring="[para(2965(a,2),6572(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2965 6572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6584">
    <literal><![CDATA[
      L(1 / x,y,y) \ 1 = x * a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,4965,a,b,6573,a),flip(a)].">
      <j1 rule="hyper" parents="39 4965 6573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6585">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = x * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(39,a,4459,a,b,6573,a),flip(a)].">
      <j1 rule="hyper" parents="39 4459 6573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6586">
    <literal><![CDATA[
      a(x * (y * (L(z / u,w,v5) \ z)),v6,v7) = a(x * (y * (L(u \ z,w,v5) \ z)),v6,v7)
    ]]></literal>
    <justification jstring="[para(6573(a,1),4040(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6573 4040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6587">
    <literal><![CDATA[
      (x * a(y,y,x)) * L((L(1 / x,y,y) \ 1) \ z,u,w) = L(1 / x,y,y) * L(L(1 / x,y,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(6584(a,1),1350(a,1,1))].">
      <j1 rule="para" parents="6584 1350"/>
    </justification>
  </clause>

  <clause id="6588">
    <literal><![CDATA[
      (x / y) * (L(1 / y,z,z) \ 1) = (y * a(z,z,y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(6584(a,2),5353(a,1,2))].">
      <j1 rule="para" parents="6584 5353"/>
    </justification>
  </clause>

  <clause id="6589">
    <literal><![CDATA[
      L(x,x \ 1,(x \ 1) \ y) = L(1 / (1 / x),x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1886,a,b,6582,a)].">
      <j1 rule="hyper" parents="316 1886 6582"/>
    </justification>
  </clause>

  <clause id="6590">
    <literal><![CDATA[
      R(x,y / (y / z),y / (y / z)) \ (x * (y / (y / z))) = y / (y / L(z,y / (y / z),L(x,y / (y / z),y / (y / z))))
    ]]></literal>
    <justification jstring="[hyper(63,a,4630,a(flip),b,6582,a)].">
      <j1 rule="hyper" parents="63 4630 6582"/>
    </justification>
  </clause>

  <clause id="6591">
    <literal><![CDATA[
      x \ (L(1 / x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(517,a,6585,a)].">
      <j1 rule="hyper" parents="517 6585"/>
    </justification>
  </clause>

  <clause id="6592">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = (L(x,y,z) \ x) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,6496,a,b,6585,a),flip(a)].">
      <j1 rule="hyper" parents="316 6496 6585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6593">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = L(x,y,z) \ (x * x)
    ]]></literal>
    <justification jstring="[hyper(316,a,1129,a,b,6585,a),flip(a)].">
      <j1 rule="hyper" parents="316 1129 6585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6594">
    <literal><![CDATA[
      1 / (x * (L(x,y,z) \ x)) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(210,a,6585,a)].">
      <j1 rule="hyper" parents="210 6585"/>
    </justification>
  </clause>

  <clause id="6595">
    <literal><![CDATA[
      x * (L(1 / y,z,u) \ 1) = x * (y * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(139,a,6585,a,b,9,a)].">
      <j1 rule="hyper" parents="139 6585 9"/>
    </justification>
  </clause>

  <clause id="6596">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * u = (x * (L(x,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,6585,a,b,11,a)].">
      <j1 rule="hyper" parents="138 6585 11"/>
    </justification>
  </clause>

  <clause id="6598">
    <literal><![CDATA[
      L(x,y,z) \ (L(1 / x,u,w) \ 1) = x * (L(x,y,z) \ (L(x,u,w) \ x))
    ]]></literal>
    <justification jstring="[hyper(133,a,6585,a,b,1128,a)].">
      <j1 rule="hyper" parents="133 6585 1128"/>
    </justification>
  </clause>

  <clause id="6599">
    <literal><![CDATA[
      (1 / x) * (L(1 / x,y,z) \ (1 / x)) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6571,a(flip),b,6585,a),flip(a)].">
      <j1 rule="hyper" parents="63 6571 6585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6600">
    <literal><![CDATA[
      L(x,x,y) \ x = x \ (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(133,a,1764,a(flip),b,6585,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 1764 6585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6601">
    <literal><![CDATA[
      L(1 / x,y \ 1,y) \ 1 = x * a(y,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(703(a,1),6585(a,2,2))].">
      <j1 rule="para" parents="703 6585"/>
    </justification>
  </clause>

  <clause id="6602">
    <literal><![CDATA[
      L(x \ R(x,y * (L(y,z,u) \ y),L(1 / y,z,u)),x,1) = a(x,L(1 / y,z,u) \ 1,L(1 / y,z,u))
    ]]></literal>
    <justification jstring="[para(6585(a,1),3425(a,1,1,2,2))].">
      <j1 rule="para" parents="6585 3425"/>
    </justification>
  </clause>

  <clause id="6603">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z))) = L(L(x,y,z) \ x,u,w) \ 1
    ]]></literal>
    <justification jstring="[para(5069(a,1),6585(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5069 6585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6604">
    <literal><![CDATA[
      a(x,y,((z * (L(z,u,w) \ z)) * v5) * v6) = a(x,y,v6 * (v5 * L(1 / z,u,w)))
    ]]></literal>
    <justification jstring="[para(6585(a,1),5901(a,1,3,1,1))].">
      <j1 rule="para" parents="6585 5901"/>
    </justification>
  </clause>

  <clause id="6605">
    <literal><![CDATA[
      a(x,y,z * ((u * (L(u,w,v5) \ u)) * v6)) = a(x,y,z * (v6 * L(1 / u,w,v5)))
    ]]></literal>
    <justification jstring="[para(6585(a,1),5902(a,1,3,2,1))].">
      <j1 rule="para" parents="6585 5902"/>
    </justification>
  </clause>

  <clause id="6606">
    <literal><![CDATA[
      a(x,y,z \ ((u * (w * (L(w,v5,v6) \ w))) * v7)) = a(x,y,z \ (v7 * (u * L(1 / w,v5,v6))))
    ]]></literal>
    <justification jstring="[para(6585(a,1),6353(a,1,3,2,1,2))].">
      <j1 rule="para" parents="6585 6353"/>
    </justification>
  </clause>

  <clause id="6607">
    <literal><![CDATA[
      x / (L(1 / y,z,u) \ 1) = x / ((L(y,z,u) \ y) * y)
    ]]></literal>
    <justification jstring="[hyper(209,a,6592,a,b,83,a)].">
      <j1 rule="hyper" parents="209 6592 83"/>
    </justification>
  </clause>

  <clause id="6608">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * L(u,x,L(x,y,z) \ x) = (L(x,y,z) \ x) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(138,a,6592,a,b,202,a)].">
      <j1 rule="hyper" parents="138 6592 202"/>
    </justification>
  </clause>

  <clause id="6610">
    <literal><![CDATA[
      (x * ((L(y,z,u) \ y) * (y \ 1))) / (y \ 1) = (x * (L(1 / y,z,u) \ 1)) / y
    ]]></literal>
    <justification jstring="[para(6592(a,2),964(a,2,1,2))].">
      <j1 rule="para" parents="6592 964"/>
    </justification>
  </clause>

  <clause id="6611">
    <literal><![CDATA[
      R(L(x,y,z) \ x,x,(x * (L(x,y,z) \ x)) \ u) \ u = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(6592(a,2),4768(a,2,2,1))].">
      <j1 rule="para" parents="6592 4768"/>
    </justification>
  </clause>

  <clause id="6613">
    <literal><![CDATA[
      (L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z))) * (x \ L(x,y,z)) = L(L(x,y,z) \ x,u,w) \ 1
    ]]></literal>
    <justification jstring="[para(5069(a,1),6592(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5069 6592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6614">
    <literal><![CDATA[
      (x \ 1) * (L(1 / x,y,z) \ 1) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(6593(a,2),5179(a,1,2))].">
      <j1 rule="para" parents="6593 5179"/>
    </justification>
  </clause>

  <clause id="6615">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ ((x * (L(x,y,z) \ x)) \ 1) = ((x * (L(x,y,z) \ x)) \ 1) * L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,6594,a(flip),b,634,a),flip(a)].">
      <j1 rule="hyper" parents="139 6594 634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6616">
    <literal><![CDATA[
      1 / ((x \ y) * (((x \ y) / y) * x)) = L(1 / (x \ y),x,y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(1656(a,1),6594(a,1,2,2))].">
      <j1 rule="para" parents="1656 6594"/>
    </justification>
  </clause>

  <clause id="6618">
    <literal><![CDATA[
      T(x / (L(a(y,z,u),w,v5) \ v6),v6) = (L(a(y,z,u),w,v5) \ v6) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,5249,a(flip),b,6475,a)].">
      <j1 rule="hyper" parents="63 5249 6475"/>
    </justification>
  </clause>

  <clause id="6619">
    <literal><![CDATA[
      x / (L(y,z,u) \ (a(w,v5,v6) \ y)) = (L(y,z,u) \ (a(w,v5,v6) \ y)) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,4999,a(flip),b,6475,a)].">
      <j1 rule="hyper" parents="63 4999 6475"/>
    </justification>
  </clause>

  <clause id="6620">
    <literal><![CDATA[
      (x / (L(y,z,u) \ w)) * (y \ w) = (y \ w) * ((L(y,z,u) \ w) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,6475,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 6475 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6622">
    <literal><![CDATA[
      (L(x,y,z) \ u) * ((x \ u) \ w) = (w / (x \ u)) * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(116(a,1),6479(a,1,2))].">
      <j1 rule="para" parents="116 6479"/>
    </justification>
  </clause>

  <clause id="6623">
    <literal><![CDATA[
      ((((x * y) / z) * L(z,y,x)) \ (x * y)) \ (x * y) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(316,a,1465,a(flip),b,6488,a),flip(a)].">
      <j1 rule="hyper" parents="316 1465 6488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6625">
    <literal><![CDATA[
      (x * y) / (L(x,z,u) * y) = (y * L(x,z,u)) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4330,a,b,6492,a)].">
      <j1 rule="hyper" parents="63 4330 6492"/>
    </justification>
  </clause>

  <clause id="6626">
    <literal><![CDATA[
      (L(x * (y \ 1),z,u) * ((x * (y \ 1)) \ (x * y))) \ (x * y) = (x * y) / (L(x * (y \ 1),z,u) * (y * y))
    ]]></literal>
    <justification jstring="[para(561(a,1),6515(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="561 6515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6627">
    <literal><![CDATA[
      (L(a(x,y,z),u \ (a(x,y,z) \ w),u) * (a(x,y,z) \ w)) \ w = w / (u * ((u \ (a(x,y,z) \ w)) * a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(2308(a,1),6515(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2308 6515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6629">
    <literal><![CDATA[
      K(x * (y * L(z,u,w)),v5) = K(x * (y * z),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3563,a(flip),b,6535,a),flip(a)].">
      <j1 rule="hyper" parents="63 3563 6535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6630">
    <literal><![CDATA[
      (K(x * (y * z),u) * x) * (y * L(z,w,v5)) = T(x * (y * L(z,w,v5)),u)
    ]]></literal>
    <justification jstring="[para(6629(a,1),2798(a,1,1,1))].">
      <j1 rule="para" parents="6629 2798"/>
    </justification>
  </clause>

  <clause id="6632">
    <literal><![CDATA[
      K(x * (a(y,z,u) \ w),v5) = K(x * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5279,a(flip),b,6556,a),flip(a)].">
      <j1 rule="hyper" parents="63 5279 6556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6634">
    <literal><![CDATA[
      K(x * (a(y,z,u) * w),v5) = K(x * w,v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),6632(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 6632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6635">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),z,u) = L(1 / (1 / T(y,x)),z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,6582,a,b,6583,a),flip(a)].">
      <j1 rule="hyper" parents="316 6582 6583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6636">
    <literal><![CDATA[
      (1 / x) * (L(x \ 1,y,z) \ (x \ 1)) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4918(a,1),6599(a,1,2))].">
      <j1 rule="para" parents="4918 6599"/>
    </justification>
  </clause>

  <clause id="6637">
    <literal><![CDATA[
      (x * y) / (L(x,z,u) * y) = (L(x,z,u) * y) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,4336,a,b,6625,a),flip(a)].">
      <j1 rule="hyper" parents="316 4336 6625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6638">
    <literal><![CDATA[
      L(T(1 / (1 / x),y),z,u) = L(1 / (K(y,x) / x),z,u)
    ]]></literal>
    <justification jstring="[para(2417(a,1),6635(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2417 6635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6639">
    <literal><![CDATA[
      (L(x,y,y \ z) * z) \ (x * z) = a(y \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6174,a(flip),b,6637,a),flip(a)].">
      <j1 rule="hyper" parents="63 6174 6637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6640">
    <literal><![CDATA[
      (L(x,L(y,z,z),a(z,z,y)) * y) \ (x * y) = a(L(y,z,z) \ y,L(y,z,z),x)
    ]]></literal>
    <justification jstring="[para(4952(a,1),6639(a,1,1,1,3))].">
      <j1 rule="para" parents="4952 6639"/>
    </justification>
  </clause>

  <clause id="6641">
    <literal><![CDATA[
      R(a(x,y,z) / u,L(u,w,v5),a(x,y,z) / u) = T(a(x,y,z) / u,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(2273(a,1),6522(a,1,1))].">
      <j1 rule="para" parents="2273 6522"/>
    </justification>
  </clause>

  <clause id="6642">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,u \ w) * w = (w / u) * (u * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(316,a,1606,a(flip),b,6493,a),flip(a)].">
      <j1 rule="hyper" parents="316 1606 6493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6643">
    <literal><![CDATA[
      (x * y) * R(L(z,u,w) \ z,y,x) = ((L(z,u,w) \ z) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4054,a(flip),b,6502,a),flip(a)].">
      <j1 rule="hyper" parents="63 4054 6502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6644">
    <literal><![CDATA[
      T(R(x * K(y,x),y,z \ L(z,u,w)),y) = (y * (z \ L(z,u,w))) \ ((y * x) * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(2746(a,2),6517(a,1,1))].">
      <j1 rule="para" parents="2746 6517"/>
    </justification>
  </clause>

  <clause id="6647">
    <literal><![CDATA[
      x \ (((y \ L(y,z,u)) * (y \ L(y,z,u))) * T(w,y \ L(y,z,u))) = (x \ w) * ((y \ L(y,z,u)) * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(133,a,6521,a,b,124,a)].">
      <j1 rule="hyper" parents="133 6521 124"/>
    </justification>
  </clause>

  <clause id="6648">
    <literal><![CDATA[
      R(x * K(y \ L(y,z,u),T(w,x)),y \ L(y,z,u),T(w,x)) = (w * (x * (y \ L(y,z,u)))) / (T(w,x) * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(6521(a,1),4488(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6521 4488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6649">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) * T(w,u) = w * (u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(5023(a,2),6521(a,1,1))].">
      <j1 rule="para" parents="5023 6521"/>
    </justification>
  </clause>

  <clause id="6650">
    <literal><![CDATA[
      x / T(y \ z,(x / z) * y) = (y \ z) \ x
    ]]></literal>
    <justification jstring="[hyper(209,a,6557,a(flip),b,2819,a)].">
      <j1 rule="hyper" parents="209 6557 2819"/>
    </justification>
  </clause>

  <clause id="6652">
    <literal><![CDATA[
      K(x,y) * (L(1 / z,u,w) \ 1) = 1 / L(z \ K(y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,4866,a(flip),b,6576,a),flip(a)].">
      <j1 rule="hyper" parents="316 4866 6576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6653">
    <literal><![CDATA[
      (x * y) * L(z \ L(z,u,w),y,x) = ((z \ L(z,u,w)) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,100,a,b,6649,a)].">
      <j1 rule="hyper" parents="316 100 6649"/>
    </justification>
  </clause>

  <clause id="6654">
    <literal><![CDATA[
      K(x,y) * (z * (L(z,u,w) \ z)) = 1 / L(z \ K(y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6595,a(flip),b,6652,a)].">
      <j1 rule="hyper" parents="63 6595 6652"/>
    </justification>
  </clause>

  <clause id="6655">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ K(u,w) = L(x \ K(u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,2973,a,b,6654,a(flip))].">
      <j1 rule="hyper" parents="36 2973 6654"/>
    </justification>
  </clause>

  <clause id="6656">
    <literal><![CDATA[
      a(x,y,(z * ((u * (L(u,w,v5) \ u)) * K(v6,v7))) \ v8) = a(x,y,(z * (1 / L(u \ K(v7,v6),w,v5))) \ v8)
    ]]></literal>
    <justification jstring="[para(6654(a,1),5685(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="6654 5685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6657">
    <literal><![CDATA[
      (x * ((L(y,z,u) \ y) * w)) / (x * w) = L(L(y,z,u) \ y,w,x)
    ]]></literal>
    <justification jstring="[para(6496(a,2),6504(a,1,1,2))].">
      <j1 rule="para" parents="6496 6504"/>
    </justification>
  </clause>

  <clause id="6658">
    <literal><![CDATA[
      (x \ (y \ L(y,z,u))) \ (y \ L(y,z,u)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,5271,a(flip),b,6561,a),flip(a)].">
      <j1 rule="hyper" parents="63 5271 6561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6659">
    <literal><![CDATA[
      (((x \ L(x,y,z)) / u) \ 1) \ 1 = u \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(350,a,6658,a),flip(a)].">
      <j1 rule="hyper" parents="350 6658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6660">
    <literal><![CDATA[
      (x \ L(x,y,z)) / (u \ 1) = (1 / u) \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(209,a,206,a(flip),b,6658,a)].">
      <j1 rule="hyper" parents="209 206 6658"/>
    </justification>
  </clause>

  <clause id="6661">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x * u) = x * ((L(x,y,z) \ x) * u)
    ]]></literal>
    <justification jstring="[hyper(138,a,5160,a(flip),b,6657,a)].">
      <j1 rule="hyper" parents="138 5160 6657"/>
    </justification>
  </clause>

  <clause id="6662">
    <literal><![CDATA[
      x * (((L(y,z,u) \ y) * x) / (x * x)) = L(L(y,z,u) \ y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,683,a(flip),b,6657,a)].">
      <j1 rule="hyper" parents="63 683 6657"/>
    </justification>
  </clause>

  <clause id="6663">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ (((L(x,y,z) \ x) * u) * w) = w * (u * K((L(x,y,z) \ x) * u,w))
    ]]></literal>
    <justification jstring="[para(6657(a,1),3951(a,1,1))].">
      <j1 rule="para" parents="6657 3951"/>
    </justification>
  </clause>

  <clause id="6665">
    <literal><![CDATA[
      (x * ((L(x,y,z) \ x) * u)) \ (((L(x,y,z) \ x) * x) * u) = a(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[para(6661(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6661 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6667">
    <literal><![CDATA[
      x * ((L(y,z,u) \ y) * (x \ 1)) = L(L(y,z,u) \ y,x,x)
    ]]></literal>
    <justification jstring="[para(562(a,1),6662(a,1,2))].">
      <j1 rule="para" parents="562 6662"/>
    </justification>
  </clause>

  <clause id="6668">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u \ 1,u) = L(L(x,y,z) \ x,u,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6528,a(flip),b,6667,a)].">
      <j1 rule="hyper" parents="63 6528 6667"/>
    </justification>
  </clause>

  <clause id="6669">
    <literal><![CDATA[
      x \ L(L(y,z,u) \ y,x,x) = (x \ 1) * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(133,a,6668,a(flip),b,271,a)].">
      <j1 rule="hyper" parents="133 6668 271"/>
    </justification>
  </clause>

  <clause id="6670">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,u) \ (L(x,y,z) \ x) = a(u,u \ 1,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(6668(a,1),703(a,1,1))].">
      <j1 rule="para" parents="6668 703"/>
    </justification>
  </clause>

  <clause id="6672">
    <literal><![CDATA[
      L((a(x,y,z) \ u) \ w,a(x,y,z) \ u,a(x,y,z) * a(x,y,z)) = ((a(x,y,z) \ 1) \ u) \ ((a(x,y,z) * a(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[para(6305(a,1),102(a,2,1))].">
      <j1 rule="para" parents="6305 102"/>
    </justification>
  </clause>

  <clause id="6674">
    <literal><![CDATA[
      x * (L(x \ L(x,y,z),u,w) \ 1) = L(x \ L(x,y,z),u,w) \ x
    ]]></literal>
    <justification jstring="[para(5019(a,1),6323(a,1,2))].">
      <j1 rule="para" parents="5019 6323"/>
    </justification>
  </clause>

  <clause id="6675">
    <literal><![CDATA[
      a(x,y,z * ((u * (w * w)) \ v5)) = a(x,y,z * (u \ ((w * w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5591,a(flip),b,6332,a),flip(a)].">
      <j1 rule="hyper" parents="316 5591 6332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6676">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * w) \ v5))) = a(x,y,(u \ v5) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5835,a(flip),b,6333,a),flip(a)].">
      <j1 rule="hyper" parents="63 5835 6333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6678">
    <literal><![CDATA[
      a(x,y,z \ ((u * (w * w)) * v5)) = a(x,y,z \ (v5 * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5833,a(flip),b,6334,a),flip(a)].">
      <j1 rule="hyper" parents="316 5833 6334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6680">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ 1))) = a(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[para(229(a,1),6678(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="229 6678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6682">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) * w)) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,6680,a)].">
      <j1 rule="hyper" parents="63 5490 6680"/>
    </justification>
  </clause>

  <clause id="6683">
    <literal><![CDATA[
      a(x,y,z \ L(u,w,w \ 1)) = a(x,y,z \ (w * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6130,a(flip),b,6680,a)].">
      <j1 rule="hyper" parents="63 6130 6680"/>
    </justification>
  </clause>

  <clause id="6684">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) * w)) = a(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5490,a,b,6682,a),flip(a)].">
      <j1 rule="hyper" parents="316 5490 6682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6685">
    <literal><![CDATA[
      a(x,y,z \ ((1 / u) * w)) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5627,a,b,6682,a)].">
      <j1 rule="hyper" parents="63 5627 6682"/>
    </justification>
  </clause>

  <clause id="6686">
    <literal><![CDATA[
      a(x,y,z \ (R(u,w,w * u) * v5)) = a(x,y,z \ ((w * ((u * w) \ 1)) * v5))
    ]]></literal>
    <justification jstring="[para(4711(a,1),6682(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="4711 6682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6687">
    <literal><![CDATA[
      a(x,y,z \ L(u,w,w \ 1)) = a(x,y,z \ L(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5843,a(flip),b,6683,a),flip(a)].">
      <j1 rule="hyper" parents="316 5843 6683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6688">
    <literal><![CDATA[
      a(x,y,z \ ((u / (w * w)) \ v5)) = a(x,y,(z \ (u \ v5)) * (w * w))
    ]]></literal>
    <justification jstring="[para(637(a,1),6338(a,2,3))].">
      <j1 rule="para" parents="637 6338"/>
    </justification>
  </clause>

  <clause id="6690">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w \ 1) \ v5))) = a(x,y,z \ (u * (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5917,a(flip),b,6344,a)].">
      <j1 rule="hyper" parents="63 5917 6344"/>
    </justification>
  </clause>

  <clause id="6692">
    <literal><![CDATA[
      a(x,y,z \ (((u \ 1) \ w) * v5)) = a(x,y,z \ (v5 * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,6690,a)].">
      <j1 rule="hyper" parents="63 5490 6690"/>
    </justification>
  </clause>

  <clause id="6693">
    <literal><![CDATA[
      a(x,y,((z * (u * u)) \ w) * v5) = a(x,y,(z \ ((u * u) \ w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,5694,a(flip),b,6361,a),flip(a)].">
      <j1 rule="hyper" parents="316 5694 6361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6694">
    <literal><![CDATA[
      a(x,y,(((z * z) \ u) \ w) * v5) = a(x,y,(u \ (w * (z * z))) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5549,a(flip),b,6363,a)].">
      <j1 rule="hyper" parents="63 5549 6363"/>
    </justification>
  </clause>

  <clause id="6695">
    <literal><![CDATA[
      a(x,y,(z \ (u * (z * z))) * w) = a(x,y,((z \ 1) \ u) * w)
    ]]></literal>
    <justification jstring="[para(281(a,1),6363(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="281 6363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6697">
    <literal><![CDATA[
      a(x,y,((z \ u) * (z * z)) * w) = a(x,y,((z \ 1) \ u) * w)
    ]]></literal>
    <justification jstring="[para(388(a,1),6695(a,1,3,1))].">
      <j1 rule="para" parents="388 6695"/>
    </justification>
  </clause>

  <clause id="6698">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * w) = a(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5874,a(flip),b,6697,a),flip(a)].">
      <j1 rule="hyper" parents="63 5874 6697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6700">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) * u) * w) = a(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6041,a,b,6698,a)].">
      <j1 rule="hyper" parents="63 6041 6698"/>
    </justification>
  </clause>

  <clause id="6701">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ w)) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,6698,a)].">
      <j1 rule="hyper" parents="63 5469 6698"/>
    </justification>
  </clause>

  <clause id="6702">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u),u,u)) = a(x,y,(z \ u) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5808,a(flip),b,6700,a)].">
      <j1 rule="hyper" parents="63 5808 6700"/>
    </justification>
  </clause>

  <clause id="6703">
    <literal><![CDATA[
      a(x,y,L(L(z,u,u),z,u)) = a(x,y,(z \ u) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5952,a,b,6702,a)].">
      <j1 rule="hyper" parents="63 5952 6702"/>
    </justification>
  </clause>

  <clause id="6704">
    <literal><![CDATA[
      a(x,y,L(L(z * K(u,w),v5,v6),v7,(v8 \ 1) \ v9)) = a(x,y,L(L(z,v7,(v8 \ K(v10,v11)) \ v9),v5,v6))
    ]]></literal>
    <justification jstring="[para(4196(a,1),6367(a,1,3))].">
      <j1 rule="para" parents="4196 6367"/>
    </justification>
  </clause>

  <clause id="6705">
    <literal><![CDATA[
      a(x,y,(z / (u * (w * w))) \ v5) = a(x,y,(u \ z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5958,a(flip),b,6393,a)].">
      <j1 rule="hyper" parents="63 5958 6393"/>
    </justification>
  </clause>

  <clause id="6707">
    <literal><![CDATA[
      a(x,y,(((z * z) * u) \ w) \ v5) = a(x,y,(u \ w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,6280,a(flip),b,6705,a)].">
      <j1 rule="hyper" parents="63 6280 6705"/>
    </justification>
  </clause>

  <clause id="6708">
    <literal><![CDATA[
      a(x,y,((z * (u * u)) \ w) \ v5) = a(x,y,(z \ w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5546,a(flip),b,6705,a)].">
      <j1 rule="hyper" parents="63 5546 6705"/>
    </justification>
  </clause>

  <clause id="6710">
    <literal><![CDATA[
      a(x,y,z \ ((u * (w / v5)) * v6)) = a(x,y,z \ ((u * (v5 \ w)) * v6))
    ]]></literal>
    <justification jstring="[para(2721(a,1),6432(a,1,3,2,1,2))].">
      <j1 rule="para" parents="2721 6432"/>
    </justification>
  </clause>

  <clause id="6711">
    <literal><![CDATA[
      R(x,y,z * ((u * (w * w)) \ v5)) = R(x,y,z * (u \ v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,6437,a(flip),b,6436,a),flip(a)].">
      <j1 rule="hyper" parents="316 6437 6436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6713">
    <literal><![CDATA[
      R(x,y,(((z * z) * u) \ w) * v5) = R(x,y,v5 * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6275,a,b,6711,a)].">
      <j1 rule="hyper" parents="63 6275 6711"/>
    </justification>
  </clause>

  <clause id="6714">
    <literal><![CDATA[
      R(x,y,z \ ((u / (w * w)) \ v5)) = R(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,1707,a(flip),b,6440,a),flip(a)].">
      <j1 rule="hyper" parents="316 1707 6440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6716">
    <literal><![CDATA[
      R(x,y,z \ ((u \ 1) \ w)) = R(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(281(a,1),6714(a,1,3,2,1))].">
      <j1 rule="para" parents="281 6714"/>
    </justification>
  </clause>

  <clause id="6717">
    <literal><![CDATA[
      R(x,y,(z * u) \ u) = R(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4776,a(flip),b,6716,a)].">
      <j1 rule="hyper" parents="63 4776 6716"/>
    </justification>
  </clause>

  <clause id="6718">
    <literal><![CDATA[
      R(x,y,R(z / u,u,z \ ((w \ 1) \ v5)) \ (w \ v5)) = R(x,y,u * (z \ ((w \ 1) \ v5)))
    ]]></literal>
    <justification jstring="[para(490(a,1),6716(a,1,3)),flip(a)].">
      <j1 rule="para" parents="490 6716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6719">
    <literal><![CDATA[
      R(x,y,x \ (y \ x)) \ x = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(6717(a,1),4768(a,1,1))].">
      <j1 rule="para" parents="6717 4768"/>
    </justification>
  </clause>

  <clause id="6720">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ K(x,x \ 1) = ((L(x,y,z) \ 1) * x) \ 1
    ]]></literal>
    <justification jstring="[para(1002(a,1),6463(a,1,1))].">
      <j1 rule="para" parents="1002 6463"/>
    </justification>
  </clause>

  <clause id="6721">
    <literal><![CDATA[
      L(x,y,z) \ (1 / (1 / x)) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(39,a,4031,a,b,6720,a(flip))].">
      <j1 rule="hyper" parents="39 4031 6720"/>
    </justification>
  </clause>

  <clause id="6722">
    <literal><![CDATA[
      K(x * (a(y,z,u) \ (w \ (v5 * a(y,z,u)))),v6) = K(x * (w \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,6536,a(flip),b,6537,a)].">
      <j1 rule="hyper" parents="63 6536 6537"/>
    </justification>
  </clause>

  <clause id="6723">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(x,y,z) \ 1) = R(1 / x,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,1033,a(flip),b,6539,a),flip(a)].">
      <j1 rule="hyper" parents="316 1033 6539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6724">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(x,y,z) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,4591,a(flip),b,6723,a),flip(a)].">
      <j1 rule="hyper" parents="316 4591 6723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6725">
    <literal><![CDATA[
      (L(x,y,z) \ 1) / (x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(209,a,4591,a(flip),b,6723,a)].">
      <j1 rule="hyper" parents="209 4591 6723"/>
    </justification>
  </clause>

  <clause id="6726">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,4591,a(flip),b,6723,a)].">
      <j1 rule="hyper" parents="139 4591 6723"/>
    </justification>
  </clause>

  <clause id="6728">
    <literal><![CDATA[
      (L(L(x,y,z) \ x,u,w) \ (L(x,y,z) \ x)) * (x \ L(x,y,z)) = L(L(x,y,z) \ x,u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,5076,a(flip),b,6724,a)].">
      <j1 rule="hyper" parents="139 5076 6724"/>
    </justification>
  </clause>

  <clause id="6730">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(138,a,6724,a(flip),b,6483,a)].">
      <j1 rule="hyper" parents="138 6724 6483"/>
    </justification>
  </clause>

  <clause id="6731">
    <literal><![CDATA[
      R(L(x,y,z) \ x,x \ 1,(L(x,y,z) \ 1) \ u) \ u = (x \ 1) * ((L(x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(6725(a,1),490(a,1,1,1))].">
      <j1 rule="para" parents="6725 490"/>
    </justification>
  </clause>

  <clause id="6732">
    <literal><![CDATA[
      R(L(x,y,z) \ x,x \ 1,(x \ 1) \ u) * u = (L(x,y,z) \ 1) * ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(6726(a,1),495(a,2,1))].">
      <j1 rule="para" parents="6726 495"/>
    </justification>
  </clause>

  <clause id="6733">
    <literal><![CDATA[
      a(x,y,((((z \ 1) \ 1) * (L(z,u,w) \ z)) * v5) * v6) = a(x,y,(v5 * (L(z,u,w) \ 1)) * v6)
    ]]></literal>
    <justification jstring="[para(6726(a,1),6092(a,2,3,1,2))].">
      <j1 rule="para" parents="6726 6092"/>
    </justification>
  </clause>

  <clause id="6735">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,L(x,y,z) \ x,x \ 1) = (L(x,y,z) \ 1) \ ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(6730(a,1),102(a,2,1))].">
      <j1 rule="para" parents="6730 102"/>
    </justification>
  </clause>

  <clause id="6737">
    <literal><![CDATA[
      a(x,y,z * ((u * (w * w)) \ v5)) = a(x,y,(u \ v5) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,6676,a(flip),b,6675,a),flip(a)].">
      <j1 rule="hyper" parents="316 6676 6675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6740">
    <literal><![CDATA[
      a(x,y,z \ ((u / (w * w)) \ v5)) = a(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,5804,a(flip),b,6688,a),flip(a)].">
      <j1 rule="hyper" parents="316 5804 6688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6743">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ w)) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(281(a,1),6740(a,1,3,2,1))].">
      <j1 rule="para" parents="281 6740"/>
    </justification>
  </clause>

  <clause id="6744">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (w / (v5 * v5))) \ v6)) = a(x,y,z \ ((u \ w) \ v6))
    ]]></literal>
    <justification jstring="[para(675(a,1),6740(a,1,3,2,1))].">
      <j1 rule="para" parents="675 6740"/>
    </justification>
  </clause>

  <clause id="6745">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) = a(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5640,a,b,6743,a)].">
      <j1 rule="hyper" parents="63 5640 6743"/>
    </justification>
  </clause>

  <clause id="6746">
    <literal><![CDATA[
      a(x,y,L(R(z,u,(z * u) \ w),R(z,u,(z * u) \ w),w)) = a(x,y,w \ (u * ((z * u) \ w)))
    ]]></literal>
    <justification jstring="[para(348(a,1),6745(a,2,3,2))].">
      <j1 rule="para" parents="348 6745"/>
    </justification>
  </clause>

  <clause id="6747">
    <literal><![CDATA[
      a(x,y,((z * (u * u)) \ w) * v5) = a(x,y,v5 * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(316,a,6373,a(flip),b,6693,a),flip(a)].">
      <j1 rule="hyper" parents="316 6373 6693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6748">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w \ 1)) \ v5)) = a(x,y,((u \ w) \ v5) * z)
    ]]></literal>
    <justification jstring="[para(584(a,1),6747(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="584 6747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6749">
    <literal><![CDATA[
      a(x,y,((z \ (u \ 1)) \ w) * v5) = a(x,y,((z \ u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,6748,a)].">
      <j1 rule="hyper" parents="63 5469 6748"/>
    </justification>
  </clause>

  <clause id="6751">
    <literal><![CDATA[
      a(x,y,(((z * z) \ u) \ w) * v5) = a(x,y,((u \ w) * (z * z)) * v5)
    ]]></literal>
    <justification jstring="[para(388(a,1),6694(a,2,3,1))].">
      <j1 rule="para" parents="388 6694"/>
    </justification>
  </clause>

  <clause id="6752">
    <literal><![CDATA[
      a(x,y,((z * (u / w)) * v5) \ ((v5 * (w \ u)) * z)) = a(x,y,a(v5,u / w,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6132,a(flip),b,6710,a),flip(a)].">
      <j1 rule="hyper" parents="63 6132 6710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6753">
    <literal><![CDATA[
      a(x,y,z \ (((u * (1 / (w / v5))) * (v5 \ w)) * v6)) = a(x,y,z \ (R(u,(w / v5) \ 1,w / v5) * v6))
    ]]></literal>
    <justification jstring="[para(2569(a,1),6710(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="2569 6710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6754">
    <literal><![CDATA[
      K(x * (y \ (z * a(u,w,v5))),v6) = K(x * (y \ z),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,6632,a(flip),b,6722,a)].">
      <j1 rule="hyper" parents="63 6632 6722"/>
    </justification>
  </clause>

  <clause id="6756">
    <literal><![CDATA[
      K(x * (y \ (a(z,u,w) \ v5)),v6) = K(x * (y \ v5),v6)
    ]]></literal>
    <justification jstring="[para(2274(a,1),6754(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2274 6754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6757">
    <literal><![CDATA[
      a(x,y,(((z * z) \ u) \ w) * v5) = a(x,y,(u \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,5874,a(flip),b,6751,a),flip(a)].">
      <j1 rule="hyper" parents="316 5874 6751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6759">
    <literal><![CDATA[
      ((x * y) * R(y,z,u)) / (x * R(y,z,u)) = y * K(R(y,z,u) * x,y)
    ]]></literal>
    <justification jstring="[para(1550(a,1),3618(a,1,1))].">
      <j1 rule="para" parents="1550 3618"/>
    </justification>
  </clause>

  <clause id="6764">
    <literal><![CDATA[
      T(x * y,x * x) / ((x \ y) * (x * x)) = (x * (x * (x \ y))) / ((x * x) * (x \ y))
    ]]></literal>
    <justification jstring="[para(674(a,1),4371(a,1,1))].">
      <j1 rule="para" parents="674 4371"/>
    </justification>
  </clause>

  <clause id="6767">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((v5 * w) * u))) = L(x,y,z \ L(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,3321,a(flip),b,4558,a),flip(a)].">
      <j1 rule="hyper" parents="316 3321 4558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6769">
    <literal><![CDATA[
      a(((x * y) \ ((z * y) * x)) \ u,w,v5) = a(L(z,y,x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,3120,a(flip),b,4565,a),flip(a)].">
      <j1 rule="hyper" parents="316 3120 4565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6771">
    <literal><![CDATA[
      a(R(x,y,z) \ u,w,v5) = a(L(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,4614,a(flip),b,6769,a)].">
      <j1 rule="hyper" parents="63 4614 6769"/>
    </justification>
  </clause>

  <clause id="6774">
    <literal><![CDATA[
      L(x,y,L(z * (u / (u * u)),w,v5)) = L(x,y,L(u \ R(z,u,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,1688,a(flip),b,4880,a)].">
      <j1 rule="hyper" parents="63 1688 4880"/>
    </justification>
  </clause>

  <clause id="6775">
    <literal><![CDATA[
      (L(a(x,x,y),L(y,x,x),L(y,x,x) \ z) * z) \ (a(x,x,y) * z) = ((L(y,x,x) \ z) * y) \ (a(x,x,y) * ((L(y,x,x) \ z) * L(y,x,x)))
    ]]></literal>
    <justification jstring="[hyper(316,a,6639,a,b,4960,a)].">
      <j1 rule="hyper" parents="316 6639 4960"/>
    </justification>
  </clause>

  <clause id="6776">
    <literal><![CDATA[
      a(x / (L(y,z,z) * K(u,w)),L(y,z,z),a(z,z,y)) = ((x / (L(y,z,z) * K(u,w))) * y) \ (a(z,z,y) * (x * K(w,u)))
    ]]></literal>
    <justification jstring="[para(3843(a,1),4960(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3843 4960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6778">
    <literal><![CDATA[
      a(x,y,L(L(z \ u,w,v5),z,z)) = a(x,y,L(u * (z \ 1),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5646,a(flip),b,5738,a),flip(a)].">
      <j1 rule="hyper" parents="63 5646 5738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6786">
    <literal><![CDATA[
      a(L(x,y * y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(70(a,1),6216(a,1,1)),flip(a)].">
      <j1 rule="para" parents="70 6216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6787">
    <literal><![CDATA[
      a(x \ ((x \ 1) * y),z,u) = a((x * x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(486(a,1),6786(a,1,1))].">
      <j1 rule="para" parents="486 6786"/>
    </justification>
  </clause>

  <clause id="6788">
    <literal><![CDATA[
      L(x,y,((z * u) \ (u * (w * z))) \ v5) = L(x,y,L(w,z,u) \ v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,3407,a(flip),b,6279,a),flip(a)].">
      <j1 rule="hyper" parents="316 3407 6279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6792">
    <literal><![CDATA[
      ((x * (y * z)) / z) / (x * y) = (x * y) \ ((x * (y * z)) / z)
    ]]></literal>
    <justification jstring="[para(4378(a,1),6310(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4378 6310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6793">
    <literal><![CDATA[
      R(x,y,(y * x) \ ((x * (y * z)) / z)) \ ((x * (y * z)) / z) = y * (((x * (y * z)) / z) / (x * y))
    ]]></literal>
    <justification jstring="[para(6792(a,2),4768(a,2,2))].">
      <j1 rule="para" parents="6792 4768"/>
    </justification>
  </clause>

  <clause id="6794">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 * w)))) = a(x,y,z \ (L(v5,w,w) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6337,a(flip),b,6347,a),flip(a)].">
      <j1 rule="hyper" parents="63 6337 6347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6796">
    <literal><![CDATA[
      (((x * (y * z)) / z) \ (x * y)) \ (x * y) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(1465(a,1),6623(a,1,1,1))].">
      <j1 rule="para" parents="1465 6623"/>
    </justification>
  </clause>

  <clause id="6797">
    <literal><![CDATA[
      (((x * (y * L(y,z,u))) / y) \ (x * L(y,z,u))) \ (x * L(y,z,u)) = (x * (L(y,z,u) * y)) / y
    ]]></literal>
    <justification jstring="[para(1469(a,1),6623(a,1,1,1))].">
      <j1 rule="para" parents="1469 6623"/>
    </justification>
  </clause>

  <clause id="6798">
    <literal><![CDATA[
      (x * y) / ((x * (y * z)) / z) = ((x * (y * z)) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(210,a,6796,a)].">
      <j1 rule="hyper" parents="210 6796"/>
    </justification>
  </clause>

  <clause id="6800">
    <literal><![CDATA[
      (((x * (L(y,z,u) * (y \ K(w,v5)))) / (y \ K(w,v5))) \ (x * L(y,z,u))) \ (x * L(y,z,u)) = (x * (K(w,v5) * (y \ L(y,z,u)))) / (y \ K(w,v5))
    ]]></literal>
    <justification jstring="[para(4379(a,1),6796(a,2,1,2))].">
      <j1 rule="para" parents="4379 6796"/>
    </justification>
  </clause>

  <clause id="6801">
    <literal><![CDATA[
      T(x * K(R(x,y,z) * u,x),u) = R(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(6759(a,1),734(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6759 734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6802">
    <literal><![CDATA[
      T(x * K(R(x,y,z) * u,x),u) = R(x,u,R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,4060,a,b,6801,a),flip(a)].">
      <j1 rule="hyper" parents="316 4060 6801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6803">
    <literal><![CDATA[
      L(R(x,y,R(T(x,y),z,u)),y,R(x,z,u)) = (R(x,z,u) * (x * y)) / (R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(6802(a,1),2750(a,1,1))].">
      <j1 rule="para" parents="6802 2750"/>
    </justification>
  </clause>

  <clause id="6805">
    <literal><![CDATA[
      L(x,y,L(z \ R(u,z,z),w,v5)) = L(x,y,L(u * (z \ 1),w,v5))
    ]]></literal>
    <justification jstring="[para(281(a,1),6774(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="281 6774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6806">
    <literal><![CDATA[
      x * L(y * K((x \ 1) \ y,x),z,u) = T(x * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3654(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6807">
    <literal><![CDATA[
      x * L(y * K(x * y,x),z,u) = T(x * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(3565(a,1),6806(a,1,2,1,2))].">
      <j1 rule="para" parents="3565 6806"/>
    </justification>
  </clause>

  <clause id="6808">
    <literal><![CDATA[
      L(x,y,z) * R(u,x,u) = T(u * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5174,a(flip),b,6807,a)].">
      <j1 rule="hyper" parents="63 5174 6807"/>
    </justification>
  </clause>

  <clause id="6809">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,1636,a,b,6808,a)].">
      <j1 rule="hyper" parents="34 1636 6808"/>
    </justification>
  </clause>

  <clause id="6810">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),x) = R(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(3422(a,2),6809(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3422 6809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6811">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,5320,a(flip),b,6810,a),flip(a)].">
      <j1 rule="hyper" parents="316 5320 6810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6812">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(1622,a,6811,a)].">
      <j1 rule="hyper" parents="1622 6811"/>
    </justification>
  </clause>

  <clause id="6816">
    <literal><![CDATA[
      x \ (y * (z * ((u * u) \ K(w,v5)))) = (x \ ((y * z) / (u * u))) * K(w,v5)
    ]]></literal>
    <justification jstring="[para(4045(a,1),4225(a,1,2,2))].">
      <j1 rule="para" parents="4045 4225"/>
    </justification>
  </clause>

  <clause id="6817">
    <literal><![CDATA[
      (x * (y * (y * L(y \ 1,z,u)))) / y = L(y \ 1,z,u) * ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(1264(a,1),4410(a,1,1,2))].">
      <j1 rule="para" parents="1264 4410"/>
    </justification>
  </clause>

  <clause id="6818">
    <literal><![CDATA[
      (x * y) / (y * (y * L(y \ 1,z,u))) = (y \ 1) * (L(y \ 1,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(1048(a,1),4425(a,1,2))].">
      <j1 rule="para" parents="1048 4425"/>
    </justification>
  </clause>

  <clause id="6819">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,z,u) \ T(x,w)) = K(x,w) * (y / L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,660,a(flip),b,4432,a),flip(a)].">
      <j1 rule="hyper" parents="316 660 4432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6820">
    <literal><![CDATA[
      (L(x,y,z) \ (u * x)) / (x * x) = x \ R(u / L(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(4394(a,1),4463(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4394 4463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6821">
    <literal><![CDATA[
      L(x,y,z) \ ((u * x) / (x * x)) = x \ R(u / L(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,675,a(flip),b,6820,a)].">
      <j1 rule="hyper" parents="63 675 6820"/>
    </justification>
  </clause>

  <clause id="6822">
    <literal><![CDATA[
      x \ R(y / L(x,z,u),x,x) = L(x,z,u) \ (y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(562(a,1),6821(a,1,2)),flip(a)].">
      <j1 rule="para" parents="562 6821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6823">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * (x \ 1))) = R(u / L(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[hyper(152,a,6822,a)].">
      <j1 rule="hyper" parents="152 6822"/>
    </justification>
  </clause>

  <clause id="6824">
    <literal><![CDATA[
      L(x,y,z) * R(u / L(x,y,z),x,x) = x * (u * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(139,a,6823,a(flip),b,1129,a)].">
      <j1 rule="hyper" parents="139 6823 1129"/>
    </justification>
  </clause>

  <clause id="6825">
    <literal><![CDATA[
      T(x \ ((K(y,z) / x) \ y),z) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(4524(a,1),2731(a,1,1))].">
      <j1 rule="para" parents="4524 2731"/>
    </justification>
  </clause>

  <clause id="6826">
    <literal><![CDATA[
      T(x \ ((1 / x) \ a(y,z,u)),w) = x \ ((1 / x) \ a(y,z,u))
    ]]></literal>
    <justification jstring="[para(2303(a,1),6825(a,1,1,2,1,1))].">
      <j1 rule="para" parents="2303 6825"/>
    </justification>
  </clause>

  <clause id="6828">
    <literal><![CDATA[
      (x \ ((1 / x) \ a(y,z,u))) * w = w * (x \ ((1 / x) \ a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(139,a,6826,a(flip),b,4310,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 6826 4310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6829">
    <literal><![CDATA[
      ((L(x,y,z) / u) * (u * T(w,x))) \ (w * L(x,y,z)) = a(u \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(4575(a,1),6639(a,1,1))].">
      <j1 rule="para" parents="4575 6639"/>
    </justification>
  </clause>

  <clause id="6830">
    <literal><![CDATA[
      (x \ y) * L(T(x \ y,x) \ y,z,u) = L(x,z,u) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(316,a,3169,a(flip),b,4870,a),flip(a)].">
      <j1 rule="hyper" parents="316 3169 4870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6831">
    <literal><![CDATA[
      (x / y) \ L((x / y) * z,u,w) = (y \ x) \ L((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(116(a,1),4884(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="116 4884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6832">
    <literal><![CDATA[
      (x \ y) \ L((x \ y) * x,z,u) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),6831(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 6831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6833">
    <literal><![CDATA[
      L(x,y,z) / (u \ x) = (x / u) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1388,a(flip),b,6832,a)].">
      <j1 rule="hyper" parents="63 1388 6832"/>
    </justification>
  </clause>

  <clause id="6834">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ x,z,u) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1355,a(flip),b,6832,a)].">
      <j1 rule="hyper" parents="63 1355 6832"/>
    </justification>
  </clause>

  <clause id="6835">
    <literal><![CDATA[
      ((x / y) \ L(x,z,u)) \ L(x,z,u) = y \ x
    ]]></literal>
    <justification jstring="[hyper(204,a,6833,a)].">
      <j1 rule="hyper" parents="204 6833"/>
    </justification>
  </clause>

  <clause id="6838">
    <literal><![CDATA[
      x \ (y * L(y \ (x * x),z,u)) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1020,a,b,6834,a)].">
      <j1 rule="hyper" parents="63 1020 6834"/>
    </justification>
  </clause>

  <clause id="6839">
    <literal><![CDATA[
      (x \ (y \ L(y,z,u))) * (x * x) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1389,a(flip),b,6838,a)].">
      <j1 rule="hyper" parents="63 1389 6838"/>
    </justification>
  </clause>

  <clause id="6840">
    <literal><![CDATA[
      (x * y) * ((z \ K(u,w)) * z) = x * (y * ((z \ K(u,w)) * z))
    ]]></literal>
    <justification jstring="[para(3934(a,1),4909(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3934 4909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6841">
    <literal><![CDATA[
      L(x,x,y \ L(y,z,u)) * (y \ L(y,z,u)) = (1 / x) \ (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,6660,a(flip),b,5064,a),flip(a)].">
      <j1 rule="hyper" parents="316 6660 5064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6842">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x \ L(x,u,w)) = L(x,y,z) \ L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,168,a(flip),b,5149,a),flip(a)].">
      <j1 rule="hyper" parents="63 168 5149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6843">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(x,y,z) \ L(x,u,w)) = x \ L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,168,a(flip),b,5149,a(flip))].">
      <j1 rule="hyper" parents="133 168 5149"/>
    </justification>
  </clause>

  <clause id="6844">
    <literal><![CDATA[
      x * ((L(x,y,z) \ u) * (x \ L(x,y,z))) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5149(a,1),5068(a,1,2))].">
      <j1 rule="para" parents="5149 5068"/>
    </justification>
  </clause>

  <clause id="6845">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x \ L(x,u,w),v5,v6) = x * (L(x,y,z) \ L(x \ L(x,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(6843(a,1),1534(a,1,2,1))].">
      <j1 rule="para" parents="6843 1534"/>
    </justification>
  </clause>

  <clause id="6846">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * (L(x,y,z) \ u)) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5112,a,b,6844,a)].">
      <j1 rule="hyper" parents="63 5112 6844"/>
    </justification>
  </clause>

  <clause id="6847">
    <literal><![CDATA[
      L(L(x,y,z) \ u,x,x \ L(x,y,z)) = L(x,y,z) \ L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(6844(a,1),5113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6844 5113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6849">
    <literal><![CDATA[
      R(x,y,L(x \ L(x,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(501,a,5157,a)].">
      <j1 rule="hyper" parents="501 5157"/>
    </justification>
  </clause>

  <clause id="6850">
    <literal><![CDATA[
      R(x,y,L(L(x,z,u) \ x,w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,1902,a,b,6849,a)].">
      <j1 rule="hyper" parents="63 1902 6849"/>
    </justification>
  </clause>

  <clause id="6851">
    <literal><![CDATA[
      (L(x,y,z) * u) * L(L(x,w,v5) \ x,v6,v7) = L(x,y,z) * (u * L(L(x,w,v5) \ x,v6,v7))
    ]]></literal>
    <justification jstring="[para(6850(a,1),400(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6850 400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6852">
    <literal><![CDATA[
      R(x,y,a(z,u,x)) = x
    ]]></literal>
    <justification jstring="[para(1561(a,2),6850(a,1,3))].">
      <j1 rule="para" parents="1561 6850"/>
    </justification>
  </clause>

  <clause id="6853">
    <literal><![CDATA[
      L(x,y,a(z,u,x)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,5371,a(flip),b,6852,a)].">
      <j1 rule="hyper" parents="63 5371 6852"/>
    </justification>
  </clause>

  <clause id="6854">
    <literal><![CDATA[
      a(x,y,z) * (z * u) = z * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(138,a,6852,a(flip),b,2497,a),flip(a)].">
      <j1 rule="hyper" parents="138 6852 2497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6855">
    <literal><![CDATA[
      a(x,y,z) * (z * u) = z * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(138,a,6852,a(flip),b,2341,a),flip(a)].">
      <j1 rule="hyper" parents="138 6852 2341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6856">
    <literal><![CDATA[
      (x * a(y,z,u)) * a(w,v5,a(y,z,u)) = a(y,z,u) * (x * a(w,v5,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(138,a,6852,a(flip),b,2335,a),flip(a)].">
      <j1 rule="hyper" parents="138 6852 2335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6857">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(w,v5,u) = u * (a(x,y,z) * a(w,v5,u))
    ]]></literal>
    <justification jstring="[hyper(138,a,6852,a(flip),b,2280,a),flip(a)].">
      <j1 rule="hyper" parents="138 6852 2280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6858">
    <literal><![CDATA[
      (x * y) * a(z,u,x) = x * (y * a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(138,a,6852,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="138 6852 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6859">
    <literal><![CDATA[
      x * (a(y,z,x) \ 1) = a(y,z,x) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,6852,a(flip),b,2629,a),flip(a)].">
      <j1 rule="hyper" parents="133 6852 2629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6860">
    <literal><![CDATA[
      (x * a(y,z,x)) \ x = a(y,z,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,6852,a(flip),b,565,a)].">
      <j1 rule="hyper" parents="133 6852 565"/>
    </justification>
  </clause>

  <clause id="6861">
    <literal><![CDATA[
      (x \ 1) * a(y,z,x) = x \ a(y,z,x)
    ]]></literal>
    <justification jstring="[para(6852(a,1),382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6852 382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6862">
    <literal><![CDATA[
      x \ (y * a(z,u,x)) = (x \ y) * a(z,u,x)
    ]]></literal>
    <justification jstring="[para(6852(a,1),492(a,1,1))].">
      <j1 rule="para" parents="6852 492"/>
    </justification>
  </clause>

  <clause id="6863">
    <literal><![CDATA[
      (L(x,y,z) * u) * a(w,v5,x) = L(x,y,z) * (u * a(w,v5,x))
    ]]></literal>
    <justification jstring="[para(6852(a,1),400(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6852 400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6865">
    <literal><![CDATA[
      (a(x,y,z) * u) * z = a(x,y,z) * (u * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,6853,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="139 6853 18"/>
    </justification>
  </clause>

  <clause id="6866">
    <literal><![CDATA[
      L(x,y,a(z,u,L(x,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,30,a,b,6853,a(flip))].">
      <j1 rule="hyper" parents="41 30 6853"/>
    </justification>
  </clause>

  <clause id="6867">
    <literal><![CDATA[
      L(R(x,y,z),u,a(w,v5,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(6853(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6853 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6868">
    <literal><![CDATA[
      L(L(x,y,z),u,a(w,v5,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(6853(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6853 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6869">
    <literal><![CDATA[
      a(x,y,z) \ (u * z) = (a(x,y,z) \ u) * z
    ]]></literal>
    <justification jstring="[para(6853(a,1),456(a,1,2,2))].">
      <j1 rule="para" parents="6853 456"/>
    </justification>
  </clause>

  <clause id="6870">
    <literal><![CDATA[
      (a(x,y,z) * u) * L(z,w,v5) = a(x,y,z) * (u * L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(6853(a,1),403(a,1,2,1))].">
      <j1 rule="para" parents="6853 403"/>
    </justification>
  </clause>

  <clause id="6871">
    <literal><![CDATA[
      L(L(L(x,y,z),u,w),v5,a(v6,v7,x)) = L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(6853(a,1),122(a,2,1,1))].">
      <j1 rule="para" parents="6853 122"/>
    </justification>
  </clause>

  <clause id="6872">
    <literal><![CDATA[
      L(x * (y * x),z,a(u,w,y)) = x * (y * x)
    ]]></literal>
    <justification jstring="[para(6853(a,1),1359(a,2,2,1))].">
      <j1 rule="para" parents="6853 1359"/>
    </justification>
  </clause>

  <clause id="6873">
    <literal><![CDATA[
      L(x \ 1,y,a(z,u,x)) = x \ 1
    ]]></literal>
    <justification jstring="[para(2534(a,1),6853(a,1,3))].">
      <j1 rule="para" parents="2534 6853"/>
    </justification>
  </clause>

  <clause id="6874">
    <literal><![CDATA[
      L(L(x,y,z),u,a(w,v5,L(x,v6,v7))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(6866(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6866 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6875">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,a(w,v5,L(x,v6,v7))) = x \ L(L(x,y,z),u,a(w,v5,L(x,v6,v7)))
    ]]></literal>
    <justification jstring="[para(6866(a,1),2138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6866 2138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6876">
    <literal><![CDATA[
      (x * y) * a(z,u,L(x,w,v5)) = x * (y * a(z,u,L(x,w,v5)))
    ]]></literal>
    <justification jstring="[para(6866(a,1),5383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6866 5383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6877">
    <literal><![CDATA[
      (a(x,y,z) * u) * (z \ 1) = (u * (z \ 1)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,6873,a(flip),b,2349,a)].">
      <j1 rule="hyper" parents="139 6873 2349"/>
    </justification>
  </clause>

  <clause id="6878">
    <literal><![CDATA[
      a(x,y,z) * ((z \ 1) * u) = (z \ 1) * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(138,a,6873,a(flip),b,5343,a),flip(a)].">
      <j1 rule="hyper" parents="138 6873 5343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6879">
    <literal><![CDATA[
      a(x,y,z) \ (u * (z \ 1)) = (a(x,y,z) \ u) * (z \ 1)
    ]]></literal>
    <justification jstring="[para(6873(a,1),456(a,1,2,2))].">
      <j1 rule="para" parents="6873 456"/>
    </justification>
  </clause>

  <clause id="6880">
    <literal><![CDATA[
      x \ (a(y,z,x) \ x) = a(y,z,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(144,a,6859,a)].">
      <j1 rule="hyper" parents="144 6859"/>
    </justification>
  </clause>

  <clause id="6881">
    <literal><![CDATA[
      T(a(x,y,z) * (u / R(z,w,v5)),R(z,w,v5)) = R(z,w,v5) \ (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(6867(a,1),4361(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6867 4361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6882">
    <literal><![CDATA[
      (x * a(y,z,u)) * L(u,w,v5) = a(y,z,u) * (x * L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(139,a,6868,a(flip),b,2353,a)].">
      <j1 rule="hyper" parents="139 6868 2353"/>
    </justification>
  </clause>

  <clause id="6883">
    <literal><![CDATA[
      L(x,y,z) * (a(u,w,x) * v5) = a(u,w,x) * (L(x,y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(138,a,6868,a(flip),b,5343,a)].">
      <j1 rule="hyper" parents="138 6868 5343"/>
    </justification>
  </clause>

  <clause id="6884">
    <literal><![CDATA[
      a(x,y,z) \ (u * L(z,w,v5)) = (a(x,y,z) \ u) * L(z,w,v5)
    ]]></literal>
    <justification jstring="[para(6868(a,1),456(a,1,2,2))].">
      <j1 rule="para" parents="6868 456"/>
    </justification>
  </clause>

  <clause id="6885">
    <literal><![CDATA[
      L(L(x,y,z) \ L(L(x,y,z),u,w),v5,a(v6,v7,x)) = L(x,y,z) \ L(L(L(x,y,z),u,w),v5,a(v6,v7,x))
    ]]></literal>
    <justification jstring="[para(6868(a,1),2138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6868 2138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6886">
    <literal><![CDATA[
      (L(x,y,z) * u) * a(w,v5,x) = L(x,y,z) * (a(w,v5,x) * u)
    ]]></literal>
    <justification jstring="[para(6868(a,1),5276(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6868 5276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6888">
    <literal><![CDATA[
      L(L(x * (y * y),z,u),w,a(v5,v6,x)) = L(x * (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(5804(a,1),6868(a,1,3))].">
      <j1 rule="para" parents="5804 6868"/>
    </justification>
  </clause>

  <clause id="6890">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ z = z * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(6880(a,1),5207(a,1,1))].">
      <j1 rule="para" parents="6880 5207"/>
    </justification>
  </clause>

  <clause id="6891">
    <literal><![CDATA[
      a((a(x,y,z) \ 1) \ z,u,w) = a(a(x,y,z) * z,u,w)
    ]]></literal>
    <justification jstring="[para(6890(a,2),2771(a,1,1))].">
      <j1 rule="para" parents="6890 2771"/>
    </justification>
  </clause>

  <clause id="6892">
    <literal><![CDATA[
      x * (a(y,z,x) * (x \ u)) = a(y,z,x) * u
    ]]></literal>
    <justification jstring="[hyper(323,a,6854,a),flip(a)].">
      <j1 rule="hyper" parents="323 6854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6893">
    <literal><![CDATA[
      a(x,y,z) \ (z * u) = z * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,160,a(flip),b,6854,a)].">
      <j1 rule="hyper" parents="133 160 6854"/>
    </justification>
  </clause>

  <clause id="6894">
    <literal><![CDATA[
      a(x,y,z) * (a(u,w,v5) * z) = z * (a(x,y,z) * a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,2293,a,b,6854,a)].">
      <j1 rule="hyper" parents="63 2293 6854"/>
    </justification>
  </clause>

  <clause id="6895">
    <literal><![CDATA[
      a(x,y,z) * (z \ (a(x,y,z) \ u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(133,a,76,a(flip),b,6854,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 76 6854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6896">
    <literal><![CDATA[
      x \ (a(y,z,x) * u) = (x \ u) * a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(543,a,6855,a)].">
      <j1 rule="hyper" parents="543 6855"/>
    </justification>
  </clause>

  <clause id="6897">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,x)) = a(z,u,x) * y
    ]]></literal>
    <justification jstring="[hyper(323,a,6855,a),flip(a)].">
      <j1 rule="hyper" parents="323 6855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6898">
    <literal><![CDATA[
      L(a(x,y,z),u,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,2307,a,b,6855,a)].">
      <j1 rule="hyper" parents="35 2307 6855"/>
    </justification>
  </clause>

  <clause id="6899">
    <literal><![CDATA[
      (a(x,y,z) * z) \ (z * (u * a(x,y,z))) = L(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,6855,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="133 6855 100"/>
    </justification>
  </clause>

  <clause id="6900">
    <literal><![CDATA[
      (x * (y * a(z,u,x))) \ ((x * a(z,u,x)) * y) = a(a(z,u,x),x,y)
    ]]></literal>
    <justification jstring="[para(6855(a,1),2351(a,1,1))].">
      <j1 rule="para" parents="6855 2351"/>
    </justification>
  </clause>

  <clause id="6901">
    <literal><![CDATA[
      L(a(x,y,L(L(z,u,w),v5,v6)),v7,L(L(z,v5,v6),u,w)) = a(x,y,L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,1699,a,b,6898,a)].">
      <j1 rule="hyper" parents="63 1699 6898"/>
    </justification>
  </clause>

  <clause id="6902">
    <literal><![CDATA[
      a(x,y,a(z,u,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,6898,a)].">
      <j1 rule="hyper" parents="53 6898"/>
    </justification>
  </clause>

  <clause id="6904">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),v5,z) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(6898(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6898 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6905">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(u,w,x) = L(x,y,z) * (x \ a(u,w,x))
    ]]></literal>
    <justification jstring="[para(6898(a,1),1135(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6898 1135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6906">
    <literal><![CDATA[
      x * (y * a(x * y,y,x)) = R(x * y,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4509,a(flip),b,6858,a),flip(a)].">
      <j1 rule="hyper" parents="63 4509 6858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6907">
    <literal><![CDATA[
      x * (((x * x) \ y) * a(z,u,x)) = (x \ L(y,x,x)) * a(z,u,x)
    ]]></literal>
    <justification jstring="[para(1118(a,1),6858(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1118 6858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6908">
    <literal><![CDATA[
      L(x \ 1,y,z) * (u * a(w,v5,L(x \ 1,y,z))) = (L(x \ 1,y,z) * u) * a(w,v5,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2655(a,1),6858(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2655 6858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6909">
    <literal><![CDATA[
      x * ((R(x,x,y) \ y) * a(z,u,x)) = L(y,x,x) * a(z,u,x)
    ]]></literal>
    <justification jstring="[para(4658(a,1),6858(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4658 6858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6913">
    <literal><![CDATA[
      (a(x,y,z) * (u * z)) * (z \ 1) = R(a(x,y,z) * u,z,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,6865,a(flip),b,569,a)].">
      <j1 rule="hyper" parents="138 6865 569"/>
    </justification>
  </clause>

  <clause id="6914">
    <literal><![CDATA[
      a(x,y,y) * (x * y) = R(x,y,y) * y
    ]]></literal>
    <justification jstring="[para(2377(a,1),6865(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2377 6865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6915">
    <literal><![CDATA[
      (x * (a(y,z,u) * u)) \ (a(y,z,u) * (x * u)) = a(x,a(y,z,u),u)
    ]]></literal>
    <justification jstring="[para(6865(a,1),2352(a,1,2))].">
      <j1 rule="para" parents="6865 2352"/>
    </justification>
  </clause>

  <clause id="6917">
    <literal><![CDATA[
      (x * y) \ (R(x,y,y) * y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,6914,a(flip),b,2290,a(flip))].">
      <j1 rule="hyper" parents="133 6914 2290"/>
    </justification>
  </clause>

  <clause id="6918">
    <literal><![CDATA[
      a(x \ y,x,z) \ y = ((y / x) * (x * z)) / z
    ]]></literal>
    <justification jstring="[hyper(136,a,2400,a(flip),b,6869,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 2400 6869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6919">
    <literal><![CDATA[
      a(x,y,z) \ (x * y) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(136,a,2315,a(flip),b,6869,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="136 2315 6869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6920">
    <literal><![CDATA[
      a(x,y,z) \ (z \ u) = z \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(35,a,5450,a(flip),b,6869,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 5450 6869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6922">
    <literal><![CDATA[
      a(x,y,y) \ (x * y) = x * L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,1439,a(flip),b,6919,a),flip(a)].">
      <j1 rule="hyper" parents="316 1439 6919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6923">
    <literal><![CDATA[
      a(x,y,z) = (x * y) / ((x * (y * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(210,a,6919,a),flip(a)].">
      <j1 rule="hyper" parents="210 6919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6925">
    <literal><![CDATA[
      a(x,y,z) = ((x * (y * z)) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(39,a,6796,a,b,6919,a),flip(a)].">
      <j1 rule="hyper" parents="39 6796 6919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6926">
    <literal><![CDATA[
      x * (a(y,z,x) \ (y * z)) = L(x,z,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(6919(a,2),4415(a,2,2)),flip(a)].">
      <j1 rule="para" parents="6919 4415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6927">
    <literal><![CDATA[
      (x * L(y,y,x)) \ (x * y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[para(6922(a,1),2301(a,1,1))].">
      <j1 rule="para" parents="6922 2301"/>
    </justification>
  </clause>

  <clause id="6928">
    <literal><![CDATA[
      (x / (y \ 1)) \ (x * y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[para(1445(a,1),6927(a,1,1))].">
      <j1 rule="para" parents="1445 6927"/>
    </justification>
  </clause>

  <clause id="6929">
    <literal><![CDATA[
      T((x * y) * ((x / (y \ 1)) \ 1),x / (y \ 1)) = R(a(x,y,y),x / (y \ 1),x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(6928(a,1),622(a,2,1))].">
      <j1 rule="para" parents="6928 622"/>
    </justification>
  </clause>

  <clause id="6930">
    <literal><![CDATA[
      ((x * (1 / y)) / (y \ 1)) \ R(x,y \ 1,y) = a(x * (1 / y),y,y)
    ]]></literal>
    <justification jstring="[para(2569(a,1),6928(a,1,2))].">
      <j1 rule="para" parents="2569 6928"/>
    </justification>
  </clause>

  <clause id="6931">
    <literal><![CDATA[
      R(x,y,((z \ 1) / (u \ 1)) \ (u * z)) = R(x,y,a(z \ 1,u,u))
    ]]></literal>
    <justification jstring="[para(6928(a,1),4746(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6928 4746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6932">
    <literal><![CDATA[
      a(x,y,(z / (u \ 1)) \ (u * z)) = a(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(6928(a,1),5490(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6928 5490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6934">
    <literal><![CDATA[
      a(R(x,y,z),y,z) = (x * y) \ (R(x,y,z) * y)
    ]]></literal>
    <justification jstring="[para(301(a,1),6925(a,2,1))].">
      <j1 rule="para" parents="301 6925"/>
    </justification>
  </clause>

  <clause id="6935">
    <literal><![CDATA[
      ((L(R(x,y,z),u,w) * (x * v5)) / v5) \ (x * L(R(x,y,z),u,w)) = a(L(R(x,y,z),u,w),x,v5)
    ]]></literal>
    <justification jstring="[para(606(a,1),6925(a,2,2)),flip(a)].">
      <j1 rule="para" parents="606 6925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6937">
    <literal><![CDATA[
      (a(x,y,z) \ (u * (w * a(x,y,z)))) \ (u * w) = a(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(2276(a,1),6925(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2276 6925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6938">
    <literal><![CDATA[
      ((x * y) / L(y,z,z)) \ (x * a(z,z,y)) = a(x,a(z,z,y),L(y,z,z))
    ]]></literal>
    <justification jstring="[para(4951(a,1),6925(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4951 6925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6939">
    <literal><![CDATA[
      x * (a(y,y \ z,x) \ z) = L(x,y \ z,y) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,4622,a(flip),b,6893,a),flip(a)].">
      <j1 rule="hyper" parents="63 4622 6893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6940">
    <literal><![CDATA[
      x * (a(y,z,x) \ ((x * x) \ u)) = a(y,z,x) \ (x \ L(u,x,x))
    ]]></literal>
    <justification jstring="[para(1118(a,1),6893(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1118 6893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6941">
    <literal><![CDATA[
      a(x,y,z) \ (a(u,u,z) \ 1) = z \ (a(x,y,z) \ L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,5088,a,b,6895,a)].">
      <j1 rule="hyper" parents="133 5088 6895"/>
    </justification>
  </clause>

  <clause id="6942">
    <literal><![CDATA[
      (a(x,y,z) * u) / z = (u / z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(136,a,6897,a(flip),b,5358,a)].">
      <j1 rule="hyper" parents="136 6897 5358"/>
    </justification>
  </clause>

  <clause id="6944">
    <literal><![CDATA[
      L(x,y,z) * (a(u,w,L(x,v5,v6)) \ 1) = a(u,w,L(x,v5,v6)) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,6874,a(flip),b,5375,a),flip(a)].">
      <j1 rule="hyper" parents="133 6874 5375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6947">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (z * v5) = z * (v5 * L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(6904(a,1),4369(a,1,1))].">
      <j1 rule="para" parents="6904 4369"/>
    </justification>
  </clause>

  <clause id="6948">
    <literal><![CDATA[
      (((x / y) * (y * z)) / z) \ x = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[para(6918(a,1),2301(a,1,1))].">
      <j1 rule="para" parents="6918 2301"/>
    </justification>
  </clause>

  <clause id="6949">
    <literal><![CDATA[
      a(R(x,y,y),y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,6917,a(flip),b,6934,a),flip(a)].">
      <j1 rule="hyper" parents="316 6917 6934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6950">
    <literal><![CDATA[
      a(L(x,y,z),y,z) = (x * y) \ (R(x,y,z) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4643,a(flip),b,6934,a)].">
      <j1 rule="hyper" parents="63 4643 6934"/>
    </justification>
  </clause>

  <clause id="6951">
    <literal><![CDATA[
      a(L(x,y,y),y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4643,a(flip),b,6949,a)].">
      <j1 rule="hyper" parents="63 4643 6949"/>
    </justification>
  </clause>

  <clause id="6952">
    <literal><![CDATA[
      a(x * (y \ 1),y,y) = a(y \ x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4651,a(flip),b,6951,a)].">
      <j1 rule="hyper" parents="63 4651 6951"/>
    </justification>
  </clause>

  <clause id="6953">
    <literal><![CDATA[
      a((x \ (x \ 1)) \ ((1 / x) * y),x \ 1,x \ 1) = a((x \ 1) \ y,x \ 1,x \ 1)
    ]]></literal>
    <justification jstring="[para(1593(a,1),6951(a,1,1))].">
      <j1 rule="para" parents="1593 6951"/>
    </justification>
  </clause>

  <clause id="6954">
    <literal><![CDATA[
      a(x * (1 / y),y,y) = a(y \ x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3150,a,b,6952,a)].">
      <j1 rule="hyper" parents="63 3150 6952"/>
    </justification>
  </clause>

  <clause id="6955">
    <literal><![CDATA[
      L(x,y,y \ x) \ x = a(y \ x,y,x)
    ]]></literal>
    <justification jstring="[para(1661(a,1),6948(a,1,1))].">
      <j1 rule="para" parents="1661 6948"/>
    </justification>
  </clause>

  <clause id="6956">
    <literal><![CDATA[
      (a(x,y,z) \ ((u / w) * (w * a(x,y,z)))) \ u = a(w \ u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(2276(a,1),6948(a,1,1))].">
      <j1 rule="para" parents="2276 6948"/>
    </justification>
  </clause>

  <clause id="6959">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,y) = a(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,3361,a,b,6950,a)].">
      <j1 rule="hyper" parents="316 3361 6950"/>
    </justification>
  </clause>

  <clause id="6960">
    <literal><![CDATA[
      a(x,y,z \ ((L(u,w \ 1,w) * 1) * v5)) = a(x,y,z \ (v5 * (u * a(w,w \ 1,u))))
    ]]></literal>
    <justification jstring="[para(6939(a,1),6353(a,1,3,2,1))].">
      <j1 rule="para" parents="6939 6353"/>
    </justification>
  </clause>

  <clause id="6961">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) \ (z * u)) = a(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5546,a(flip),b,6932,a)].">
      <j1 rule="hyper" parents="63 5546 6932"/>
    </justification>
  </clause>

  <clause id="6962">
    <literal><![CDATA[
      a(x,y,z) \ ((z \ 1) * u) = (z \ 1) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,160,a(flip),b,6878,a)].">
      <j1 rule="hyper" parents="133 160 6878"/>
    </justification>
  </clause>

  <clause id="6963">
    <literal><![CDATA[
      T(a(x,y,z) \ z,z \ 1) = (z \ 1) \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(390,a,168,a(flip),b,6879,a(flip))].">
      <j1 rule="hyper" parents="390 168 6879"/>
    </justification>
  </clause>

  <clause id="6964">
    <literal><![CDATA[
      a(x,y,z) \ ((z \ 1) \ u) = (z \ 1) \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(35,a,5450,a(flip),b,6879,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 5450 6879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6965">
    <literal><![CDATA[
      (x \ (a(y,z,x) \ 1)) * x = (x \ 1) * (a(y,z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5450,a(flip),b,6962,a)].">
      <j1 rule="hyper" parents="63 5450 6962"/>
    </justification>
  </clause>

  <clause id="6966">
    <literal><![CDATA[
      (x \ (a(y,x,L(x,z,u)) \ 1)) * x = (x \ 1) * (a(y,L(x,z,u),x) \ x)
    ]]></literal>
    <justification jstring="[para(2548(a,1),6965(a,1,1,2,1))].">
      <j1 rule="para" parents="2548 6965"/>
    </justification>
  </clause>

  <clause id="6967">
    <literal><![CDATA[
      ((x * y) * (y \ 1)) * a(z,u,y) = R(a(z,u,y) * x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6877,a(flip),b,6913,a)].">
      <j1 rule="hyper" parents="63 6877 6913"/>
    </justification>
  </clause>

  <clause id="6968">
    <literal><![CDATA[
      R(a(x,y,z) * u,z,z) = R(u,z,z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(565(a,1),6967(a,1,1)),flip(a)].">
      <j1 rule="para" parents="565 6967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6969">
    <literal><![CDATA[
      L(a(x,y,z),u,L(z,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(463,a,6863,a)].">
      <j1 rule="hyper" parents="463 6863"/>
    </justification>
  </clause>

  <clause id="6970">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ L(z,u,w) = L(z,u,w) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,5047,a,b,6863,a)].">
      <j1 rule="hyper" parents="35 5047 6863"/>
    </justification>
  </clause>

  <clause id="6971">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,6863,a(flip),b,2330,a),flip(a)].">
      <j1 rule="hyper" parents="134 6863 2330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6972">
    <literal><![CDATA[
      L(x,y,z) \ (x * (z * y)) = (z * y) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,4928,a(flip),b,6863,a(flip))].">
      <j1 rule="hyper" parents="133 4928 6863"/>
    </justification>
  </clause>

  <clause id="6973">
    <literal><![CDATA[
      a((x * y) \ x,z,a(u,w,y \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(232(a,1),6971(a,1,1))].">
      <j1 rule="para" parents="232 6971"/>
    </justification>
  </clause>

  <clause id="6975">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),v5,L(z,v6,v7)) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(6969(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6969 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6976">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,u,w) * v5) = L(z,u,w) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(6969(a,1),2541(a,1,1))].">
      <j1 rule="para" parents="6969 2541"/>
    </justification>
  </clause>

  <clause id="6977">
    <literal><![CDATA[
      a((x * y) \ x,z,a(u,w,y)) = 1
    ]]></literal>
    <justification jstring="[para(2534(a,1),6973(a,1,3))].">
      <j1 rule="para" parents="2534 6973"/>
    </justification>
  </clause>

  <clause id="6978">
    <literal><![CDATA[
      a((x * y) \ y,z,a(u,w,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,4176,a,b,6977,a)].">
      <j1 rule="hyper" parents="63 4176 6977"/>
    </justification>
  </clause>

  <clause id="6979">
    <literal><![CDATA[
      x * (L(x,y,z) \ (z * y)) = (z * y) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1129,a(flip),b,6972,a)].">
      <j1 rule="hyper" parents="63 1129 6972"/>
    </justification>
  </clause>

  <clause id="6981">
    <literal><![CDATA[
      x * (L(x,y,z) \ (z * y)) = a(z,y,x) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2290,a,b,6979,a),flip(a)].">
      <j1 rule="hyper" parents="316 2290 6979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6982">
    <literal><![CDATA[
      (x * y) \ (L(z / (x * y),y,x) \ z) = a(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(133,a,6574,a(flip),b,6979,a(flip))].">
      <j1 rule="hyper" parents="133 6574 6979"/>
    </justification>
  </clause>

  <clause id="6983">
    <literal><![CDATA[
      (a(x,y,z) * L(z,u,w)) \ L(z,u,w) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,5205,a,b,6970,a)].">
      <j1 rule="hyper" parents="39 5205 6970"/>
    </justification>
  </clause>

  <clause id="6985">
    <literal><![CDATA[
      (a(x,y,z) * (u * L(z,w,v5))) / (a(x,y,z) * L(z,w,v5)) = R(u,a(x,y,z),L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(6870(a,1),2280(a,1,1))].">
      <j1 rule="para" parents="6870 2280"/>
    </justification>
  </clause>

  <clause id="6986">
    <literal><![CDATA[
      (x * (a(y,z,u) * L(u,w,v5))) \ (a(y,z,u) * (x * L(u,w,v5))) = a(x,a(y,z,u),L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(6870(a,1),2352(a,1,2))].">
      <j1 rule="para" parents="6870 2352"/>
    </justification>
  </clause>

  <clause id="6987">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),v5,z) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(463,a,6876,a)].">
      <j1 rule="hyper" parents="463 6876"/>
    </justification>
  </clause>

  <clause id="6988">
    <literal><![CDATA[
      a(x,y,a(z,u,L(x,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,6876,a(flip),b,2330,a),flip(a)].">
      <j1 rule="hyper" parents="134 6876 2330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6989">
    <literal><![CDATA[
      a(x \ y,z,a(u,w,x * y)) = 1
    ]]></literal>
    <justification jstring="[para(5811(a,1),6988(a,1,3))].">
      <j1 rule="para" parents="5811 6988"/>
    </justification>
  </clause>

  <clause id="6990">
    <literal><![CDATA[
      L(a(x,y,z * u),w,z \ u) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(52,a,6989,a)].">
      <j1 rule="hyper" parents="52 6989"/>
    </justification>
  </clause>

  <clause id="6992">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ a(u,w,x * L(x,y,z)) = x * (L(x,y,z) \ a(u,w,x * L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(133,a,6990,a(flip),b,6846,a)].">
      <j1 rule="hyper" parents="133 6990 6846"/>
    </justification>
  </clause>

  <clause id="6993">
    <literal><![CDATA[
      a(a(x,x,y),L(y,x,x),z) \ (y * z) = L(y,x,x) * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,4959,a,b,6883,a)].">
      <j1 rule="hyper" parents="316 4959 6883"/>
    </justification>
  </clause>

  <clause id="6994">
    <literal><![CDATA[
      L(x,y,z) * (a(u,w,x) * (x \ v5)) = a(u,w,x) * ((v5 / x) * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,4326,a(flip),b,6883,a),flip(a)].">
      <j1 rule="hyper" parents="316 4326 6883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6995">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * ((a(x,y,z) \ u) * L(z,w,v5)) = (a(x,y,z) \ 1) \ (u * L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(139,a,6884,a(flip),b,6304,a)].">
      <j1 rule="hyper" parents="139 6884 6304"/>
    </justification>
  </clause>

  <clause id="6996">
    <literal><![CDATA[
      L(x,y,z) \ (a(u,w,x) \ v5) = a(u,w,x) \ (L(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(35,a,5450,a(flip),b,6884,a(flip))].">
      <j1 rule="hyper" parents="35 5450 6884"/>
    </justification>
  </clause>

  <clause id="6997">
    <literal><![CDATA[
      L(x,a(y,z,u),u) = L(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2496,a(flip),b,6899,a)].">
      <j1 rule="hyper" parents="63 2496 6899"/>
    </justification>
  </clause>

  <clause id="6998">
    <literal><![CDATA[
      L(a(x,y,z) \ u,z,a(x,y,z)) = (z * a(x,y,z)) \ (z * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,102,a(flip),b,6997,a),flip(a)].">
      <j1 rule="hyper" parents="63 102 6997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6999">
    <literal><![CDATA[
      L(x,y,z) * (x \ a(u,w,x)) = a(u,w,x) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a,b,6905,a),flip(a)].">
      <j1 rule="hyper" parents="63 2290 6905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7000">
    <literal><![CDATA[
      L(L(x,y,z) \ (L(x,y,z) \ x),y,z) * (a(u,w,L(x,y,z) \ (L(x,y,z) \ x)) \ v5) = a(u,w,L(x,y,z) \ (L(x,y,z) \ x)) \ ((L(x,y,z) \ 1) * v5)
    ]]></literal>
    <justification jstring="[para(1371(a,1),6976(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1371 6976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7002">
    <literal><![CDATA[
      L(a(x,y,z) \ (L(z,u,w) \ v5),L(z,u,w),a(x,y,z)) = (a(x,y,z) * L(z,u,w)) \ v5
    ]]></literal>
    <justification jstring="[para(6996(a,1),298(a,1,1))].">
      <j1 rule="para" parents="6996 298"/>
    </justification>
  </clause>

  <clause id="7003">
    <literal><![CDATA[
      x \ L(a(y,z,x) * u,x,x) = (x \ L(u,x,x)) * a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6127,a(flip),b,6907,a)].">
      <j1 rule="hyper" parents="63 6127 6907"/>
    </justification>
  </clause>

  <clause id="7004">
    <literal><![CDATA[
      L(a(x,y,z) * u,z,z) = L(u,z,z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(38,a,6862,a,b,7003,a),flip(a)].">
      <j1 rule="hyper" parents="38 6862 7003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7005">
    <literal><![CDATA[
      x * ((R(x,x,y) \ y) * a(z,u,x)) = L(a(z,u,x) * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,6909,a,b,7004,a)].">
      <j1 rule="hyper" parents="316 6909 7004"/>
    </justification>
  </clause>

  <clause id="7006">
    <literal><![CDATA[
      R(x,y,((z \ 1) / (u \ 1)) \ (u * z)) = L(x,y,a(z \ 1,u,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5371,a(flip),b,6931,a),flip(a)].">
      <j1 rule="hyper" parents="316 5371 6931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7007">
    <literal><![CDATA[
      x * (a(y,z,x) \ ((x * x) \ u)) = x \ (a(y,z,x) \ L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,6920,a(flip),b,6940,a),flip(a)].">
      <j1 rule="hyper" parents="316 6920 6940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7009">
    <literal><![CDATA[
      a(a(x,y,z),z,u) = a(z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2350,a(flip),b,6900,a),flip(a)].">
      <j1 rule="hyper" parents="63 2350 6900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7010">
    <literal><![CDATA[
      a(a(x,y,z),z,u) * w = w * a(z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(138,a,7009,a,b,2287,a)].">
      <j1 rule="hyper" parents="138 7009 2287"/>
    </justification>
  </clause>

  <clause id="7011">
    <literal><![CDATA[
      a(x,a(y,z,u),u) = a(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2544,a(flip),b,6915,a),flip(a)].">
      <j1 rule="hyper" parents="63 2544 6915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7012">
    <literal><![CDATA[
      L(a(x,a(y,z,u),u),w,L(u,v5,v6)) = a(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6969,a,b,7011,a)].">
      <j1 rule="hyper" parents="63 6969 7011"/>
    </justification>
  </clause>

  <clause id="7013">
    <literal><![CDATA[
      x \ (y * a(z,x,a(u,w,x))) = (x \ y) * a(z,a(u,w,x),x)
    ]]></literal>
    <justification jstring="[para(7011(a,1),6862(a,1,2,2))].">
      <j1 rule="para" parents="7011 6862"/>
    </justification>
  </clause>

  <clause id="7014">
    <literal><![CDATA[
      x * (a(y,z,x) * a(x * a(y,z,x),x,a(y,z,x))) = R(x * a(y,z,x),a(y,z,x),x)
    ]]></literal>
    <justification jstring="[para(7011(a,1),6906(a,1,2,2))].">
      <j1 rule="para" parents="7011 6906"/>
    </justification>
  </clause>

  <clause id="7016">
    <literal><![CDATA[
      L(a(x,y,a(z,u,y)),w,L(y,v5,v6)) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(7011(a,1),7012(a,1,1))].">
      <j1 rule="para" parents="7011 7012"/>
    </justification>
  </clause>

  <clause id="7017">
    <literal><![CDATA[
      L(x,y,z) \ (u * a(w,x,a(v5,v6,x))) = (L(x,y,z) \ u) * a(w,x,a(v5,v6,x))
    ]]></literal>
    <justification jstring="[para(7016(a,1),456(a,1,2,2))].">
      <j1 rule="para" parents="7016 456"/>
    </justification>
  </clause>

  <clause id="7018">
    <literal><![CDATA[
      x \ (y * a(z,x,a(u,w,x))) = (x \ y) * a(z,x,a(u,w,x))
    ]]></literal>
    <justification jstring="[para(7011(a,1),7013(a,2,2))].">
      <j1 rule="para" parents="7011 7013"/>
    </justification>
  </clause>

  <clause id="7019">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ R(x,y \ 1,y) = a(x * (1 / y),y,y)
    ]]></literal>
    <justification jstring="[para(3242(a,1),6930(a,1,1))].">
      <j1 rule="para" parents="3242 6930"/>
    </justification>
  </clause>

  <clause id="7020">
    <literal><![CDATA[
      (x * (L(x,y,y) \ z)) \ (z * a(y,y,x)) = a(z,a(y,y,x),L(x,y,y))
    ]]></literal>
    <justification jstring="[para(4390(a,1),6938(a,1,1))].">
      <j1 rule="para" parents="4390 6938"/>
    </justification>
  </clause>

  <clause id="7021">
    <literal><![CDATA[
      a(a(x,x,y),L(y,x,x),z) = a(L(y,x,x),a(x,x,y),z)
    ]]></literal>
    <justification jstring="[hyper(39,a,4968,a,b,6993,a),flip(a)].">
      <j1 rule="hyper" parents="39 4968 6993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7022">
    <literal><![CDATA[
      a(a(x,x,x \ y),L(x \ y,x,x),z) = a(y * (x \ 1),a(x,x,x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(316,a,4651,a(flip),b,7021,a),flip(a)].">
      <j1 rule="hyper" parents="316 4651 7021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7024">
    <literal><![CDATA[
      R(x,y,(z / (u \ 1)) * L(z / (u \ 1),u \ 1,u)) = R(x,y,((u \ 1) \ z) \ (u * z))
    ]]></literal>
    <justification jstring="[para(474(a,1),5193(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="474 5193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7025">
    <literal><![CDATA[
      x * T(y * (a(z,u,w) \ 1),x) = y * ((x * ((a(z,u,w) \ 1) * y)) / y)
    ]]></literal>
    <justification jstring="[para(5364(a,2),5273(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5364 5273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7026">
    <literal><![CDATA[
      (a(x,y,z) \ (a(x,y,z) \ 1)) * u = u / (a(x,y,z) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,434,a(flip),b,5303,a),flip(a)].">
      <j1 rule="hyper" parents="316 434 5303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7027">
    <literal><![CDATA[
      (a(x,y,z) \ (a(x,y,z) \ 1)) * u = (a(x,y,z) * a(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(316,a,5362,a(flip),b,7026,a),flip(a)].">
      <j1 rule="hyper" parents="316 5362 7026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7028">
    <literal><![CDATA[
      ((a(x,y,z) * a(x,y,z)) \ (u * w)) / T(u,w) = ((a(x,y,z) \ (a(x,y,z) \ 1)) * (w * u)) / u
    ]]></literal>
    <justification jstring="[para(7027(a,2),3975(a,2,1))].">
      <j1 rule="para" parents="7027 3975"/>
    </justification>
  </clause>

  <clause id="7029">
    <literal><![CDATA[
      K(x,y) \ ((z \ 1) * (z * y)) = 1 \ T((z \ 1) * (z * y),x)
    ]]></literal>
    <justification jstring="[para(217(a,1),5339(a,1,1,2))].">
      <j1 rule="para" parents="217 5339"/>
    </justification>
  </clause>

  <clause id="7030">
    <literal><![CDATA[
      K(x \ y,z) \ ((u \ 1) * (u * z)) = 1 \ T((u \ 1) * (u * z),((y \ 1) * x) \ 1)
    ]]></literal>
    <justification jstring="[para(3704(a,2),7029(a,2,2))].">
      <j1 rule="para" parents="3704 7029"/>
    </justification>
  </clause>

  <clause id="7032">
    <literal><![CDATA[
      L(((a(x,y,z) \ 1) \ u) / w,w,a(x,y,z)) = u / (w * (a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(4993(a,1),5381(a,2,1))].">
      <j1 rule="para" parents="4993 5381"/>
    </justification>
  </clause>

  <clause id="7034">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ (u * w) = u * ((a(x,y,z) * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5362,a(flip),b,5454,a)].">
      <j1 rule="hyper" parents="63 5362 5454"/>
    </justification>
  </clause>

  <clause id="7035">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * (u * w) = u * ((a(x,y,z) * a(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[para(5345(a,2),5456(a,2,2))].">
      <j1 rule="para" parents="5345 5456"/>
    </justification>
  </clause>

  <clause id="7036">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) * ((u * w) \ w))) = a(x,y,z \ (w \ (w / (u \ 1))))
    ]]></literal>
    <justification jstring="[hyper(316,a,5497,a(flip),b,5619,a),flip(a)].">
      <j1 rule="hyper" parents="316 5497 5619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7037">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,(z \ 1) \ u)) = a(x,y,(u / (z \ 1)) * (z * u))
    ]]></literal>
    <justification jstring="[para(474(a,1),5657(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="474 5657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7038">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,(z \ 1) \ u)) = a(x,y,(z * u) * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,7037,a),flip(a)].">
      <j1 rule="hyper" parents="316 5469 7037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7039">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,(z \ 1) \ u)) = a(x,y,(z * u) * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5481,a(flip),b,7038,a),flip(a)].">
      <j1 rule="hyper" parents="316 5481 7038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7040">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,z \ u)) = a(x,y,(z * u) * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(5814(a,1),7039(a,1,3))].">
      <j1 rule="para" parents="5814 7039"/>
    </justification>
  </clause>

  <clause id="7041">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,z \ u)) = a(x,y,(z \ u) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,6701,a(flip),b,7040,a),flip(a)].">
      <j1 rule="hyper" parents="316 6701 7040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7042">
    <literal><![CDATA[
      a(x,y,a(z \ u,z,u)) = a(x,y,a(z,z \ 1,z \ u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5909,a(flip),b,7041,a)].">
      <j1 rule="hyper" parents="316 5909 7041"/>
    </justification>
  </clause>

  <clause id="7043">
    <literal><![CDATA[
      a(x,y,(z \ (u \ (w \ v5))) * (w * w)) = a(x,y,z \ (u \ (v5 / (w \ 1))))
    ]]></literal>
    <justification jstring="[para(637(a,1),5704(a,1,3))].">
      <j1 rule="para" parents="637 5704"/>
    </justification>
  </clause>

  <clause id="7045">
    <literal><![CDATA[
      a(x,y,L(z * (u * (K(w,v5) / w)),v6,v7)) = a(x,y,L(z * (u * (1 / w)),v6,v7))
    ]]></literal>
    <justification jstring="[para(3108(a,1),5713(a,1,3,1,2,2))].">
      <j1 rule="para" parents="3108 5713"/>
    </justification>
  </clause>

  <clause id="7046">
    <literal><![CDATA[
      a(x,y,((z * (u \ 1)) \ w) * v5) = a(x,y,((z * u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,6757,a(flip),b,5715,a),flip(a)].">
      <j1 rule="hyper" parents="63 6757 5715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7048">
    <literal><![CDATA[
      a(x,y,(z / (u \ 1)) * L(z / (u \ 1),u \ 1,u)) = a(x,y,((u \ 1) \ z) \ (u * z))
    ]]></literal>
    <justification jstring="[para(474(a,1),5726(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="474 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7049">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * (v5 \ 1)))) = a(x,y,(u \ (w * v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6676,a(flip),b,5728,a),flip(a)].">
      <j1 rule="hyper" parents="63 6676 5728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7051">
    <literal><![CDATA[
      a(x,y,(z \ ((u \ 1) * w)) * v5) = a(x,y,(z \ (w * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5665,a,b,7049,a)].">
      <j1 rule="hyper" parents="63 5665 7049"/>
    </justification>
  </clause>

  <clause id="7052">
    <literal><![CDATA[
      a(x,y,(z \ (u * a(w,w,u))) * v5) = a(x,y,v5 * (z \ L(u,w,w)))
    ]]></literal>
    <justification jstring="[para(5093(a,1),7049(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="5093 7049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7053">
    <literal><![CDATA[
      a(x,y,z * (u * L((w / v5) * v6,v7,v8))) = a(x,y,z * (u * L((v5 \ w) * v6,v7,v8)))
    ]]></literal>
    <justification jstring="[para(2774(a,1),5916(a,1,3,2,2,1))].">
      <j1 rule="para" parents="2774 5916"/>
    </justification>
  </clause>

  <clause id="7054">
    <literal><![CDATA[
      a(x,y,z * (((u / (w * w)) \ 1) \ v5)) = a(x,y,z * ((u \ (w * w)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,5643,a(flip),b,5937,a),flip(a)].">
      <j1 rule="hyper" parents="316 5643 5937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7055">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * (v5 \ (1 / v6))) = a(x,y,(v5 \ v6) * ((w * u) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5591,a,b,5979,a)].">
      <j1 rule="hyper" parents="63 5591 5979"/>
    </justification>
  </clause>

  <clause id="7056">
    <literal><![CDATA[
      a(x,y,z * L((u \ K(w,v5)) * (v6 * v6),v7,v8)) = a(x,y,z * L(u \ (v6 * v6),v7,v8))
    ]]></literal>
    <justification jstring="[para(388(a,1),6052(a,1,3,2,1))].">
      <j1 rule="para" parents="388 6052"/>
    </justification>
  </clause>

  <clause id="7057">
    <literal><![CDATA[
      a(x,y,L(z * ((u * u) * w),v5,v6)) = a(x,y,L(z * w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5817,a(flip),b,6071,a),flip(a)].">
      <j1 rule="hyper" parents="63 5817 6071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7059">
    <literal><![CDATA[
      a(x,y,((1 / z) * (u * L(u,w,v5))) * v6) = a(x,y,v6 * ((u \ L(u,w,v5)) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5906,a(flip),b,6089,a),flip(a)].">
      <j1 rule="hyper" parents="63 5906 6089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7060">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ (L(x,u,w) \ v5)) * L(x,u,w) = (x \ L(x,y,z)) \ ((x \ v5) * x)
    ]]></literal>
    <justification jstring="[para(4409(a,1),6163(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4409 6163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7063">
    <literal><![CDATA[
      x / (L(y \ L(y,z,u),w,v5) \ 1) = (L(y \ L(y,z,u),w,v5) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(346,a,6505,a)].">
      <j1 rule="hyper" parents="346 6505"/>
    </justification>
  </clause>

  <clause id="7064">
    <literal><![CDATA[
      (L(x \ L(x,y,z),u,w) \ 1) * x = L(x \ L(x,y,z),u,w) \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,6674,a(flip),b,6505,a),flip(a)].">
      <j1 rule="hyper" parents="316 6674 6505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7065">
    <literal><![CDATA[
      x / L((y \ T(x,z)) * K(z,x),u,w) = L(T(x,z) / y,u,w) \ T(x,z)
    ]]></literal>
    <justification jstring="[para(4837(a,2),6575(a,1,2))].">
      <j1 rule="para" parents="4837 6575"/>
    </justification>
  </clause>

  <clause id="7066">
    <literal><![CDATA[
      ((L(x,y,z) \ (a(u,w,v5) \ x)) \ v6) \ v6 = L(x,y,z) \ (a(u,w,v5) \ x)
    ]]></literal>
    <justification jstring="[hyper(204,a,6619,a)].">
      <j1 rule="hyper" parents="204 6619"/>
    </justification>
  </clause>

  <clause id="7067">
    <literal><![CDATA[
      (K(x * (y \ L(y,z,u)),w) * x) * (L(y,z,u) * L(y \ 1,v5,v6)) = T(x * (L(y,z,u) * L(y \ 1,v5,v6)),w)
    ]]></literal>
    <justification jstring="[para(969(a,1),6630(a,1,1,1,1,2))].">
      <j1 rule="para" parents="969 6630"/>
    </justification>
  </clause>

  <clause id="7070">
    <literal><![CDATA[
      (x * y) * ((z * z) \ K(u,w)) = x * (y * ((z * z) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(38,a,4238,a,b,6816,a)].">
      <j1 rule="hyper" parents="38 4238 6816"/>
    </justification>
  </clause>

  <clause id="7071">
    <literal><![CDATA[
      (x * y) * (z \ (z \ K(u,w))) = x * (y * ((z * z) \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(4208(a,1),7070(a,1,2))].">
      <j1 rule="para" parents="4208 7070"/>
    </justification>
  </clause>

  <clause id="7072">
    <literal><![CDATA[
      (x * y) * (z \ (z \ K(u,w))) = x * (y * (z \ (z \ K(u,w))))
    ]]></literal>
    <justification jstring="[para(4208(a,1),7071(a,2,2,2))].">
      <j1 rule="para" parents="4208 7071"/>
    </justification>
  </clause>

  <clause id="7073">
    <literal><![CDATA[
      (x * (y * (y \ L(y,z,u)))) / y = L(y \ 1,z,u) * ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(1064(a,1),6817(a,1,1,2,2))].">
      <j1 rule="para" parents="1064 6817"/>
    </justification>
  </clause>

  <clause id="7074">
    <literal><![CDATA[
      L(x \ 1,y,z) * ((x \ 1) \ u) = (u * L(x,y,z)) / x
    ]]></literal>
    <justification jstring="[para(10(a,1),7073(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 7073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7075">
    <literal><![CDATA[
      L(x \ 1,y,z) * ((x \ 1) \ u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4377,a(flip),b,7074,a),flip(a)].">
      <j1 rule="hyper" parents="316 4377 7074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7078">
    <literal><![CDATA[
      (x / (y \ 1)) * L(y \ 1,z,u) = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4325,a(flip),b,7075,a)].">
      <j1 rule="hyper" parents="63 4325 7075"/>
    </justification>
  </clause>

  <clause id="7079">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) * (x \ u)) = L(x \ 1,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(139,a,7075,a(flip),b,1126,a)].">
      <j1 rule="hyper" parents="139 7075 1126"/>
    </justification>
  </clause>

  <clause id="7080">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) / L(x \ 1,y,z) = u / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(136,a,7075,a(flip),b,4325,a(flip))].">
      <j1 rule="hyper" parents="136 7075 4325"/>
    </justification>
  </clause>

  <clause id="7081">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ (L(x,u,w) * (x \ v5))) = L(x \ 1,y,z) \ (L(x \ 1,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(7075(a,1),1139(a,1,2,2))].">
      <j1 rule="para" parents="7075 1139"/>
    </justification>
  </clause>

  <clause id="7082">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * (((x \ L(x,y,z)) \ 1) \ v5) = L(x \ L(x,y,z),u,w) * ((x \ L(x,y,z)) \ v5)
    ]]></literal>
    <justification jstring="[para(1894(a,1),7075(a,1,1,1))].">
      <j1 rule="para" parents="1894 7075"/>
    </justification>
  </clause>

  <clause id="7083">
    <literal><![CDATA[
      (x / (y \ 1)) * L(y \ 1,z,u) = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4325,a(flip),b,7078,a),flip(a)].">
      <j1 rule="hyper" parents="316 4325 7078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7084">
    <literal><![CDATA[
      (L(x,y,z) \ u) / (x \ 1) = (x \ u) / L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(136,a,1131,a(flip),b,7078,a),flip(a)].">
      <j1 rule="hyper" parents="136 1131 7078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7085">
    <literal><![CDATA[
      x * (L(y,y,x) \ L(L(y,y,x),z,u)) = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2023,a,b,7078,a)].">
      <j1 rule="hyper" parents="63 2023 7078"/>
    </justification>
  </clause>

  <clause id="7086">
    <literal><![CDATA[
      a(x,y,z \ (u * (L(u,w,v5) * (u \ v6)))) = a(x,y,z \ (L(u \ 1,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(7079(a,1),6682(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="7079 6682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7087">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) / (x \ 1) = L(x,y,z) * (x \ (u / (x \ 1)))
    ]]></literal>
    <justification jstring="[para(7080(a,1),5176(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7080 5176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7088">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ (x \ u)) = L(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(37,a,4333,a,b,7084,a)].">
      <j1 rule="hyper" parents="37 4333 7084"/>
    </justification>
  </clause>

  <clause id="7089">
    <literal><![CDATA[
      ((x \ y) / L(x \ 1,z,u)) \ ((L(x,z,u) \ y) * x) = a(L(x,z,u) \ y,x,x)
    ]]></literal>
    <justification jstring="[para(7084(a,1),6928(a,1,1))].">
      <j1 rule="para" parents="7084 6928"/>
    </justification>
  </clause>

  <clause id="7090">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(34,a,6730,a,b,7088,a),flip(a)].">
      <j1 rule="hyper" parents="34 6730 7088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7091">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (L(x,y,z) \ x) = L(x \ 1,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(4595(a,1),7088(a,1,2))].">
      <j1 rule="para" parents="4595 7088"/>
    </justification>
  </clause>

  <clause id="7092">
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) \ x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(7090(a,1),6636(a,1,2))].">
      <j1 rule="para" parents="7090 6636"/>
    </justification>
  </clause>

  <clause id="7093">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (1 / x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6496,a,b,7092,a)].">
      <j1 rule="hyper" parents="63 6496 7092"/>
    </justification>
  </clause>

  <clause id="7094">
    <literal><![CDATA[
      ((x * (L(y,z,u) \ y)) / (1 / L(y,z,u))) * (1 / y) = (1 / y) * R((1 / y) \ x,1 / y,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(7092(a,1),733(a,1,1,2))].">
      <j1 rule="para" parents="7092 733"/>
    </justification>
  </clause>

  <clause id="7095">
    <literal><![CDATA[
      L((1 / x) \ y,1 / x,L(x,z,u) \ x) = (1 / L(x,z,u)) \ ((L(x,z,u) \ x) * y)
    ]]></literal>
    <justification jstring="[para(7093(a,1),102(a,2,1))].">
      <j1 rule="para" parents="7093 102"/>
    </justification>
  </clause>

  <clause id="7096">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),y,x) = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[para(2136(a,1),7085(a,1,2))].">
      <j1 rule="para" parents="2136 7085"/>
    </justification>
  </clause>

  <clause id="7097">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),y,x) = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4325,a(flip),b,7096,a),flip(a)].">
      <j1 rule="hyper" parents="316 4325 7096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7098">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) = u \ (L(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(144,a,7096,a),flip(a)].">
      <j1 rule="hyper" parents="144 7096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7099">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,z * y) = (z * y) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,4378,a(flip),b,7096,a),flip(a)].">
      <j1 rule="hyper" parents="133 4378 7096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7100">
    <literal><![CDATA[
      L((x \ y) \ L(x \ y,z,u),x \ y,y) = y \ (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,4340,a(flip),b,7096,a),flip(a)].">
      <j1 rule="hyper" parents="133 4340 7096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7101">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) = u \ ((u / x) * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,4325,a(flip),b,7096,a),flip(a)].">
      <j1 rule="hyper" parents="133 4325 7096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7102">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) \ w = (u \ ((u / x) * L(x,y,z))) \ w
    ]]></literal>
    <justification jstring="[para(7097(a,1),166(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7097 166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7103">
    <literal><![CDATA[
      T(L(x \ L(x,y,z),x,L(x,y,z) * u),w) = L(T(u \ (x \ (L(x,y,z) * u)),w),u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(7098(a,2),483(a,1,1))].">
      <j1 rule="para" parents="7098 483"/>
    </justification>
  </clause>

  <clause id="7104">
    <literal><![CDATA[
      x \ (L(y,z,z) * (y \ x)) = L(a(z,z,y) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(5088(a,2),7098(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5088 7098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7105">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,x \ u) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,1602,a,b,7101,a)].">
      <j1 rule="hyper" parents="316 1602 7101"/>
    </justification>
  </clause>

  <clause id="7106">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,x * u) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,1612,a(flip),b,7101,a),flip(a)].">
      <j1 rule="hyper" parents="316 1612 7101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7107">
    <literal><![CDATA[
      (x * y) \ (L(x,z,u) * y) = y \ ((y / x) * L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4404,a(flip),b,7101,a)].">
      <j1 rule="hyper" parents="63 4404 7101"/>
    </justification>
  </clause>

  <clause id="7108">
    <literal><![CDATA[
      x \ ((x / (x \ y)) * L(x \ y,z,u)) = y \ (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,475,a(flip),b,7101,a),flip(a)].">
      <j1 rule="hyper" parents="63 475 7101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7109">
    <literal><![CDATA[
      (x * y) \ (x * L(y,z,u)) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,102,a(flip),b,7101,a)].">
      <j1 rule="hyper" parents="63 102 7101"/>
    </justification>
  </clause>

  <clause id="7111">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,y,y \ z) = L(a(x,x,y) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5166,a,b,7104,a)].">
      <j1 rule="hyper" parents="63 5166 7104"/>
    </justification>
  </clause>

  <clause id="7113">
    <literal><![CDATA[
      (x * (L(x,y,z) \ L(x \ L(x,y,z),x,u))) * (L(x,y,z) \ x) = L(x / L(x,y,z),x,x \ u)
    ]]></literal>
    <justification jstring="[para(7105(a,1),1927(a,1,1,2,2))].">
      <j1 rule="para" parents="7105 1927"/>
    </justification>
  </clause>

  <clause id="7114">
    <literal><![CDATA[
      (x * x) \ (((x * x) / y) * L(y,z,u)) = ((y * (x * x)) \ L(y,z,u)) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,388,a(flip),b,7107,a),flip(a)].">
      <j1 rule="hyper" parents="63 388 7107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7115">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (L(L(x,w,v5),y,z) * u) = u \ ((u / L(x,y,z)) * L(L(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(30(a,1),7107(a,1,2,1))].">
      <j1 rule="para" parents="30 7107"/>
    </justification>
  </clause>

  <clause id="7116">
    <literal><![CDATA[
      L(x \ 1,x,y) \ L((y * x) \ y,z,u) = y \ ((y / x) * L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1861,a,b,7109,a)].">
      <j1 rule="hyper" parents="63 1861 7109"/>
    </justification>
  </clause>

  <clause id="7117">
    <literal><![CDATA[
      K(x,y) * (x \ ((x / y) * L(y,z,u))) = (y * x) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,7109,a(flip),b,6235,a)].">
      <j1 rule="hyper" parents="139 7109 6235"/>
    </justification>
  </clause>

  <clause id="7118">
    <literal><![CDATA[
      L((x * y) \ x,z,u) \ ((x * y) \ x) = (x \ ((x / y) * L(y,z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(7109(a,1),1906(a,2,1))].">
      <j1 rule="para" parents="7109 1906"/>
    </justification>
  </clause>

  <clause id="7119">
    <literal><![CDATA[
      K(x,x \ y) \ ((K(x,x \ y) / ((x \ y) / z)) * L((x \ y) / z,u,w)) = ((y / x) / z) \ (K(x,x \ y) * L((x \ y) / z,u,w))
    ]]></literal>
    <justification jstring="[para(2776(a,1),7109(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2776 7109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7123">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,y * z) = (z * y) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1668,a,b,7099,a)].">
      <j1 rule="hyper" parents="63 1668 7099"/>
    </justification>
  </clause>

  <clause id="7124">
    <literal><![CDATA[
      (a(x,y,z) * u) \ ((a(x,y,z) * (u * w)) / w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5386,a(flip),b,7099,a),flip(a)].">
      <j1 rule="hyper" parents="63 5386 7099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7125">
    <literal><![CDATA[
      (x * y) \ ((x * (y * (y \ z))) / (y \ z)) = ((x * y) * (y \ z)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,537,a(flip),b,7099,a),flip(a)].">
      <j1 rule="hyper" parents="63 537 7099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7126">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (y * z)) = (x * y) \ ((x * (y * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,489,a(flip),b,7099,a)].">
      <j1 rule="hyper" parents="63 489 7099"/>
    </justification>
  </clause>

  <clause id="7127">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),x,z * y) = L((z * y) \ ((z * (y * x)) / x),u,w)
    ]]></literal>
    <justification jstring="[para(7099(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7099 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7128">
    <literal><![CDATA[
      L(x \ (y * L(y \ x,z,u)),x \ y,u * z) = (u * z) \ ((u * (z * (x \ y))) / (x \ y))
    ]]></literal>
    <justification jstring="[para(1252(a,1),7099(a,1,1))].">
      <j1 rule="para" parents="1252 7099"/>
    </justification>
  </clause>

  <clause id="7130">
    <literal><![CDATA[
      L(K(x,y) * (z \ L(z,u,w)),z,w * u) = K(x,y) * ((w * u) \ ((w * (u * z)) / z))
    ]]></literal>
    <justification jstring="[para(7099(a,1),4850(a,2,2))].">
      <j1 rule="para" parents="7099 4850"/>
    </justification>
  </clause>

  <clause id="7131">
    <literal><![CDATA[
      L((x * y) \ ((x * (y * z)) / z),u,z) = L(z \ L(z,y,x),z,x * y)
    ]]></literal>
    <justification jstring="[para(7099(a,1),5156(a,1,1))].">
      <j1 rule="para" parents="7099 5156"/>
    </justification>
  </clause>

  <clause id="7132">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,w),z,w * u)) = a(x,y,(w * u) \ (z \ (w * (u * z))))
    ]]></literal>
    <justification jstring="[para(7099(a,2),5497(a,1,3))].">
      <j1 rule="para" parents="7099 5497"/>
    </justification>
  </clause>

  <clause id="7133">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,w),z,w * u)) = a(x,y,(w * u) \ ((w * (u * z)) / z))
    ]]></literal>
    <justification jstring="[para(7123(a,1),5557(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7123 5557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7134">
    <literal><![CDATA[
      (x * (y / z)) \ ((x * ((y / z) * z)) / z) = ((x * (y / z)) * z) \ (x * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),7126(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 7126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7135">
    <literal><![CDATA[
      (x * y) \ ((x * (y * T(z,y))) / T(z,y)) = ((x * y) * T(z,y)) \ (x * (z * y))
    ]]></literal>
    <justification jstring="[para(114(a,1),7126(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="114 7126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7137">
    <literal><![CDATA[
      R(x,y,((z * u) * w) \ (z * (w * u))) = R(x,y,(z * u) \ ((z * (u * w)) / w))
    ]]></literal>
    <justification jstring="[para(7126(a,1),4976(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7126 4976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7138">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ ((u * w) * z)) = a(x,y,(z * u) \ ((z * (u * w)) / w))
    ]]></literal>
    <justification jstring="[para(7126(a,1),5490(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7126 5490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7139">
    <literal><![CDATA[
      x \ ((T(x,y) / y) * L(y,z,u)) = (y * x) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3189,a(flip),b,7117,a)].">
      <j1 rule="hyper" parents="63 3189 7117"/>
    </justification>
  </clause>

  <clause id="7140">
    <literal><![CDATA[
      (x * y) \ (y * L(x,z,u)) = y \ (x \ (y * L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(4420(a,1),7139(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4420 7139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7141">
    <literal><![CDATA[
      (x * y) \ (z \ ((x * y) * L(z,y,x))) = (z * (x * y)) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(100(a,1),7140(a,1,2)),flip(a)].">
      <j1 rule="para" parents="100 7140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7143">
    <literal><![CDATA[
      (x * a(y,z,u)) \ ((a(y,z,u) * (x * w)) / w) = a(w,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2324,a(flip),b,7124,a)].">
      <j1 rule="hyper" parents="63 2324 7124"/>
    </justification>
  </clause>

  <clause id="7144">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (w \ (a(x,y,z) * (w * u))) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(5447(a,1),7124(a,1,2))].">
      <j1 rule="para" parents="5447 7124"/>
    </justification>
  </clause>

  <clause id="7145">
    <literal><![CDATA[
      (x * a(y,z,u)) \ ((a(y,z,u) * (x * w)) / w) = a(w \ 1,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(964(a,1),7143(a,1,2))].">
      <j1 rule="para" parents="964 7143"/>
    </justification>
  </clause>

  <clause id="7146">
    <literal><![CDATA[
      (a(x,y,z) * (u \ (a(x,y,z) \ w))) \ (u \ w) = a(u,u \ (a(x,y,z) \ w),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(76(a,1),7144(a,1,2,2))].">
      <j1 rule="para" parents="76 7144"/>
    </justification>
  </clause>

  <clause id="7147">
    <literal><![CDATA[
      (a(x,y,z) * (u \ w)) \ (u \ (w * a(x,y,z))) = a(u,u \ w,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(2297(a,1),7144(a,1,2,2))].">
      <j1 rule="para" parents="2297 7144"/>
    </justification>
  </clause>

  <clause id="7148">
    <literal><![CDATA[
      ((x * y) \ x) \ L((x * y) \ x,z,u) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,358,a(flip),b,7116,a)].">
      <j1 rule="hyper" parents="63 358 7116"/>
    </justification>
  </clause>

  <clause id="7149">
    <literal><![CDATA[
      (x * (1 / ((y * z) \ ((y * (z * x)) / x)))) \ x = L(x \ L(x,z,y),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2674,a(flip),b,7131,a)].">
      <j1 rule="hyper" parents="63 2674 7131"/>
    </justification>
  </clause>

  <clause id="7150">
    <literal><![CDATA[
      (x * (y * z)) \ (y * (z * x)) = (y * z) \ (x \ (y * (z * x)))
    ]]></literal>
    <justification jstring="[para(100(a,1),7141(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="100 7141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7152">
    <literal><![CDATA[
      (x * y) / (y * (y \ L(y,z,u))) = (y \ 1) * (L(y \ 1,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(1064(a,1),6818(a,1,2,2))].">
      <j1 rule="para" parents="1064 6818"/>
    </justification>
  </clause>

  <clause id="7153">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ u) = (u * x) / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),7152(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 7152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7154">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4390,a(flip),b,7153,a),flip(a)].">
      <j1 rule="hyper" parents="316 4390 7153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7155">
    <literal><![CDATA[
      R(x,y,y) * L(y,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(138,a,3677,a(flip),b,7153,a(flip))].">
      <j1 rule="hyper" parents="138 3677 7153"/>
    </justification>
  </clause>

  <clause id="7157">
    <literal><![CDATA[
      R(x,y,y) \ (x * y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,7155,a)].">
      <j1 rule="hyper" parents="144 7155"/>
    </justification>
  </clause>

  <clause id="7158">
    <literal><![CDATA[
      x * (L(x,x,y) \ y) = R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,4393,a,b,7155,a)].">
      <j1 rule="hyper" parents="35 4393 7155"/>
    </justification>
  </clause>

  <clause id="7159">
    <literal><![CDATA[
      L(x,x,L(y,x,x)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,4632,a,b,7155,a)].">
      <j1 rule="hyper" parents="34 4632 7155"/>
    </justification>
  </clause>

  <clause id="7161">
    <literal><![CDATA[
      ((R(x,y,y) * (L(y,y,x) * z)) / z) \ (R(x,y,y) * L(y,y,x)) = (x * y) / ((R(x,y,y) * (L(y,y,x) * z)) / z)
    ]]></literal>
    <justification jstring="[para(7155(a,1),6798(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7155 6798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7162">
    <literal><![CDATA[
      ((x * (y * z)) / L(z,z,y)) \ (x * R(y,z,z)) = a(x,R(y,z,z),L(z,z,y))
    ]]></literal>
    <justification jstring="[para(7155(a,1),6925(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7155 6925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7163">
    <literal><![CDATA[
      ((R(x,y,y) * (L(y,y,x) * z)) / z) \ (x * y) = a(R(x,y,y),L(y,y,x),z)
    ]]></literal>
    <justification jstring="[para(7155(a,1),6925(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7155 6925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7164">
    <literal><![CDATA[
      L(x / (x / y),y,L(z,y,y)) = x / (x / L(y,y,z))
    ]]></literal>
    <justification jstring="[para(7159(a,1),6582(a,2,2,2))].">
      <j1 rule="para" parents="7159 6582"/>
    </justification>
  </clause>

  <clause id="7165">
    <literal><![CDATA[
      R(x / y,y,y) \ x = L(y,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3308,a(flip),b,7157,a)].">
      <j1 rule="hyper" parents="63 3308 7157"/>
    </justification>
  </clause>

  <clause id="7166">
    <literal><![CDATA[
      x * (R(x,y,y) \ y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1169,a(flip),b,7157,a)].">
      <j1 rule="hyper" parents="63 1169 7157"/>
    </justification>
  </clause>

  <clause id="7167">
    <literal><![CDATA[
      L(x,x,y) * R(y,x,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(138,a,7157,a(flip),b,4228,a)].">
      <j1 rule="hyper" parents="138 7157 4228"/>
    </justification>
  </clause>

  <clause id="7169">
    <literal><![CDATA[
      L(x,x,y) \ y = x \ R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,7158,a),flip(a)].">
      <j1 rule="hyper" parents="144 7158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7170">
    <literal><![CDATA[
      L(x,y,L(L(z,z,u) \ u,z,z)) = L(x,y,R(u,z,z) * (z \ 1))
    ]]></literal>
    <justification jstring="[para(7158(a,1),3441(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="7158 3441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7171">
    <literal><![CDATA[
      L(x,y,L(L(z,z,u) \ u,w,v5)) = L(x,y,L(u * (z \ 1),w,v5))
    ]]></literal>
    <justification jstring="[para(7169(a,2),6805(a,1,3,1))].">
      <j1 rule="para" parents="7169 6805"/>
    </justification>
  </clause>

  <clause id="7172">
    <literal><![CDATA[
      L(x,x,x \ y) = (y * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(563(a,1),7165(a,1,1)),flip(a)].">
      <j1 rule="para" parents="563 7165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7173">
    <literal><![CDATA[
      L(T(x,x \ 1),x \ 1,y) = L(x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(316,a,367,a,b,7172,a)].">
      <j1 rule="hyper" parents="316 367 7172"/>
    </justification>
  </clause>

  <clause id="7174">
    <literal><![CDATA[
      L(x * y,x * y,L(y \ 1,y,x)) = (x * ((x * y) \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(232(a,2),7172(a,1,3))].">
      <j1 rule="para" parents="232 7172"/>
    </justification>
  </clause>

  <clause id="7175">
    <literal><![CDATA[
      L(x,y,L(z,z,z \ u)) = L(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[para(7172(a,2),1696(a,2,3)),flip(a)].">
      <j1 rule="para" parents="7172 1696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7177">
    <literal><![CDATA[
      L(T(x,x \ 1),x \ 1,y * x) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1584,a(flip),b,7173,a),flip(a)].">
      <j1 rule="hyper" parents="316 1584 7173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7178">
    <literal><![CDATA[
      (x \ 1) * L(x,x,x \ y) = x \ L(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(7173(a,1),972(a,1,2))].">
      <j1 rule="para" parents="7173 972"/>
    </justification>
  </clause>

  <clause id="7179">
    <literal><![CDATA[
      L(x,y,L(z,z \ 1,u)) = L(x,y,L(z,z,z \ u))
    ]]></literal>
    <justification jstring="[para(7173(a,1),1585(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7173 1585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7180">
    <literal><![CDATA[
      L(1 / (1 / x),x,x \ y) = L(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(38,a,1295,a,b,7178,a(flip))].">
      <j1 rule="hyper" parents="38 1295 7178"/>
    </justification>
  </clause>

  <clause id="7181">
    <literal><![CDATA[
      x \ L(x,x \ 1,x * y) = (x \ 1) * L(x,x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),7178(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="9 7178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7182">
    <literal><![CDATA[
      L(x,y,L(z,z \ 1,u)) = L(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,7175,a(flip),b,7179,a),flip(a)].">
      <j1 rule="hyper" parents="316 7175 7179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7183">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z \ 1,u)) = L(x,y,L(z \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(2675(a,1),7182(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2675 7182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7184">
    <literal><![CDATA[
      L(x / (x / y),y,L(z,y,y)) = L(x / (x / y),y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,6582,a,b,7164,a),flip(a)].">
      <j1 rule="hyper" parents="316 6582 7164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7185">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ 1) \ ((L(x \ L(x,y,z),u,w) \ v5) * (x \ L(x,y,z))) = L((x \ L(x,y,z)) \ 1,u,w) \ v5
    ]]></literal>
    <justification jstring="[hyper(133,a,5023,a(flip),b,7154,a)].">
      <j1 rule="hyper" parents="133 5023 7154"/>
    </justification>
  </clause>

  <clause id="7187">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * L(x \ 1,y,z) = u * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(138,a,7154,a(flip),b,4390,a)].">
      <j1 rule="hyper" parents="138 7154 4390"/>
    </justification>
  </clause>

  <clause id="7188">
    <literal><![CDATA[
      (x \ (x \ 1)) * (L(x \ 1,y,z) \ (1 / L(x \ 1,y,z))) = L(x,y,z) \ (1 / L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,697,a,b,7154,a(flip))].">
      <j1 rule="hyper" parents="34 697 7154"/>
    </justification>
  </clause>

  <clause id="7189">
    <literal><![CDATA[
      (x \ 1) * ((x \ 1) * (L(x \ 1,y,z) \ u)) = x * (L(x,y,z) \ ((x \ 1) * u))
    ]]></literal>
    <justification jstring="[para(1129(a,1),7154(a,1,2))].">
      <j1 rule="para" parents="1129 7154"/>
    </justification>
  </clause>

  <clause id="7190">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (L((L(x,y,z) \ x) \ 1,u,w) \ v5) = (L(x,y,z) \ x) * (L(L(x,y,z) \ x,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(5076(a,1),7154(a,1,1))].">
      <j1 rule="para" parents="5076 7154"/>
    </justification>
  </clause>

  <clause id="7191">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z,z \ u)) = L(x,y,L(z \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3405,a(flip),b,7183,a)].">
      <j1 rule="hyper" parents="63 3405 7183"/>
    </justification>
  </clause>

  <clause id="7192">
    <literal><![CDATA[
      (x * L(y,z,u)) * (y \ 1) = (x * y) * L(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(4328(a,1),7187(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4328 7187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7193">
    <literal><![CDATA[
      a(x,y,L(z * u,z * u,L(u,u,z))) = a(x,y,(z * ((z * u) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(7174(a,1),6377(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7174 6377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7194">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,z,u) \ T(x,w)) = K(x,w) * (L(y / x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(6568(a,1),6819(a,2,2))].">
      <j1 rule="para" parents="6568 6819"/>
    </justification>
  </clause>

  <clause id="7195">
    <literal><![CDATA[
      (x \ (a(y,x,L(x,z,u)) \ 1)) * x = (x \ 1) * (a(y,x,L(x,z,u)) \ x)
    ]]></literal>
    <justification jstring="[para(2548(a,1),6966(a,2,2,1))].">
      <j1 rule="para" parents="2548 6966"/>
    </justification>
  </clause>

  <clause id="7197">
    <literal><![CDATA[
      x * ((y * ((a(z,u,w) \ 1) * x)) / x) = (x * (a(z,u,w) \ 1)) * y
    ]]></literal>
    <justification jstring="[hyper(290,a,7025,a),flip(a)].">
      <j1 rule="hyper" parents="290 7025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7200">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) * ((u * w) \ w))) = a(x,y,z \ (w \ ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5606,a(flip),b,7036,a),flip(a)].">
      <j1 rule="hyper" parents="316 5606 7036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7201">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w / (v5 \ 1)))) = a(x,y,z \ (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5804,a(flip),b,7043,a),flip(a)].">
      <j1 rule="hyper" parents="63 5804 7043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7203">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w \ 1) \ v5))) = a(x,y,z \ (u \ (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5606,a(flip),b,7201,a)].">
      <j1 rule="hyper" parents="63 5606 7201"/>
    </justification>
  </clause>

  <clause id="7204">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ a(w,v5,v6)))) = a(x,y,z \ (u \ (w * a(w,v5,v6))))
    ]]></literal>
    <justification jstring="[para(2474(a,1),7201(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="2474 7201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7205">
    <literal><![CDATA[
      a(x,y,((z / (u * u)) \ w) * v5) = a(x,y,v5 * ((z \ (u * u)) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6701,a(flip),b,7054,a)].">
      <j1 rule="hyper" parents="63 6701 7054"/>
    </justification>
  </clause>

  <clause id="7206">
    <literal><![CDATA[
      a(x,y,(((z * z) \ u) \ w) * v5) = a(x,y,v5 * ((u \ (z * z)) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5549,a(flip),b,7205,a)].">
      <j1 rule="hyper" parents="63 5549 7205"/>
    </justification>
  </clause>

  <clause id="7207">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w * w)) \ v5)) = a(x,y,(u \ v5) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6757,a(flip),b,7206,a),flip(a)].">
      <j1 rule="hyper" parents="63 6757 7206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7209">
    <literal><![CDATA[
      a(x,y,((z \ (u * u)) \ w) * v5) = a(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,7207,a)].">
      <j1 rule="hyper" parents="63 5469 7207"/>
    </justification>
  </clause>

  <clause id="7210">
    <literal><![CDATA[
      a(x,y,(z \ (1 / u)) * (w * ((v5 * v6) \ K(v7,v8)))) = a(x,y,(z \ u) * ((v6 * v5) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6050,a,b,7055,a)].">
      <j1 rule="hyper" parents="63 6050 7055"/>
    </justification>
  </clause>

  <clause id="7211">
    <literal><![CDATA[
      (L(x \ L(x,y,z),u,w) \ 1) \ x = x * L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5169,a(flip),b,7063,a),flip(a)].">
      <j1 rule="hyper" parents="63 5169 7063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7212">
    <literal><![CDATA[
      x * L(x \ L(x,y,y \ 1),z,u) = a(y \ 1,y,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(2409(a,1),7211(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2409 7211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7213">
    <literal><![CDATA[
      L(T(x,y) / z,u,w) \ T(x,y) = x / L(z \ x,u,w)
    ]]></literal>
    <justification jstring="[para(3849(a,1),7065(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3849 7065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7214">
    <literal><![CDATA[
      L(T(x,y) / z,u,w) \ T(x,y) = L(x / z,u,w) \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,6568,a(flip),b,7213,a),flip(a)].">
      <j1 rule="hyper" parents="316 6568 7213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7216">
    <literal><![CDATA[
      L((x \ y) / z,u,w) \ T(y / x,x) = L((y / x) / z,u,w) \ (y / x)
    ]]></literal>
    <justification jstring="[para(116(a,1),7214(a,1,1,1,1))].">
      <j1 rule="para" parents="116 7214"/>
    </justification>
  </clause>

  <clause id="7217">
    <literal><![CDATA[
      ((x * y) * (y \ z)) \ (x * z) = (x * y) \ ((x * z) / (y \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),7125(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 7125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7218">
    <literal><![CDATA[
      (x * y) \ ((x * (x \ z)) / (y \ (x \ z))) = ((x * y) * (y \ (x \ z))) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,168,a(flip),b,7217,a),flip(a)].">
      <j1 rule="hyper" parents="63 168 7217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7219">
    <literal><![CDATA[
      ((x / y) * y) \ (((x / y) * z) / (y \ z)) = (x * (y \ z)) \ ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(12(a,1),7217(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 7217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7221">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * a(x,y,z)) \ (((a(x,y,z) \ u) * w) / (a(x,y,z) \ w)) = (u * (a(x,y,z) \ w)) \ ((a(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(2274(a,1),7217(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2274 7217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7222">
    <literal><![CDATA[
      (x * a(y \ 1,y,z)) \ ((x * z) / (a(y \ 1,y,z) \ z)) = ((x * a(y \ 1,y,z)) * L(z,y,y \ 1)) \ (x * z)
    ]]></literal>
    <justification jstring="[para(2406(a,1),7217(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2406 7217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7223">
    <literal><![CDATA[
      (a(x,x,y) * L(y,x,x)) \ ((a(x,x,y) * z) / (L(y,x,x) \ z)) = (y * (L(y,x,x) \ z)) \ (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(4951(a,1),7217(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4951 7217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7224">
    <literal><![CDATA[
      ((x * (y / z)) * z) \ (x * y) = (x * (y / z)) \ ((x * y) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),7134(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 7134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7225">
    <literal><![CDATA[
      ((x * y) * T(z,y)) \ (x * (z * y)) = (x * ((z * y) / z)) \ ((x * (((z * y) / z) * z)) / z)
    ]]></literal>
    <justification jstring="[para(3893(a,1),7134(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3893 7134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7226">
    <literal><![CDATA[
      a(x \ 1,y,a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7143,a(flip),b,7145,a),flip(a)].">
      <j1 rule="hyper" parents="63 7143 7145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7227">
    <literal><![CDATA[
      (a(x,y,z) * (u \ (w * ((v5 * a(x,y,z)) / v5)))) \ (u \ ((w * a(x,y,z)) * ((v5 * a(x,y,z)) / v5))) = a(u,u \ (w * ((v5 * a(x,y,z)) / v5)),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(1396(a,1),7147(a,1,2,2))].">
      <j1 rule="para" parents="1396 7147"/>
    </justification>
  </clause>

  <clause id="7228">
    <literal><![CDATA[
      a(x,y,L(z * u,z * u,L(u,u,z))) = a(x,y,z \ (((z * u) \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5772,a(flip),b,7193,a),flip(a)].">
      <j1 rule="hyper" parents="316 5772 7193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7230">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w \ 1) \ u))) = a(x,y,z \ ((w * u) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5833,a(flip),b,7200,a),flip(a)].">
      <j1 rule="hyper" parents="63 5833 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7232">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) \ w)) = a(x,y,z \ (w \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7203,a(flip),b,7230,a),flip(a)].">
      <j1 rule="hyper" parents="63 7203 7230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7233">
    <literal><![CDATA[
      a(x,y,z \ (z \ (u \ z))) = a(x,y,R(u,z,z) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6067,a(flip),b,7232,a),flip(a)].">
      <j1 rule="hyper" parents="63 6067 7232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7234">
    <literal><![CDATA[
      L((x / y) / z,u,w) \ (x / y) = L((y \ x) / z,u,w) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(116(a,1),7216(a,1,2)),flip(a)].">
      <j1 rule="para" parents="116 7216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7235">
    <literal><![CDATA[
      ((x * y) * (y \ (x \ z))) \ z = (x * y) \ (z / (y \ (x \ z)))
    ]]></literal>
    <justification jstring="[para(10(a,1),7218(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 7218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7237">
    <literal><![CDATA[
      (x * y) \ (1 / (y \ (x \ 1))) = a(x,y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[para(2401(a,1),7235(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2401 7235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7238">
    <literal><![CDATA[
      (x * (y \ z)) \ ((x / y) * z) = x \ (((x / y) * z) / (y \ z))
    ]]></literal>
    <justification jstring="[para(12(a,1),7219(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 7219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7239">
    <literal><![CDATA[
      a(x,y,L(z * u,z * u,L(u,u,z))) = a(x,y,z \ ((z * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(316,a,6743,a(flip),b,7228,a),flip(a)].">
      <j1 rule="hyper" parents="316 6743 7228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7240">
    <literal><![CDATA[
      a((x \ 1) \ (x \ y),x \ 1,x) = ((y / x) / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(2551(a,1),3346(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2551 3346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7241">
    <literal><![CDATA[
      (x * y) \ x = (y \ 1) * (y * L(y \ 1,y,x))
    ]]></literal>
    <justification jstring="[hyper(35,a,3592,a(flip),b,3470,a)].">
      <j1 rule="hyper" parents="35 3592 3470"/>
    </justification>
  </clause>

  <clause id="7242">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * x) \ y)) = (y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(316,a,711,a(flip),b,7241,a)].">
      <j1 rule="hyper" parents="316 711 7241"/>
    </justification>
  </clause>

  <clause id="7244">
    <literal><![CDATA[
      L((x * y) \ x,y,y \ 1) \ ((x * y) \ x) = T((y \ 1) * y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,7242,a(flip),b,4363,a)].">
      <j1 rule="hyper" parents="133 7242 4363"/>
    </justification>
  </clause>

  <clause id="7245">
    <literal><![CDATA[
      (L(x \ 1,x,(y * x) \ y) * (x * ((y * x) \ y))) \ ((y * x) \ y) = a((y * x) \ y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(7242(a,1),5784(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7242 5784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7246">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * w) / T(u,w) = u \ ((a(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(5249(a,1),3721(a,1,2))].">
      <j1 rule="para" parents="5249 3721"/>
    </justification>
  </clause>

  <clause id="7247">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) / w = w \ ((a(y,z,u) \ w) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5355,a(flip),b,7246,a)].">
      <j1 rule="hyper" parents="63 5355 7246"/>
    </justification>
  </clause>

  <clause id="7249">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u) \ w) * w = (x * a(y,z,u)) * (a(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(138,a,2512,a(flip),b,7247,a)].">
      <j1 rule="hyper" parents="138 2512 7247"/>
    </justification>
  </clause>

  <clause id="7250">
    <literal><![CDATA[
      L(x,1 / x,(1 / x) \ (x \ y)) = (y / x) \ ((y / ((x \ 1) \ 1)) / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,3243,a(flip),b,4233,a)].">
      <j1 rule="hyper" parents="63 3243 4233"/>
    </justification>
  </clause>

  <clause id="7251">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((v5 * w) * u))) = L(x,y,(z \ R(v5,w,u)) * K(w,u))
    ]]></literal>
    <justification jstring="[para(4605(a,1),4490(a,2,3))].">
      <j1 rule="para" parents="4605 4490"/>
    </justification>
  </clause>

  <clause id="7252">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (y * K(z * (x \ y),x)) * z
    ]]></literal>
    <justification jstring="[para(3521(a,1),4505(a,2,1,2))].">
      <j1 rule="para" parents="3521 4505"/>
    </justification>
  </clause>

  <clause id="7253">
    <literal><![CDATA[
      (x * K(y * (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,2575,a(flip),b,7252,a),flip(a)].">
      <j1 rule="hyper" parents="63 2575 7252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7254">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x = (y \ (z * x)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,6292,a,b,7253,a)].">
      <j1 rule="hyper" parents="63 6292 7253"/>
    </justification>
  </clause>

  <clause id="7255">
    <literal><![CDATA[
      ((((x \ 1) \ ((y \ ((x \ 1) * z)) * y)) / x) \ u) * (((x \ 1) \ ((y \ ((x \ 1) * z)) * y)) / x) = (((y \ (z * (x \ 1))) * y) \ u) * (((x \ 1) \ ((y \ ((x \ 1) * z)) * y)) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(7254(a,1),3469(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7254 3469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7256">
    <literal><![CDATA[
      K(x,y) * (z * L(x,T(x,y) \ 1,T(x,y))) = T(1 / (1 / x),y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(2417(a,1),4598(a,2,1))].">
      <j1 rule="para" parents="2417 4598"/>
    </justification>
  </clause>

  <clause id="7257">
    <literal><![CDATA[
      a(x \ ((y * y) \ (y * (x * y))),z,u) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,2788,a(flip),b,4620,a),flip(a)].">
      <j1 rule="hyper" parents="316 2788 4620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7259">
    <literal><![CDATA[
      a(x \ L(T(x,y),y,y),z,u) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[para(247(a,1),7257(a,1,1,2))].">
      <j1 rule="para" parents="247 7257"/>
    </justification>
  </clause>

  <clause id="7260">
    <literal><![CDATA[
      a(x \ L(x,y,y),z,u) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3322,a(flip),b,7259,a)].">
      <j1 rule="hyper" parents="63 3322 7259"/>
    </justification>
  </clause>

  <clause id="7262">
    <literal><![CDATA[
      (x * y) * L(z,R(x,y,y) \ (x * y),L(x,y,y)) = R(x,y,y) * (L(y,y,L(x,y,y)) * z)
    ]]></literal>
    <justification jstring="[para(4630(a,2),4631(a,2,2,1))].">
      <j1 rule="para" parents="4630 4631"/>
    </justification>
  </clause>

  <clause id="7263">
    <literal><![CDATA[
      R(x,y,z * ((u * z) * u)) = R(x,y,a(u * z,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4675,a(flip),b,4732,a),flip(a)].">
      <j1 rule="hyper" parents="63 4675 4732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7265">
    <literal><![CDATA[
      R(x,y,z * ((u * z) * u)) = L(x,y,a(u * z,u,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5371,a(flip),b,7263,a),flip(a)].">
      <j1 rule="hyper" parents="316 5371 7263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7266">
    <literal><![CDATA[
      R(x,y,z * R(z,u,u)) = L(x,y,a(u * z,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4811,a(flip),b,7265,a)].">
      <j1 rule="hyper" parents="63 4811 7265"/>
    </justification>
  </clause>

  <clause id="7267">
    <literal><![CDATA[
      L(x * K(y \ (x \ L(x,z,u)),y),z,u) = ((y \ (x \ L(x,z,u))) * y) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,2715,a,b,4873,a),flip(a)].">
      <j1 rule="hyper" parents="316 2715 4873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7268">
    <literal><![CDATA[
      ((a(x,y,z) \ u) \ w) * K(u,(u \ a(x,y,z)) * w) = w / (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(3713(a,1),5285(a,1,2))].">
      <j1 rule="para" parents="3713 5285"/>
    </justification>
  </clause>

  <clause id="7269">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ ((u * v5) * w))) = a(x,y,z * R(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5596,a(flip),b,5583,a),flip(a)].">
      <j1 rule="hyper" parents="63 5596 5583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7272">
    <literal><![CDATA[
      a(x,y,z * R(u,w,v5)) = a(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,6128,a(flip),b,7269,a),flip(a)].">
      <j1 rule="hyper" parents="63 6128 7269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7274">
    <literal><![CDATA[
      a(x,y,(z \ 1) * R(z,u,w)) = a(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5532,a(flip),b,7272,a),flip(a)].">
      <j1 rule="hyper" parents="316 5532 7272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7275">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * v5) = a(x,y,v5 * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,7272,a)].">
      <j1 rule="hyper" parents="63 5469 7272"/>
    </justification>
  </clause>

  <clause id="7276">
    <literal><![CDATA[
      a(x,y,z * L(z,u,u)) = a(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5573,a(flip),b,7272,a),flip(a)].">
      <j1 rule="hyper" parents="63 5573 7272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7277">
    <literal><![CDATA[
      a(x,y,z * L((u / w) / v5,v5,w)) = a(x,y,z * (u / (v5 * w)))
    ]]></literal>
    <justification jstring="[para(303(a,1),7272(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="303 7272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7279">
    <literal><![CDATA[
      a(x,y,z * (u * (z * u))) = a(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5942,a,b,7276,a)].">
      <j1 rule="hyper" parents="63 5942 7276"/>
    </justification>
  </clause>

  <clause id="7280">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4962,a(flip),b,7276,a),flip(a)].">
      <j1 rule="hyper" parents="63 4962 7276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7282">
    <literal><![CDATA[
      a(x,y,a((z * z) \ u,(z * z) \ u,w)) = a(x,y,a(w,(z * z) \ u,u))
    ]]></literal>
    <justification jstring="[para(5802(a,1),7280(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5802 7280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7283">
    <literal><![CDATA[
      a(x * y,z,a(x,y,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,5727,a(flip),b,7279,a),flip(a)].">
      <j1 rule="hyper" parents="63 5727 7279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7284">
    <literal><![CDATA[
      a(x,y,a(z,u,z * u)) = a(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5187,a(flip),b,7279,a)].">
      <j1 rule="hyper" parents="63 5187 7279"/>
    </justification>
  </clause>

  <clause id="7285">
    <literal><![CDATA[
      a(x * y,z,a(y,x,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,2771,a,b,7283,a)].">
      <j1 rule="hyper" parents="63 2771 7283"/>
    </justification>
  </clause>

  <clause id="7286">
    <literal><![CDATA[
      L(a(x,y,y),z,x * y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(52,a,7283,a)].">
      <j1 rule="hyper" parents="52 7283"/>
    </justification>
  </clause>

  <clause id="7287">
    <literal><![CDATA[
      a(x * y,z,a(x,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,7280,a(flip),b,7285,a)].">
      <j1 rule="hyper" parents="63 7280 7285"/>
    </justification>
  </clause>

  <clause id="7289">
    <literal><![CDATA[
      L(a(x,x,y),z,x * y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(52,a,7287,a)].">
      <j1 rule="hyper" parents="52 7287"/>
    </justification>
  </clause>

  <clause id="7290">
    <literal><![CDATA[
      L(x,x,y) \ x = a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,1562,a(flip),b,7286,a)].">
      <j1 rule="hyper" parents="41 1562 7286"/>
    </justification>
  </clause>

  <clause id="7291">
    <literal><![CDATA[
      (x * y) \ (z * a(x,y,y)) = ((x * y) \ z) * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(7286(a,1),456(a,1,2,2))].">
      <j1 rule="para" parents="7286 456"/>
    </justification>
  </clause>

  <clause id="7292">
    <literal><![CDATA[
      R(x,y,(z * u) \ a(z,u,u)) = R(x,y,a(z,u,u) * (z * u))
    ]]></literal>
    <justification jstring="[para(7286(a,1),4801(a,1,3,2))].">
      <j1 rule="para" parents="7286 4801"/>
    </justification>
  </clause>

  <clause id="7293">
    <literal><![CDATA[
      L(x,x,y) \ x = (a(y,x,x) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(316,a,2301,a,b,7290,a),flip(a)].">
      <j1 rule="hyper" parents="316 2301 7290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7294">
    <literal><![CDATA[
      L(x,x,y) * a(y,x,x) = x
    ]]></literal>
    <justification jstring="[hyper(152,a,7290,a)].">
      <j1 rule="hyper" parents="152 7290"/>
    </justification>
  </clause>

  <clause id="7295">
    <literal><![CDATA[
      (L(x,x,y) \ x) * y = R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(138,a,7290,a,b,2376,a)].">
      <j1 rule="hyper" parents="138 7290 2376"/>
    </justification>
  </clause>

  <clause id="7296">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (x \ 1) = a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7090,a,b,7290,a)].">
      <j1 rule="hyper" parents="63 7090 7290"/>
    </justification>
  </clause>

  <clause id="7297">
    <literal><![CDATA[
      a(x,y,y) \ y = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,7290,a)].">
      <j1 rule="hyper" parents="39 2301 7290"/>
    </justification>
  </clause>

  <clause id="7298">
    <literal><![CDATA[
      a(x,y,y) * L(y,y,x) = y
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,7290,a)].">
      <j1 rule="hyper" parents="38 2295 7290"/>
    </justification>
  </clause>

  <clause id="7299">
    <literal><![CDATA[
      L(1 / x,x,y) \ 1 = x * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,7290,a(flip),b,6591,a),flip(a)].">
      <j1 rule="hyper" parents="139 7290 6591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7300">
    <literal><![CDATA[
      L(x,x,y) \ 1 = x \ a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,7290,a(flip),b,1002,a),flip(a)].">
      <j1 rule="hyper" parents="133 7290 1002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7302">
    <literal><![CDATA[
      a(x,y,z * L(z,z,u)) = a(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[para(7290(a,1),2652(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7290 2652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7303">
    <literal><![CDATA[
      (x * a(y,x,x)) \ 1 = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(7290(a,1),4459(a,1,1,2))].">
      <j1 rule="para" parents="7290 4459"/>
    </justification>
  </clause>

  <clause id="7304">
    <literal><![CDATA[
      a(x,y,y) \ 1 = y \ L(y,y,x)
    ]]></literal>
    <justification jstring="[para(7290(a,1),5076(a,1,1))].">
      <j1 rule="para" parents="7290 5076"/>
    </justification>
  </clause>

  <clause id="7306">
    <literal><![CDATA[
      L(1 / x,x,y) \ 1 = a(y,x,x) * x
    ]]></literal>
    <justification jstring="[para(7290(a,1),6592(a,2,1))].">
      <j1 rule="para" parents="7290 6592"/>
    </justification>
  </clause>

  <clause id="7308">
    <literal><![CDATA[
      (x * a(y,x,x)) \ K(z,u) = L(x \ K(z,u),x,y)
    ]]></literal>
    <justification jstring="[para(7290(a,1),6655(a,1,1,2))].">
      <j1 rule="para" parents="7290 6655"/>
    </justification>
  </clause>

  <clause id="7310">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * L(w,w,v5)))) = a(x,y,z \ (u * a(v5,w,w)))
    ]]></literal>
    <justification jstring="[para(7290(a,1),6354(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="7290 6354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7311">
    <literal><![CDATA[
      x * L(y,a(z,x,x),L(x,x,z)) = L(x,x,z) * (a(z,x,x) * y)
    ]]></literal>
    <justification jstring="[hyper(138,a,7294,a(flip),b,202,a)].">
      <j1 rule="hyper" parents="138 7294 202"/>
    </justification>
  </clause>

  <clause id="7312">
    <literal><![CDATA[
      L(K(a(x,y,y),L(y,y,x)) * z,L(y,y,x),a(x,y,y)) = y \ (a(x,y,y) * (L(y,y,x) * z))
    ]]></literal>
    <justification jstring="[para(7294(a,1),3299(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7294 3299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7315">
    <literal><![CDATA[
      a(L(x,x,y) * (a(y,x,x) * a(y,x,x)),z,u) = a((a(y,x,x) \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(7297(a,1),1828(a,1,1,1))].">
      <j1 rule="para" parents="7297 1828"/>
    </justification>
  </clause>

  <clause id="7316">
    <literal><![CDATA[
      a(x,y \ 1,y) \ (y \ 1) = L(y \ 1,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(2534(a,1),7297(a,1,1))].">
      <j1 rule="para" parents="2534 7297"/>
    </justification>
  </clause>

  <clause id="7317">
    <literal><![CDATA[
      a(x,y,y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      L(y,y,x) = z
    ]]></literal>
    <justification jstring="[para(7298(a,1),321(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7298 321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7318">
    <literal><![CDATA[
      ((x * y) / L(y,y,z)) \ (x * a(z,y,y)) = a(x,a(z,y,y),L(y,y,z))
    ]]></literal>
    <justification jstring="[para(7298(a,1),6925(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7298 6925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7319">
    <literal><![CDATA[
      L(x,x,y) * L(x \ a(y,x,x),z,u) = L(x,x,y) \ L(L(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7300(a,1),1064(a,1,2,1))].">
      <j1 rule="para" parents="7300 1064"/>
    </justification>
  </clause>

  <clause id="7320">
    <literal><![CDATA[
      x \ (y * L(y \ x,x \ y,z)) = a(z,x \ y,x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,1252,a(flip),b,7304,a)].">
      <j1 rule="hyper" parents="316 1252 7304"/>
    </justification>
  </clause>

  <clause id="7321">
    <literal><![CDATA[
      x \ (a(y,x,x) \ 1) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,7304,a,b,1064,a)].">
      <j1 rule="hyper" parents="133 7304 1064"/>
    </justification>
  </clause>

  <clause id="7322">
    <literal><![CDATA[
      K(x,y) * (a(z,x,x) \ 1) = x \ L(T(x,y),x,z)
    ]]></literal>
    <justification jstring="[para(7304(a,2),4350(a,1,2))].">
      <j1 rule="para" parents="7304 4350"/>
    </justification>
  </clause>

  <clause id="7323">
    <literal><![CDATA[
      (a(x,y,y) \ 1) * K(z,u) = y * L(y \ K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(7304(a,2),4852(a,1,1))].">
      <j1 rule="para" parents="7304 4852"/>
    </justification>
  </clause>

  <clause id="7326">
    <literal><![CDATA[
      a(x,y,(z \ (u \ L(u,u,w))) * v5) = a(x,y,v5 * (z \ a(w,u,u)))
    ]]></literal>
    <justification jstring="[para(7304(a,1),5884(a,1,3,1,2))].">
      <j1 rule="para" parents="7304 5884"/>
    </justification>
  </clause>

  <clause id="7327">
    <literal><![CDATA[
      a(x,y,z \ ((u \ L(u,u,w)) * v5)) = a(x,y,z \ (v5 * a(w,u,u)))
    ]]></literal>
    <justification jstring="[para(7304(a,1),6684(a,1,3,2,1))].">
      <j1 rule="para" parents="7304 6684"/>
    </justification>
  </clause>

  <clause id="7328">
    <literal><![CDATA[
      x \ L(x,x,a(y,z,u)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,5385,a,b,7289,a)].">
      <j1 rule="hyper" parents="41 5385 7289"/>
    </justification>
  </clause>

  <clause id="7329">
    <literal><![CDATA[
      x \ R(x,x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,3422,a(flip),b,7289,a)].">
      <j1 rule="hyper" parents="41 3422 7289"/>
    </justification>
  </clause>

  <clause id="7330">
    <literal><![CDATA[
      a(x,x,y) * ((x * y) * z) = (x * y) * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(138,a,7289,a(flip),b,2454,a)].">
      <j1 rule="hyper" parents="138 7289 2454"/>
    </justification>
  </clause>

  <clause id="7331">
    <literal><![CDATA[
      L(L(a(x,x,y),z,u),w,x * y) = L(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7289(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7289 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7332">
    <literal><![CDATA[
      x * a(x,x,y) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(152,a,7329,a)].">
      <j1 rule="hyper" parents="152 7329"/>
    </justification>
  </clause>

  <clause id="7333">
    <literal><![CDATA[
      a(x,x,y) * x = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,7329,a)].">
      <j1 rule="hyper" parents="38 2295 7329"/>
    </justification>
  </clause>

  <clause id="7334">
    <literal><![CDATA[
      x * (L(x,y,z) \ a(x,x,u)) = L(x,y,z) \ R(x,x,u)
    ]]></literal>
    <justification jstring="[para(7329(a,1),1130(a,1,2,2))].">
      <j1 rule="para" parents="7329 1130"/>
    </justification>
  </clause>

  <clause id="7335">
    <literal><![CDATA[
      (x \ a(x,x,y)) * x = (x \ 1) * R(x,x,y)
    ]]></literal>
    <justification jstring="[para(7329(a,1),3248(a,1,1,2))].">
      <j1 rule="para" parents="7329 3248"/>
    </justification>
  </clause>

  <clause id="7337">
    <literal><![CDATA[
      R(x,x,y) * L(z,a(x,x,y),x) = x * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(138,a,7332,a(flip),b,202,a)].">
      <j1 rule="hyper" parents="138 7332 202"/>
    </justification>
  </clause>

  <clause id="7338">
    <literal><![CDATA[
      (a(x,x,y) \ (z * R(x,x,y))) \ (z * x) = a(z,x,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(7332(a,1),6937(a,1,1,2,2))].">
      <j1 rule="para" parents="7332 6937"/>
    </justification>
  </clause>

  <clause id="7339">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * x = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5371,a(flip),b,7333,a),flip(a)].">
      <j1 rule="hyper" parents="316 5371 7333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7340">
    <literal><![CDATA[
      a(x,y,y) \ (1 / ((x * y) \ x)) = y
    ]]></literal>
    <justification jstring="[hyper(39,a,6600,a(flip),b,7293,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 6600 7293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7341">
    <literal><![CDATA[
      a(x,x \ y,x \ y) \ 1 = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(39,a,1905,a(flip),b,7293,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 1905 7293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7342">
    <literal><![CDATA[
      1 / (x \ (x / y)) = y * a(y \ x,y,y)
    ]]></literal>
    <justification jstring="[hyper(209,a,1603,a(flip),b,7303,a)].">
      <j1 rule="hyper" parents="209 1603 7303"/>
    </justification>
  </clause>

  <clause id="7343">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(209,a,356,a(flip),b,7303,a),flip(a)].">
      <j1 rule="hyper" parents="209 356 7303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7344">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z,u) \ 1) = L(x,y,z * a(u,z,z))
    ]]></literal>
    <justification jstring="[para(7303(a,1),1580(a,1,3,1))].">
      <j1 rule="para" parents="7303 1580"/>
    </justification>
  </clause>

  <clause id="7345">
    <literal><![CDATA[
      x * ((L(1 / y,y,z) \ 1) \ u) = x * ((y * a(z,y,y)) \ u)
    ]]></literal>
    <justification jstring="[para(7306(a,2),2394(a,1,2,1))].">
      <j1 rule="para" parents="7306 2394"/>
    </justification>
  </clause>

  <clause id="7347">
    <literal><![CDATA[
      ((x * (L(1 / y,y,z) \ 1)) / y) \ (x * a(z,y,y)) = a(x,a(z,y,y),y)
    ]]></literal>
    <justification jstring="[para(7306(a,2),6925(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7306 6925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7348">
    <literal><![CDATA[
      x * ((y * x) \ y) = a(y,x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,232,a(flip),b,7321,a)].">
      <j1 rule="hyper" parents="139 232 7321"/>
    </justification>
  </clause>

  <clause id="7349">
    <literal><![CDATA[
      a(x,y,y \ 1) \ 1 = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(2383(a,2),7348(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2383 7348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7350">
    <literal><![CDATA[
      x * (a(y,z,u) \ (x \ a(y,z,u))) = a(a(y,z,u),x,x) \ 1
    ]]></literal>
    <justification jstring="[para(5451(a,1),7348(a,1,2))].">
      <j1 rule="para" parents="5451 7348"/>
    </justification>
  </clause>

  <clause id="7351">
    <literal><![CDATA[
      L(x,y,z * ((z * u) \ u)) = L(x,y,a(u,z,z) \ 1)
    ]]></literal>
    <justification jstring="[para(7348(a,1),6237(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7348 6237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7352">
    <literal><![CDATA[
      R(x,y,z * ((z * u) \ u)) = R(x,y,a(u,z,z) \ 1)
    ]]></literal>
    <justification jstring="[para(7348(a,1),6241(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7348 6241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7354">
    <literal><![CDATA[
      (x * (1 / (y \ (y / z)))) / a(z \ y,z,z) = (x * (z * (a(z \ y,z,z) \ 1))) / (a(z \ y,z,z) \ 1)
    ]]></literal>
    <justification jstring="[para(7342(a,2),964(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7342 964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7355">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ ((x \ (x / y)) \ ((x \ (x / y)) \ 1)) = (y * a(y \ x,y,y)) \ ((x \ (x / y)) \ (1 / (x \ (x / y))))
    ]]></literal>
    <justification jstring="[para(7342(a,1),3215(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7342 3215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7356">
    <literal><![CDATA[
      L(x,y \ (y / z),(y \ (y / z)) \ 1) * 1 = x * (((z * a(z \ y,z,z)) * ((y \ (y / z)) * x)) / x)
    ]]></literal>
    <justification jstring="[para(7342(a,1),4494(a,2,2,1,1))].">
      <j1 rule="para" parents="7342 4494"/>
    </justification>
  </clause>

  <clause id="7357">
    <literal><![CDATA[
      (x * ((x * y) \ y)) * a(1 / ((x * y) \ y),x * ((x * y) \ y),x * ((x * y) \ y)) = 1 / (x \ (x / (x * ((x * y) \ y))))
    ]]></literal>
    <justification jstring="[para(6277(a,1),7342(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6277 7342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7358">
    <literal><![CDATA[
      a(x,y,a(z,z \ u,z \ u)) = a(x,y,a(z,z \ u,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),7284(a,1,3,3)),flip(a)].">
      <j1 rule="para" parents="10 7284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7359">
    <literal><![CDATA[
      a(x,y,z * ((z * u) \ u)) = a(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6037,a(flip),b,7302,a)].">
      <j1 rule="hyper" parents="63 6037 7302"/>
    </justification>
  </clause>

  <clause id="7360">
    <literal><![CDATA[
      a(a(x,y,z),u,u) \ 1 = a(u,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7304,a,b,7328,a)].">
      <j1 rule="hyper" parents="63 7304 7328"/>
    </justification>
  </clause>

  <clause id="7361">
    <literal><![CDATA[
      L(x \ L(x,L(x,y,z),a(u,w,v5)),y,z) = a(L(x,y,z),L(x,y,z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,2136,a(flip),b,7328,a)].">
      <j1 rule="hyper" parents="63 2136 7328"/>
    </justification>
  </clause>

  <clause id="7362">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) * L(x \ 1,w,v5) = a(x,x,a(y,z,u)) * (x \ L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(7328(a,1),5133(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7328 5133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7363">
    <literal><![CDATA[
      (x \ a(x,x,a(y,z,u))) * x = (x \ 1) * L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(5264(a,1),7335(a,2,2))].">
      <j1 rule="para" parents="5264 7335"/>
    </justification>
  </clause>

  <clause id="7371">
    <literal><![CDATA[
      ((x * (y \ x)) / (y * ((y \ x) * (y \ x)))) \ 1 = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(2328(a,2),7341(a,1,1))].">
      <j1 rule="para" parents="2328 7341"/>
    </justification>
  </clause>

  <clause id="7372">
    <literal><![CDATA[
      a(x,x \ y,x \ y) * (x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a,b,7343,a)].">
      <j1 rule="hyper" parents="63 2290 7343"/>
    </justification>
  </clause>

  <clause id="7373">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,(x \ y) \ 1) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[para(2383(a,2),7343(a,1,2))].">
      <j1 rule="para" parents="2383 7343"/>
    </justification>
  </clause>

  <clause id="7375">
    <literal><![CDATA[
      a(x,y,R(L(z,u,w),v5,v6) * v7) = a(x,y,L(L(z,v5,v6),u,w) * v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,5531,a,b,7275,a),flip(a)].">
      <j1 rule="hyper" parents="316 5531 7275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7376">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * v5) = a(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,7275,a),flip(a)].">
      <j1 rule="hyper" parents="316 5469 7275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7377">
    <literal><![CDATA[
      (x * a(y,x,x)) \ K(z,u * a(w,v5,v5)) = L(x \ K(z,u),x,y)
    ]]></literal>
    <justification jstring="[para(3732(a,1),7308(a,2,1,2))].">
      <j1 rule="para" parents="3732 7308"/>
    </justification>
  </clause>

  <clause id="7379">
    <literal><![CDATA[
      x \ (a(y,x \ 1,x) \ 1) = L(x \ 1,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6920,a(flip),b,7316,a)].">
      <j1 rule="hyper" parents="63 6920 7316"/>
    </justification>
  </clause>

  <clause id="7380">
    <literal><![CDATA[
      a(x,y,y) \ K(y,z) = y \ L(T(y,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2466,a(flip),b,7322,a)].">
      <j1 rule="hyper" parents="63 2466 7322"/>
    </justification>
  </clause>

  <clause id="7381">
    <literal><![CDATA[
      a(x,y,R(R(z,u,w),v5,v6) * (u * w)) = a(x,y,(L(z,v5,v6) * u) * w)
    ]]></literal>
    <justification jstring="[para(400(a,1),7376(a,2,3))].">
      <j1 rule="para" parents="400 7376"/>
    </justification>
  </clause>

  <clause id="7382">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * R(1 / v5,v5,v5 \ R(z,u,w))) = a(x,y,v5 \ T(R(z,u,w),v5 \ 1))
    ]]></literal>
    <justification jstring="[para(3139(a,1),7376(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3139 7376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7383">
    <literal><![CDATA[
      a(x,y \ 1,y) \ 1 = y \ L(y,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(38,a,1065,a,b,7379,a),flip(a)].">
      <j1 rule="hyper" parents="38 1065 7379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7384">
    <literal><![CDATA[
      L(x,x \ 1,y) \ x = a(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,5076,a,b,7383,a)].">
      <j1 rule="hyper" parents="39 5076 7383"/>
    </justification>
  </clause>

  <clause id="7385">
    <literal><![CDATA[
      a(x,y \ 1,y) \ y = L(y,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(38,a,6880,a,b,7383,a(flip))].">
      <j1 rule="hyper" parents="38 6880 7383"/>
    </justification>
  </clause>

  <clause id="7386">
    <literal><![CDATA[
      R(x,y,z * ((z * u) \ u)) = R(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,1033,a(flip),b,7352,a),flip(a)].">
      <j1 rule="hyper" parents="316 1033 7352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7387">
    <literal><![CDATA[
      R(x,y,z * ((z * u) \ u)) = L(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5371,a(flip),b,7386,a),flip(a)].">
      <j1 rule="hyper" parents="316 5371 7386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7388">
    <literal><![CDATA[
      R(x,y,z * (u \ (z \ u))) = L(x,y,a(z \ u,z,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),7387(a,1,3,2,1))].">
      <j1 rule="para" parents="10 7387"/>
    </justification>
  </clause>

  <clause id="7389">
    <literal><![CDATA[
      (x \ y) * (x \ (y * ((x \ y) \ 1))) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[para(704(a,1),7373(a,1,2))].">
      <j1 rule="para" parents="704 7373"/>
    </justification>
  </clause>

  <clause id="7390">
    <literal><![CDATA[
      a(x,y,z \ R(z,u,w)) = a(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5474,a(flip),b,7274,a)].">
      <j1 rule="hyper" parents="63 5474 7274"/>
    </justification>
  </clause>

  <clause id="7391">
    <literal><![CDATA[
      a(x,y,x \ R(x,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(316,a,5145,a(flip),b,7390,a),flip(a)].">
      <j1 rule="hyper" parents="316 5145 7390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7392">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(52,a,7391,a)].">
      <j1 rule="hyper" parents="52 7391"/>
    </justification>
  </clause>

  <clause id="7393">
    <literal><![CDATA[
      L(x \ (y * ((x \ y) \ 1)),z,x) = x \ R(x,x \ y,x \ y)
    ]]></literal>
    <justification jstring="[para(568(a,1),7392(a,1,1,2))].">
      <j1 rule="para" parents="568 7392"/>
    </justification>
  </clause>

  <clause id="7394">
    <literal><![CDATA[
      ((x * y) \ (z * a(x,y,y))) / a(x,y,y) = (x * y) \ z
    ]]></literal>
    <justification jstring="[hyper(136,a,7291,a,b,xx)].">
      <j1 rule="hyper" parents="136 7291"/>
    </justification>
  </clause>

  <clause id="7395">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * a(x,y,y)) = L(z,y,x) * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(18(a,2),7291(a,2,1))].">
      <j1 rule="para" parents="18 7291"/>
    </justification>
  </clause>

  <clause id="7396">
    <literal><![CDATA[
      x * L(x \ K(y,z),x,u) = a(u,x,x) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3780,a(flip),b,7323,a),flip(a)].">
      <j1 rule="hyper" parents="63 3780 7323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7397">
    <literal><![CDATA[
      x * ((y * x) \ T(y,z)) = a(y,x,x) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(2823(a,1),7396(a,1,2))].">
      <j1 rule="para" parents="2823 7396"/>
    </justification>
  </clause>

  <clause id="7398">
    <literal><![CDATA[
      a(x,y,y) \ K(x,y) = y * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[para(2875(a,1),7397(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2875 7397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7399">
    <literal><![CDATA[
      a(x,y,(z * ((z * u) \ u)) * w) = a(x,y,a(u,z,z) * w)
    ]]></literal>
    <justification jstring="[para(7398(a,1),5733(a,1,3,1))].">
      <j1 rule="para" parents="7398 5733"/>
    </justification>
  </clause>

  <clause id="7401">
    <literal><![CDATA[
      a(x,y,(z * (u * ((u * w) \ w))) \ v5) = a(x,y,(z * a(w,u,u)) \ v5)
    ]]></literal>
    <justification jstring="[para(7398(a,1),6068(a,1,3,1,2))].">
      <j1 rule="para" parents="7398 6068"/>
    </justification>
  </clause>

  <clause id="7402">
    <literal><![CDATA[
      L(x * y,z,a(x,x,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(35,a,5275,a,b,7330,a(flip))].">
      <j1 rule="hyper" parents="35 5275 7330"/>
    </justification>
  </clause>

  <clause id="7403">
    <literal><![CDATA[
      L((a(x,y,x) / z) * (a(x,y,x) \ u),w,a(a(x,y,x) / z,a(x,y,x) / z,a(x,y,x) \ u)) = (1 / z) * u
    ]]></literal>
    <justification jstring="[hyper(316,a,5428,a(flip),b,7402,a),flip(a)].">
      <j1 rule="hyper" parents="316 5428 7402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7405">
    <literal><![CDATA[
      ((x * y) \ z) / a(x,y,y) = (x * y) \ (a(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[para(2274(a,1),7394(a,1,1,2))].">
      <j1 rule="para" parents="2274 7394"/>
    </justification>
  </clause>

  <clause id="7407">
    <literal><![CDATA[
      a(x,y,y) \ ((x * y) \ z) = (x * y) \ (a(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2276,a(flip),b,7405,a)].">
      <j1 rule="hyper" parents="63 2276 7405"/>
    </justification>
  </clause>

  <clause id="7411">
    <literal><![CDATA[
      R(x,y,(z * u) \ a(z,u,u)) = R(x,y,R(z,u,u) * u)
    ]]></literal>
    <justification jstring="[para(6914(a,1),7292(a,2,3))].">
      <j1 rule="para" parents="6914 7292"/>
    </justification>
  </clause>

  <clause id="7413">
    <literal><![CDATA[
      x * (a(y,z,u) \ (x \ a(y,z,u))) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,7360,a(flip),b,7350,a),flip(a)].">
      <j1 rule="hyper" parents="316 7360 7350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7414">
    <literal><![CDATA[
      L(x \ (y * ((x \ y) \ 1)),z,x) = x \ (y * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(568(a,1),7393(a,2,2))].">
      <j1 rule="para" parents="568 7393"/>
    </justification>
  </clause>

  <clause id="7415">
    <literal><![CDATA[
      x * ((x \ y) * (x \ (z * ((x \ z) \ 1)))) = y * (x \ (z * ((x \ z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(139,a,7414,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="139 7414 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7416">
    <literal><![CDATA[
      a(x,y,z * L((u / w) / v5,v5,w)) = a(x,y,z * ((v5 * w) \ u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5481,a(flip),b,7277,a),flip(a)].">
      <j1 rule="hyper" parents="316 5481 7277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7418">
    <literal><![CDATA[
      a(x,y,z * L(u \ (w / v5),u,v5)) = a(x,y,z * ((u * v5) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5560,a(flip),b,7416,a)].">
      <j1 rule="hyper" parents="63 5560 7416"/>
    </justification>
  </clause>

  <clause id="7419">
    <literal><![CDATA[
      a(x,y,(z \ (u * L(u,u,w))) * v5) = a(x,y,v5 * (z \ a(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6375,a(flip),b,7326,a)].">
      <j1 rule="hyper" parents="63 6375 7326"/>
    </justification>
  </clause>

  <clause id="7420">
    <literal><![CDATA[
      ((x * ((y \ x) \ 1)) / y) \ 1 = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(639(a,1),7371(a,1,1))].">
      <j1 rule="para" parents="639 7371"/>
    </justification>
  </clause>

  <clause id="7421">
    <literal><![CDATA[
      (x \ (y * ((x \ y) \ 1))) \ 1 = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(2221(a,1),7420(a,1,1))].">
      <j1 rule="para" parents="2221 7420"/>
    </justification>
  </clause>

  <clause id="7422">
    <literal><![CDATA[
      a(x,y,L(R(z,u,w),v5,v6) * v7) = a(x,y,L(L(z,u,w),v5,v6) * v7)
    ]]></literal>
    <justification jstring="[para(29(a,1),7375(a,1,3,1))].">
      <j1 rule="para" parents="29 7375"/>
    </justification>
  </clause>

  <clause id="7423">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),v5,v6) * (v6 * v5)) = a(x,y,v6 * (v5 * R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5472,a(flip),b,7422,a),flip(a)].">
      <j1 rule="hyper" parents="63 5472 7422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7424">
    <literal><![CDATA[
      (x * (L(x,x,y) \ z)) \ (z * a(y,x,x)) = a(z,a(y,x,x),L(x,x,y))
    ]]></literal>
    <justification jstring="[para(4390(a,1),7318(a,1,1))].">
      <j1 rule="para" parents="4390 7318"/>
    </justification>
  </clause>

  <clause id="7425">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) * v5) * v6) = a(x,y,(L(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(397(a,1),7381(a,1,3))].">
      <j1 rule="para" parents="397 7381"/>
    </justification>
  </clause>

  <clause id="7426">
    <literal><![CDATA[
      a(x,y,(R(L(z,u,w),v5,v6) * v7) * v8) = a(x,y,(L(L(z,v5,v6),u,w) * v7) * v8)
    ]]></literal>
    <justification jstring="[para(30(a,1),7425(a,2,3,1,1))].">
      <j1 rule="para" parents="30 7425"/>
    </justification>
  </clause>

  <clause id="7428">
    <literal><![CDATA[
      a(x,y,(L(z,u,w \ 1) * v5) * v6) = a(x,y,(R(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(1033(a,1),7425(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="1033 7425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7429">
    <literal><![CDATA[
      a(x,y,(L(z,u,w \ 1) * v5) * v6) = a(x,y,(L(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,7425,a(flip),b,7428,a),flip(a)].">
      <j1 rule="hyper" parents="316 7425 7428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7431">
    <literal><![CDATA[
      a(x,y,(L(T(z,u),u,u) * w) * v5) = a(x,y,(((1 / u) * (z * u)) * w) * v5)
    ]]></literal>
    <justification jstring="[para(892(a,1),7429(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="892 7429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7432">
    <literal><![CDATA[
      a(x,y,((z * ((z * u) \ u)) * w) \ v5) = a(x,y,(w * a(u,z,z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5626,a,b,7401,a)].">
      <j1 rule="hyper" parents="63 5626 7401"/>
    </justification>
  </clause>

  <clause id="7433">
    <literal><![CDATA[
      a(x,y,z * (u * R(w,v5,v6))) = a(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5472,a(flip),b,7423,a),flip(a)].">
      <j1 rule="hyper" parents="63 5472 7423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7434">
    <literal><![CDATA[
      a(x,y,z * (u * L(T(w,v5),v6,v7))) = a(x,y,(u * R(w,v6,v7)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5731,a(flip),b,7433,a),flip(a)].">
      <j1 rule="hyper" parents="63 5731 7433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7435">
    <literal><![CDATA[
      a(x,y,(z * (u * R(w,v5,v6))) * a(v7,v7,z * (u * L(w,v5,v6)))) = a(x,y,L(z * (u * R(w,v5,v6)),v7,v7))
    ]]></literal>
    <justification jstring="[para(7433(a,1),5100(a,1,3,2))].">
      <j1 rule="para" parents="7433 5100"/>
    </justification>
  </clause>

  <clause id="7436">
    <literal><![CDATA[
      a(x,y,(z * R(u,w,v5)) * v6) = a(x,y,(z * L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5669,a(flip),b,7434,a),flip(a)].">
      <j1 rule="hyper" parents="63 5669 7434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7437">
    <literal><![CDATA[
      L(x,x,y) * L(x \ a(y,x,x),z,u) = L(x \ L(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2136,a(flip),b,7319,a),flip(a)].">
      <j1 rule="hyper" parents="316 2136 7319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7438">
    <literal><![CDATA[
      x * (y \ (x * ((y \ x) \ 1))) = y * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(7389(a,1),7415(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7389 7415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7439">
    <literal><![CDATA[
      a(x,y,(z \ u) \ ((1 / z) * u)) = a(x,y,(z \ u) * ((1 / z) * u))
    ]]></literal>
    <justification jstring="[para(887(a,1),5722(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="887 5722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7440">
    <literal><![CDATA[
      a(x,y,(z \ u) \ ((1 / z) * u)) = a(x,y,(z \ u) * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5642,a(flip),b,7439,a),flip(a)].">
      <j1 rule="hyper" parents="316 5642 7439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7441">
    <literal><![CDATA[
      a(x,y,(z \ u) \ ((1 / z) * u)) = a(x,y,(z \ u) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5902,a(flip),b,7440,a),flip(a)].">
      <j1 rule="hyper" parents="316 5902 7440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7442">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * L(L(z,u,w),v5,v6)) = a(x,y,L(z * L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5893,a(flip),b,5724,a),flip(a)].">
      <j1 rule="hyper" parents="316 5893 5724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7443">
    <literal><![CDATA[
      (L(x,y,x) * (y * L(x,z,u))) \ (x * (y * L(x,z,u))) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(4917(a,1),5785(a,1,1))].">
      <j1 rule="para" parents="4917 5785"/>
    </justification>
  </clause>

  <clause id="7446">
    <literal><![CDATA[
      a(x,y,((z * u) \ (z * (w * u))) * (v5 * v5)) = a(x,y,L(w,u * (v5 * v5),z))
    ]]></literal>
    <justification jstring="[para(837(a,1),6034(a,1,3))].">
      <j1 rule="para" parents="837 6034"/>
    </justification>
  </clause>

  <clause id="7447">
    <literal><![CDATA[
      a(x,y,(z * ((u * (w \ 1)) * w)) * v5) = a(x,y,(z * L(u,w \ 1,w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,7436,a(flip),b,6070,a),flip(a)].">
      <j1 rule="hyper" parents="316 7436 6070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7448">
    <literal><![CDATA[
      L(x \ 1,x,y) * T(z,y / (y * x)) = T(z * ((y * x) \ y),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6184,a(flip),b,6195,a),flip(a)].">
      <j1 rule="hyper" parents="63 6184 6195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7449">
    <literal><![CDATA[
      (T(x,y) \ (z \ u)) \ L(T(x,y) \ (z \ u),x,z) = (((z * x) \ u) \ (x \ (z \ u))) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),6227(a,2,1,1,2))].">
      <j1 rule="para" parents="10 6227"/>
    </justification>
  </clause>

  <clause id="7450">
    <literal><![CDATA[
      a(x,y,((z * u) * (1 / w)) \ (z * (u * w))) = a(x,y,a(1 / w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6352,a(flip),b,6336,a)].">
      <j1 rule="hyper" parents="63 6352 6336"/>
    </justification>
  </clause>

  <clause id="7451">
    <literal><![CDATA[
      a(x,y,((z * u) * (w \ 1)) \ (z * (u * w))) = a(x,y,a(1 / w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5684,a(flip),b,7450,a)].">
      <j1 rule="hyper" parents="63 5684 7450"/>
    </justification>
  </clause>

  <clause id="7452">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ (z * (u * w))) = a(x,y,a(1 / w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5970,a(flip),b,7451,a)].">
      <j1 rule="hyper" parents="63 5970 7451"/>
    </justification>
  </clause>

  <clause id="7453">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * L((v5 * v5) \ v6,w,u))) = a(x,y,z \ (u * (w * v6)))
    ]]></literal>
    <justification jstring="[para(1120(a,2),6346(a,1,3,2,2))].">
      <j1 rule="para" parents="1120 6346"/>
    </justification>
  </clause>

  <clause id="7454">
    <literal><![CDATA[
      a(x,y,R(z,z,u * w) \ (w * u)) = a(x,y,(R(w,w,u) \ u) * z)
    ]]></literal>
    <justification jstring="[para(4802(a,1),6350(a,1,3,1))].">
      <j1 rule="para" parents="4802 6350"/>
    </justification>
  </clause>

  <clause id="7455">
    <literal><![CDATA[
      a(x,y,(R(z,z,u) \ u) * w) = a(x,y,(u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5856,a(flip),b,7454,a),flip(a)].">
      <j1 rule="hyper" parents="63 5856 7454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7456">
    <literal><![CDATA[
      a(x,y,(z \ L(u,z,z)) * w) = a(x,y,(u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6057,a(flip),b,7455,a)].">
      <j1 rule="hyper" parents="63 6057 7455"/>
    </justification>
  </clause>

  <clause id="7457">
    <literal><![CDATA[
      a(x,y,(z * L(z \ u,z,z)) * w) = a(x,y,((z * u) * z) * w)
    ]]></literal>
    <justification jstring="[para(1355(a,1),7456(a,1,3,1))].">
      <j1 rule="para" parents="1355 7456"/>
    </justification>
  </clause>

  <clause id="7458">
    <literal><![CDATA[
      a(x,y,(z * L(z \ u,z,z)) * w) = a(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,6131,a(flip),b,7457,a),flip(a)].">
      <j1 rule="hyper" parents="316 6131 7457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7459">
    <literal><![CDATA[
      (x * y) \ ((x * (L(z,u,w) \ z)) * y) = R(L(z,u,w) \ z,x,y)
    ]]></literal>
    <justification jstring="[para(6484(a,1),6548(a,2,1))].">
      <j1 rule="para" parents="6484 6548"/>
    </justification>
  </clause>

  <clause id="7460">
    <literal><![CDATA[
      R(L(x,y,z) \ x,L(x,y,z),u) = (L(x,y,z) * u) \ (x * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),7459(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 7459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7462">
    <literal><![CDATA[
      (L(x,y,z) * L(x,y,z)) \ (x * L(x,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,1382,a(flip),b,7460,a),flip(a)].">
      <j1 rule="hyper" parents="63 1382 7460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7463">
    <literal><![CDATA[
      (L(x,y,z) * L(x,y,z)) * (L(x,y,z) \ x) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,1382,a(flip),b,7460,a(flip))].">
      <j1 rule="hyper" parents="139 1382 7460"/>
    </justification>
  </clause>

  <clause id="7464">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ z) * v5) = a(x,y,(z * L(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(7462(a,1),5851(a,1,3,1))].">
      <j1 rule="para" parents="7462 5851"/>
    </justification>
  </clause>

  <clause id="7465">
    <literal><![CDATA[
      a(x,y,L(z * (L(u,w,v5) \ u),v6,v7)) = a(x,y,L(z * (u * L(u,w,v5)),v6,v7))
    ]]></literal>
    <justification jstring="[para(7463(a,1),7057(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="7463 7057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7466">
    <literal><![CDATA[
      a(x,y,(z * L(z,u \ 1,u)) * w) = a(x,y,a(u,u \ 1,z) * w)
    ]]></literal>
    <justification jstring="[para(703(a,1),7464(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="703 7464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7467">
    <literal><![CDATA[
      a(x,y,(z * L(z,u,u)) * w) = a(x,y,a(u,u,z) * w)
    ]]></literal>
    <justification jstring="[para(4952(a,1),7464(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4952 7464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7468">
    <literal><![CDATA[
      a(x,x \ 1,L(y,z,u) \ y) = a(x,x,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4952,a(flip),b,6670,a),flip(a)].">
      <j1 rule="hyper" parents="63 4952 6670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7469">
    <literal><![CDATA[
      a(x,x \ 1,y * L(y,z,u)) = a(x,x,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2652,a(flip),b,7468,a)].">
      <j1 rule="hyper" parents="63 2652 7468"/>
    </justification>
  </clause>

  <clause id="7470">
    <literal><![CDATA[
      a(x,x \ 1,y * L(y,z,u)) = a(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,2652,a(flip),b,7469,a),flip(a)].">
      <j1 rule="hyper" parents="316 2652 7469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7471">
    <literal><![CDATA[
      a(x,y,((z * (u / T(w,v5))) * v6) \ (z * (v6 * (w \ u)))) = a(x,y,a(v6,u / T(w,v5),z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6433,a(flip),b,6752,a)].">
      <j1 rule="hyper" parents="63 6433 6752"/>
    </justification>
  </clause>

  <clause id="7473">
    <literal><![CDATA[
      R(x,y,z) \ (a(u,w,x) * v5) = (R(x,y,z) \ v5) * a(u,w,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5347,a(flip),b,6881,a),flip(a)].">
      <j1 rule="hyper" parents="63 5347 6881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7474">
    <literal><![CDATA[
      x * (R(x,x,y) \ (a(z,u,x) * y)) = L(a(z,u,x) * y,x,x)
    ]]></literal>
    <justification jstring="[para(7473(a,2),7005(a,1,2))].">
      <j1 rule="para" parents="7473 7005"/>
    </justification>
  </clause>

  <clause id="7475">
    <literal><![CDATA[
      ((R(x,y,y) * (L(y,y,x) * z)) / z) \ (x * y) = a(L(x,y,y),L(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(316,a,4643,a(flip),b,7163,a),flip(a)].">
      <j1 rule="hyper" parents="316 4643 7163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7479">
    <literal><![CDATA[
      L(x,1 / x,(x \ 1) \ (x \ y)) = (y / x) \ ((y / ((x \ 1) \ 1)) / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,3218,a(flip),b,7250,a)].">
      <j1 rule="hyper" parents="63 3218 7250"/>
    </justification>
  </clause>

  <clause id="7480">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((v5 * w) * u))) = L(x,y,z \ R(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,1676,a(flip),b,7251,a),flip(a)].">
      <j1 rule="hyper" parents="316 1676 7251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7482">
    <literal><![CDATA[
      L(x,y,z \ R(u,w,v5)) = L(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,6767,a(flip),b,7480,a),flip(a)].">
      <j1 rule="hyper" parents="63 6767 7480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7483">
    <literal><![CDATA[
      L(x,y,z \ R(L(u,w,v5),v6,v7)) = L(x,y,z \ L(L(u,v6,v7),w,v5))
    ]]></literal>
    <justification jstring="[para(30(a,1),7482(a,2,3,2))].">
      <j1 rule="para" parents="30 7482"/>
    </justification>
  </clause>

  <clause id="7484">
    <literal><![CDATA[
      L(x,y,z \ L(z,u,u)) = L(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(2380(a,1),7482(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2380 7482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7485">
    <literal><![CDATA[
      L(x,y,L(z \ u,z,u \ R(w,v5,v6)) \ L(w,v5,v6)) = L(x,y,T((R(w,v5,v6) / u) * z,z \ u))
    ]]></literal>
    <justification jstring="[para(3740(a,1),7482(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3740 7482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7486">
    <literal><![CDATA[
      L(x,y,R(1 / z,z,L(u,w,v5)) \ L(u,w,v5)) = L(x,y,z * R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(4896(a,1),7482(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4896 7482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7488">
    <literal><![CDATA[
      L(x,y,z \ L(z,z,u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(7329(a,1),7482(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7329 7482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7489">
    <literal><![CDATA[
      x * L(y,x,x \ L(x,x,z)) = L(x * y,x,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1558,a(flip),b,7488,a)].">
      <j1 rule="hyper" parents="63 1558 7488"/>
    </justification>
  </clause>

  <clause id="7490">
    <literal><![CDATA[
      L(x,y,a(z,u,u) \ 1) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(7304(a,2),7488(a,1,3))].">
      <j1 rule="para" parents="7304 7488"/>
    </justification>
  </clause>

  <clause id="7491">
    <literal><![CDATA[
      L(x,y,z * ((z * u) \ u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7351,a,b,7490,a)].">
      <j1 rule="hyper" parents="63 7351 7490"/>
    </justification>
  </clause>

  <clause id="7493">
    <literal><![CDATA[
      L(x * y,x,a(x,x,z)) = x * L(y,x,a(x,x,z))
    ]]></literal>
    <justification jstring="[para(7488(a,1),7489(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7488 7489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7494">
    <literal><![CDATA[
      L(x,y,z \ L(R(u,w,v5),v6,v7)) = L(x,y,z \ L(L(u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(29(a,1),7483(a,1,3,2))].">
      <j1 rule="para" parents="29 7483"/>
    </justification>
  </clause>

  <clause id="7495">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ L(R(z,v5,v6),u,w)) = L(x,y,L(z \ L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(2138(a,1),7494(a,2,3))].">
      <j1 rule="para" parents="2138 7494"/>
    </justification>
  </clause>

  <clause id="7496">
    <literal><![CDATA[
      L(x,y,z * R(u,w,v5)) = L(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(369(a,1),7486(a,1,3)),flip(a)].">
      <j1 rule="para" parents="369 7486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7497">
    <literal><![CDATA[
      T(1 / (1 / x),y) * T(z,x) = K(x,y) * (z * (1 / (1 / x)))
    ]]></literal>
    <justification jstring="[para(2419(a,1),7256(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2419 7256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7499">
    <literal><![CDATA[
      ((a(x,y,z) \ u) \ w) * K(u,u \ w) = w / (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5367(a,1),7268(a,1,2))].">
      <j1 rule="para" parents="5367 7268"/>
    </justification>
  </clause>

  <clause id="7500">
    <literal><![CDATA[
      (x * y) / (a(z,u,w) \ y) = (a(z,u,w) \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3976,a(flip),b,7499,a),flip(a)].">
      <j1 rule="hyper" parents="63 3976 7499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7501">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ K(u,u \ 1) = 1 / (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3780,a(flip),b,7499,a)].">
      <j1 rule="hyper" parents="63 3780 7499"/>
    </justification>
  </clause>

  <clause id="7503">
    <literal><![CDATA[
      (a(x,y,z) \ (1 / (1 / u))) \ 1 = 1 / (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4031,a,b,7501,a)].">
      <j1 rule="hyper" parents="63 4031 7501"/>
    </justification>
  </clause>

  <clause id="7504">
    <literal><![CDATA[
      a(x,y,(((1 / z) * (u * z)) * w) * v5) = a(x,y,(L(u,z,z) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5552,a(flip),b,7431,a),flip(a)].">
      <j1 rule="hyper" parents="63 5552 7431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7506">
    <literal><![CDATA[
      a(x,y,(z * ((u * w) * w)) * v5) = a(x,y,(L(u,w,w) * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,6360,a(flip),b,7504,a)].">
      <j1 rule="hyper" parents="63 6360 7504"/>
    </justification>
  </clause>

  <clause id="7507">
    <literal><![CDATA[
      a(x,y,z * (((u * w) * w) * v5)) = a(x,y,(L(u,w,w) * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5623,a(flip),b,7506,a)].">
      <j1 rule="hyper" parents="63 5623 7506"/>
    </justification>
  </clause>

  <clause id="7508">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4938,a(flip),b,7443,a),flip(a)].">
      <j1 rule="hyper" parents="63 4938 7443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7510">
    <literal><![CDATA[
      a(x,y,z \ (x \ z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6745,a(flip),b,7508,a)].">
      <j1 rule="hyper" parents="63 6745 7508"/>
    </justification>
  </clause>

  <clause id="7514">
    <literal><![CDATA[
      a(x,y,L(T(z,u),u,w) * (v5 * v5)) = a(x,y,L(z,u * (v5 * v5),w))
    ]]></literal>
    <justification jstring="[para(247(a,1),7446(a,1,3,1))].">
      <j1 rule="para" parents="247 7446"/>
    </justification>
  </clause>

  <clause id="7515">
    <literal><![CDATA[
      a(x,y,L(T(z,u),u,w)) = a(x,y,L(z,u * (v5 * v5),w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5804,a(flip),b,7514,a)].">
      <j1 rule="hyper" parents="63 5804 7514"/>
    </justification>
  </clause>

  <clause id="7517">
    <literal><![CDATA[
      a(x,y,L(z,u * (w * w),v5)) = a(x,y,L(z,u,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5503,a(flip),b,7515,a),flip(a)].">
      <j1 rule="hyper" parents="63 5503 7515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7519">
    <literal><![CDATA[
      a(x,y,L(z,u \ 1,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(229(a,1),7517(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="229 7517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7520">
    <literal><![CDATA[
      a(x,y,L(z,u \ 1,w \ 1)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5761,a(flip),b,7519,a),flip(a)].">
      <j1 rule="hyper" parents="316 5761 7519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7521">
    <literal><![CDATA[
      a(x,y,L(L(z,u \ 1,w),v5,v6)) = a(x,y,L(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5952,a,b,7519,a)].">
      <j1 rule="hyper" parents="63 5952 7519"/>
    </justification>
  </clause>

  <clause id="7522">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * ((v5 * v5) \ v6)))) = a(x,y,z \ (u * (w * v6)))
    ]]></literal>
    <justification jstring="[para(100(a,1),7453(a,1,3,2))].">
      <j1 rule="para" parents="100 7453"/>
    </justification>
  </clause>

  <clause id="7523">
    <literal><![CDATA[
      L(x,x \ 1,(x \ 1) \ (x \ y)) = (y / x) \ ((y / ((x \ 1) \ 1)) / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,2673,a(flip),b,7479,a)].">
      <j1 rule="hyper" parents="63 2673 7479"/>
    </justification>
  </clause>

  <clause id="7524">
    <literal><![CDATA[
      (x / y) \ ((x / ((y \ 1) \ 1)) / (y \ 1)) = L(1 / (1 / y),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6589,a(flip),b,7523,a),flip(a)].">
      <j1 rule="hyper" parents="63 6589 7523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7525">
    <literal><![CDATA[
      (x / y) \ ((x / ((y \ 1) \ 1)) / (y \ 1)) = L(y,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,7180,a(flip),b,7524,a),flip(a)].">
      <j1 rule="hyper" parents="316 7180 7524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7526">
    <literal><![CDATA[
      (x / y) \ ((x / y) / (1 / y)) = L(y,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(4009(a,1),7525(a,1,2))].">
      <j1 rule="para" parents="4009 7525"/>
    </justification>
  </clause>

  <clause id="7527">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) / (1 / x)) = L(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3177,a(flip),b,7526,a)].">
      <j1 rule="hyper" parents="63 3177 7526"/>
    </justification>
  </clause>

  <clause id="7528">
    <literal><![CDATA[
      L((x \ 1) \ (y / x),z,u) \ (((x \ 1) \ (L(y,z,u) / x)) / (1 / (x \ 1))) = L(x \ 1,(x \ 1) \ 1,L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(1354(a,2),7527(a,1,1))].">
      <j1 rule="para" parents="1354 7527"/>
    </justification>
  </clause>

  <clause id="7529">
    <literal><![CDATA[
      (x * y) \ (K(z,u) * T(K(u,z) * x,y)) = (y * (K(u,z) * x)) \ (K(u,z) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3009,a(flip),b,2921,a)].">
      <j1 rule="hyper" parents="63 3009 2921"/>
    </justification>
  </clause>

  <clause id="7531">
    <literal><![CDATA[
      L(x,y,z \ ((u \ 1) \ (w * (v5 * (u \ 1))))) = L(x,y,z \ (u \ (w * (v5 * u))))
    ]]></literal>
    <justification jstring="[hyper(316,a,3243,a(flip),b,3253,a),flip(a)].">
      <j1 rule="hyper" parents="316 3243 3253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7534">
    <literal><![CDATA[
      x * ((1 / x) * K(y \ (1 / x),x * y)) = ((x * y) \ K(x,x \ 1)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3774,a(flip),b,4286,a)].">
      <j1 rule="hyper" parents="63 3774 4286"/>
    </justification>
  </clause>

  <clause id="7536">
    <literal><![CDATA[
      (1 / L(x,y,z)) * ((x \ u) * x) = T((1 / L(x,y,z)) * u,x)
    ]]></literal>
    <justification jstring="[para(4409(a,1),4312(a,1,2))].">
      <j1 rule="para" parents="4409 4312"/>
    </justification>
  </clause>

  <clause id="7538">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ (a(w,v5,v6) \ v7)) * (a(w,v5,v6) \ v7) = ((v7 / a(w,v5,v6)) / u) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,3251,a(flip),b,4355,a),flip(a)].">
      <j1 rule="hyper" parents="316 3251 4355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7539">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) \ ((x / y) * L(y,z,u)) = a(y,y \ L(y,z,u),y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5066,a(flip),b,4388,a)].">
      <j1 rule="hyper" parents="63 5066 4388"/>
    </justification>
  </clause>

  <clause id="7540">
    <literal><![CDATA[
      (x * y) \ (a(z,u,z) \ (x * (a(z,u,z) * (y * w)))) = L(w,a(z,u,z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5409,a(flip),b,4544,a)].">
      <j1 rule="hyper" parents="63 5409 4544"/>
    </justification>
  </clause>

  <clause id="7541">
    <literal><![CDATA[
      (a(x,y,x) * ((z * u) * w)) / (a(x,y,x) * (u * w)) = R(z,a(x,y,x) * u,w)
    ]]></literal>
    <justification jstring="[para(5403(a,1),4549(a,1,1))].">
      <j1 rule="para" parents="5403 4549"/>
    </justification>
  </clause>

  <clause id="7542">
    <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(4540(a,1),4552(a,1,2))].">
      <j1 rule="para" parents="4540 4552"/>
    </justification>
  </clause>

  <clause id="7543">
    <literal><![CDATA[
      L(x,y,z) * R(u,x,L(x,y,z) * (x \ 1)) = (u * x) * (x \ L(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(25(a,2),4674(a,2,2,2))].">
      <j1 rule="para" parents="25 4674"/>
    </justification>
  </clause>

  <clause id="7544">
    <literal><![CDATA[
      T((x * y) * ((x / (y \ 1)) \ 1),x * y) = (x * y) * ((x / (y \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2894,a(flip),b,4901,a)].">
      <j1 rule="hyper" parents="63 2894 4901"/>
    </justification>
  </clause>

  <clause id="7545">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (u * L(x \ 1,y,z)) = R(u / x,x,L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(1064(a,1),4990(a,1,1))].">
      <j1 rule="para" parents="1064 4990"/>
    </justification>
  </clause>

  <clause id="7546">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (u * L(x \ 1,y,z)) = R(u / x,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,1713,a(flip),b,7545,a),flip(a)].">
      <j1 rule="hyper" parents="316 1713 7545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7548">
    <literal><![CDATA[
      L(x \ y,x,z \ L(z,u,w)) = (x * (z \ L(z,u,w))) \ (y * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5025,a(flip),b,5028,a),flip(a)].">
      <j1 rule="hyper" parents="316 5025 5028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7549">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * (u * w)) / (w * (a(x,y,z) \ 1)) = R(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,1033,a(flip),b,5035,a),flip(a)].">
      <j1 rule="hyper" parents="316 1033 5035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7550">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * (u * w)) / ((a(x,y,z) \ 1) * w) = R(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(5006(a,2),7549(a,1,2))].">
      <j1 rule="para" parents="5006 7549"/>
    </justification>
  </clause>

  <clause id="7551">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * w)) / (w * (x \ L(x,y,z))) = R(u,w,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,1718,a(flip),b,5037,a),flip(a)].">
      <j1 rule="hyper" parents="316 1718 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7552">
    <literal><![CDATA[
      (1 / x) \ (y * (x \ L(x,z,u))) = ((1 / x) \ y) * (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[para(1066(a,1),5159(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1066 5159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7553">
    <literal><![CDATA[
      L(a(x,x,y),z,u) \ a(x,x,y) = a(x,x,y) \ a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,5099,a(flip),b,5185,a),flip(a)].">
      <j1 rule="hyper" parents="133 5099 5185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7554">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(y,z,z)) = a(z,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4952,a(flip),b,7553,a),flip(a)].">
      <j1 rule="hyper" parents="63 4952 7553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7559">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ (w * (v5 * (u \ 1))))) = a(x,y,z \ (u \ (w * (v5 * u))))
    ]]></literal>
    <justification jstring="[hyper(316,a,5497,a(flip),b,5639,a),flip(a)].">
      <j1 rule="hyper" parents="316 5497 5639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7560">
    <literal><![CDATA[
      a(x,y,(((z * (u * u)) \ w) * v5) * v6) = a(x,y,((z \ (w / (u * u))) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5547,a(flip),b,5791,a)].">
      <j1 rule="hyper" parents="63 5547 5791"/>
    </justification>
  </clause>

  <clause id="7561">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w * (v5 * v5)) * v6))) = a(x,y,(z \ (u \ (v6 * w))) * (v5 * v5))
    ]]></literal>
    <justification jstring="[para(637(a,1),5922(a,2,3))].">
      <j1 rule="para" parents="637 5922"/>
    </justification>
  </clause>

  <clause id="7562">
    <literal><![CDATA[
      a(x,y,z \ (((u * (w * w)) \ v5) \ v6)) = a(x,y,z \ ((u \ (v5 / (w * w))) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5629,a(flip),b,5929,a)].">
      <j1 rule="hyper" parents="63 5629 5929"/>
    </justification>
  </clause>

  <clause id="7564">
    <literal><![CDATA[
      a(x,y,(z \ ((u / (w * w)) \ v5)) * v6) = a(x,y,(z \ (u \ (v5 * (w * w)))) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5694,a(flip),b,5949,a)].">
      <j1 rule="hyper" parents="63 5694 5949"/>
    </justification>
  </clause>

  <clause id="7565">
    <literal><![CDATA[
      a(x,y,L((z \ (u \ w)) * (u * u),v5,v6)) = a(x,y,L(z \ (w / (u \ 1)),v5,v6))
    ]]></literal>
    <justification jstring="[para(388(a,1),5951(a,1,3,1))].">
      <j1 rule="para" parents="388 5951"/>
    </justification>
  </clause>

  <clause id="7566">
    <literal><![CDATA[
      a(x,y,z * (u * ((w / (v5 * v5)) * v6))) = a(x,y,(u * (w * v6)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6019,a(flip),b,5980,a),flip(a)].">
      <j1 rule="hyper" parents="63 6019 5980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7568">
    <literal><![CDATA[
      a(x,y,(z * ((u / (w * w)) * v5)) * v6) = a(x,y,(z * (u * v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,7566,a)].">
      <j1 rule="hyper" parents="63 5469 7566"/>
    </justification>
  </clause>

  <clause id="7569">
    <literal><![CDATA[
      a(x,y,z * (u * ((w * (v5 \ 1)) * v6))) = a(x,y,(u * ((w * v5) * v6)) * z)
    ]]></literal>
    <justification jstring="[para(562(a,1),7566(a,1,3,2,2,1))].">
      <j1 rule="para" parents="562 7566"/>
    </justification>
  </clause>

  <clause id="7571">
    <literal><![CDATA[
      a(x,y,(z * ((u * (w \ 1)) * v5)) * v6) = a(x,y,(z * ((u * w) * v5)) * v6)
    ]]></literal>
    <justification jstring="[para(562(a,1),7568(a,1,3,1,2,1))].">
      <j1 rule="para" parents="562 7568"/>
    </justification>
  </clause>

  <clause id="7572">
    <literal><![CDATA[
      a(x,y,z * (u * ((w * (v5 \ 1)) * v6))) = a(x,y,(u * (v6 * (w * v5))) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5691,a,b,7569,a),flip(a)].">
      <j1 rule="hyper" parents="316 5691 7569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7573">
    <literal><![CDATA[
      a(x,y,(z * L(u,w \ 1,w)) * v5) = a(x,y,(z * ((u * w) * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,7447,a(flip),b,7571,a)].">
      <j1 rule="hyper" parents="63 7447 7571"/>
    </justification>
  </clause>

  <clause id="7574">
    <literal><![CDATA[
      a(x,y,(z * L(u,w \ 1,w)) * v5) = a(x,y,(L(u,w,w) * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,7506,a(flip),b,7573,a),flip(a)].">
      <j1 rule="hyper" parents="316 7506 7573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7575">
    <literal><![CDATA[
      a(x,y,(L(z,u \ 1,u) * w) * v5) = a(x,y,(L(z,u,u) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5542,a,b,7574,a)].">
      <j1 rule="hyper" parents="63 5542 7574"/>
    </justification>
  </clause>

  <clause id="7576">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,u) * w) = a(x,y,(L(u,z,z) * u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,7466,a(flip),b,7574,a)].">
      <j1 rule="hyper" parents="63 7466 7574"/>
    </justification>
  </clause>

  <clause id="7578">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,u) * w) = a(x,y,(u * L(u,z,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,5542,a,b,7576,a),flip(a)].">
      <j1 rule="hyper" parents="316 5542 7576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7579">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,u) * w) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,7467,a(flip),b,7578,a),flip(a)].">
      <j1 rule="hyper" parents="316 7467 7578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7580">
    <literal><![CDATA[
      a(x,y,z * ((((u \ 1) * w) * v5) * v6)) = a(x,y,(v6 * (v5 * (w * u))) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6002,a,b,7572,a)].">
      <j1 rule="hyper" parents="63 6002 7572"/>
    </justification>
  </clause>

  <clause id="7581">
    <literal><![CDATA[
      a(x,y,(z * (((u \ 1) * w) * v5)) * v6) = a(x,y,(z * (v5 * (w * u))) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5623,a,b,7580,a)].">
      <j1 rule="hyper" parents="63 5623 7580"/>
    </justification>
  </clause>

  <clause id="7583">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x \ L(x,w,v5)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(6159(a,1),6161(a,2,2))].">
      <j1 rule="para" parents="6159 6161"/>
    </justification>
  </clause>

  <clause id="7588">
    <literal><![CDATA[
      a(x,y,(((z * (u * u)) * w) \ v5) \ v6) = a(x,y,((w * z) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,6708,a(flip),b,6281,a),flip(a)].">
      <j1 rule="hyper" parents="316 6708 6281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7590">
    <literal><![CDATA[
      a(x,y,((z * (u \ 1)) \ w) \ v5) = a(x,y,((u * z) \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(229(a,1),7588(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="229 7588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7593">
    <literal><![CDATA[
      R(x,y,(((z * z) * (z \ u)) \ w) * v5) = R(x,y,((u / (z \ 1)) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,4727,a(flip),b,6283,a),flip(a)].">
      <j1 rule="hyper" parents="63 4727 6283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7595">
    <literal><![CDATA[
      R(x,y,(((z * z) * (z \ u)) \ w) * v5) = R(x,y,(((z \ 1) \ u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,4729,a(flip),b,7593,a),flip(a)].">
      <j1 rule="hyper" parents="316 4729 7593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7596">
    <literal><![CDATA[
      R(x,y,(((z \ 1) \ u) \ w) * v5) = R(x,y,v5 * ((z \ u) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6713,a(flip),b,7595,a),flip(a)].">
      <j1 rule="hyper" parents="63 6713 7595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7598">
    <literal><![CDATA[
      ((x \ y) * x) * L(((x \ y) * x) \ z,u,w) = y * L(y \ z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),6284(a,2,2,1,1))].">
      <j1 rule="para" parents="10 6284"/>
    </justification>
  </clause>

  <clause id="7599">
    <literal><![CDATA[
      (x \ y) * (x * L(x \ ((x \ y) \ z),u,w)) = y * L(y \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,879,a(flip),b,7598,a)].">
      <j1 rule="hyper" parents="63 879 7598"/>
    </justification>
  </clause>

  <clause id="7600">
    <literal><![CDATA[
      T((x \ y) * L((x \ y) \ z,u,w),x) = x \ (y * L(y \ (z * x),u,w))
    ]]></literal>
    <justification jstring="[hyper(390,a,7598,a(flip),b,1528,a(flip))].">
      <j1 rule="hyper" parents="390 7598 1528"/>
    </justification>
  </clause>

  <clause id="7602">
    <literal><![CDATA[
      ((x * x) \ y) * L(((x * x) \ y) \ z,u,w) = y * L(y \ z,u,w)
    ]]></literal>
    <justification jstring="[para(1113(a,1),7599(a,1,2))].">
      <j1 rule="para" parents="1113 7599"/>
    </justification>
  </clause>

  <clause id="7604">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ L(u,a(x,y,z),a(x,y,z)) = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(2273(a,1),6324(a,2,2))].">
      <j1 rule="para" parents="2273 6324"/>
    </justification>
  </clause>

  <clause id="7608">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * (u * w)) / ((L(x,y,z) \ x) * w) = R(u,w,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(6496(a,2),6543(a,1,1))].">
      <j1 rule="para" parents="6496 6543"/>
    </justification>
  </clause>

  <clause id="7609">
    <literal><![CDATA[
      a(x,y,((z * (L(z,u,w) \ z)) * v5) * v6) = a(x,y,v6 * (v5 * L(z \ 1,u,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5705,a(flip),b,6604,a),flip(a)].">
      <j1 rule="hyper" parents="316 5705 6604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7610">
    <literal><![CDATA[
      a(x,y,z * ((u * (L(u,w,v5) \ u)) * v6)) = a(x,y,z * (v6 * L(u \ 1,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5705,a(flip),b,6605,a),flip(a)].">
      <j1 rule="hyper" parents="316 5705 6605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7611">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * L(u,x,L(x,y,z) \ x) = x * ((L(x,y,z) \ x) * u)
    ]]></literal>
    <justification jstring="[hyper(316,a,6661,a(flip),b,6608,a),flip(a)].">
      <j1 rule="hyper" parents="316 6661 6608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7612">
    <literal><![CDATA[
      (x * (L(1 / y,z,u) \ 1)) / y = (x * (L(y,z,u) \ 1)) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(6726(a,1),6610(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6726 6610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7613">
    <literal><![CDATA[
      (a(x,x,y) * (z * L(y,x,x))) \ (z * y) = a(L(y,x,x) \ y,L(y,x,x),z)
    ]]></literal>
    <justification jstring="[para(5448(a,1),6640(a,1,1))].">
      <j1 rule="para" parents="5448 6640"/>
    </justification>
  </clause>

  <clause id="7614">
    <literal><![CDATA[
      (a(x,x,y) * (z * L(y,x,x))) \ (z * y) = a(a(x,x,y),L(y,x,x),z)
    ]]></literal>
    <justification jstring="[para(4952(a,1),7613(a,2,1))].">
      <j1 rule="para" parents="4952 7613"/>
    </justification>
  </clause>

  <clause id="7615">
    <literal><![CDATA[
      R(a(x,y,z) / u,L(u,w,v5),u \ a(x,y,z)) = T(a(x,y,z) / u,L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,4680,a(flip),b,6641,a)].">
      <j1 rule="hyper" parents="63 4680 6641"/>
    </justification>
  </clause>

  <clause id="7616">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (x * T(u,x))) \ (u * L(x,y,z)) = a(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(1272(a,1),6829(a,1,1,1))].">
      <j1 rule="para" parents="1272 6829"/>
    </justification>
  </clause>

  <clause id="7618">
    <literal><![CDATA[
      L(x,y,z) \ (a(u,x,a(w,v5,x)) * v6) = (L(x,y,z) \ v6) * a(u,x,a(w,v5,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,2296,a,b,7017,a)].">
      <j1 rule="hyper" parents="63 2296 7017"/>
    </justification>
  </clause>

  <clause id="7619">
    <literal><![CDATA[
      a(x,y,z * ((u \ L(u,w,v5)) * v6)) = a(x,y,z * ((u * L(u,w,v5)) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5906,a(flip),b,7059,a),flip(a)].">
      <j1 rule="hyper" parents="63 5906 7059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7620">
    <literal><![CDATA[
      a(x,y,z \ (L(u \ 1,w,v5) * v6)) = a(x,y,z \ (L(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(1127(a,1),7086(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="1127 7086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7621">
    <literal><![CDATA[
      ((x * (y * y)) \ L(x,z,u)) * (y * y) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6202,a(flip),b,7114,a),flip(a)].">
      <j1 rule="hyper" parents="63 6202 7114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7623">
    <literal><![CDATA[
      ((x * y) * T(z,y)) \ (x * (z * y)) = (x * y) \ ((x * (y * z)) / z)
    ]]></literal>
    <justification jstring="[para(4048(a,1),7135(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4048 7135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7625">
    <literal><![CDATA[
      R(x,y,((z * u) * w) \ (z * (w * u))) = R(x,y,(z * u) \ (w \ (z * (u * w))))
    ]]></literal>
    <justification jstring="[hyper(316,a,4695,a(flip),b,7137,a),flip(a)].">
      <j1 rule="hyper" parents="316 4695 7137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7626">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ ((u * w) * z)) = a(x,y,(z * u) \ (w \ (z * (u * w))))
    ]]></literal>
    <justification jstring="[hyper(316,a,5497,a(flip),b,7138,a),flip(a)].">
      <j1 rule="hyper" parents="316 5497 7138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7627">
    <literal><![CDATA[
      (x \ 1) * (x * (L(x,y,z) \ u)) = x * (L(x,y,z) \ ((x \ 1) * u))
    ]]></literal>
    <justification jstring="[para(7154(a,1),7189(a,1,2))].">
      <j1 rule="para" parents="7154 7189"/>
    </justification>
  </clause>

  <clause id="7628">
    <literal><![CDATA[
      (x \ 1) * (x * (L(x,y,z) \ u)) = L(x,y,z) \ L(u,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,1141,a(flip),b,7627,a),flip(a)].">
      <j1 rule="hyper" parents="316 1141 7627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7629">
    <literal><![CDATA[
      L(x,y,y \ 1) \ L(K(y,y \ 1),x \ 1,x) = (x \ 1) * (x * (((y \ 1) * (y * x)) \ 1))
    ]]></literal>
    <justification jstring="[para(2452(a,1),7628(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2452 7628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7630">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) * L(x \ 1,u,w) = a(x,x,a(z,y,y)) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(7280(a,2),7362(a,2,1))].">
      <j1 rule="para" parents="7280 7362"/>
    </justification>
  </clause>

  <clause id="7631">
    <literal><![CDATA[
      a(x,y,(L(R(z,u,w),v5,v6) * v7) * v8) = a(x,y,(L(L(z,u,w),v5,v6) * v7) * v8)
    ]]></literal>
    <justification jstring="[para(29(a,1),7426(a,1,3,1,1))].">
      <j1 rule="para" parents="29 7426"/>
    </justification>
  </clause>

  <clause id="7632">
    <literal><![CDATA[
      ((x * y) \ T(x * K(z,u),y)) * K(u,z) = (y * (K(z,u) * x)) \ (K(z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4907,a(flip),b,7529,a)].">
      <j1 rule="hyper" parents="63 4907 7529"/>
    </justification>
  </clause>

  <clause id="7634">
    <literal><![CDATA[
      x \ (((x / y) * L(y,z,u)) / (y \ L(y,z,u))) = a(y,y \ L(y,z,u),y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7238,a(flip),b,7539,a)].">
      <j1 rule="hyper" parents="63 7238 7539"/>
    </justification>
  </clause>

  <clause id="7635">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = (w * u) \ (w * (u * x))
    ]]></literal>
    <justification jstring="[para(5396(a,1),7540(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5396 7540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7636">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,18,a,b,7635,a),flip(a)].">
      <j1 rule="hyper" parents="316 18 7635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7638">
    <literal><![CDATA[
      L(x,R(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(4545(a,1),7636(a,1,2))].">
      <j1 rule="para" parents="4545 7636"/>
    </justification>
  </clause>

  <clause id="7639">
    <literal><![CDATA[
      L(x,L(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(4934(a,1),7636(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4934 7636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7641">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(1040(a,1),7638(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1040 7638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7643">
    <literal><![CDATA[
      (x * L(y,z,y)) * L(u,y,x) = x * (L(y,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,7639,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="139 7639 18"/>
    </justification>
  </clause>

  <clause id="7644">
    <literal><![CDATA[
      L(x,y \ (y * z),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(353(a,1),7639(a,1,2))].">
      <j1 rule="para" parents="353 7639"/>
    </justification>
  </clause>

  <clause id="7645">
    <literal><![CDATA[
      L(1 / x,x \ 1,y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1452,a(flip),b,7641,a),flip(a)].">
      <j1 rule="hyper" parents="63 1452 7641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7647">
    <literal><![CDATA[
      L(1 / x,x \ 1,y) * K(y / x,z) = y \ T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,7645,a,b,3898,a)].">
      <j1 rule="hyper" parents="138 7645 3898"/>
    </justification>
  </clause>

  <clause id="7648">
    <literal><![CDATA[
      L(1 / (x \ y),(x \ y) \ 1,y) = y \ x
    ]]></literal>
    <justification jstring="[para(80(a,1),7645(a,2,2))].">
      <j1 rule="para" parents="80 7645"/>
    </justification>
  </clause>

  <clause id="7649">
    <literal><![CDATA[
      1 / (R(x,y,z) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,7392,a,b,7648,a),flip(a)].">
      <j1 rule="hyper" parents="41 7392 7648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7650">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(204,a,7649,a)].">
      <j1 rule="hyper" parents="204 7649"/>
    </justification>
  </clause>

  <clause id="7651">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ 1 = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3514,a(flip),b,7649,a)].">
      <j1 rule="hyper" parents="63 3514 7649"/>
    </justification>
  </clause>

  <clause id="7652">
    <literal><![CDATA[
      1 / (x \ R(x,y,z)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(209,a,7649,a(flip),b,3514,a(flip))].">
      <j1 rule="hyper" parents="209 7649 3514"/>
    </justification>
  </clause>

  <clause id="7653">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) * u = (R(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[para(7649(a,1),207(a,1,1,1))].">
      <j1 rule="para" parents="7649 207"/>
    </justification>
  </clause>

  <clause id="7654">
    <literal><![CDATA[
      R(x,y,y \ 1) \ x = a(x,y,y \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(706(a,1),7650(a,1,1)),flip(a)].">
      <j1 rule="para" parents="706 7650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7655">
    <literal><![CDATA[
      (1 \ (L(x \ R(x,y,z),u,w) * ((x \ R(x,y,z)) \ 1))) \ 1 = L(1 \ (R(x,y,z) \ x),u,w) \ (1 \ ((x \ R(x,y,z)) \ 1))
    ]]></literal>
    <justification jstring="[para(7650(a,1),1907(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7650 1907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7656">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x * (R(x,y,z) \ L(x \ R(x,y,z),u,w))) = 1 * L(1 \ ((x \ R(x,y,z)) \ 1),u,w)
    ]]></literal>
    <justification jstring="[para(7650(a,2),2016(a,2,2,1,2))].">
      <j1 rule="para" parents="7650 2016"/>
    </justification>
  </clause>

  <clause id="7657">
    <literal><![CDATA[
      R(x,y,y) \ x = a(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[para(2380(a,1),7650(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2380 7650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7658">
    <literal><![CDATA[
      R(x,x,y) \ x = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(7329(a,1),7650(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7329 7650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7659">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x \ (R(x,y,z) * L(R(x,y,z) \ x,u,w))) = 1 * L(1 \ ((x \ R(x,y,z)) \ 1),u,w)
    ]]></literal>
    <justification jstring="[para(7650(a,1),5134(a,1,1))].">
      <j1 rule="para" parents="7650 5134"/>
    </justification>
  </clause>

  <clause id="7660">
    <literal><![CDATA[
      R(x,y,y) \ x = y \ L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,7304,a(flip),b,7657,a),flip(a)].">
      <j1 rule="hyper" parents="316 7304 7657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7661">
    <literal><![CDATA[
      R(x,y,y) * (y \ L(y,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,7304,a(flip),b,7657,a)].">
      <j1 rule="hyper" parents="139 7304 7657"/>
    </justification>
  </clause>

  <clause id="7663">
    <literal><![CDATA[
      (R(x,y,y) \ x) * K(z,u) = a(x,y,y) \ K(z,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,7657,a,b,3803,a)].">
      <j1 rule="hyper" parents="138 7657 3803"/>
    </justification>
  </clause>

  <clause id="7664">
    <literal><![CDATA[
      a(x,x \ y,x \ y) \ 1 = (y * ((x \ y) \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(568(a,1),7657(a,1,1)),flip(a)].">
      <j1 rule="para" parents="568 7657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7666">
    <literal><![CDATA[
      R(x,x,y) \ x = y \ L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,5088,a(flip),b,7658,a),flip(a)].">
      <j1 rule="hyper" parents="316 5088 7658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7671">
    <literal><![CDATA[
      (x \ L(x,y,y)) * R(y,y,x) = y
    ]]></literal>
    <justification jstring="[hyper(138,a,7666,a(flip),b,1772,a)].">
      <j1 rule="hyper" parents="138 7666 1772"/>
    </justification>
  </clause>

  <clause id="7672">
    <literal><![CDATA[
      L((x \ L(x,y,y)) \ z,R(y,y,x) \ y,R(y,y,x)) = y \ (R(y,y,x) * z)
    ]]></literal>
    <justification jstring="[para(7666(a,1),475(a,1,1,1))].">
      <j1 rule="para" parents="7666 475"/>
    </justification>
  </clause>

  <clause id="7673">
    <literal><![CDATA[
      x * L(y,R(x,x,z),z \ L(z,x,x)) = (x / R(x,x,z)) * (R(x,x,z) * y)
    ]]></literal>
    <justification jstring="[para(7666(a,1),1606(a,1,2,3))].">
      <j1 rule="para" parents="7666 1606"/>
    </justification>
  </clause>

  <clause id="7675">
    <literal><![CDATA[
      R(x,x,y) * ((y \ L(y,x,x)) * L((y \ L(y,x,x)) \ z,R(x,x,y),y \ L(y,x,x))) = (y \ L(y,x,x)) * (R(x,x,y) * (x \ (R(x,x,y) * z)))
    ]]></literal>
    <justification jstring="[para(7671(a,1),6230(a,2,2,2,1))].">
      <j1 rule="para" parents="7671 6230"/>
    </justification>
  </clause>

  <clause id="7676">
    <literal><![CDATA[
      (L(R(x,y,z),u,w) \ L(x,u,w)) \ 1 = L(x,u,w) \ R(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(29(a,1),7651(a,1,1,1))].">
      <j1 rule="para" parents="29 7651"/>
    </justification>
  </clause>

  <clause id="7677">
    <literal><![CDATA[
      (R(R(x,y,z),u,w) \ R(x,y,z)) \ 1 = R(x,y,z) \ R(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(31(a,1),7651(a,2,2))].">
      <j1 rule="para" parents="31 7651"/>
    </justification>
  </clause>

  <clause id="7678">
    <literal><![CDATA[
      R(x,y,y \ 1) \ x = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,7349,a(flip),b,7654,a),flip(a)].">
      <j1 rule="hyper" parents="316 7349 7654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7679">
    <literal><![CDATA[
      R(x,y,x \ (y \ x)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(39,a,6719,a,b,7678,a)].">
      <j1 rule="hyper" parents="39 6719 7678"/>
    </justification>
  </clause>

  <clause id="7680">
    <literal><![CDATA[
      R(x,y,x \ (y \ x)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1033,a(flip),b,7679,a),flip(a)].">
      <j1 rule="hyper" parents="316 1033 7679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7681">
    <literal><![CDATA[
      R(x,y,y) \ ((x * y) * (x \ (y \ x))) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(7680(a,1),199(a,1,1))].">
      <j1 rule="para" parents="7680 199"/>
    </justification>
  </clause>

  <clause id="7683">
    <literal><![CDATA[
      a(x,y,y) \ K(x,z) = R(x,y,y) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3846,a(flip),b,7663,a),flip(a)].">
      <j1 rule="hyper" parents="63 3846 7663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7684">
    <literal><![CDATA[
      a(x,y,y) \ K(x,y) = ((y * x) * (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,3401,a(flip),b,7683,a),flip(a)].">
      <j1 rule="hyper" parents="316 3401 7683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7685">
    <literal><![CDATA[
      ((x * y) * (x \ 1)) \ y = x * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7398,a(flip),b,7684,a),flip(a)].">
      <j1 rule="hyper" parents="63 7398 7684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7686">
    <literal><![CDATA[
      ((L(x,y,z) * u) * (u \ 1)) \ L(T(x,u),y,z) = u * ((u * L(T(x,u),y,z)) \ L(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(251(a,1),7685(a,1,1,1))].">
      <j1 rule="para" parents="251 7685"/>
    </justification>
  </clause>

  <clause id="7687">
    <literal><![CDATA[
      ((R(x,y,z) * u) * (u \ 1)) \ R(T(x,u),y,z) = u * ((u * R(T(x,u),y,z)) \ R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(252(a,1),7685(a,1,1,1))].">
      <j1 rule="para" parents="252 7685"/>
    </justification>
  </clause>

  <clause id="7688">
    <literal><![CDATA[
      R(x \ 1,x * y,x * ((x * y) \ y)) \ y = (x * y) * (((x \ 1) * (x * y)) \ y)
    ]]></literal>
    <justification jstring="[para(7685(a,1),4768(a,1,1,3))].">
      <j1 rule="para" parents="7685 4768"/>
    </justification>
  </clause>

  <clause id="7689">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,L(x,y,z),z * L(y,u,y)) = (z * (L(y,u,y) * x)) \ (z * L(y,u,y))
    ]]></literal>
    <justification jstring="[para(7643(a,1),232(a,2,1))].">
      <j1 rule="para" parents="7643 232"/>
    </justification>
  </clause>

  <clause id="7690">
    <literal><![CDATA[
      (x * ((y \ x) \ 1)) \ y = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7341,a(flip),b,7664,a),flip(a)].">
      <j1 rule="hyper" parents="63 7341 7664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7691">
    <literal><![CDATA[
      ((x / y) \ x) * (x \ (x / y)) = (x * (y \ 1)) \ (x / y)
    ]]></literal>
    <justification jstring="[para(83(a,1),7690(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 7690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7693">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x / y) = y * (x \ (x / y))
    ]]></literal>
    <justification jstring="[hyper(558,a,7691,a),flip(a)].">
      <j1 rule="hyper" parents="558 7691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7695">
    <literal><![CDATA[
      R(x / y,y,x \ (y \ x)) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(39,a,4759,a,b,7693,a)].">
      <j1 rule="hyper" parents="39 4759 7693"/>
    </justification>
  </clause>

  <clause id="7696">
    <literal><![CDATA[
      (x * (y \ 1)) * (y * (x \ (y \ x))) = y \ x
    ]]></literal>
    <justification jstring="[hyper(138,a,7695,a(flip),b,349,a(flip))].">
      <j1 rule="hyper" parents="138 7695 349"/>
    </justification>
  </clause>

  <clause id="7697">
    <literal><![CDATA[
      (x * (y \ 1)) \ (y \ x) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(7695(a,1),490(a,1,1))].">
      <j1 rule="para" parents="7695 490"/>
    </justification>
  </clause>

  <clause id="7698">
    <literal><![CDATA[
      (x \ y) \ R(y * (x \ 1),x * (y \ (x \ y)),x * (y \ (x \ y))) = (x * (y \ (x \ y))) \ 1
    ]]></literal>
    <justification jstring="[para(7696(a,1),570(a,1,1))].">
      <j1 rule="para" parents="7696 570"/>
    </justification>
  </clause>

  <clause id="7699">
    <literal><![CDATA[
      a(x,y,((z * u) \ (u \ z)) * w) = a(x,y,(u * (z \ (u \ z))) * w)
    ]]></literal>
    <justification jstring="[para(7697(a,1),7046(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="7697 7046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7700">
    <literal><![CDATA[
      L((1 / x) * K(y / x,z),x \ 1,y) = y \ T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4837,a,b,7647,a)].">
      <j1 rule="hyper" parents="63 4837 7647"/>
    </justification>
  </clause>

  <clause id="7701">
    <literal><![CDATA[
      (L(R(x,y,z),u,w) \ L(x,u,w)) \ 1 = L(x,u,w) \ L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29(a,1),7676(a,2,2))].">
      <j1 rule="para" parents="29 7676"/>
    </justification>
  </clause>

  <clause id="7702">
    <literal><![CDATA[
      L((x \ L(x,y,y)) \ z,R(y,y,x) \ y,L(y,y,x)) = y \ (R(y,y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4628,a(flip),b,7672,a)].">
      <j1 rule="hyper" parents="63 4628 7672"/>
    </justification>
  </clause>

  <clause id="7703">
    <literal><![CDATA[
      R(R(x,y,z),y * z,a(u,w,u)) = R(x,a(u,w,u) * y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2515,a(flip),b,7541,a)].">
      <j1 rule="hyper" parents="63 2515 7541"/>
    </justification>
  </clause>

  <clause id="7704">
    <literal><![CDATA[
      R(x,a(y,z,y) * u,w) = R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(5387,a,7703,a),flip(a)].">
      <j1 rule="hyper" parents="5387 7703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7706">
    <literal><![CDATA[
      R(x,R(y,z,y),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(4545(a,1),7704(a,1,2))].">
      <j1 rule="para" parents="4545 7704"/>
    </justification>
  </clause>

  <clause id="7707">
    <literal><![CDATA[
      R(x,L(y,z,y),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(4934(a,1),7704(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4934 7704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7709">
    <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(63,a,460,a(flip),b,7542,a)].">
      <j1 rule="hyper" parents="63 460 7542"/>
    </justification>
  </clause>

  <clause id="7710">
    <literal><![CDATA[
      L(x,y,a(z,u,z) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(4542,a,7709,a),flip(a)].">
      <j1 rule="hyper" parents="4542 7709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7712">
    <literal><![CDATA[
      L(x,y,a(z,u,z) \ w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),7710(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 7710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7713">
    <literal><![CDATA[
      L(x,y,z \ a(u,w,u)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(5395(a,1),7710(a,1,3))].">
      <j1 rule="para" parents="5395 7710"/>
    </justification>
  </clause>

  <clause id="7714">
    <literal><![CDATA[
      L(x,y,(z * u) * (z \ 1)) = L(x,y,z * (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(2536(a,1),7712(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2536 7712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7715">
    <literal><![CDATA[
      L(x,y,z * L(u,w,u)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(4939(a,1),7712(a,1,3))].">
      <j1 rule="para" parents="4939 7712"/>
    </justification>
  </clause>

  <clause id="7716">
    <literal><![CDATA[
      L(x,y,z * (u * (z \ 1))) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3441,a(flip),b,7714,a),flip(a)].">
      <j1 rule="hyper" parents="63 3441 7714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7717">
    <literal><![CDATA[
      L(x,y,L((z \ 1) \ u,z,z)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2781,a(flip),b,7716,a),flip(a)].">
      <j1 rule="hyper" parents="63 2781 7716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7718">
    <literal><![CDATA[
      L(x,y,L(z,u \ 1,u)) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1665,a(flip),b,7716,a)].">
      <j1 rule="hyper" parents="63 1665 7716"/>
    </justification>
  </clause>

  <clause id="7719">
    <literal><![CDATA[
      L(x,y,(z \ (z \ 1)) \ ((1 / z) * u)) = L(x,y,L(u / (z \ 1),z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4639,a,b,7718,a)].">
      <j1 rule="hyper" parents="63 4639 7718"/>
    </justification>
  </clause>

  <clause id="7720">
    <literal><![CDATA[
      L(x,y,(z \ (z \ 1)) \ ((1 / z) * u)) = L(x,y,L((z \ 1) \ u,z,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,1591,a(flip),b,7719,a),flip(a)].">
      <j1 rule="hyper" parents="316 1591 7719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7721">
    <literal><![CDATA[
      L(x,y,(z \ (z \ 1)) \ ((z \ 1) * u)) = L(x,y,L((z \ 1) \ u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4174,a(flip),b,7720,a)].">
      <j1 rule="hyper" parents="63 4174 7720"/>
    </justification>
  </clause>

  <clause id="7722">
    <literal><![CDATA[
      L(x,y,((z \ 1) * u) * (z * z)) = L(x,y,L((z \ 1) \ u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1592,a(flip),b,7721,a)].">
      <j1 rule="hyper" parents="63 1592 7721"/>
    </justification>
  </clause>

  <clause id="7723">
    <literal><![CDATA[
      L(x,y,(z \ 1) * (u * (z * z))) = L(x,y,L((z \ 1) \ u,z,z))
    ]]></literal>
    <justification jstring="[para(32(a,1),7722(a,1,3))].">
      <j1 rule="para" parents="32 7722"/>
    </justification>
  </clause>

  <clause id="7724">
    <literal><![CDATA[
      L(x,y,(z \ 1) * (u * (z * z))) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,7717,a(flip),b,7723,a),flip(a)].">
      <j1 rule="hyper" parents="316 7717 7723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7725">
    <literal><![CDATA[
      L(x,y,z) * R(u,x,L(x,y,z) * (x \ 1)) = (x * u) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,6258,a(flip),b,7543,a),flip(a)].">
      <j1 rule="hyper" parents="316 6258 7543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7726">
    <literal><![CDATA[
      L(x,y,z) * R(u,x,x \ L(x,y,z)) = (x * u) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(969(a,1),7725(a,1,2,3))].">
      <j1 rule="para" parents="969 7725"/>
    </justification>
  </clause>

  <clause id="7727">
    <literal><![CDATA[
      R(x,y,y \ L(y,z,u)) = L(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(34,a,5106,a,b,7726,a),flip(a)].">
      <j1 rule="hyper" parents="34 5106 7726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7728">
    <literal><![CDATA[
      R(x,y,y * L(y,z,u)) = L(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1718,a(flip),b,7727,a)].">
      <j1 rule="hyper" parents="63 1718 7727"/>
    </justification>
  </clause>

  <clause id="7729">
    <literal><![CDATA[
      L(x \ L(x,y,y \ L(y,z,u)),x,L(y,z,u)) = a(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7727(a,1),3426(a,1,1,2))].">
      <j1 rule="para" parents="7727 3426"/>
    </justification>
  </clause>

  <clause id="7730">
    <literal><![CDATA[
      L(x \ L(x,y,y \ L(y,z,u)),x,L(y,z,u)) = a(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5566,a(flip),b,7729,a),flip(a)].">
      <j1 rule="hyper" parents="316 5566 7729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7732">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) \ ((x * w) * (y \ L(y,z,u))) = L(w,x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),7548(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 7548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7733">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w * (v5 * v5)) * v6))) = a(x,y,z \ (u \ (v6 * w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5804,a(flip),b,7561,a),flip(a)].">
      <j1 rule="hyper" parents="316 5804 7561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7735">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((1 / w) * v5))) = a(x,y,z \ (u \ (v5 * w)))
    ]]></literal>
    <justification jstring="[para(233(a,1),7733(a,1,3,2,2,1))].">
      <j1 rule="para" parents="233 7733"/>
    </justification>
  </clause>

  <clause id="7736">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w \ 1) * v5))) = a(x,y,z \ (u \ (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5924,a(flip),b,7735,a)].">
      <j1 rule="hyper" parents="63 5924 7735"/>
    </justification>
  </clause>

  <clause id="7737">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * (v5 \ 1)))) = a(x,y,z \ (u \ (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5602,a,b,7736,a)].">
      <j1 rule="hyper" parents="63 5602 7736"/>
    </justification>
  </clause>

  <clause id="7738">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w * (L(w,v5,v6) \ w)) * v7))) = a(x,y,z \ (u \ (v7 * L(1 / w,v5,v6))))
    ]]></literal>
    <justification jstring="[para(6585(a,1),7736(a,1,3,2,2,1))].">
      <j1 rule="para" parents="6585 7736"/>
    </justification>
  </clause>

  <clause id="7739">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * a(v5,v5,w)))) = a(x,y,z \ (u \ L(w,v5,v5)))
    ]]></literal>
    <justification jstring="[para(5093(a,1),7737(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="5093 7737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7740">
    <literal><![CDATA[
      a(x,y,z \ (((u * (w * w)) \ v5) \ v6)) = a(x,y,z \ ((u \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,6744,a(flip),b,7562,a),flip(a)].">
      <j1 rule="hyper" parents="316 6744 7562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7742">
    <literal><![CDATA[
      a(x,y,z \ (((u / (w * w)) \ v5) \ v6)) = a(x,y,z \ ((u \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(12(a,1),7740(a,1,3,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 7740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7743">
    <literal><![CDATA[
      a(x,y,z \ (((u \ 1) \ w) \ v5)) = a(x,y,z \ ((u \ w) \ v5))
    ]]></literal>
    <justification jstring="[para(229(a,1),7740(a,1,3,2,1,1)),flip(a)].">
      <j1 rule="para" parents="229 7740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7745">
    <literal><![CDATA[
      a(x,y,z \ (((u * (w \ 1)) \ v5) \ v6)) = a(x,y,z \ (((u * w) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(562(a,1),7742(a,1,3,2,1,1))].">
      <j1 rule="para" parents="562 7742"/>
    </justification>
  </clause>

  <clause id="7746">
    <literal><![CDATA[
      a(x,y,(z \ ((u / (w * w)) \ v5)) * v6) = a(x,y,((z \ (u \ v5)) * (w * w)) * v6)
    ]]></literal>
    <justification jstring="[para(637(a,1),7564(a,2,3,1))].">
      <j1 rule="para" parents="637 7564"/>
    </justification>
  </clause>

  <clause id="7747">
    <literal><![CDATA[
      a(x,y,L(z \ (u / (w \ 1)),v5,v6)) = a(x,y,L(z \ (w \ u),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5817,a(flip),b,7565,a),flip(a)].">
      <j1 rule="hyper" parents="63 5817 7565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7749">
    <literal><![CDATA[
      a(x,y,L(z \ ((u \ 1) \ w),v5,v6)) = a(x,y,L(z \ (u \ w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5710,a(flip),b,7747,a)].">
      <j1 rule="hyper" parents="63 5710 7747"/>
    </justification>
  </clause>

  <clause id="7750">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u),w,v5)) = a(x,y,L(u \ (z \ u),w,v5))
    ]]></literal>
    <justification jstring="[para(1447(a,2),7747(a,1,3,1))].">
      <j1 rule="para" parents="1447 7747"/>
    </justification>
  </clause>

  <clause id="7752">
    <literal><![CDATA[
      a(x,y,L(L(z \ 1,z,u),w,v5)) = a(x,y,L(u \ (z \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5891,a,b,7750,a)].">
      <j1 rule="hyper" parents="63 5891 7750"/>
    </justification>
  </clause>

  <clause id="7753">
    <literal><![CDATA[
      a(x,y,L((z * u) \ z,w,v5)) = a(x,y,L(z \ (u \ z),w,v5))
    ]]></literal>
    <justification jstring="[para(232(a,1),7752(a,1,3,1))].">
      <j1 rule="para" parents="232 7752"/>
    </justification>
  </clause>

  <clause id="7754">
    <literal><![CDATA[
      a(x,y,L((z * u) \ u,w,v5)) = a(x,y,L(u \ (z \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,6255,a,b,7753,a)].">
      <j1 rule="hyper" parents="63 6255 7753"/>
    </justification>
  </clause>

  <clause id="7755">
    <literal><![CDATA[
      a(x,y,L((z / (u \ 1)) \ L(u,u,z),w,v5)) = a(x,y,L(((z / (u \ 1)) * z) \ (z / (u \ 1)),w,v5))
    ]]></literal>
    <justification jstring="[para(1447(a,2),7753(a,2,3,1,2)),flip(a)].">
      <j1 rule="para" parents="1447 7753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7756">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u) \ (u \ L(z,z,u)),w,v5)) = a(x,y,L((u / (z \ 1)) \ L(z,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(1445(a,1),7754(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="1445 7754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7757">
    <literal><![CDATA[
      a(x,y,L((((z \ 1) \ u) \ L((z \ 1) \ u,w,v5)) \ (z \ u),v6,v7)) = a(x,y,L(L(1 / ((z \ 1) \ u),w,v5) \ 1,v6,v7))
    ]]></literal>
    <justification jstring="[para(5126(a,2),7749(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5126 7749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7759">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * (u * w)) / ((L(x,y,z) \ x) * w) = R(u,w,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,1721,a(flip),b,7608,a),flip(a)].">
      <j1 rule="hyper" parents="316 1721 7608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7761">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,x,L(x,y,z) \ x) = (L(1 / x,y,z) \ 1) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(133,a,160,a(flip),b,7611,a),flip(a)].">
      <j1 rule="hyper" parents="133 160 7611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7762">
    <literal><![CDATA[
      R(a(x,y,z) / x,L(x,u,w),x * a(x,y,z)) = T(a(x,y,z) / x,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,4809,a(flip),b,7615,a)].">
      <j1 rule="hyper" parents="63 4809 7615"/>
    </justification>
  </clause>

  <clause id="7763">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) \ (u * L(x,y,z)) = a(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(114(a,1),7616(a,1,1,2))].">
      <j1 rule="para" parents="114 7616"/>
    </justification>
  </clause>

  <clause id="7764">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) * a(x,x \ L(x,y,z),u) = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,2579,a(flip),b,7763,a)].">
      <j1 rule="hyper" parents="139 2579 7763"/>
    </justification>
  </clause>

  <clause id="7765">
    <literal><![CDATA[
      R(x,y,(z * u) \ (w \ (z * (u * w)))) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5373,a(flip),b,7625,a),flip(a)].">
      <j1 rule="hyper" parents="63 5373 7625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7767">
    <literal><![CDATA[
      R(x,y,(z * u) \ (w \ (u * (z * w)))) = L(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4752,a,b,7765,a)].">
      <j1 rule="hyper" parents="63 4752 7765"/>
    </justification>
  </clause>

  <clause id="7768">
    <literal><![CDATA[
      L(x,x,a(y,z,z)) = L(x,x,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,7362,a,b,7630,a)].">
      <j1 rule="hyper" parents="35 7362 7630"/>
    </justification>
  </clause>

  <clause id="7769">
    <literal><![CDATA[
      a(x,y,(L(L(z,u,w),v5,v6) * (v6 * v5)) * v7) = a(x,y,(v6 * (v5 * R(z,u,w))) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,5647,a(flip),b,7631,a),flip(a)].">
      <j1 rule="hyper" parents="63 5647 7631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7770">
    <literal><![CDATA[
      x \ ((y \ L(y,z,u)) \ ((x / y) * L(y,z,u))) = a(y,y \ L(y,z,u),y \ x)
    ]]></literal>
    <justification jstring="[para(5015(a,1),7634(a,1,2))].">
      <j1 rule="para" parents="5015 7634"/>
    </justification>
  </clause>

  <clause id="7772">
    <literal><![CDATA[
      a(x,y,(z \ ((u / (w * w)) \ v5)) * v6) = a(x,y,(z \ (u \ v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,5874,a(flip),b,7746,a),flip(a)].">
      <j1 rule="hyper" parents="316 5874 7746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7774">
    <literal><![CDATA[
      a(x,y,(z \ ((u \ 1) \ w)) * v5) = a(x,y,(z \ (u \ w)) * v5)
    ]]></literal>
    <justification jstring="[para(281(a,1),7772(a,1,3,1,2,1))].">
      <j1 rule="para" parents="281 7772"/>
    </justification>
  </clause>

  <clause id="7775">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * w) = a(x,y,(u \ (z \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5950,a,b,7774,a)].">
      <j1 rule="hyper" parents="63 5950 7774"/>
    </justification>
  </clause>

  <clause id="7776">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ 1) \ v5))) = a(x,y,(u \ (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,7774,a)].">
      <j1 rule="hyper" parents="63 5469 7774"/>
    </justification>
  </clause>

  <clause id="7777">
    <literal><![CDATA[
      a(x,y,((z * u) \ z) * w) = a(x,y,(z \ (u \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5879,a(flip),b,7775,a)].">
      <j1 rule="hyper" parents="63 5879 7775"/>
    </justification>
  </clause>

  <clause id="7778">
    <literal><![CDATA[
      a(x,y,((z * u) \ u) * w) = a(x,y,(u \ (z \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5948,a,b,7777,a)].">
      <j1 rule="hyper" parents="63 5948 7777"/>
    </justification>
  </clause>

  <clause id="7779">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * (w \ 1)) = a(x,y,w * ((u * z) \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5529,a(flip),b,7778,a),flip(a)].">
      <j1 rule="hyper" parents="63 5529 7778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7780">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ 1) \ v5))) = a(x,y,z * (u \ (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,7776,a),flip(a)].">
      <j1 rule="hyper" parents="316 5469 7776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7781">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ w)) = a(x,y,z * (w \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5529,a(flip),b,7779,a),flip(a)].">
      <j1 rule="hyper" parents="63 5529 7779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7782">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ 1) \ R(w,v5,v5)))) = a(x,y,z * (u \ a(w,v5,v5)))
    ]]></literal>
    <justification jstring="[para(2380(a,1),7780(a,2,3,2,2))].">
      <j1 rule="para" parents="2380 7780"/>
    </justification>
  </clause>

  <clause id="7783">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ (v5 \ (w \ v5))))) = a(x,y,z * (u \ (w * (v5 \ (w \ v5)))))
    ]]></literal>
    <justification jstring="[para(4734(a,1),7780(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="4734 7780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7784">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * R(w,v5,v5)))) = a(x,y,z * (u \ a(w,v5,v5)))
    ]]></literal>
    <justification jstring="[para(3362(a,1),7782(a,1,3,2,2))].">
      <j1 rule="para" parents="3362 7782"/>
    </justification>
  </clause>

  <clause id="7785">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * (u * x)) / (L(1 / x,y,z) \ 1) = R(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6607,a,b,7759,a)].">
      <j1 rule="hyper" parents="63 6607 7759"/>
    </justification>
  </clause>

  <clause id="7787">
    <literal><![CDATA[
      R(a(x,y,z) / x,L(x,u,w),x * a(x,y,z)) = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,4309,a(flip),b,7762,a),flip(a)].">
      <j1 rule="hyper" parents="316 4309 7762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7789">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * (u * x)) / (L(1 / x,y,z) \ 1) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,7728,a(flip),b,7785,a),flip(a)].">
      <j1 rule="hyper" parents="316 7728 7785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7790">
    <literal><![CDATA[
      K(x / ((x * y) / (z * y)),u) * (x * (z * y)) = (x * y) * T(L(T(z,y),y,x),u)
    ]]></literal>
    <justification jstring="[para(3393(a,1),3129(a,1,1))].">
      <j1 rule="para" parents="3393 3129"/>
    </justification>
  </clause>

  <clause id="7792">
    <literal><![CDATA[
      K(x,x \ 1) * (y / L((1 / x) * y,x,a(x,x \ 1,y))) = a(x,1 / x,y) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,660,a(flip),b,3468,a)].">
      <j1 rule="hyper" parents="63 660 3468"/>
    </justification>
  </clause>

  <clause id="7793">
    <literal><![CDATA[
      L(x,y \ z,a(u,w,v5) * y) * ((a(u,w,v5) * y) * (y \ z)) = (a(u,w,v5) * y) * ((y \ z) * T(x,z))
    ]]></literal>
    <justification jstring="[para(5239(a,1),3526(a,2,2,2))].">
      <j1 rule="para" parents="5239 3526"/>
    </justification>
  </clause>

  <clause id="7794">
    <literal><![CDATA[
      ((R(x,y,z) \ u) \ w) * (R(x,y,z) \ u) = w * K(x * (w / u),u / x)
    ]]></literal>
    <justification jstring="[para(3551(a,1),4607(a,2,2))].">
      <j1 rule="para" parents="3551 4607"/>
    </justification>
  </clause>

  <clause id="7795">
    <literal><![CDATA[
      ((R(x,y,z) \ u) \ w) * (R(x,y,z) \ u) = ((x \ u) \ w) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4573,a(flip),b,7794,a),flip(a)].">
      <j1 rule="hyper" parents="316 4573 7794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7797">
    <literal><![CDATA[
      L(L(x,y,y),a(y,y,x),x \ z) \ z = T((z / x) * a(y,y,x),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5249,a(flip),b,4956,a),flip(a)].">
      <j1 rule="hyper" parents="63 5249 4956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7799">
    <literal><![CDATA[
      L(L(x,y,y),a(y,y,x),x \ z) \ z = (x \ z) * a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,5333,a(flip),b,7797,a),flip(a)].">
      <j1 rule="hyper" parents="316 5333 7797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7800">
    <literal><![CDATA[
      L(L((a(x,x,y) * a(x,x,y)) * y,x,x),a(x,x,y),a(x,x,y)) = a(x,x,y) * y
    ]]></literal>
    <justification jstring="[para(1115(a,2),4957(a,1,1))].">
      <j1 rule="para" parents="1115 4957"/>
    </justification>
  </clause>

  <clause id="7801">
    <literal><![CDATA[
      R(L(T(1 / x,y),z,x),R(x,z,x),R(x,z,x) \ y) = y \ (1 * (R(x,z,x) \ y))
    ]]></literal>
    <justification jstring="[para(25(a,2),5439(a,1,1))].">
      <j1 rule="para" parents="25 5439"/>
    </justification>
  </clause>

  <clause id="7803">
    <literal><![CDATA[
      a(x,x,y * L(y,z,u)) \ (y \ L(y,z,u)) = L(y \ L(y,z,u),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(7470(a,1),5723(a,1,1))].">
      <j1 rule="para" parents="7470 5723"/>
    </justification>
  </clause>

  <clause id="7804">
    <literal><![CDATA[
      L(x \ L(x,y,z),u \ 1,u) = L(x \ L(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5725,a(flip),b,7803,a),flip(a)].">
      <j1 rule="hyper" parents="63 5725 7803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7805">
    <literal><![CDATA[
      L(x \ (y * L(y \ x,z,u)),w \ 1,w) = L((y / x) \ L(y / x,z,u),w,w)
    ]]></literal>
    <justification jstring="[para(5189(a,1),7804(a,1,1))].">
      <j1 rule="para" parents="5189 7804"/>
    </justification>
  </clause>

  <clause id="7807">
    <literal><![CDATA[
      L(x \ (y * L(y \ x,z,u)),w \ 1,w) = L(x \ (y * L(y \ x,z,u)),w,w)
    ]]></literal>
    <justification jstring="[para(5189(a,1),7805(a,2,1))].">
      <j1 rule="para" parents="5189 7805"/>
    </justification>
  </clause>

  <clause id="7808">
    <literal><![CDATA[
      a(x,y,z \ (u * (R(w,v5,v5) \ (v5 \ 1)))) = a(x,y,z \ (u * (((w * v5) * v5) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5599,a(flip),b,5918,a),flip(a)].">
      <j1 rule="hyper" parents="316 5599 5918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7809">
    <literal><![CDATA[
      K(x,x \ y) * (z \ (x \ L(y,u,w))) = T(z \ (L(y,u,w) / x),K(x,y))
    ]]></literal>
    <justification jstring="[para(5180(a,1),6200(a,1,1))].">
      <j1 rule="para" parents="5180 6200"/>
    </justification>
  </clause>

  <clause id="7811">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (u * K(x * (L(x,y,z) \ u),w)) = T(u * (L(x,y,z) \ x),w)
    ]]></literal>
    <justification jstring="[para(3567(a,1),6494(a,1,2,2))].">
      <j1 rule="para" parents="3567 6494"/>
    </justification>
  </clause>

  <clause id="7812">
    <literal><![CDATA[
      R(T(x,y),y,L(a(z,u,w),v5,v6)) = L(T(x,y),y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(5239(a,1),6523(a,1,1))].">
      <j1 rule="para" parents="5239 6523"/>
    </justification>
  </clause>

  <clause id="7815">
    <literal><![CDATA[
      T(x * (L(y \ x,z,u) \ 1),(x / y) \ x) = x * (L(y \ x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,6471,a(flip),b,6577,a)].">
      <j1 rule="hyper" parents="63 6471 6577"/>
    </justification>
  </clause>

  <clause id="7817">
    <literal><![CDATA[
      T(x * (L(y \ x,z,u) \ 1),y) = x * (L(y \ x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(83(a,1),7815(a,1,2))].">
      <j1 rule="para" parents="83 7815"/>
    </justification>
  </clause>

  <clause id="7818">
    <literal><![CDATA[
      R(L(x,y,z) \ x,x \ 1,x \ u) * u = (L(x,y,z) \ 1) * ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(4789(a,1),6732(a,1,1))].">
      <j1 rule="para" parents="4789 6732"/>
    </justification>
  </clause>

  <clause id="7820">
    <literal><![CDATA[
      L(x \ 1,x * y,a(y,x,x)) \ y = (x * y) * (((x \ 1) * (x * y)) \ y)
    ]]></literal>
    <justification jstring="[para(7387(a,1),7688(a,1,1))].">
      <j1 rule="para" parents="7387 7688"/>
    </justification>
  </clause>

  <clause id="7821">
    <literal><![CDATA[
      (x * y) * (((x \ 1) * (x * y)) \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(6873(a,1),7820(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6873 7820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7823">
    <literal><![CDATA[
      a(x,y,(z * (u * R(w,v5,v6))) * v7) = a(x,y,(z * (u * L(w,v5,v6))) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,5647,a(flip),b,7769,a),flip(a)].">
      <j1 rule="hyper" parents="63 5647 7769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7824">
    <literal><![CDATA[
      K(x / ((x * y) / (z * y)),u) * (x * (z * y)) = x * (y * T(T(z,y),u))
    ]]></literal>
    <justification jstring="[hyper(316,a,408,a(flip),b,7790,a),flip(a)].">
      <j1 rule="hyper" parents="316 408 7790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7825">
    <literal><![CDATA[
      K(x / ((x * y) / (z * y)),u) * (x * (z * y)) = x * (T(z,u) * y)
    ]]></literal>
    <justification jstring="[para(250(a,1),7824(a,2,2))].">
      <j1 rule="para" parents="250 7824"/>
    </justification>
  </clause>

  <clause id="7826">
    <literal><![CDATA[
      L(x,y,(z * (T(u,w) * v5)) \ v6) = L(x,y,(z * (u * v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(7825(a,1),4172(a,1,3,1))].">
      <j1 rule="para" parents="7825 4172"/>
    </justification>
  </clause>

  <clause id="7827">
    <literal><![CDATA[
      a(x \ (y * (z * (T(u,w) * v5))),v6,v7) = a(x \ (y * (z * (u * v5))),v6,v7)
    ]]></literal>
    <justification jstring="[para(7825(a,1),4556(a,1,1,2,2))].">
      <j1 rule="para" parents="7825 4556"/>
    </justification>
  </clause>

  <clause id="7829">
    <literal><![CDATA[
      L(x,y,(L(z,u,w) * (w * u)) \ v5) = L(x,y,(w * (z * u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,4564,a(flip),b,7826,a)].">
      <j1 rule="hyper" parents="63 4564 7826"/>
    </justification>
  </clause>

  <clause id="7831">
    <literal><![CDATA[
      L(x,y,(z * (u * w)) \ (u * (w * z))) = L(x,y,a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5786,a(flip),b,7829,a),flip(a)].">
      <j1 rule="hyper" parents="63 5786 7829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7832">
    <literal><![CDATA[
      L(x,y,((z * u) * w) \ (z * (u * w))) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4173,a,b,7831,a)].">
      <j1 rule="hyper" parents="63 4173 7831"/>
    </justification>
  </clause>

  <clause id="7833">
    <literal><![CDATA[
      L(x,y,(z * u) \ (w \ (z * (u * w)))) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(7150(a,1),7831(a,1,3))].">
      <j1 rule="para" parents="7150 7831"/>
    </justification>
  </clause>

  <clause id="7834">
    <literal><![CDATA[
      L(x,y,L(z \ L(z,u,w),z,w * u)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(489(a,2),7832(a,1,3))].">
      <j1 rule="para" parents="489 7832"/>
    </justification>
  </clause>

  <clause id="7835">
    <literal><![CDATA[
      L(x,y,(z * u) \ (w \ ((v5 * v5) \ (z * (u * (w * (v5 * v5))))))) = L(x,y,a(w * (v5 * v5),u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4559,a(flip),b,7833,a)].">
      <j1 rule="hyper" parents="63 4559 7833"/>
    </justification>
  </clause>

  <clause id="7836">
    <literal><![CDATA[
      L(x,y,(z * u) \ L(z * u,u,z)) = L(x,y,a(z * u,u,z))
    ]]></literal>
    <justification jstring="[para(18(a,2),7833(a,1,3,2))].">
      <j1 rule="para" parents="18 7833"/>
    </justification>
  </clause>

  <clause id="7837">
    <literal><![CDATA[
      L(x,y,a(z \ K(u,w),v5,v6)) = L(x,y,(v6 * v5) \ ((z \ 1) \ (v6 * (v5 * (z \ 1)))))
    ]]></literal>
    <justification jstring="[para(3806(a,2),7833(a,2,3)),flip(a)].">
      <j1 rule="para" parents="3806 7833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7838">
    <literal><![CDATA[
      L(x,y,L(z \ L(z,u,w),z,u * w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(1668(a,1),7834(a,1,3))].">
      <j1 rule="para" parents="1668 7834"/>
    </justification>
  </clause>

  <clause id="7840">
    <literal><![CDATA[
      a(x \ (L(y,x \ (z * (T(u,w) * v5)),x) * (z * (u * v5))),v6,v7) = a((x \ (z * (T(u,w) * v5))) * T(y,z * (T(u,w) * v5)),v6,v7)
    ]]></literal>
    <justification jstring="[para(714(a,1),7827(a,1,1)),flip(a)].">
      <j1 rule="para" parents="714 7827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7841">
    <literal><![CDATA[
      K(x,x \ 1) * (y / L((1 / x) * y,x,a(x,x \ 1,y))) = a(x,x \ 1,y) * x
    ]]></literal>
    <justification jstring="[para(3467(a,1),7792(a,2,1))].">
      <j1 rule="para" parents="3467 7792"/>
    </justification>
  </clause>

  <clause id="7842">
    <literal><![CDATA[
      L(L(x * (a(y,y,x) * a(y,y,x)),y,y),a(y,y,x),a(y,y,x)) = a(y,y,x) * x
    ]]></literal>
    <justification jstring="[para(5345(a,1),7800(a,1,1,1))].">
      <j1 rule="para" parents="5345 7800"/>
    </justification>
  </clause>

  <clause id="7843">
    <literal><![CDATA[
      R(L(T(1 / x,y),z,x),x,R(x,z,x) \ y) = y \ (1 * (R(x,z,x) \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7706,a(flip),b,7801,a)].">
      <j1 rule="hyper" parents="63 7706 7801"/>
    </justification>
  </clause>

  <clause id="7845">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) * (x \ T(x * (L(x,y,z) \ u),w))) = T(u * (L(x,y,z) \ x),w)
    ]]></literal>
    <justification jstring="[para(3926(a,1),7811(a,1,2))].">
      <j1 rule="para" parents="3926 7811"/>
    </justification>
  </clause>

  <clause id="7846">
    <literal><![CDATA[
      L(x,y,a(z \ K(u,w),v5,v6)) = L(x,y,(v6 * v5) \ (z \ (v6 * (v5 * z))))
    ]]></literal>
    <justification jstring="[hyper(316,a,7531,a(flip),b,7837,a),flip(a)].">
      <j1 rule="hyper" parents="316 7531 7837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7847">
    <literal><![CDATA[
      L(x,y,a(z \ K(u,w),v5,v6)) = L(x,y,a(z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,7833,a(flip),b,7846,a),flip(a)].">
      <j1 rule="hyper" parents="316 7833 7846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7848">
    <literal><![CDATA[
      L(x,y,a(z \ 1,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(180(a,1),7847(a,1,3,1,2))].">
      <j1 rule="para" parents="180 7847"/>
    </justification>
  </clause>

  <clause id="7849">
    <literal><![CDATA[
      R(x,y,((z \ 1) / (u \ 1)) \ (u * z)) = L(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7006,a,b,7848,a)].">
      <j1 rule="hyper" parents="63 7006 7848"/>
    </justification>
  </clause>

  <clause id="7850">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ (u \ 1)) \ (z * u)) = L(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4728,a(flip),b,7849,a)].">
      <j1 rule="hyper" parents="63 4728 7849"/>
    </justification>
  </clause>

  <clause id="7851">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ u) \ (z * u)) = L(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4822,a(flip),b,7850,a)].">
      <j1 rule="hyper" parents="63 4822 7850"/>
    </justification>
  </clause>

  <clause id="7852">
    <literal><![CDATA[
      L(x * (a(y,y,x) * a(y,y,x)),y,y) = a(y,y,x) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,6888,a(flip),b,7842,a)].">
      <j1 rule="hyper" parents="63 6888 7842"/>
    </justification>
  </clause>

  <clause id="7854">
    <literal><![CDATA[
      a(x,y,(z * (a(u,u,w) * w)) * v5) = a(x,y,(z * L(w,u,u)) * v5)
    ]]></literal>
    <justification jstring="[para(7852(a,1),5997(a,1,3,1,2))].">
      <j1 rule="para" parents="7852 5997"/>
    </justification>
  </clause>

  <clause id="7855">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) * (w / ((x \ y) \ w)) = L(x,z,u) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(316,a,6830,a(flip),b,3231,a),flip(a)].">
      <j1 rule="hyper" parents="316 6830 3231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7856">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) * (x \ y) = L(x,z,u) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(540,a,7855,a)].">
      <j1 rule="hyper" parents="540 7855"/>
    </justification>
  </clause>

  <clause id="7857">
    <literal><![CDATA[
      L((R(x,y,z) \ (u * x)) \ (u * x),w,v5) * (R(x,y,z) \ (u * x)) = L(R(x,y,z),w,v5) * (R(x,y,z) \ (x * u))
    ]]></literal>
    <justification jstring="[para(4228(a,1),7856(a,2,2))].">
      <j1 rule="para" parents="4228 7856"/>
    </justification>
  </clause>

  <clause id="7862">
    <literal><![CDATA[
      (L(x * (x * y),z,u) * (x \ 1)) \ L(x * (x * y),z,u) = L(x,x,x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1367(a,2),3458(a,1,2))].">
      <j1 rule="para" parents="1367 3458"/>
    </justification>
  </clause>

  <clause id="7863">
    <literal><![CDATA[
      x * ((y * K(x \ 1,x)) * K(x * y,z)) = T(x * (y * K(x \ 1,x)),z)
    ]]></literal>
    <justification jstring="[para(3568(a,1),3651(a,1,2,2))].">
      <j1 rule="para" parents="3568 3651"/>
    </justification>
  </clause>

  <clause id="7864">
    <literal><![CDATA[
      x * (y * ((x \ 1) * (x * K(x * y,z)))) = T(x * (y * K(x \ 1,x)),z)
    ]]></literal>
    <justification jstring="[para(4205(a,1),7863(a,1,2))].">
      <j1 rule="para" parents="4205 7863"/>
    </justification>
  </clause>

  <clause id="7865">
    <literal><![CDATA[
      (x \ y) / ((z * T(y / (x \ 1),x)) / (x * x)) = (y / (x \ 1)) / (z * (y / (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,676,a(flip),b,3969,a)].">
      <j1 rule="hyper" parents="63 676 3969"/>
    </justification>
  </clause>

  <clause id="7866">
    <literal><![CDATA[
      ((1 / x) * (T(y,x \ 1) * K(z,u))) * x = (y * (x \ K(z,u))) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3780(a,1),4069(a,2,1,2))].">
      <j1 rule="para" parents="3780 4069"/>
    </justification>
  </clause>

  <clause id="7867">
    <literal><![CDATA[
      R(x,(y * (z \ 1)) \ 1,y * z) * 1 = (x * R(z / y,y,z)) * (y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(1711(a,1),4482(a,1,1))].">
      <j1 rule="para" parents="1711 4482"/>
    </justification>
  </clause>

  <clause id="7868">
    <literal><![CDATA[
      (x * R(y / z,z,y)) * (z * (y \ 1)) = R(x,(z * (y \ 1)) \ 1,z * y)
    ]]></literal>
    <justification jstring="[hyper(146,a,7867,a),flip(a)].">
      <j1 rule="hyper" parents="146 7867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7869">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ (a(y,z,y) * ((x * u) * w)) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[para(5403(a,1),4550(a,1,2))].">
      <j1 rule="para" parents="5403 4550"/>
    </justification>
  </clause>

  <clause id="7871">
    <literal><![CDATA[
      L(x,y,L(z * (u * u),w,v5) \ (u * u)) = L(x,y,T(L(z,w,v5) \ 1,u * u))
    ]]></literal>
    <justification jstring="[para(427(a,1),4816(a,2,3))].">
      <j1 rule="para" parents="427 4816"/>
    </justification>
  </clause>

  <clause id="7872">
    <literal><![CDATA[
      L(x,y,L(z * (u * u),w,v5) \ (u * u)) = L(x,y,L(z,w,v5) \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,1581,a(flip),b,7871,a),flip(a)].">
      <j1 rule="hyper" parents="316 1581 7871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7874">
    <literal><![CDATA[
      (x * (a(y,y,x) \ z)) / (a(y,y,x) \ (L(x,y,y) * z)) = R(a(y,y,x),L(x,y,y),z)
    ]]></literal>
    <justification jstring="[para(6893(a,1),4958(a,1,1))].">
      <j1 rule="para" parents="6893 4958"/>
    </justification>
  </clause>

  <clause id="7875">
    <literal><![CDATA[
      x \ (K(y,T(z,u)) * L(L(u,w,v5),v6,v7)) = (x \ L(L(u,v6,v7),w,v5)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4126(a,1),4972(a,1,2,1))].">
      <j1 rule="para" parents="4126 4972"/>
    </justification>
  </clause>

  <clause id="7876">
    <literal><![CDATA[
      x \ L(K(y,T(z,u)) * L(u,w,v5),v6,v7) = (x \ L(L(u,v6,v7),w,v5)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4850(a,2),7875(a,1,2))].">
      <j1 rule="para" parents="4850 7875"/>
    </justification>
  </clause>

  <clause id="7877">
    <literal><![CDATA[
      x \ L(L(K(y,T(z,u)) * u,w,v5),v6,v7) = (x \ L(L(u,v6,v7),w,v5)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4850(a,2),7876(a,1,2,1))].">
      <j1 rule="para" parents="4850 7876"/>
    </justification>
  </clause>

  <clause id="7878">
    <literal><![CDATA[
      x \ L(L(y * K(z,u),w,v5),v6,v7) = (x \ L(L(y,v6,v7),w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[para(4127(a,1),7877(a,1,2,1,1))].">
      <j1 rule="para" parents="4127 7877"/>
    </justification>
  </clause>

  <clause id="7879">
    <literal><![CDATA[
      (1 / x) * L(L(x \ 1,y,z) * x,u,w) = x \ L(x * L(x \ 1,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,1075,a(flip),b,4980,a),flip(a)].">
      <j1 rule="hyper" parents="316 1075 4980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7880">
    <literal><![CDATA[
      (1 / x) * L((x \ 1) * L(x,y,z),u,w) = x \ L(x * L(x \ 1,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(4442(a,1),7879(a,1,2,1))].">
      <j1 rule="para" parents="4442 7879"/>
    </justification>
  </clause>

  <clause id="7881">
    <literal><![CDATA[
      (1 / x) * L((x \ 1) * L(x,y,z),u,w) = x \ L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1064(a,1),7880(a,2,2,1))].">
      <j1 rule="para" parents="1064 7880"/>
    </justification>
  </clause>

  <clause id="7882">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u * (w * (a(x,y,z) \ 1))) = a(x,y,z) \ (u * (w * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(316,a,2276,a(flip),b,5051,a),flip(a)].">
      <j1 rule="hyper" parents="316 2276 5051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7884">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ u) * (L(x,y,z) \ x) = u / (L(x,y,z) * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(5133(a,1),5075(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 5075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7885">
    <literal><![CDATA[
      (L(x,y,z) \ x) * ((x \ L(x,y,z)) \ u) = u / (L(x,y,z) * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6496,a,b,7884,a)].">
      <j1 rule="hyper" parents="63 6496 7884"/>
    </justification>
  </clause>

  <clause id="7887">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((L(x,y,z) \ x) \ u) = u * (L(x,y,z) * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(138,a,75,a(flip),b,7885,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="138 75 7885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7890">
    <literal><![CDATA[
      x * ((L(y,z,u) \ y) * (L(y,z,u) \ y)) = x / (L(y,z,u) * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(6312(a,1),5083(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6312 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7892">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) \ x) = x * (L(x,y,z) \ (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(34,a,6316,a,b,7890,a),flip(a)].">
      <j1 rule="hyper" parents="34 6316 7890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7893">
    <literal><![CDATA[
      L(((L(x,y,z) \ x) * (L(x,y,z) \ x)) \ u,w,v5) = (x * (L(x,y,z) \ (L(x,y,z) \ x))) \ L(u,w,v5)
    ]]></literal>
    <justification jstring="[para(7892(a,1),1120(a,2,1))].">
      <j1 rule="para" parents="7892 1120"/>
    </justification>
  </clause>

  <clause id="7897">
    <literal><![CDATA[
      (x * (y * (z \ L(z,u,w)))) / T((z \ L(z,u,w)) * x,y) = L(y,z \ L(z,u,w),x)
    ]]></literal>
    <justification jstring="[para(5023(a,2),5119(a,1,2,1))].">
      <j1 rule="para" parents="5023 5119"/>
    </justification>
  </clause>

  <clause id="7898">
    <literal><![CDATA[
      ((x * (a(y,z,y) * (u * w))) \ ((x * u) * w)) * a(y,z,y) = a(x,u,a(y,z,y) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5422,a(flip),b,5402,a)].">
      <j1 rule="hyper" parents="63 5422 5402"/>
    </justification>
  </clause>

  <clause id="7899">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ ((x * (a(y,z,y) * u)) * w) = a(x * a(y,z,y),u,w)
    ]]></literal>
    <justification jstring="[para(5398(a,1),5419(a,1,2,1))].">
      <j1 rule="para" parents="5398 5419"/>
    </justification>
  </clause>

  <clause id="7900">
    <literal><![CDATA[
      (1 / x) \ (((a(y,z,y) / x) * u) * w) = (x \ 1) \ (((x \ a(y,z,y)) * u) * w)
    ]]></literal>
    <justification jstring="[para(5427(a,1),5440(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5427 5440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7901">
    <literal><![CDATA[
      a(x,y,z \ (u * R(K(w,v5) * v6,v7,v8))) = a(x,y,z \ (R(v6,v7,v8) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5496,a(flip),b,5617,a),flip(a)].">
      <j1 rule="hyper" parents="63 5496 5617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7903">
    <literal><![CDATA[
      a(x,y,z \ (u * L(K(w,v5) * v6,v7,v8))) = a(x,y,z \ (L(v6,v7,v8) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5496,a(flip),b,5622,a),flip(a)].">
      <j1 rule="hyper" parents="63 5496 5622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7905">
    <literal><![CDATA[
      a(x,y,(z \ R(K(u,w) * v5,v6,v7)) * v8) = a(x,y,v8 * ((z \ R(v5,v6,v7)) * K(u,w)))
    ]]></literal>
    <justification jstring="[para(3781(a,1),5734(a,2,3,2))].">
      <j1 rule="para" parents="3781 5734"/>
    </justification>
  </clause>

  <clause id="7906">
    <literal><![CDATA[
      a(x,y,z * ((u * L(u,w,v5)) * (v6 * u))) = a(x,y,z * (u * (v6 * (u \ L(u,w,v5)))))
    ]]></literal>
    <justification jstring="[hyper(63,a,7619,a(flip),b,5797,a)].">
      <j1 rule="hyper" parents="63 7619 5797"/>
    </justification>
  </clause>

  <clause id="7907">
    <literal><![CDATA[
      a(x,y,(z \ L(K(u,w) * v5,v6,v7)) * v8) = a(x,y,v8 * ((z \ L(v5,v6,v7)) * K(u,w)))
    ]]></literal>
    <justification jstring="[para(3781(a,1),5940(a,2,3,2))].">
      <j1 rule="para" parents="3781 5940"/>
    </justification>
  </clause>

  <clause id="7909">
    <literal><![CDATA[
      a(x,y,z \ (((u \ (w \ v5)) * (w * w)) * v6)) = a(x,y,z \ (v6 * (u \ (v5 / (w \ 1)))))
    ]]></literal>
    <justification jstring="[para(388(a,1),6102(a,1,3,2,1))].">
      <j1 rule="para" parents="388 6102"/>
    </justification>
  </clause>

  <clause id="7910">
    <literal><![CDATA[
      a(x,y,(z * ((L(u,w,v5) \ u) * v6)) * v7) = a(x,y,v7 * (z * (v6 * (u \ L(u,w,v5)))))
    ]]></literal>
    <justification jstring="[hyper(316,a,5666,a(flip),b,6109,a),flip(a)].">
      <j1 rule="hyper" parents="316 5666 6109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7911">
    <literal><![CDATA[
      ((x / y) \ z) \ L((x / y) \ u,w,v5) = ((y \ x) \ z) \ L((y \ x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(116(a,1),6228(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="116 6228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7912">
    <literal><![CDATA[
      x * ((x \ y) * (L(z,u,w) * L(z \ 1,u,w))) = y * (L(z,u,w) * L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(631,a,6319,a),flip(a)].">
      <j1 rule="hyper" parents="631 6319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7913">
    <literal><![CDATA[
      L(L(x,y,z) * L(x \ 1,y,z),u,w) = L(x,y,z) * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(463,a,6319,a)].">
      <j1 rule="hyper" parents="463 6319"/>
    </justification>
  </clause>

  <clause id="7914">
    <literal><![CDATA[
      (((x * y) / x) * x) * (L(z,u,w) * L(z \ 1,u,w)) = y * (T(x,y) * (L(z,u,w) * L(z \ 1,u,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,3076,a(flip),b,6319,a),flip(a)].">
      <j1 rule="hyper" parents="316 3076 6319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7916">
    <literal><![CDATA[
      x \ (y * (L(z,u,w) * L(z \ 1,u,w))) = (x \ y) * (L(z,u,w) * L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(133,a,158,a(flip),b,6319,a(flip))].">
      <j1 rule="hyper" parents="133 158 6319"/>
    </justification>
  </clause>

  <clause id="7917">
    <literal><![CDATA[
      K(L(x,y,z) * L(x \ 1,y,z),u * w) * ((u * (w * (L(x,y,z) * L(x \ 1,y,z)))) / v5) = ((L(x,y,z) * L(x \ 1,y,z)) * (u * w)) / v5
    ]]></literal>
    <justification jstring="[para(6319(a,1),2766(a,1,2,1))].">
      <j1 rule="para" parents="6319 2766"/>
    </justification>
  </clause>

  <clause id="7918">
    <literal><![CDATA[
      (x * y) / (L(z,u,w) * L(z \ 1,u,w)) = x * (y / (L(z,u,w) * L(z \ 1,u,w)))
    ]]></literal>
    <justification jstring="[hyper(209,a,7913,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="209 7913 104"/>
    </justification>
  </clause>

  <clause id="7921">
    <literal><![CDATA[
      a(x,y,z \ (R(L(u,w,u),u,v5) \ v5)) = a(x,y,z \ (u * (a(u,w,u) \ v5)))
    ]]></literal>
    <justification jstring="[para(7707(a,1),6351(a,1,3,2,1))].">
      <j1 rule="para" parents="7707 6351"/>
    </justification>
  </clause>

  <clause id="7922">
    <literal><![CDATA[
      a(x,y,z \ (L(R(u,u,w),v5,u) \ w)) = a(x,y,z \ (u * (a(u,v5,u) \ w)))
    ]]></literal>
    <justification jstring="[para(29(a,1),7921(a,1,3,2,1))].">
      <j1 rule="para" parents="29 7921"/>
    </justification>
  </clause>

  <clause id="7924">
    <literal><![CDATA[
      a(x * (y * (L(1 / z,u,w) \ 1)),v5,v6) = a(x * (y * (z * (L(z,u,w) \ z))),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,4555,a(flip),b,6586,a),flip(a)].">
      <j1 rule="hyper" parents="316 4555 6586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7925">
    <literal><![CDATA[
      a(L(x,y,z) \ x,x,u) = a(x,L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6546,a(flip),b,6665,a),flip(a)].">
      <j1 rule="hyper" parents="63 6546 6665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7927">
    <literal><![CDATA[
      (x * (x * (x \ y))) / ((x * x) * (x \ y)) = ((x * x) \ (x * y)) / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,673,a(flip),b,6764,a),flip(a)].">
      <j1 rule="hyper" parents="63 673 6764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7928">
    <literal><![CDATA[
      (x * (x * (x \ y))) / ((x * x) * (x \ y)) = L(x \ y,x,x) / (x \ y)
    ]]></literal>
    <justification jstring="[para(102(a,2),7927(a,2,1))].">
      <j1 rule="para" parents="102 7927"/>
    </justification>
  </clause>

  <clause id="7929">
    <literal><![CDATA[
      (x * (x * (x \ y))) / ((x * x) * (x \ y)) = (x \ y) \ L(x \ y,x,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,1272,a(flip),b,7928,a),flip(a)].">
      <j1 rule="hyper" parents="316 1272 7928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7930">
    <literal><![CDATA[
      (x * y) / ((x * x) * (x \ y)) = (x \ y) \ L(x \ y,x,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),7929(a,1,1,2))].">
      <j1 rule="para" parents="10 7929"/>
    </justification>
  </clause>

  <clause id="7932">
    <literal><![CDATA[
      L(R(x,y,R(T(x,y),z,u)),y,R(x,z,u)) = (x * (R(x,z,u) * y)) / (R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(1166(a,1),6803(a,2,1))].">
      <j1 rule="para" parents="1166 6803"/>
    </justification>
  </clause>

  <clause id="7933">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,a(w,v5,L(x,v6,v7))) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(6874(a,1),6875(a,2,2))].">
      <j1 rule="para" parents="6874 6875"/>
    </justification>
  </clause>

  <clause id="7934">
    <literal><![CDATA[
      ((x * y) * L(y \ 1,z,u)) / (y \ L(y,z,u)) = a(x,y,L(y \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[para(7933(a,1),2677(a,1,2))].">
      <j1 rule="para" parents="7933 2677"/>
    </justification>
  </clause>

  <clause id="7936">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ ((u * x) * L(x \ 1,y,z)) = a(u,x,L(x \ 1,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,5015,a(flip),b,7934,a)].">
      <j1 rule="hyper" parents="63 5015 7934"/>
    </justification>
  </clause>

  <clause id="7938">
    <literal><![CDATA[
      R((x * y) / y,y,L(y,z,u)) = a(x,y,L(y \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,7546,a(flip),b,7936,a)].">
      <j1 rule="hyper" parents="63 7546 7936"/>
    </justification>
  </clause>

  <clause id="7939">
    <literal><![CDATA[
      a(x,y,L(y \ 1,z,u)) * x = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),7938(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 7938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7940">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) * x = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(2655(a,1),7939(a,1,1))].">
      <j1 rule="para" parents="2655 7939"/>
    </justification>
  </clause>

  <clause id="7941">
    <literal><![CDATA[
      a((x \ (x \ 1)) \ ((1 / x) * y),x \ 1,x) = a((x \ 1) \ y,x \ 1,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2534,a(flip),b,6953,a)].">
      <j1 rule="hyper" parents="63 2534 6953"/>
    </justification>
  </clause>

  <clause id="7942">
    <literal><![CDATA[
      a((x \ (x \ 1)) \ ((x \ 1) * y),x \ 1,x) = a((x \ 1) \ y,x \ 1,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,4177,a(flip),b,7941,a)].">
      <j1 rule="hyper" parents="63 4177 7941"/>
    </justification>
  </clause>

  <clause id="7943">
    <literal><![CDATA[
      a(((x \ 1) * y) * (x * x),x \ 1,x) = a((x \ 1) \ y,x \ 1,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1817,a(flip),b,7942,a)].">
      <j1 rule="hyper" parents="63 1817 7942"/>
    </justification>
  </clause>

  <clause id="7944">
    <literal><![CDATA[
      a((x \ 1) * (y * (x * x)),x \ 1,x) = a((x \ 1) \ y,x \ 1,x \ 1)
    ]]></literal>
    <justification jstring="[para(32(a,1),7943(a,1,1))].">
      <j1 rule="para" parents="32 7943"/>
    </justification>
  </clause>

  <clause id="7945">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * a(v5,v5 \ 1,w)))) = a(x,y,z \ (L(w,v5 \ 1,v5) * u))
    ]]></literal>
    <justification jstring="[para(8(a,1),6960(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="8 6960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7946">
    <literal><![CDATA[
      K(x \ 1,y) \ ((z \ 1) * (z * y)) = 1 \ T((z \ 1) * (z * y),((u \ 1) * (u * x)) \ 1)
    ]]></literal>
    <justification jstring="[para(3589(a,1),7030(a,1,1))].">
      <j1 rule="para" parents="3589 7030"/>
    </justification>
  </clause>

  <clause id="7947">
    <literal><![CDATA[
      a(x,y,z * L(u \ K(w,v5),v6,v7)) = a(x,y,z * L(u \ (v8 * v8),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,6104,a(flip),b,7056,a)].">
      <j1 rule="hyper" parents="63 6104 7056"/>
    </justification>
  </clause>

  <clause id="7949">
    <literal><![CDATA[
      a(x,y,z * L(u \ (w * w),v5,v6)) = a(x,y,L(u,v5,v6) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6359,a(flip),b,7947,a),flip(a)].">
      <j1 rule="hyper" parents="63 6359 7947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7950">
    <literal><![CDATA[
      a(x,y,L(z \ (u * u),w,v5) * v6) = a(x,y,L(z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,7949,a)].">
      <j1 rule="hyper" parents="63 5469 7949"/>
    </justification>
  </clause>

  <clause id="7951">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ z,v5,v6) * v7) = a(x,y,L(z * L(z,u,w),v5,v6) * v7)
    ]]></literal>
    <justification jstring="[para(5161(a,1),7950(a,1,3,1,1))].">
      <j1 rule="para" parents="5161 7950"/>
    </justification>
  </clause>

  <clause id="7952">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ (L(x,u,w) \ v5)) * L(x,u,w) = ((x \ L(x,y,z)) \ (x \ v5)) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,6154,a(flip),b,7060,a),flip(a)].">
      <j1 rule="hyper" parents="316 6154 7060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7960">
    <literal><![CDATA[
      (x \ y) / (z * (T(y / (x \ 1),x) / (x * x))) = (y / (x \ 1)) / (z * (y / (x \ 1)))
    ]]></literal>
    <justification jstring="[para(683(a,1),7865(a,1,2))].">
      <j1 rule="para" parents="683 7865"/>
    </justification>
  </clause>

  <clause id="7961">
    <literal><![CDATA[
      a(x,y,x) \ ((z * (u * w)) \ (a(x,y,x) * ((z * u) * w))) = a(z,a(x,y,x) * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5431,a(flip),b,7869,a)].">
      <j1 rule="hyper" parents="63 5431 7869"/>
    </justification>
  </clause>

  <clause id="7963">
    <literal><![CDATA[
      (x * (a(y,y,x) \ z)) / (L(x,y,y) * (a(y,y,x) \ z)) = R(a(y,y,x),L(x,y,y),z)
    ]]></literal>
    <justification jstring="[para(6976(a,1),7874(a,1,2))].">
      <j1 rule="para" parents="6976 7874"/>
    </justification>
  </clause>

  <clause id="7964">
    <literal><![CDATA[
      L(a(x,y,z) \ (u * (w * a(x,y,z))),a(x,y,z) \ 1,a(x,y,z)) = 1 \ (a(x,y,z) * (u * (w * (a(x,y,z) \ 1))))
    ]]></literal>
    <justification jstring="[para(7882(a,1),475(a,1,1))].">
      <j1 rule="para" parents="7882 475"/>
    </justification>
  </clause>

  <clause id="7965">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u * ((a(x,y,z) \ 1) * w)) = a(x,y,z) \ (u * (w * a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(5006(a,2),7882(a,1,2,2))].">
      <j1 rule="para" parents="5006 7882"/>
    </justification>
  </clause>

  <clause id="7969">
    <literal><![CDATA[
      (a(x,y,x) \ ((z * (u * w)) \ ((z * u) * w))) * a(x,y,x) = a(z,u,a(x,y,x) * w)
    ]]></literal>
    <justification jstring="[para(5431(a,1),7898(a,1,1))].">
      <j1 rule="para" parents="5431 7898"/>
    </justification>
  </clause>

  <clause id="7970">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,4550,a(flip),b,7899,a),flip(a)].">
      <j1 rule="hyper" parents="63 4550 7899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7971">
    <literal><![CDATA[
      a(a(x,y,x) \ z,a(x,y,x) * u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2783,a(flip),b,7970,a),flip(a)].">
      <j1 rule="hyper" parents="63 2783 7970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7973">
    <literal><![CDATA[
      a(x,y,(z \ R(K(u,w) * v5,v6,v7)) * v8) = a(x,y,v8 * (z \ R(v5,v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5488,a(flip),b,7905,a),flip(a)].">
      <j1 rule="hyper" parents="316 5488 7905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7975">
    <literal><![CDATA[
      a(x,y,(z * u) * (u * (z * (u \ L(u,w,v5))))) = a(x,y,L(u * L(u,w,v5),z * u,z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5826,a(flip),b,7906,a),flip(a)].">
      <j1 rule="hyper" parents="63 5826 7906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7976">
    <literal><![CDATA[
      a(x,y,(z \ L(K(u,w) * v5,v6,v7)) * v8) = a(x,y,v8 * (z \ L(v5,v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5488,a(flip),b,7907,a),flip(a)].">
      <j1 rule="hyper" parents="316 5488 7907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7982">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ (v5 / (v6 \ 1))))) = a(x,y,z \ (u * (w \ (v6 \ v5))))
    ]]></literal>
    <justification jstring="[hyper(63,a,6678,a(flip),b,7909,a),flip(a)].">
      <j1 rule="hyper" parents="63 6678 7909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7984">
    <literal><![CDATA[
      a(x,y,z * (u * (w * (L(v5,v6,v7) \ v5)))) = a(x,y,z * (u * (w * (v5 \ L(v5,v6,v7)))))
    ]]></literal>
    <justification jstring="[hyper(63,a,5666,a(flip),b,7910,a)].">
      <j1 rule="hyper" parents="63 5666 7910"/>
    </justification>
  </clause>

  <clause id="7986">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ u) * (L(x,y,z) * L(x \ 1,y,z)) = (L(x,y,z) \ x) \ u
    ]]></literal>
    <justification jstring="[hyper(34,a,7887,a,b,7912,a),flip(a)].">
      <j1 rule="hyper" parents="34 7887 7912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7987">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (u * (x \ L(x,y,z))) = u * (L(x,y,z) * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(5014(a,1),7986(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5014 7986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7989">
    <literal><![CDATA[
      L(R(x,y,R(T(x,y),z,u)),y,R(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,11,a(flip),b,7932,a),flip(a)].">
      <j1 rule="hyper" parents="316 11 7932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7991">
    <literal><![CDATA[
      L(R(x,y,R(x,z,u)),y,R(x,z,u)) = x
    ]]></literal>
    <justification jstring="[para(4060(a,1),7989(a,1,1))].">
      <j1 rule="para" parents="4060 7989"/>
    </justification>
  </clause>

  <clause id="7992">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,z,u)) = x
    ]]></literal>
    <justification jstring="[para(4895(a,1),7991(a,1,1))].">
      <j1 rule="para" parents="4895 7991"/>
    </justification>
  </clause>

  <clause id="7993">
    <literal><![CDATA[
      L(x,y,R(x,z,u)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(7992(a,1),1618(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7992 1618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7995">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4628,a(flip),b,7993,a)].">
      <j1 rule="hyper" parents="63 4628 7993"/>
    </justification>
  </clause>

  <clause id="7996">
    <literal><![CDATA[
      L(R(x,y,z),u,L(x,w,v5)) = R(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(7995(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7995 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7997">
    <literal><![CDATA[
      L(L(x,y,z),u,L(x,w,v5)) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(7995(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7995 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7998">
    <literal><![CDATA[
      L((x \ y) \ z,u,(x \ y) \ z) = L((x \ y) \ z,u,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(475(a,1),7995(a,1,3)),flip(a)].">
      <j1 rule="para" parents="475 7995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7999">
    <literal><![CDATA[
      L(x,y,x) \ L(L(x,y,L(x,z,u)),w,v5) = L(x \ L(x,w,v5),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(7995(a,1),2136(a,1,1))].">
      <j1 rule="para" parents="7995 2136"/>
    </justification>
  </clause>

  <clause id="8000">
    <literal><![CDATA[
      L(1 / x,y,L(x,z,u)) = 1 / (x * (L(x,y,x) \ x))
    ]]></literal>
    <justification jstring="[para(7995(a,1),6594(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7995 6594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8001">
    <literal><![CDATA[
      L(R(x,y,z),u,L(x,w,v5)) = L(R(x,y,z),u,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,29,a(flip),b,7996,a),flip(a)].">
      <j1 rule="hyper" parents="316 29 7996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8002">
    <literal><![CDATA[
      R(a(x,y,x) \ x,z,u) = L(R(x,z,u),y,L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(4935(a,2),7996(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4935 7996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8003">
    <literal><![CDATA[
      a(x,y,L(L(z,u,z),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(7997(a,1),5574(a,1,3))].">
      <j1 rule="para" parents="7997 5574"/>
    </justification>
  </clause>

  <clause id="8004">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),v5,z)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5952,a,b,8003,a)].">
      <j1 rule="hyper" parents="63 5952 8003"/>
    </justification>
  </clause>

  <clause id="8005">
    <literal><![CDATA[
      a(x,y,L(L(L(z,u,z),w,v5),v6,v7)) = a(x,y,L(L(z,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(7997(a,1),8003(a,1,3,1))].">
      <j1 rule="para" parents="7997 8003"/>
    </justification>
  </clause>

  <clause id="8006">
    <literal><![CDATA[
      L(1 / x,y,L(x,z,u)) = L(1 / x,y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,6594,a(flip),b,8000,a),flip(a)].">
      <j1 rule="hyper" parents="316 6594 8000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8007">
    <literal><![CDATA[
      L(1 / (x \ 1),y,L(x \ 1,z,u)) = L(1 / (x \ 1),y,x \ a(w,v5,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,7713,a,b,8006,a),flip(a)].">
      <j1 rule="hyper" parents="316 7713 8006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8009">
    <literal><![CDATA[
      L(R(x,y,z),u,L(x,w,v5)) \ v6 = (R(x,y,z) \ v6) * a(x,u,x)
    ]]></literal>
    <justification jstring="[para(8002(a,1),6115(a,1,1))].">
      <j1 rule="para" parents="8002 6115"/>
    </justification>
  </clause>

  <clause id="8010">
    <literal><![CDATA[
      a(x,y,L(L(L(z,u,w),v5,v6),v7,z)) = a(x,y,L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(122(a,2),8005(a,1,3))].">
      <j1 rule="para" parents="122 8005"/>
    </justification>
  </clause>

  <clause id="8011">
    <literal><![CDATA[
      (R(x,y,z) \ u) * a(x,w,x) = L(R(x,y,z),w,x) \ u
    ]]></literal>
    <justification jstring="[para(155(a,1),8009(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="155 8009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8012">
    <literal><![CDATA[
      R(x,y,z) * (L(R(x,y,z),u,x) \ w) = w * a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,8011,a(flip),b,5393,a)].">
      <j1 rule="hyper" parents="139 8011 5393"/>
    </justification>
  </clause>

  <clause id="8013">
    <literal><![CDATA[
      L((x \ y) \ 1,y,y \ (x * 1)) * y = y * T((x \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(7998(a,1),2851(a,1,1))].">
      <j1 rule="para" parents="7998 2851"/>
    </justification>
  </clause>

  <clause id="8014">
    <literal><![CDATA[
      L((x \ y) \ 1,y,y \ x) * y = y * T((x \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),8013(a,1,1,3,2))].">
      <j1 rule="para" parents="8 8013"/>
    </justification>
  </clause>

  <clause id="8015">
    <literal><![CDATA[
      L(((x * y) \ y) \ 1,y,y \ (x * y)) = T(((y * x) \ y) \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(35,a,6269,a,b,8014,a),flip(a)].">
      <j1 rule="hyper" parents="35 6269 8014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8016">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,y * x) = L(((y * x) \ x) \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1584,a(flip),b,8015,a),flip(a)].">
      <j1 rule="hyper" parents="63 1584 8015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8018">
    <literal><![CDATA[
      L(1 / (x \ 1),y,x \ a(z,u,z)) = L(x,y,L(x \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(80(a,1),8007(a,1,1)),flip(a)].">
      <j1 rule="para" parents="80 8007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8021">
    <literal><![CDATA[
      L(x,y,L(x \ 1,z,u)) = L(x,y,x \ a(w,v5,w))
    ]]></literal>
    <justification jstring="[para(80(a,1),8018(a,1,1)),flip(a)].">
      <j1 rule="para" parents="80 8018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8023">
    <literal><![CDATA[
      L(x,y,L(x \ 1,z,u)) = L(x,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,7713,a(flip),b,8021,a),flip(a)].">
      <j1 rule="hyper" parents="316 7713 8021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8024">
    <literal><![CDATA[
      L(x \ y,z,(x \ y) \ 1) = L(x \ y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(356(a,1),8023(a,1,3)),flip(a)].">
      <j1 rule="para" parents="356 8023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8025">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,L(x,w,v5)) = L(x,u,x) \ L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(7995(a,1),7999(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7995 7999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8026">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,L(x,w,v5)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5154,a(flip),b,8025,a),flip(a)].">
      <j1 rule="hyper" parents="316 5154 8025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8029">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),v5,L(x,v6,v7)) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(8026(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8026 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8030">
    <literal><![CDATA[
      L(x \ (L(y,z,u) * (y \ x)),w,L(y,v5,v6)) = L(y \ L(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(7098(a,1),8029(a,1,1))].">
      <j1 rule="para" parents="7098 8029"/>
    </justification>
  </clause>

  <clause id="8036">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((x \ L(x,u,w)) \ (x \ v5))) = (x \ L(x,u,w)) \ (L(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(35,a,4393,a,b,7952,a)].">
      <j1 rule="hyper" parents="35 4393 7952"/>
    </justification>
  </clause>

  <clause id="8037">
    <literal><![CDATA[
      (x / (y \ 1)) / (z * (x / (y \ 1))) = (y \ x) / (z * (y \ x))
    ]]></literal>
    <justification jstring="[para(672(a,1),7960(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="672 7960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8038">
    <literal><![CDATA[
      ((x \ 1) \ y) / (z * ((x \ 1) \ y)) = (x \ y) / (z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4525,a(flip),b,8037,a)].">
      <j1 rule="hyper" parents="63 4525 8037"/>
    </justification>
  </clause>

  <clause id="8039">
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = (x * (u * w)) \ ((x * u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5415,a(flip),b,7961,a),flip(a)].">
      <j1 rule="hyper" parents="63 5415 7961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8041">
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,14,a,b,8039,a),flip(a)].">
      <j1 rule="hyper" parents="316 14 8039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8042">
    <literal><![CDATA[
      a(a(x,y,x) \ z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,7971,a(flip),b,8041,a),flip(a)].">
      <j1 rule="hyper" parents="63 7971 8041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8043">
    <literal><![CDATA[
      a(x,R(y,z,y),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(4545(a,1),8041(a,1,2))].">
      <j1 rule="para" parents="4545 8041"/>
    </justification>
  </clause>

  <clause id="8044">
    <literal><![CDATA[
      a(x,L(y,z,y),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(4934(a,1),8041(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4934 8041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8045">
    <literal><![CDATA[
      a(x,y \ a(z,u,z),w) = a(x,y \ 1,w)
    ]]></literal>
    <justification jstring="[para(5395(a,1),8041(a,1,2))].">
      <j1 rule="para" parents="5395 8041"/>
    </justification>
  </clause>

  <clause id="8046">
    <literal><![CDATA[
      a(x,L(a(y,z,y) * u,w,v5),v6) = a(x,L(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(6141(a,2),8041(a,1,2))].">
      <j1 rule="para" parents="6141 8041"/>
    </justification>
  </clause>

  <clause id="8047">
    <literal><![CDATA[
      a(x,(y \ 1) \ 1,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1037(a,1),8043(a,1,2))].">
      <j1 rule="para" parents="1037 8043"/>
    </justification>
  </clause>

  <clause id="8048">
    <literal><![CDATA[
      a(x,y \ (y * z),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(353(a,1),8044(a,1,2))].">
      <j1 rule="para" parents="353 8044"/>
    </justification>
  </clause>

  <clause id="8049">
    <literal><![CDATA[
      a(x,L(y \ 1,y,z) \ 1,u) = a(x,y * a(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(7303(a,1),8047(a,1,2,1))].">
      <j1 rule="para" parents="7303 8047"/>
    </justification>
  </clause>

  <clause id="8050">
    <literal><![CDATA[
      a(x,L(y \ 1,y,z),u) = a(x,(z * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(362(a,1),8048(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="362 8048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8052">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),8042(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 8042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8053">
    <literal><![CDATA[
      a(x \ (a(y,z,y) \ u),w,v5) = a(x \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(5414(a,1),8042(a,1,1))].">
      <j1 rule="para" parents="5414 8042"/>
    </justification>
  </clause>

  <clause id="8054">
    <literal><![CDATA[
      a(L(a(x,y,x) * z,u,w),v5,v6) = a(L(z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(6142(a,1),8042(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6142 8042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8056">
    <literal><![CDATA[
      a(x \ a(y,z,y),u,w) = a(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(5395(a,1),8052(a,1,1))].">
      <j1 rule="para" parents="5395 8052"/>
    </justification>
  </clause>

  <clause id="8058">
    <literal><![CDATA[
      a(a(x,y,x) / z,u,w) = a(z \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1813,a,b,8056,a)].">
      <j1 rule="hyper" parents="63 1813 8056"/>
    </justification>
  </clause>

  <clause id="8059">
    <literal><![CDATA[
      a(x \ (y * ((z * y) \ y)),u,w) = a(x \ (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(4947(a,1),8053(a,1,1,2))].">
      <j1 rule="para" parents="4947 8053"/>
    </justification>
  </clause>

  <clause id="8060">
    <literal><![CDATA[
      a(x,L(y \ a(z,u,z),w,v5),v6) = a(x,L(y \ 1,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(5395(a,1),8046(a,1,2,1))].">
      <j1 rule="para" parents="5395 8046"/>
    </justification>
  </clause>

  <clause id="8061">
    <literal><![CDATA[
      a(L(x \ a(y,z,y),u,w),v5,v6) = a(L(x \ 1,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(5395(a,1),8054(a,1,1,1))].">
      <j1 rule="para" parents="5395 8054"/>
    </justification>
  </clause>

  <clause id="8063">
    <literal><![CDATA[
      a((x * y) \ y,z,u) = a(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),8059(a,1,1))].">
      <j1 rule="para" parents="9 8059"/>
    </justification>
  </clause>

  <clause id="8064">
    <literal><![CDATA[
      a((x * y) \ x,z,u) = a(x \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4176,a,b,8063,a)].">
      <j1 rule="hyper" parents="63 4176 8063"/>
    </justification>
  </clause>

  <clause id="8065">
    <literal><![CDATA[
      a(L(x \ 1,x,y),z,u) = a(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[para(232(a,2),8064(a,1,1))].">
      <j1 rule="para" parents="232 8064"/>
    </justification>
  </clause>

  <clause id="8066">
    <literal><![CDATA[
      (L(x,y,y) * (a(y,y,x) \ z)) \ (x * (a(y,y,x) \ z)) = R(a(y,y,x),L(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6637,a(flip),b,7963,a)].">
      <j1 rule="hyper" parents="63 6637 7963"/>
    </justification>
  </clause>

  <clause id="8067">
    <literal><![CDATA[
      L((a(x,y,z) \ (u * (w * a(x,y,z)))) \ v5,(a(x,y,z) \ 1) \ (u * ((a(x,y,z) \ 1) * w)),a(x,y,z) \ 1) = (u * ((a(x,y,z) \ 1) * w)) \ ((a(x,y,z) \ 1) * v5)
    ]]></literal>
    <justification jstring="[para(7965(a,1),475(a,1,1,1))].">
      <j1 rule="para" parents="7965 475"/>
    </justification>
  </clause>

  <clause id="8069">
    <literal><![CDATA[
      (a(x,y,x) \ a(z,u,w)) * a(x,y,x) = a(z,u,a(x,y,x) * w)
    ]]></literal>
    <justification jstring="[para(14(a,2),7969(a,1,1,2))].">
      <j1 rule="para" parents="14 7969"/>
    </justification>
  </clause>

  <clause id="8070">
    <literal><![CDATA[
      a(x,y,a(z,u,z) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2274,a(flip),b,8069,a),flip(a)].">
      <j1 rule="hyper" parents="63 2274 8069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8073">
    <literal><![CDATA[
      a(x,y,z * (u * (a(w,v5,w) * v6))) = a(x,y,(u * v6) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5534,a(flip),b,8070,a)].">
      <j1 rule="hyper" parents="63 5534 8070"/>
    </justification>
  </clause>

  <clause id="8074">
    <literal><![CDATA[
      a(x,y,a(z,u,z) \ w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),8070(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 8070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8075">
    <literal><![CDATA[
      a(x,y,(a(z,u,z) \ w) * v5) = a(x,y,w * v5)
    ]]></literal>
    <justification jstring="[para(4539(a,1),8070(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4539 8070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8076">
    <literal><![CDATA[
      a(x,y,z \ (u * (a(w,v5,w) \ v6))) = a(x,y,z \ (u * v6))
    ]]></literal>
    <justification jstring="[para(5424(a,1),8070(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5424 8070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8077">
    <literal><![CDATA[
      a(x,y,L(a(z,u,z) * w,v5,v6)) = a(x,y,L(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(6141(a,2),8070(a,1,3))].">
      <j1 rule="para" parents="6141 8070"/>
    </justification>
  </clause>

  <clause id="8080">
    <literal><![CDATA[
      a(x,y,(L(z,u,z) \ w) * v5) = a(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[para(4940(a,1),8075(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4940 8075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8081">
    <literal><![CDATA[
      a(x,y,L(a(z,u,z) * L(w \ 1,v5,v6),v7,v8)) = a(x,y,L(L(w,v5,v6),v7,v8))
    ]]></literal>
    <justification jstring="[hyper(316,a,5891,a(flip),b,8077,a),flip(a)].">
      <j1 rule="hyper" parents="316 5891 8077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8082">
    <literal><![CDATA[
      a(x,y,L(L(z * a(u,w,u),v5,v6),v7,v8)) = a(x,y,L(L(z,v5,v6),v7,v8))
    ]]></literal>
    <justification jstring="[para(6139(a,2),8077(a,1,3,1))].">
      <j1 rule="para" parents="6139 8077"/>
    </justification>
  </clause>

  <clause id="8085">
    <literal><![CDATA[
      a(x,y,(L((z * u) * w,v5,(z * u) * w) \ ((z * u) * R(w,u,z))) * v6) = a(x,y,a(w,u,z) * v6)
    ]]></literal>
    <justification jstring="[para(3428(a,2),8080(a,2,3,1))].">
      <j1 rule="para" parents="3428 8080"/>
    </justification>
  </clause>

  <clause id="8087">
    <literal><![CDATA[
      a(x,y,z \ (L(R(u,u,w),v5,u) \ w)) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7922,a,b,8076,a)].">
      <j1 rule="hyper" parents="63 7922 8076"/>
    </justification>
  </clause>

  <clause id="8089">
    <literal><![CDATA[
      a(x,y,z \ (L(R(u,u,L(w,v5,v6)),v7,u) \ R(w,v5,v6))) = a(x,y,z \ (u * R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(4893(a,1),8087(a,1,3,2,1,1))].">
      <j1 rule="para" parents="4893 8087"/>
    </justification>
  </clause>

  <clause id="8090">
    <literal><![CDATA[
      a(x,y,L(L(a(z,u,z) * (w \ 1),v5,v6),v7,v8)) = a(x,y,L(L(w,v5,v6),v7,v8))
    ]]></literal>
    <justification jstring="[para(6141(a,2),8081(a,1,3,1))].">
      <j1 rule="para" parents="6141 8081"/>
    </justification>
  </clause>

  <clause id="8091">
    <literal><![CDATA[
      a(x,y,L(L(z \ a(u,w,u),v5,v6),v7,v8)) = a(x,y,L(L(z,v5,v6),v7,v8))
    ]]></literal>
    <justification jstring="[para(5395(a,1),8090(a,1,3,1,1))].">
      <j1 rule="para" parents="5395 8090"/>
    </justification>
  </clause>

  <clause id="8092">
    <literal><![CDATA[
      x * (L(x,y,z) \ (x \ ((x \ L(x,u,w)) \ v5))) = (x \ L(x,u,w)) \ (L(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(1501(a,1),8036(a,1,2,2))].">
      <j1 rule="para" parents="1501 8036"/>
    </justification>
  </clause>

  <clause id="8093">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ L(x,u,w)) \ v5) = (x \ L(x,u,w)) \ (L(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,1130,a(flip),b,8092,a)].">
      <j1 rule="hyper" parents="63 1130 8092"/>
    </justification>
  </clause>

  <clause id="8094">
    <literal><![CDATA[
      L(x,y,z) \ (R(x \ L(x,u,w),x \ L(x,u,w),v5) * v5) = (x \ L(x,u,w)) \ (L(x,y,z) \ (((x \ L(x,u,w)) * (x \ L(x,u,w))) * v5))
    ]]></literal>
    <justification jstring="[para(1164(a,1),8093(a,1,2))].">
      <j1 rule="para" parents="1164 8093"/>
    </justification>
  </clause>

  <clause id="8095">
    <literal><![CDATA[
      L((1 / x) * K(y * (x \ 1),x \ 1),x \ 1,y) = (y * (x \ (x \ 1))) / (y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(1951(a,1),3336(a,1,1,2))].">
      <j1 rule="para" parents="1951 3336"/>
    </justification>
  </clause>

  <clause id="8097">
    <literal><![CDATA[
      L(x,y,z) * (T(u,x) * T(x \ L(x,w,v5),u * L(x,y,z))) = (x \ L(x,w,v5)) * (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(8026(a,1),4318(a,2,1))].">
      <j1 rule="para" parents="8026 4318"/>
    </justification>
  </clause>

  <clause id="8099">
    <literal><![CDATA[
      (L(x,y,z) * u) / T(x * u,x \ L(x,y,z)) = (x * u) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(3694(a,1),4419(a,1,2))].">
      <j1 rule="para" parents="3694 4419"/>
    </justification>
  </clause>

  <clause id="8101">
    <literal><![CDATA[
      (L(x,y,z) * u) / (x * u) = (x * u) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(4992(a,1),8099(a,1,2))].">
      <j1 rule="para" parents="4992 8099"/>
    </justification>
  </clause>

  <clause id="8102">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) / (x * (z * y)) = ((z * y) * x) \ (z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(316,a,4493,a(flip),b,8101,a),flip(a)].">
      <j1 rule="hyper" parents="316 4493 8101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8103">
    <literal><![CDATA[
      (L(x,y,z) * u) / ((x * (u \ 1)) * (u * u)) = (x * (u \ 1)) \ (L(x,y,z) * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,639,a,b,8101,a)].">
      <j1 rule="hyper" parents="63 639 8101"/>
    </justification>
  </clause>

  <clause id="8105">
    <literal><![CDATA[
      (x * (y * z)) / ((x * y) * z) = ((x * y) * z) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4371,a(flip),b,8102,a)].">
      <j1 rule="hyper" parents="63 4371 8102"/>
    </justification>
  </clause>

  <clause id="8107">
    <literal><![CDATA[
      x / (((x * y) * y) / (y * y)) = ((x * y) * y) \ (x * (y * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,676,a(flip),b,8105,a)].">
      <j1 rule="hyper" parents="63 676 8105"/>
    </justification>
  </clause>

  <clause id="8108">
    <literal><![CDATA[
      ((x * y) * (y \ z)) \ (x * (y * (y \ z))) = (x * z) / ((x * y) * (y \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),8105(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 8105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8109">
    <literal><![CDATA[
      ((x * y) * T(z,y)) \ (x * (y * T(z,y))) = (x * (z * y)) / ((x * y) * T(z,y))
    ]]></literal>
    <justification jstring="[para(114(a,1),8105(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="114 8105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8110">
    <literal><![CDATA[
      ((x * y) * y) \ (x * (y * y)) = x / R(x,y,y)
    ]]></literal>
    <justification jstring="[para(20(a,2),8107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 8107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8111">
    <literal><![CDATA[
      ((x * y) * y) \ (x * (y * y)) = R(x,y,y) \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,1772,a(flip),b,8110,a),flip(a)].">
      <j1 rule="hyper" parents="316 1772 8110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8112">
    <literal><![CDATA[
      (x * y) / ((x * z) * (z \ y)) = ((x * z) * (z \ y)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),8108(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 8108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8113">
    <literal><![CDATA[
      ((x * x) * (x \ y)) \ (x * y) = (x \ y) \ L(x \ y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7930,a(flip),b,8112,a),flip(a)].">
      <j1 rule="hyper" parents="63 7930 8112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8115">
    <literal><![CDATA[
      ((x * x) * (x \ y)) \ (x * y) = a(x,x,x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,5088,a,b,8113,a),flip(a)].">
      <j1 rule="hyper" parents="316 5088 8113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8116">
    <literal><![CDATA[
      a(x,y,a(z,z,z \ u) \ 1) = a(x,y,(z * u) / (z \ u))
    ]]></literal>
    <justification jstring="[para(8115(a,1),5957(a,1,3))].">
      <j1 rule="para" parents="8115 5957"/>
    </justification>
  </clause>

  <clause id="8117">
    <literal><![CDATA[
      a(x,y,a(z,z,z \ u)) = a(x,y,(z * u) / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2534,a(flip),b,8116,a)].">
      <j1 rule="hyper" parents="63 2534 8116"/>
    </justification>
  </clause>

  <clause id="8118">
    <literal><![CDATA[
      a(x,y,a(z,z,z \ u)) = a(x,y,(z \ u) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5477,a(flip),b,8117,a),flip(a)].">
      <j1 rule="hyper" parents="316 5477 8117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8119">
    <literal><![CDATA[
      (x * (y * z)) / ((x * z) * T(y,z)) = ((x * z) * T(y,z)) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(114(a,1),8109(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="114 8109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8120">
    <literal><![CDATA[
      (x * (y * z)) / ((x * z) * T(y,z)) = (x * z) \ ((x * (z * y)) / y)
    ]]></literal>
    <justification jstring="[hyper(316,a,7623,a(flip),b,8119,a),flip(a)].">
      <j1 rule="hyper" parents="316 7623 8119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8121">
    <literal><![CDATA[
      (L(x,y,z) * u) / (x * ((u \ 1) * (u * u))) = (x * (u \ 1)) \ (L(x,y,z) * (u \ 1))
    ]]></literal>
    <justification jstring="[para(32(a,1),8103(a,1,2))].">
      <j1 rule="para" parents="32 8103"/>
    </justification>
  </clause>

  <clause id="8122">
    <literal><![CDATA[
      (x * (y \ 1)) \ (L(x,z,u) * (y \ 1)) = (L(x,z,u) * y) / (x * y)
    ]]></literal>
    <justification jstring="[para(229(a,1),8121(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="229 8121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8123">
    <literal><![CDATA[
      (x * (y \ 1)) \ (L(x,z,u) * (y \ 1)) = (x * y) \ (L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,8101,a(flip),b,8122,a),flip(a)].">
      <j1 rule="hyper" parents="316 8101 8122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8124">
    <literal><![CDATA[
      (x \ 1) \ (((x \ 1) / y) * L(y,z,u)) = (y * x) \ (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7107,a(flip),b,8123,a)].">
      <j1 rule="hyper" parents="63 7107 8123"/>
    </justification>
  </clause>

  <clause id="8125">
    <literal><![CDATA[
      (x \ 1) \ (((x \ 1) / y) * L(y,z,u)) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,7107,a(flip),b,8124,a),flip(a)].">
      <j1 rule="hyper" parents="316 7107 8124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8126">
    <literal><![CDATA[
      (((x \ y) \ z) \ u) * ((x \ y) \ z) = ((y \ (x * z)) \ u) * (y \ (x * z))
    ]]></literal>
    <justification jstring="[para(475(a,1),4441(a,1,2)),flip(a)].">
      <j1 rule="para" parents="475 4441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8127">
    <literal><![CDATA[
      x * K((y \ (z \ u)) * x,(u \ z) * y) = ((u \ (z * y)) \ x) * (u \ (z * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4574,a,b,8126,a)].">
      <j1 rule="hyper" parents="63 4574 8126"/>
    </justification>
  </clause>

  <clause id="8128">
    <literal><![CDATA[
      (T(x,x \ y) \ z) * ((x \ y) \ y) = ((y \ (x * y)) \ z) * (y \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,632,a,b,8126,a)].">
      <j1 rule="hyper" parents="63 632 8126"/>
    </justification>
  </clause>

  <clause id="8129">
    <literal><![CDATA[
      x / (y \ (z * L(z \ y,u,w))) = (y \ (z * L(z \ y,u,w))) \ x
    ]]></literal>
    <justification jstring="[hyper(136,a,5013,a(flip),b,8126,a(flip))].">
      <j1 rule="hyper" parents="136 5013 8126"/>
    </justification>
  </clause>

  <clause id="8131">
    <literal><![CDATA[
      (x \ ((y \ x) * L((y \ x) \ x,z,u))) \ w = w / (x \ (L(y,z,u) * (y \ x)))
    ]]></literal>
    <justification jstring="[para(604(a,1),8129(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="604 8129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8132">
    <literal><![CDATA[
      (T(x,x \ y) \ z) * ((x \ y) \ y) = (T(x,y) \ z) * (y \ (x * y))
    ]]></literal>
    <justification jstring="[para(22(a,2),8128(a,2,1,1))].">
      <j1 rule="para" parents="22 8128"/>
    </justification>
  </clause>

  <clause id="8133">
    <literal><![CDATA[
      (T(x,x \ y) \ z) * ((x \ y) \ y) = (T(x,y) \ z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(22(a,2),8132(a,2,2))].">
      <j1 rule="para" parents="22 8132"/>
    </justification>
  </clause>

  <clause id="8134">
    <literal><![CDATA[
      (((x \ y) \ y) \ z) * ((x \ y) \ y) = (T(x,y) \ z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,632,a(flip),b,8133,a)].">
      <j1 rule="hyper" parents="63 632 8133"/>
    </justification>
  </clause>

  <clause id="8135">
    <literal><![CDATA[
      x / (y \ (L(z,u,w) * (z \ y))) = (y \ (L(z,u,w) * (z \ y))) \ x
    ]]></literal>
    <justification jstring="[para(604(a,1),8131(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="604 8131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8136">
    <literal><![CDATA[
      T(x \ (L(y,z,u) * (y \ x)),w) = x \ (L(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(137,a,242,a(flip),b,8135,a)].">
      <j1 rule="hyper" parents="137 242 8135"/>
    </justification>
  </clause>

  <clause id="8138">
    <literal><![CDATA[
      ((x * y) \ (L(z,y,x) * (z \ (x * y)))) \ u = u / ((x * y) \ ((x * (y * z)) / z))
    ]]></literal>
    <justification jstring="[para(4378(a,1),8135(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4378 8135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8139">
    <literal><![CDATA[
      T(x \ ((x / y) * L(y,z,u)),w) = x \ (L(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[para(4325(a,1),8136(a,1,1,2))].">
      <j1 rule="para" parents="4325 8136"/>
    </justification>
  </clause>

  <clause id="8140">
    <literal><![CDATA[
      L(T(x \ ((x / y) * L(y,z,u)),w),v5,L(y,v6,v7)) = L(y \ L(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(8139(a,2),8030(a,1,1))].">
      <j1 rule="para" parents="8139 8030"/>
    </justification>
  </clause>

  <clause id="8141">
    <literal><![CDATA[
      x / ((y * z) \ ((y * (z * u)) / u)) = ((y * z) \ ((y * (z * u)) / u)) \ x
    ]]></literal>
    <justification jstring="[para(4378(a,1),8138(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4378 8138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8142">
    <literal><![CDATA[
      (x * (((y * z) \ ((y * (z * x)) / x)) \ 1)) \ x = L(x \ L(x,z,y),x,y * z)
    ]]></literal>
    <justification jstring="[para(8141(a,1),7149(a,1,1,2))].">
      <j1 rule="para" parents="8141 7149"/>
    </justification>
  </clause>

  <clause id="8143">
    <literal><![CDATA[
      L(T(x,a(y,z,u) \ 1),u \ L(u,z,y),u) = u * (L(u,z,y) \ (x * (u \ L(u,z,y))))
    ]]></literal>
    <justification jstring="[hyper(316,a,1129,a(flip),b,4670,a),flip(a)].">
      <j1 rule="hyper" parents="316 1129 4670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8144">
    <literal><![CDATA[
      T((((x \ 1) \ y) * z) * (((x \ 1) \ y) \ 1),x * y) = R(z,(x \ 1) \ y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3525,a(flip),b,4792,a)].">
      <j1 rule="hyper" parents="63 3525 4792"/>
    </justification>
  </clause>

  <clause id="8145">
    <literal><![CDATA[
      R(x * K(y * z,x),(y \ 1) \ z,y \ z) = (((y \ 1) \ z) * x) * (((y \ 1) \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(40,a,2735,a,b,8144,a)].">
      <j1 rule="hyper" parents="40 2735 8144"/>
    </justification>
  </clause>

  <clause id="8150">
    <literal><![CDATA[
      L((x * y) \ L(x * y,z,u),x * y,y) = ((y * x) * y) \ (L(y * x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(4886(a,1),5211(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4886 5211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8151">
    <literal><![CDATA[
      L((x * y) \ L(x * y,z,u),x * y,y) = y \ ((y / (y * x)) * L(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,7107,a(flip),b,8150,a),flip(a)].">
      <j1 rule="hyper" parents="316 7107 8150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8152">
    <literal><![CDATA[
      x \ ((x / (y * x)) * L(y * x,z,u)) = x \ ((x / (x * y)) * L(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7101,a(flip),b,8151,a)].">
      <j1 rule="hyper" parents="63 7101 8151"/>
    </justification>
  </clause>

  <clause id="8153">
    <literal><![CDATA[
      ((x * y) * (z * a(u,w,u))) / ((y * z) * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5372,a(flip),b,5412,a),flip(a)].">
      <j1 rule="hyper" parents="316 5372 5412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8155">
    <literal><![CDATA[
      ((x * y) * (z * a(u,w,u))) / (y * (z * a(u,w,u))) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5391(a,1),8153(a,1,2))].">
      <j1 rule="para" parents="5391 8153"/>
    </justification>
  </clause>

  <clause id="8156">
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,20,a,b,8155,a)].">
      <j1 rule="hyper" parents="63 20 8155"/>
    </justification>
  </clause>

  <clause id="8157">
    <literal><![CDATA[
      R(x,y,R(z,u,z) \ w) = R(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(5432(a,1),8156(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5432 8156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8158">
    <literal><![CDATA[
      R(L(T(1 / x,y),z,x),x,x \ y) = y \ (1 * (R(x,z,x) \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7843,a(flip),b,8157,a),flip(a)].">
      <j1 rule="hyper" parents="63 7843 8157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8160">
    <literal><![CDATA[
      L(R(T(1 / x,y),x,x \ y),z,x) = y \ (1 * (R(x,z,x) \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,29,a(flip),b,8158,a)].">
      <j1 rule="hyper" parents="63 29 8158"/>
    </justification>
  </clause>

  <clause id="8161">
    <literal><![CDATA[
      x \ (1 * (R(y,z,y) \ x)) = L(x \ (y \ x),z,y)
    ]]></literal>
    <justification jstring="[para(827(a,1),8160(a,1,1)),flip(a)].">
      <j1 rule="para" parents="827 8160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8162">
    <literal><![CDATA[
      L(x \ (y \ x),z,y) = x \ (R(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(328,a,8161,a),flip(a)].">
      <j1 rule="hyper" parents="328 8161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8163">
    <literal><![CDATA[
      a(x,y,x) \ (z \ (x \ z)) = L(z \ (x \ z),y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,5433,a,b,8162,a)].">
      <j1 rule="hyper" parents="316 5433 8162"/>
    </justification>
  </clause>

  <clause id="8164">
    <literal><![CDATA[
      (L(x,y,x) * y) \ y = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(38,a,5441,a(flip),b,8163,a)].">
      <j1 rule="hyper" parents="38 5441 8163"/>
    </justification>
  </clause>

  <clause id="8165">
    <literal><![CDATA[
      (L(x,y / x,x) * (y / x)) \ (y / x) = (x \ y) \ (x \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(316,a,3215,a(flip),b,8164,a),flip(a)].">
      <j1 rule="hyper" parents="316 3215 8164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8166">
    <literal><![CDATA[
      x / (x \ (y \ x)) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(210,a,8164,a)].">
      <j1 rule="hyper" parents="210 8164"/>
    </justification>
  </clause>

  <clause id="8167">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * L(u,x \ R(x,y,z),u)) \ (x \ R(x,y,z)) = (x \ R(x,y,z)) \ (u \ (x \ R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,2264,a,b,8164,a)].">
      <j1 rule="hyper" parents="63 2264 8164"/>
    </justification>
  </clause>

  <clause id="8168">
    <literal><![CDATA[
      (x / (x \ (y \ x))) * z = (L(y,x,y) * x) * z
    ]]></literal>
    <justification jstring="[para(8164(a,1),198(a,1,1,2))].">
      <j1 rule="para" parents="8164 198"/>
    </justification>
  </clause>

  <clause id="8169">
    <literal><![CDATA[
      ((x * (y * x)) / x) \ y = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(1623(a,2),8164(a,1,1))].">
      <j1 rule="para" parents="1623 8164"/>
    </justification>
  </clause>

  <clause id="8170">
    <literal><![CDATA[
      (x / (L(y,x,y) * x)) * L(L(y,x,y) * x,z,u) = L(L(y,x,y) * x,z,u) * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(8164(a,1),4325(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8164 4325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8172">
    <literal><![CDATA[
      L(L(x,y,x) * y,z,u) * (y \ (x \ y)) = (y \ (x \ y)) * L((y \ (x \ y)) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(8166(a,1),602(a,1,1,1))].">
      <j1 rule="para" parents="8166 602"/>
    </justification>
  </clause>

  <clause id="8173">
    <literal><![CDATA[
      (x \ ((x / (x \ (y \ x))) * L(x \ (y \ x),z,u))) * x = (L(y,x,y) * x) * L(x \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(8166(a,1),5130(a,2,1))].">
      <j1 rule="para" parents="8166 5130"/>
    </justification>
  </clause>

  <clause id="8174">
    <literal><![CDATA[
      (x * y) * (x \ (y \ x)) = K(x * y,y) * x
    ]]></literal>
    <justification jstring="[para(8169(a,1),3010(a,1,2))].">
      <j1 rule="para" parents="8169 3010"/>
    </justification>
  </clause>

  <clause id="8175">
    <literal><![CDATA[
      L(x,y,z * ((u \ (u * (w * u))) \ w)) = L(x,y,z * (w \ (u \ w)))
    ]]></literal>
    <justification jstring="[para(8169(a,1),3219(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="8169 3219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8176">
    <literal><![CDATA[
      (L(L(x,y,z) \ x,u,w) \ (L(L(x,y,z) \ x,u,w) * (v5 * L(L(x,y,z) \ x,u,w)))) \ v5 = v5 \ (L(L(x,y,z) \ x,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(6486(a,1),8169(a,1,1))].">
      <j1 rule="para" parents="6486 8169"/>
    </justification>
  </clause>

  <clause id="8177">
    <literal><![CDATA[
      (x * y) * (x \ (y \ x)) = x * K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,3640,a(flip),b,8174,a),flip(a)].">
      <j1 rule="hyper" parents="316 3640 8174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8178">
    <literal><![CDATA[
      (x * y) * (x \ (y \ x)) = x * K(x * y,y)
    ]]></literal>
    <justification jstring="[para(3549(a,2),8177(a,2,2))].">
      <j1 rule="para" parents="3549 8177"/>
    </justification>
  </clause>

  <clause id="8179">
    <literal><![CDATA[
      R(x,y,y) \ (x * K(x * y,y)) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(8178(a,1),7681(a,1,2))].">
      <j1 rule="para" parents="8178 7681"/>
    </justification>
  </clause>

  <clause id="8180">
    <literal><![CDATA[
      (R(x,y,y) \ x) * K(x * y,y) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3781,a(flip),b,8179,a)].">
      <j1 rule="hyper" parents="63 3781 8179"/>
    </justification>
  </clause>

  <clause id="8181">
    <literal><![CDATA[
      a(x,y,y) \ K(x * y,y) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,7663,a(flip),b,8180,a)].">
      <j1 rule="hyper" parents="63 7663 8180"/>
    </justification>
  </clause>

  <clause id="8182">
    <literal><![CDATA[
      a(x,y,y) \ K(y * x,y) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(3549(a,1),8181(a,1,2))].">
      <j1 rule="para" parents="3549 8181"/>
    </justification>
  </clause>

  <clause id="8183">
    <literal><![CDATA[
      a(x * (y \ (x \ y)),z,u) = a(a(y,x,x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(8181(a,1),3806(a,1,1))].">
      <j1 rule="para" parents="8181 3806"/>
    </justification>
  </clause>

  <clause id="8184">
    <literal><![CDATA[
      a(x,y,(z * (u \ (z \ u))) * w) = a(x,y,a(u,z,z) * w)
    ]]></literal>
    <justification jstring="[para(8181(a,1),5733(a,1,3,1))].">
      <j1 rule="para" parents="8181 5733"/>
    </justification>
  </clause>

  <clause id="8185">
    <literal><![CDATA[
      a(x,y,(z * (u * (w \ (u \ w)))) \ v5) = a(x,y,(z * a(w,u,u)) \ v5)
    ]]></literal>
    <justification jstring="[para(8181(a,1),6068(a,1,3,1,2))].">
      <j1 rule="para" parents="8181 6068"/>
    </justification>
  </clause>

  <clause id="8186">
    <literal><![CDATA[
      L(x \ K(x * y,x),x,y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(34,a,7396,a,b,8182,a(flip))].">
      <j1 rule="hyper" parents="34 7396 8182"/>
    </justification>
  </clause>

  <clause id="8187">
    <literal><![CDATA[
      (x * a(y,x,x)) \ K(x * y,x * a(z,u,u)) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7377,a,b,8186,a)].">
      <j1 rule="hyper" parents="63 7377 8186"/>
    </justification>
  </clause>

  <clause id="8188">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w) \ 1,L(a(x,y,z),u,w),v5) = v5 \ (L(a(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(2438(a,1),8186(a,1,1,2))].">
      <j1 rule="para" parents="2438 8186"/>
    </justification>
  </clause>

  <clause id="8189">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w \ u)) * w)) = a(x,y,a(u,w,w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5623,a(flip),b,8184,a)].">
      <j1 rule="hyper" parents="63 5623 8184"/>
    </justification>
  </clause>

  <clause id="8190">
    <literal><![CDATA[
      T(x * a(y,x,x),x * y) = 1 / (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(209,a,8187,a(flip),b,2944,a),flip(a)].">
      <j1 rule="hyper" parents="209 8187 2944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8191">
    <literal><![CDATA[
      (L(x,x \ y,x) * (y / x)) \ (y / x) = (x \ y) \ (x \ (x \ y))
    ]]></literal>
    <justification jstring="[para(3296(a,1),8165(a,1,1,1))].">
      <j1 rule="para" parents="3296 8165"/>
    </justification>
  </clause>

  <clause id="8192">
    <literal><![CDATA[
      (x * (y / R(x,x \ y,x))) \ (y / x) = (x \ y) \ (x \ (x \ y))
    ]]></literal>
    <justification jstring="[para(5435(a,1),8191(a,1,1))].">
      <j1 rule="para" parents="5435 8191"/>
    </justification>
  </clause>

  <clause id="8193">
    <literal><![CDATA[
      (x * (K(x,y) * (x \ y))) \ (y / x) = (x \ y) \ (x \ (x \ y))
    ]]></literal>
    <justification jstring="[para(3026(a,1),8192(a,1,1,2))].">
      <j1 rule="para" parents="3026 8192"/>
    </justification>
  </clause>

  <clause id="8194">
    <literal><![CDATA[
      (T(x,y) * (x \ y)) \ (y / x) = (x \ y) \ (x \ (x \ y))
    ]]></literal>
    <justification jstring="[para(2867(a,1),8193(a,1,1))].">
      <j1 rule="para" parents="2867 8193"/>
    </justification>
  </clause>

  <clause id="8195">
    <literal><![CDATA[
      (x \ y) \ (x \ (x \ y)) = (y * K(x,y)) \ (y / x)
    ]]></literal>
    <justification jstring="[para(2824(a,1),8194(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2824 8194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8196">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ u)) = L(x,y,z * (u \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(9(a,1),8175(a,1,3,2,1))].">
      <j1 rule="para" parents="9 8175"/>
    </justification>
  </clause>

  <clause id="8197">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ w)) = L(x,y,z * (w \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6251,a,b,8196,a)].">
      <j1 rule="hyper" parents="63 6251 8196"/>
    </justification>
  </clause>

  <clause id="8199">
    <literal><![CDATA[
      L(x,y,z * (u \ (z \ u))) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7491,a(flip),b,8197,a),flip(a)].">
      <j1 rule="hyper" parents="63 7491 8197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8200">
    <literal><![CDATA[
      a(x,y,((z * (u \ (z \ u))) * w) \ v5) = a(x,y,(w * a(u,z,z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5626,a,b,8185,a)].">
      <j1 rule="hyper" parents="63 5626 8185"/>
    </justification>
  </clause>

  <clause id="8201">
    <literal><![CDATA[
      a(x,y,((z * ((u * w) / u)) * u) \ (z * (u * w))) = a(x,y,a(u,(u * w) / u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6075,a(flip),b,6134,a)].">
      <j1 rule="hyper" parents="63 6075 6134"/>
    </justification>
  </clause>

  <clause id="8203">
    <literal><![CDATA[
      a(x,y,(z * ((u * w) / u)) \ ((z * (u * w)) / u)) = a(x,y,a(u,(u * w) / u,z))
    ]]></literal>
    <justification jstring="[para(7224(a,1),8201(a,1,3))].">
      <j1 rule="para" parents="7224 8201"/>
    </justification>
  </clause>

  <clause id="8204">
    <literal><![CDATA[
      (L(x,y,z) \ (L(x,y,z) \ x)) * L(x,y,z) = L(T(x,L(x,y,z) \ 1),y,z) \ x
    ]]></literal>
    <justification jstring="[para(1003(a,1),6566(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1003 6566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8205">
    <literal><![CDATA[
      (L(x,y,z) \ (L(x,y,z) \ x)) * L(x,y,z) = L(T(x,x \ 1),y,z) \ x
    ]]></literal>
    <justification jstring="[para(4471(a,1),8204(a,2,1,1))].">
      <j1 rule="para" parents="4471 8204"/>
    </justification>
  </clause>

  <clause id="8206">
    <literal><![CDATA[
      L(T(x,x \ 1),y,z) \ x = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,4424,a(flip),b,8205,a),flip(a)].">
      <j1 rule="hyper" parents="63 4424 8205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8209">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ x = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(115(a,1),8206(a,1,1,1))].">
      <j1 rule="para" parents="115 8206"/>
    </justification>
  </clause>

  <clause id="8210">
    <literal><![CDATA[
      R(x,y,R(z / u,u,z \ (w \ v5)) \ (w \ v5)) = R(x,y,u * (z \ ((w \ 1) \ v5)))
    ]]></literal>
    <justification jstring="[para(6716(a,1),6718(a,1,3,1))].">
      <j1 rule="para" parents="6716 6718"/>
    </justification>
  </clause>

  <clause id="8211">
    <literal><![CDATA[
      R(x,y,z * (u \ ((w \ 1) \ v5))) = R(x,y,z * (u \ (w \ v5)))
    ]]></literal>
    <justification jstring="[para(490(a,1),8210(a,1,3)),flip(a)].">
      <j1 rule="para" parents="490 8210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8212">
    <literal><![CDATA[
      R(x,y,z * ((u * w) \ w)) = R(x,y,z * (w \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,4978,a(flip),b,8211,a)].">
      <j1 rule="hyper" parents="63 4978 8211"/>
    </justification>
  </clause>

  <clause id="8213">
    <literal><![CDATA[
      R(x,y,z * (u \ (z \ u))) = L(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7387,a(flip),b,8212,a),flip(a)].">
      <j1 rule="hyper" parents="63 7387 8212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8214">
    <literal><![CDATA[
      L(x,y,a(z \ u,z,z)) = L(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7388,a(flip),b,8213,a)].">
      <j1 rule="hyper" parents="63 7388 8213"/>
    </justification>
  </clause>

  <clause id="8215">
    <literal><![CDATA[
      R(x,a(y,z,u),L(u,w,v5)) = L(x,L(u,w,v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5343,a(flip),b,6985,a),flip(a)].">
      <j1 rule="hyper" parents="63 5343 6985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8216">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ u) \ (z * u)) = R(x,y,(u / (z \ 1)) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4744,a(flip),b,7024,a),flip(a)].">
      <j1 rule="hyper" parents="63 4744 7024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8217">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ u) \ (z * u)) = R(x,y,(z * u) * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(316,a,4676,a,b,8216,a),flip(a)].">
      <j1 rule="hyper" parents="316 4676 8216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8218">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ u) \ (z * u)) = R(x,y,(z * u) * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(316,a,4683,a(flip),b,8217,a),flip(a)].">
      <j1 rule="hyper" parents="316 4683 8217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8219">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,(z \ 1) \ u)) = a(x,y,((z \ 1) \ u) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5539,a(flip),b,7048,a)].">
      <j1 rule="hyper" parents="63 5539 7048"/>
    </justification>
  </clause>

  <clause id="8220">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,z \ u)) = a(x,y,((z \ 1) \ u) \ (z * u))
    ]]></literal>
    <justification jstring="[para(5814(a,1),8219(a,1,3))].">
      <j1 rule="para" parents="5814 8219"/>
    </justification>
  </clause>

  <clause id="8221">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,z \ u)) = a(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,6961,a(flip),b,8220,a),flip(a)].">
      <j1 rule="hyper" parents="316 6961 8220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8222">
    <literal><![CDATA[
      a(x,y,a(z \ u,z,u)) = a(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7042,a,b,8221,a)].">
      <j1 rule="hyper" parents="63 7042 8221"/>
    </justification>
  </clause>

  <clause id="8223">
    <literal><![CDATA[
      a(x \ y,z,a(y,x,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,6902,a(flip),b,8221,a),flip(a)].">
      <j1 rule="hyper" parents="63 6902 8221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8224">
    <literal><![CDATA[
      L(a(x,y,y),z,y \ x) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(52,a,8223,a)].">
      <j1 rule="hyper" parents="52 8223"/>
    </justification>
  </clause>

  <clause id="8225">
    <literal><![CDATA[
      a(x,y,a(R(z,u,u),z * u,z * u)) = a(x,y,a(u \ 1,z * u,R(z,u,u)))
    ]]></literal>
    <justification jstring="[para(570(a,1),8222(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="570 8222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8226">
    <literal><![CDATA[
      a(x,y,a(R(z,u,u),z * u,z * u)) = a(x,y,a(u \ 1,z * u,L(z,u,u)))
    ]]></literal>
    <justification jstring="[para(5746(a,1),8225(a,2,3))].">
      <j1 rule="para" parents="5746 8225"/>
    </justification>
  </clause>

  <clause id="8227">
    <literal><![CDATA[
      a(x,y,((z * (u / T(w * w,v5))) * v6) \ (z * (v6 * u))) = a(x,y,a(v6,u / T(w * w,v5),z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7522,a(flip),b,7471,a)].">
      <j1 rule="hyper" parents="63 7522 7471"/>
    </justification>
  </clause>

  <clause id="8229">
    <literal><![CDATA[
      L((1 / x) * K(y / x,x \ 1),x \ 1,y) = (y * (x \ (x \ 1))) / (y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(3392(a,1),8095(a,1,1,2))].">
      <j1 rule="para" parents="3392 8095"/>
    </justification>
  </clause>

  <clause id="8230">
    <literal><![CDATA[
      L(T(x,a(y,z,u) \ 1),u \ L(u,z,y),u) = R(x,u \ L(u,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4426,a(flip),b,8143,a),flip(a)].">
      <j1 rule="hyper" parents="316 4426 8143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8231">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),y) = L(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(4989(a,1),8230(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4989 8230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8232">
    <literal><![CDATA[
      L(x \ L(x,y \ L(y,z,u),y),x,L(y,z,u)) = a(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(8231(a,1),3425(a,1,1,2))].">
      <j1 rule="para" parents="8231 3425"/>
    </justification>
  </clause>

  <clause id="8233">
    <literal><![CDATA[
      L(x \ L(x,y,y \ L(y,z,u)),x,L(y,z,u)) = a(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(1537(a,1),8232(a,1,1,2))].">
      <j1 rule="para" parents="1537 8232"/>
    </justification>
  </clause>

  <clause id="8234">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),y) = a(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7730,a(flip),b,8233,a),flip(a)].">
      <j1 rule="hyper" parents="63 7730 8233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8235">
    <literal><![CDATA[
      x \ L(x,y,y \ L(y,z,u)) = a(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(41,a,6969,a,b,8233,a),flip(a)].">
      <j1 rule="hyper" parents="41 6969 8233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8236">
    <literal><![CDATA[
      L(a(x,y \ L(y,z,u),y),w,y) = a(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6898,a,b,8234,a)].">
      <j1 rule="hyper" parents="63 6898 8234"/>
    </justification>
  </clause>

  <clause id="8237">
    <literal><![CDATA[
      a(x,(y * z) \ L(y * z,u,w),z * y) = a(x,y * z,(y * z) * L(y * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,8234,a)].">
      <j1 rule="hyper" parents="63 5469 8234"/>
    </justification>
  </clause>

  <clause id="8238">
    <literal><![CDATA[
      a(x,(y * y) * z,((y * y) * z) * L((y * y) * z,u,w)) = a(x,((y * y) * z) \ L((y * y) * z,u,w),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5803,a(flip),b,8234,a),flip(a)].">
      <j1 rule="hyper" parents="63 5803 8234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8239">
    <literal><![CDATA[
      a(x,(y \ 1) * z,((y \ 1) * z) * L((y \ 1) * z,u,w)) = a(x,((y \ 1) * z) \ L((y \ 1) * z,u,w),y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5564,a(flip),b,8234,a),flip(a)].">
      <j1 rule="hyper" parents="63 5564 8234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8241">
    <literal><![CDATA[
      x \ L(x,y,y \ L(y,z,u)) = a(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,8234,a(flip),b,8235,a),flip(a)].">
      <j1 rule="hyper" parents="316 8234 8235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8243">
    <literal><![CDATA[
      x \ L(x,y * z,(y * z) \ L(y * z,z,y)) = a(x,y * z,y * (z * (y * z)))
    ]]></literal>
    <justification jstring="[para(100(a,1),8241(a,2,3))].">
      <j1 rule="para" parents="100 8241"/>
    </justification>
  </clause>

  <clause id="8244">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) * (x \ y) = L(x \ y,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(8241(a,1),1853(a,1,1))].">
      <j1 rule="para" parents="8241 1853"/>
    </justification>
  </clause>

  <clause id="8245">
    <literal><![CDATA[
      L(a(x,y,y * L(y,z,u)),w,y) = a(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(8234(a,1),8236(a,1,1))].">
      <j1 rule="para" parents="8234 8236"/>
    </justification>
  </clause>

  <clause id="8246">
    <literal><![CDATA[
      x \ L(x,y * z,a(y * z,z,y)) = a(x,y * z,y * (z * (y * z)))
    ]]></literal>
    <justification jstring="[para(7836(a,1),8243(a,1,2))].">
      <j1 rule="para" parents="7836 8243"/>
    </justification>
  </clause>

  <clause id="8247">
    <literal><![CDATA[
      x \ L(x,y * z,a(y * z,z,y)) = a(x,y * z,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,7279,a(flip),b,8246,a),flip(a)].">
      <j1 rule="hyper" parents="316 7279 8246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8248">
    <literal><![CDATA[
      L(L(x,y,x) * y,z,u) * (y \ (x \ y)) = ((x \ y) / y) \ L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,6834,a(flip),b,8172,a),flip(a)].">
      <j1 rule="hyper" parents="316 6834 8172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8249">
    <literal><![CDATA[
      ((x \ 1) * ((1 / x) * (((1 / x) * y) \ y))) / (x \ 1) = ((y / x) / y) / (1 / x)
    ]]></literal>
    <justification jstring="[para(83(a,1),3341(a,2,1,1,2))].">
      <j1 rule="para" parents="83 3341"/>
    </justification>
  </clause>

  <clause id="8251">
    <literal><![CDATA[
      R(x,y,z \ ((L(L(u,w,v5),v6,v7) \ 1) * (u \ 1))) = R(x,y,z \ (u \ L(L(u,w,v5),v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(63,a,4775,a(flip),b,4915,a)].">
      <j1 rule="hyper" parents="63 4775 4915"/>
    </justification>
  </clause>

  <clause id="8252">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) / w) * R(w,u,a(x,y,z)) = w \ ((w * u) * (a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(1033(a,1),5039(a,1,2))].">
      <j1 rule="para" parents="1033 5039"/>
    </justification>
  </clause>

  <clause id="8253">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) / w) * L(w,u,a(x,y,z)) = w \ ((w * u) * (a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(5371(a,1),8252(a,1,2))].">
      <j1 rule="para" parents="5371 8252"/>
    </justification>
  </clause>

  <clause id="8254">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * ((a(z,u,w) \ 1) * y) = (x * y) * (a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(38,a,4382,a,b,8253,a(flip))].">
      <j1 rule="hyper" parents="38 4382 8253"/>
    </justification>
  </clause>

  <clause id="8255">
    <literal><![CDATA[
      L(x,a(y,z,u) \ 1,w) * ((a(y,z,u) \ 1) * w) = (x * (a(y,z,u) \ 1)) * w
    ]]></literal>
    <justification jstring="[hyper(316,a,7197,a(flip),b,5060,a),flip(a)].">
      <j1 rule="hyper" parents="316 7197 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8256">
    <literal><![CDATA[
      R(x,a(y,z,u) \ 1,w) = L(x,a(y,z,u) \ 1,w)
    ]]></literal>
    <justification jstring="[hyper(35,a,109,a,b,8255,a)].">
      <j1 rule="hyper" parents="35 109 8255"/>
    </justification>
  </clause>

  <clause id="8260">
    <literal><![CDATA[
      x \ (L(x,y,z) * L(L(x,y,z) \ x,u,w)) = x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,1252,a(flip),b,5155,a)].">
      <j1 rule="hyper" parents="63 1252 5155"/>
    </justification>
  </clause>

  <clause id="8261">
    <literal><![CDATA[
      x * (x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))) = L(x,y,z) * L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,5155,a(flip),b,1252,a(flip))].">
      <j1 rule="hyper" parents="139 5155 1252"/>
    </justification>
  </clause>

  <clause id="8265">
    <literal><![CDATA[
      L(x,y,z \ ((T(u,w) * u) * (T(u,w) \ v5))) = L(x,y,z \ (v5 / (T(u,w) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3319,a(flip),b,5173,a),flip(a)].">
      <j1 rule="hyper" parents="63 3319 5173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8267">
    <literal><![CDATA[
      L(x,y,z \ ((T(u,w) * u) * (T(u,w) \ v5))) = L(x,y,z \ ((T(u,w) \ 1) \ v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,3243,a(flip),b,8265,a),flip(a)].">
      <j1 rule="hyper" parents="316 3243 8265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8268">
    <literal><![CDATA[
      a(x,y,z \ (u \ (((w * (v5 * v6)) / v6) * v6))) = a(x,y,z \ (u \ (w * (v5 * (v6 \ 1)))))
    ]]></literal>
    <justification jstring="[hyper(63,a,7736,a(flip),b,5779,a)].">
      <j1 rule="hyper" parents="63 7736 5779"/>
    </justification>
  </clause>

  <clause id="8269">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * (v5 * (v6 \ 1))))) = a(x,y,z \ (u \ (w * (v5 * v6))))
    ]]></literal>
    <justification jstring="[para(12(a,1),8268(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="12 8268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8271">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w * (v5 \ 1)) * v6))) = a(x,y,z \ (u \ (v6 * (w * v5))))
    ]]></literal>
    <justification jstring="[hyper(63,a,5602,a,b,8269,a)].">
      <j1 rule="hyper" parents="63 5602 8269"/>
    </justification>
  </clause>

  <clause id="8273">
    <literal><![CDATA[
      a(x,y,(((z \ K(u,w)) \ (v5 \ 1)) \ v6) * v7) = a(x,y,(((z \ 1) \ (v5 \ K(w,u))) \ v6) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,5549,a(flip),b,5793,a)].">
      <j1 rule="hyper" parents="63 5549 5793"/>
    </justification>
  </clause>

  <clause id="8275">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ (((v5 * v6) \ v5) \ 1)))) = a(x,y,z \ (u * (w \ ((v6 * v5) \ v5))))
    ]]></literal>
    <justification jstring="[hyper(63,a,6343,a(flip),b,6270,a),flip(a)].">
      <j1 rule="hyper" parents="63 6343 6270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8277">
    <literal><![CDATA[
      a(x,y,(((z * z) * (z \ u)) \ w) \ v5) = a(x,y,((v6 * v6) * (T(u / (z \ 1),z) \ w)) \ v5)
    ]]></literal>
    <attribute><![CDATA[
      label(flip_matches_hint)
    ]]></attribute>
    <justification jstring="[hyper(63,a,5958,a(flip),b,6446,a)].">
      <j1 rule="hyper" parents="63 5958 6446"/>
    </justification>
  </clause>

  <clause id="8279">
    <literal><![CDATA[
      R(L(x,y,z) \ x,x,L(x,y,z) \ u) \ u = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(4829(a,1),6611(a,1,1))].">
      <j1 rule="para" parents="4829 6611"/>
    </justification>
  </clause>

  <clause id="8280">
    <literal><![CDATA[
      R(L(x,y,z) \ x,x \ 1,L(x,y,z) \ u) \ u = (x \ 1) * ((L(x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(4789(a,1),6731(a,1,1))].">
      <j1 rule="para" parents="4789 6731"/>
    </justification>
  </clause>

  <clause id="8281">
    <literal><![CDATA[
      a(x,y,((L(z \ 1,u,w) \ 1) * v5) * v6) = a(x,y,(v5 * (L(z,u,w) \ 1)) * v6)
    ]]></literal>
    <justification jstring="[para(7091(a,1),6733(a,1,3,1,1))].">
      <j1 rule="para" parents="7091 6733"/>
    </justification>
  </clause>

  <clause id="8282">
    <literal><![CDATA[
      a(x,y,(z * (L(u,w,v5) \ 1)) * v6) = a(x,y,v6 * (z * L(u \ 1,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5901,a(flip),b,8281,a),flip(a)].">
      <j1 rule="hyper" parents="63 5901 8281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8283">
    <literal><![CDATA[
      a(x,y,z * (u * L(w \ 1,v5,v6))) = a(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5896,a(flip),b,8282,a),flip(a)].">
      <j1 rule="hyper" parents="63 5896 8282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8284">
    <literal><![CDATA[
      a(x,y,z * ((u * (L(u,w,v5) \ u)) * v6)) = a(x,y,z * (v6 * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7610,a,b,8283,a)].">
      <j1 rule="hyper" parents="63 7610 8283"/>
    </justification>
  </clause>

  <clause id="8285">
    <literal><![CDATA[
      a(x,y,((z * (L(z,u,w) \ z)) * v5) * v6) = a(x,y,v6 * (v5 * L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7609,a,b,8283,a)].">
      <j1 rule="hyper" parents="63 7609 8283"/>
    </justification>
  </clause>

  <clause id="8286">
    <literal><![CDATA[
      a(x,y,(z * ((L((u \ 1) * w,v5,v6) \ ((u \ 1) * w)) * (w * u))) * v7) = a(x,y,v7 * (z * L((u \ 1) * w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7580,a(flip),b,8284,a)].">
      <j1 rule="hyper" parents="63 7580 8284"/>
    </justification>
  </clause>

  <clause id="8293">
    <literal><![CDATA[
      T((x * y) * ((x / (y \ 1)) \ 1),x * y) = R(a(x,y,y),x / (y \ 1),x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,2894,a(flip),b,6929,a)].">
      <j1 rule="hyper" parents="63 2894 6929"/>
    </justification>
  </clause>

  <clause id="8294">
    <literal><![CDATA[
      T((x * y) * ((x / (y \ 1)) \ 1),x * y) = R(a(x,y,y),x / (y \ 1),(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,4680,a(flip),b,8293,a),flip(a)].">
      <j1 rule="hyper" parents="316 4680 8293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8295">
    <literal><![CDATA[
      T((x * y) * ((x / (y \ 1)) \ 1),x * y) = R(a(x,y,y),x / (y \ 1),y \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,4789,a(flip),b,8294,a),flip(a)].">
      <j1 rule="hyper" parents="316 4789 8294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8296">
    <literal><![CDATA[
      (x * (x \ y)) \ ((x * ((x \ y) * (x \ y))) / (x \ y)) = L((x \ y) * (y \ x),x \ y,x * (x \ y))
    ]]></literal>
    <justification jstring="[para(456(a,1),7128(a,1,1)),flip(a)].">
      <j1 rule="para" parents="456 7128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8299">
    <literal><![CDATA[
      (x * ((y * z) / y)) \ ((x * (((y * z) / y) * y)) / y) = (x * z) \ ((x * (z * y)) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7623,a(flip),b,7225,a),flip(a)].">
      <j1 rule="hyper" parents="63 7623 7225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8300">
    <literal><![CDATA[
      (x * ((y * z) / y)) \ ((x * (y * z)) / y) = (x * z) \ ((x * (z * y)) / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),8299(a,1,2,1,2))].">
      <j1 rule="para" parents="12 8299"/>
    </justification>
  </clause>

  <clause id="8302">
    <literal><![CDATA[
      a(x,y,a(z,(z * u) / z,w)) = a(x,y,(w * u) \ ((w * (u * z)) / z))
    ]]></literal>
    <justification jstring="[para(8300(a,1),8203(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8300 8203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8303">
    <literal><![CDATA[
      a(x,y,a(z,(z * u) / z,w)) = a(x,y,(w * u) \ (z \ (w * (u * z))))
    ]]></literal>
    <justification jstring="[hyper(316,a,5497,a(flip),b,8302,a),flip(a)].">
      <j1 rule="hyper" parents="316 5497 8302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8305">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * R(1 / v5,v5,v5 \ R(z,u,w))) = a(x,y,v5 \ R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5487,a(flip),b,7382,a),flip(a)].">
      <j1 rule="hyper" parents="316 5487 7382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8307">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * L(1 / v5,v5,v5 \ R(z,u,w))) = a(x,y,v5 \ R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7272,a(flip),b,8305,a)].">
      <j1 rule="hyper" parents="63 7272 8305"/>
    </justification>
  </clause>

  <clause id="8308">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * L(1 / v5,v5,v5 \ L(z,u,w))) = a(x,y,v5 \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(7482(a,1),8307(a,1,3,2))].">
      <j1 rule="para" parents="7482 8307"/>
    </justification>
  </clause>

  <clause id="8309">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) / v5) * (v5 * (1 / v5))) = a(x,y,v5 \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(1606(a,1),8308(a,1,3))].">
      <j1 rule="para" parents="1606 8308"/>
    </justification>
  </clause>

  <clause id="8310">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) / v5) * K(v5,v5 \ 1)) = a(x,y,v5 \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(1085(a,2),8309(a,1,3,2))].">
      <j1 rule="para" parents="1085 8309"/>
    </justification>
  </clause>

  <clause id="8312">
    <literal><![CDATA[
      L(x,y,y \ 1) \ K(y,y \ 1) = (x \ 1) * (x * (((y \ 1) * (y * x)) \ 1))
    ]]></literal>
    <justification jstring="[para(3747(a,1),7629(a,1,2))].">
      <j1 rule="para" parents="3747 7629"/>
    </justification>
  </clause>

  <clause id="8314">
    <literal><![CDATA[
      (x \ 1) * (x * (((y \ 1) * (y * x)) \ 1)) = ((y \ 1) * (y * x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,2452,a(flip),b,8312,a),flip(a)].">
      <j1 rule="hyper" parents="63 2452 8312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8315">
    <literal><![CDATA[
      L((x * (((y \ 1) * (y * x)) \ 1)) \ z,x * (((y \ 1) * (y * x)) \ 1),x \ 1) = (((y \ 1) * (y * x)) \ 1) \ ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(8314(a,1),102(a,2,1))].">
      <j1 rule="para" parents="8314 102"/>
    </justification>
  </clause>

  <clause id="8316">
    <literal><![CDATA[
      (((x \ 1) * (x * y)) \ 1) \ R(y \ 1,y * (((x \ 1) * (x * y)) \ 1),y * (((x \ 1) * (x * y)) \ 1)) = (y * (((x \ 1) * (x * y)) \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(8314(a,1),570(a,1,1))].">
      <j1 rule="para" parents="8314 570"/>
    </justification>
  </clause>

  <clause id="8317">
    <literal><![CDATA[
      (x * L(y,z,y)) \ (L(a(u,w,v5),y,x) \ (x * L(y,z,y))) = (x * (L(y,z,y) * a(u,w,v5))) \ (x * L(y,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8188,a(flip),b,7689,a)].">
      <j1 rule="hyper" parents="63 8188 7689"/>
    </justification>
  </clause>

  <clause id="8318">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,L(x,y,z),z * y) = (z * (L(y,u,y) * x)) \ (z * L(y,u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7715,a(flip),b,7689,a)].">
      <j1 rule="hyper" parents="63 7715 7689"/>
    </justification>
  </clause>

  <clause id="8320">
    <literal><![CDATA[
      (x * (L(y,z,y) * u)) \ (x * L(y,z,y)) = (x * (y * u)) \ ((x * y) * 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,488,a(flip),b,8318,a),flip(a)].">
      <j1 rule="hyper" parents="63 488 8318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8321">
    <literal><![CDATA[
      (x * (L(y,z,y) * u)) \ (x * L(y,z,y)) = (x * (y * u)) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,169,a(flip),b,8320,a),flip(a)].">
      <j1 rule="hyper" parents="316 169 8320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8322">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w * (L(w,v5,v6) \ w)) * v7))) = a(x,y,z \ (u \ (v7 * L(w \ 1,v5,v6))))
    ]]></literal>
    <justification jstring="[hyper(316,a,6044,a(flip),b,7738,a),flip(a)].">
      <j1 rule="hyper" parents="316 6044 7738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8323">
    <literal><![CDATA[
      1 \ T((x \ 1) * (x * y),((z \ 1) * (z * u)) \ 1) = K(y,u \ 1) * ((x \ 1) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(3014,a,7946,a),flip(a)].">
      <j1 rule="hyper" parents="3014 7946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8325">
    <literal><![CDATA[
      R(x,y,z \ ((L(L(u,w,v5),v6,v7) \ 1) * u)) = R(x,y,z \ (u \ L(L(u,w,v5),v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(63,a,1728,a(flip),b,8251,a)].">
      <j1 rule="hyper" parents="63 1728 8251"/>
    </justification>
  </clause>

  <clause id="8326">
    <literal><![CDATA[
      R(x,y,z \ (u \ L(L(u,w,v5),v6,v7))) = R(x,y,z \ (u * L(L(u,w,v5),v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(63,a,4746,a(flip),b,8325,a),flip(a)].">
      <j1 rule="hyper" parents="63 4746 8325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8327">
    <literal><![CDATA[
      R(x,y,z \ (L(L(u,w,v5),v6,v7) \ u)) = R(x,y,z \ (u \ L(L(u,w,v5),v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(316,a,1850,a,b,8326,a)].">
      <j1 rule="hyper" parents="316 1850 8326"/>
    </justification>
  </clause>

  <clause id="8328">
    <literal><![CDATA[
      R(x,y,z \ (u * L(L(u \ 1,w,v5),v6,v7))) = R(x,y,z \ (L(L(u,w,v5),v6,v7) \ u))
    ]]></literal>
    <justification jstring="[para(1372(a,2),8327(a,2,3,2)),flip(a)].">
      <j1 rule="para" parents="1372 8327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8329">
    <literal><![CDATA[
      R(x,y,z \ (L(L(z,u,w),v5,v6) \ z)) = R(x,y,L(L(z \ 1,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(9(a,1),8328(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 8328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8330">
    <literal><![CDATA[
      R(x,y,L(L(z \ 1,u,w),v5,v6)) = R(x,y,L(L(z,u,w),v5,v6) \ 1)
    ]]></literal>
    <justification jstring="[para(1849(a,1),8329(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1849 8329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8331">
    <literal><![CDATA[
      R(x,y,L(L(z \ 1,u,w),v5,v6)) = R(x,y,L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,1033,a(flip),b,8330,a),flip(a)].">
      <j1 rule="hyper" parents="316 1033 8330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8333">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,y,z) = x * (x * L(L(x,y,z) \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(2140(a,1),8261(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2140 8261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8334">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,y,z) = L(x * (x * (L(x,y,z) \ 1)),y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1367,a,b,8333,a),flip(a)].">
      <j1 rule="hyper" parents="316 1367 8333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8335">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,y,z) = L(x * (L(x,y,z) \ x),y,z)
    ]]></literal>
    <justification jstring="[para(1002(a,1),8334(a,2,1,2))].">
      <j1 rule="para" parents="1002 8334"/>
    </justification>
  </clause>

  <clause id="8336">
    <literal><![CDATA[
      a(x,y,(((z \ 1) \ (u \ K(w,v5))) \ v6) * v7) = a(x,y,(((z \ K(v5,w)) \ u) \ v6) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,6749,a(flip),b,8273,a),flip(a)].">
      <j1 rule="hyper" parents="63 6749 8273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8338">
    <literal><![CDATA[
      a(x,y,((z * z) * (T(u / (w \ 1),w) \ v5)) \ v6) = a(x,y,((w \ u) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,6707,a(flip),b,8277,a),flip(a)].">
      <j1 rule="hyper" parents="63 6707 8277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8340">
    <literal><![CDATA[
      a(x,y,((z * z) * ((u / (w \ 1)) \ v5)) \ v6) = a(x,y,((w \ u) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5947,a(flip),b,8338,a)].">
      <j1 rule="hyper" parents="63 5947 8338"/>
    </justification>
  </clause>

  <clause id="8342">
    <literal><![CDATA[
      a(x,y,((z / (u \ 1)) \ w) \ v5) = a(x,y,((u \ z) \ w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5954,a(flip),b,8340,a)].">
      <j1 rule="hyper" parents="63 5954 8340"/>
    </justification>
  </clause>

  <clause id="8343">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) \ w) * L(L(z,z,u) \ w,L(z,z,u),u)) = a(x,y,((z \ u) \ (u * w)) \ (L(z,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,2661,a,b,8342,a)].">
      <j1 rule="hyper" parents="63 2661 8342"/>
    </justification>
  </clause>

  <clause id="8344">
    <literal><![CDATA[
      1 \ T((x \ 1) * (x * y),((z \ 1) * (z * y)) \ 1) = (x \ 1) * (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(316,a,4218,a(flip),b,8323,a),flip(a)].">
      <j1 rule="hyper" parents="316 4218 8323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8345">
    <literal><![CDATA[
      1 \ ((((x \ 1) * (x * y)) \ 1) \ 1) = (x \ 1) * (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,311,a(flip),b,8344,a)].">
      <j1 rule="hyper" parents="63 311 8344"/>
    </justification>
  </clause>

  <clause id="8346">
    <literal><![CDATA[
      (((x \ 1) * (x * y)) \ 1) \ 1 = (x \ 1) * (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(179,a,8345,a)].">
      <j1 rule="hyper" parents="179 8345"/>
    </justification>
  </clause>

  <clause id="8349">
    <literal><![CDATA[
      R(x * K(y / z,x),y * (z \ 1),y * z) = ((y * (z \ 1)) * x) * ((y * (z \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(3392(a,1),3152(a,1,1,2))].">
      <j1 rule="para" parents="3392 3152"/>
    </justification>
  </clause>

  <clause id="8350">
    <literal><![CDATA[
      T(((x * (y \ 1)) * z) * ((x * (y \ 1)) \ 1),x / y) = R(z,x * (y \ 1),x * y)
    ]]></literal>
    <justification jstring="[para(8349(a,1),2735(a,1,1))].">
      <j1 rule="para" parents="8349 2735"/>
    </justification>
  </clause>

  <clause id="8353">
    <literal><![CDATA[
      (K(x,y) * (z * u)) / (z * (K((z \ (x \ z)) \ 1,y) * u)) = a(z,K((z \ (x \ z)) \ 1,y),u)
    ]]></literal>
    <justification jstring="[para(406(a,1),3655(a,1,1))].">
      <j1 rule="para" parents="406 3655"/>
    </justification>
  </clause>

  <clause id="8354">
    <literal><![CDATA[
      (x * (L(L(x,y,z),u,w) * v5)) / T(x * L(L(x,u,w),y,z),v5) = L(v5,x,L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(1844(a,1),4373(a,1,1))].">
      <j1 rule="para" parents="1844 4373"/>
    </justification>
  </clause>

  <clause id="8355">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ u) * L(x \ R(x,y,z),x,z * y) = (x \ R(x,y,z)) \ (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(2194(a,1),4418(a,1,1))].">
      <j1 rule="para" parents="2194 4418"/>
    </justification>
  </clause>

  <clause id="8356">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * T(w,x * (L(x,y,z) \ u)) = w * (((x \ L(x,y,z)) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(1894(a,1),4497(a,1,1,1))].">
      <j1 rule="para" parents="1894 4497"/>
    </justification>
  </clause>

  <clause id="8357">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * T(w,x * (L(x,y,z) \ u)) = w * ((L(x,y,z) \ x) * u)
    ]]></literal>
    <justification jstring="[para(1894(a,1),8356(a,2,2,1))].">
      <j1 rule="para" parents="1894 8356"/>
    </justification>
  </clause>

  <clause id="8358">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * T(w,y * (L(y,z,u) \ x)) = w * ((L(y,z,u) \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6498,a(flip),b,8357,a)].">
      <j1 rule="hyper" parents="63 6498 8357"/>
    </justification>
  </clause>

  <clause id="8359">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * T(w,x) = w * ((L(y,z,u) \ y) * x)
    ]]></literal>
    <justification jstring="[para(6513(a,1),8358(a,1,2))].">
      <j1 rule="para" parents="6513 8358"/>
    </justification>
  </clause>

  <clause id="8360">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(253,a,8359,a(flip),b,6498,a)].">
      <j1 rule="hyper" parents="253 8359 6498"/>
    </justification>
  </clause>

  <clause id="8361">
    <literal><![CDATA[
      (x * ((L(y,z,u) \ y) * w)) / ((L(y,z,u) \ y) * T(x,w)) = R(w,L(y,z,u) \ y,T(x,w))
    ]]></literal>
    <justification jstring="[hyper(136,a,8359,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="136 8359 109"/>
    </justification>
  </clause>

  <clause id="8362">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * (L(u,w,v5) \ u)) * v6 = v6 * ((L(u,w,v5) \ u) * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(6477(a,1),8359(a,1,2))].">
      <j1 rule="para" parents="6477 8359"/>
    </justification>
  </clause>

  <clause id="8364">
    <literal><![CDATA[
      T(x / ((L(y,z,u) \ y) * w),w) = ((L(y,z,u) \ y) * w) \ x
    ]]></literal>
    <justification jstring="[hyper(377,a,8360,a),flip(a)].">
      <j1 rule="hyper" parents="377 8360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8365">
    <literal><![CDATA[
      1 / T((L(x,y,z) \ x) \ (1 / u),u) = ((L(x,y,z) \ x) \ (1 / u)) \ 1
    ]]></literal>
    <justification jstring="[para(8360(a,1),2892(a,1,2))].">
      <j1 rule="para" parents="8360 2892"/>
    </justification>
  </clause>

  <clause id="8366">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * (u * w)) / ((L(x,y,z) \ x) * w) = L(u,w,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(40,a,708,a(flip),b,8364,a),flip(a)].">
      <j1 rule="hyper" parents="40 708 8364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8367">
    <literal><![CDATA[
      R(x,y,z * L(z,u,w)) = L(x,y,L(z,u,w) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7759,a(flip),b,8366,a)].">
      <j1 rule="hyper" parents="63 7759 8366"/>
    </justification>
  </clause>

  <clause id="8370">
    <literal><![CDATA[
      x \ L(x,y \ L(y,z,u),L(y,z,u) \ y) = a(x,y \ L(y,z,u),y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,8367,a(flip),b,5721,a)].">
      <j1 rule="hyper" parents="133 8367 5721"/>
    </justification>
  </clause>

  <clause id="8374">
    <literal><![CDATA[
      (x * (L(x,y,z) \ (L(x,y,z) \ x))) * u = u * ((L(x,y,z) \ x) * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(7892(a,1),8362(a,1,1))].">
      <j1 rule="para" parents="7892 8362"/>
    </justification>
  </clause>

  <clause id="8376">
    <literal><![CDATA[
      (x * (L(x,y,z) \ (L(x,y,z) \ x))) * u = u / (L(x,y,z) * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,7890,a(flip),b,8374,a),flip(a)].">
      <j1 rule="hyper" parents="316 7890 8374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8377">
    <literal><![CDATA[
      (x * (L(x,y,z) \ (L(x,y,z) \ x))) \ u = u * (L(x,y,z) * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,11,a(flip),b,8376,a)].">
      <j1 rule="hyper" parents="133 11 8376"/>
    </justification>
  </clause>

  <clause id="8379">
    <literal><![CDATA[
      (x * y) * R(z \ L(z,u,w),y,x) = ((z \ L(z,u,w)) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5524,a(flip),b,5115,a),flip(a)].">
      <j1 rule="hyper" parents="63 5524 5115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8380">
    <literal><![CDATA[
      R(x \ L(x,y,z),u,w) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(34,a,6653,a,b,8379,a),flip(a)].">
      <j1 rule="hyper" parents="34 6653 8379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8381">
    <literal><![CDATA[
      R(x,y,z) \ L(R(x,y,z),u,w) = L(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2158,a,b,8380,a)].">
      <j1 rule="hyper" parents="63 2158 8380"/>
    </justification>
  </clause>

  <clause id="8382">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,(w \ 1) \ v5) = R(x \ L(x,y,z),u,w \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,4789,a(flip),b,8380,a),flip(a)].">
      <j1 rule="hyper" parents="63 4789 8380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8383">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,((w \ 1) * v5) * v6) = R(x \ L(x,y,z),u,v6 * (v5 * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,4766,a(flip),b,8380,a),flip(a)].">
      <j1 rule="hyper" parents="63 4766 8380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8384">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w * ((v5 * v5) * v6)) = R(x \ L(x,y,z),u,w * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,4751,a(flip),b,8380,a),flip(a)].">
      <j1 rule="hyper" parents="63 4751 8380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8386">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w \ 1) = R(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1033,a(flip),b,8380,a),flip(a)].">
      <j1 rule="hyper" parents="63 1033 8380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8387">
    <literal><![CDATA[
      R(x,y,z) * L(x \ L(x,u,w),y,z) = L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,8380,a(flip),b,2158,a)].">
      <j1 rule="hyper" parents="139 8380 2158"/>
    </justification>
  </clause>

  <clause id="8388">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * (u * w) = ((x \ L(x,y,z)) * u) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,8380,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="138 8380 20"/>
    </justification>
  </clause>

  <clause id="8391">
    <literal><![CDATA[
      L(x,x,y \ L(y,z,u)) * L(y \ L(y,z,u),x,x) = x * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(8380(a,1),7167(a,1,2))].">
      <j1 rule="para" parents="8380 7167"/>
    </justification>
  </clause>

  <clause id="8392">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w \ 1) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,8380,a(flip),b,8386,a),flip(a)].">
      <j1 rule="hyper" parents="316 8380 8386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8393">
    <literal><![CDATA[
      L((T(x,y) \ z) \ L(T(x,y) \ z,u,w),v5,v6) = L((x \ z) \ L(x \ z,u,w),v5,v6 \ 1)
    ]]></literal>
    <justification jstring="[para(4869(a,1),8392(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4869 8392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8394">
    <literal><![CDATA[
      L(x \ L(x,y,y \ L(y,z,u)),w,v5) = a(R(x,w,v5),y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8241,a(flip),b,8381,a),flip(a)].">
      <j1 rule="hyper" parents="63 8241 8381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8395">
    <literal><![CDATA[
      L(R(x,y,z),u,w) \ R(x,y,z) = L(x \ L(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(8381(a,1),1894(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8381 1894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8396">
    <literal><![CDATA[
      L(x,y,L(x \ L(x,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(8381(a,1),6158(a,1,3))].">
      <j1 rule="para" parents="8381 6158"/>
    </justification>
  </clause>

  <clause id="8397">
    <literal><![CDATA[
      L(x,y,a(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,7838,a(flip),b,8396,a)].">
      <j1 rule="hyper" parents="63 7838 8396"/>
    </justification>
  </clause>

  <clause id="8398">
    <literal><![CDATA[
      R(x,y,a(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,5371,a,b,8397,a)].">
      <j1 rule="hyper" parents="63 5371 8397"/>
    </justification>
  </clause>

  <clause id="8399">
    <literal><![CDATA[
      L(x \ 1,y,a(x,z,u)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,7848,a(flip),b,8397,a)].">
      <j1 rule="hyper" parents="63 7848 8397"/>
    </justification>
  </clause>

  <clause id="8400">
    <literal><![CDATA[
      a(x,y,z) * (1 / x) = a(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(209,a,8397,a(flip),b,2674,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="209 8397 2674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8401">
    <literal><![CDATA[
      (x * a(y,z,u)) * y = a(y,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,8397,a(flip),b,2353,a)].">
      <j1 rule="hyper" parents="139 8397 2353"/>
    </justification>
  </clause>

  <clause id="8402">
    <literal><![CDATA[
      (a(x,y,z) * u) * x = a(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(139,a,8397,a(flip),b,7635,a(flip))].">
      <j1 rule="hyper" parents="139 8397 7635"/>
    </justification>
  </clause>

  <clause id="8403">
    <literal><![CDATA[
      a(x,y,z) * (x * u) = x * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(138,a,8397,a(flip),b,5343,a),flip(a)].">
      <j1 rule="hyper" parents="138 8397 5343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8404">
    <literal><![CDATA[
      x * (a(x,y,z) \ 1) = a(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,8397,a(flip),b,5375,a),flip(a)].">
      <j1 rule="hyper" parents="133 8397 5375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8405">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * x = a(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,8397,a(flip),b,271,a),flip(a)].">
      <j1 rule="hyper" parents="133 8397 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8407">
    <literal><![CDATA[
      L(R(x,y,z),u,a(x,w,v5)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(8397(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8397 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8408">
    <literal><![CDATA[
      L(L(x,y,z),u,a(x,w,v5)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8397(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8397 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8409">
    <literal><![CDATA[
      (a(x,y,z) * u) * L(x,w,v5) = a(x,y,z) * (u * L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(8397(a,1),403(a,1,2,1))].">
      <j1 rule="para" parents="8397 403"/>
    </justification>
  </clause>

  <clause id="8410">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * R(x,u,w) = a(x,y,z) \ R(x,u,w)
    ]]></literal>
    <justification jstring="[para(8397(a,1),525(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8397 525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8411">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,a(x,w,v5)) = x \ L(L(x,y,z),u,a(x,w,v5))
    ]]></literal>
    <justification jstring="[para(8397(a,1),2138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8397 2138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8412">
    <literal><![CDATA[
      (x * y) * a(x,z,u) = x * (a(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(8397(a,1),5276(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8397 5276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8413">
    <literal><![CDATA[
      a(x,y,z) * (x * u) = x * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(8397(a,1),5382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8397 5382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8414">
    <literal><![CDATA[
      (x * y) * a(x,z,u) = x * (y * a(x,z,u))
    ]]></literal>
    <justification jstring="[para(8397(a,1),5383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8397 5383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8415">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (x * u) = x * (u * (a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(138,a,8398,a(flip),b,7549,a),flip(a)].">
      <j1 rule="hyper" parents="138 8398 7549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8416">
    <literal><![CDATA[
      x * ((y * z) * a(x,y,z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,8398,a(flip),b,688,a)].">
      <j1 rule="hyper" parents="138 8398 688"/>
    </justification>
  </clause>

  <clause id="8417">
    <literal><![CDATA[
      x * ((x \ y) * a(x,z,u)) = y * a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,8398,a(flip),b,106,a(flip))].">
      <j1 rule="hyper" parents="138 8398 106"/>
    </justification>
  </clause>

  <clause id="8418">
    <literal><![CDATA[
      R(R(x,y,z),u,a(x,w,v5)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(8398(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8398 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8419">
    <literal><![CDATA[
      (x \ 1) * a(x,y,z) = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(8398(a,1),382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8398 382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8420">
    <literal><![CDATA[
      x \ (y * a(x,z,u)) = (x \ y) * a(x,z,u)
    ]]></literal>
    <justification jstring="[para(8398(a,1),492(a,1,1))].">
      <j1 rule="para" parents="8398 492"/>
    </justification>
  </clause>

  <clause id="8422">
    <literal><![CDATA[
      x \ ((x * y) * z) = (y * z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(8398(a,1),689(a,1,1))].">
      <j1 rule="para" parents="8398 689"/>
    </justification>
  </clause>

  <clause id="8423">
    <literal><![CDATA[
      L(x,y,z) \ (u * a(x,w,v5)) = (L(x,y,z) \ u) * a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(8398(a,1),723(a,1,1,1))].">
      <j1 rule="para" parents="8398 723"/>
    </justification>
  </clause>

  <clause id="8425">
    <literal><![CDATA[
      a(x,y,z) * ((x \ 1) * u) = (x \ 1) * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(138,a,8399,a(flip),b,5343,a),flip(a)].">
      <j1 rule="hyper" parents="138 8399 5343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8426">
    <literal><![CDATA[
      ((x \ 1) * y) * a(x,z,u) = (x \ 1) * (a(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(8399(a,1),5276(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8399 5276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8427">
    <literal><![CDATA[
      a(x,y,z) \ (a(x,y,z) / x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(144,a,8400,a)].">
      <j1 rule="hyper" parents="144 8400"/>
    </justification>
  </clause>

  <clause id="8428">
    <literal><![CDATA[
      (1 / x) * a(x,y,z) = a(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a(flip),b,8400,a)].">
      <j1 rule="hyper" parents="63 2290 8400"/>
    </justification>
  </clause>

  <clause id="8429">
    <literal><![CDATA[
      x \ (a(x,y,z) \ x) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(144,a,8404,a)].">
      <j1 rule="hyper" parents="144 8404"/>
    </justification>
  </clause>

  <clause id="8430">
    <literal><![CDATA[
      x * (y \ L(y,y,x)) = a(x,y,y) \ x
    ]]></literal>
    <justification jstring="[para(7304(a,1),8404(a,1,2))].">
      <j1 rule="para" parents="7304 8404"/>
    </justification>
  </clause>

  <clause id="8431">
    <literal><![CDATA[
      a(x,y,z) \ (u * R(x,w,v5)) = (a(x,y,z) \ u) * R(x,w,v5)
    ]]></literal>
    <justification jstring="[para(8407(a,1),456(a,1,2,2))].">
      <j1 rule="para" parents="8407 456"/>
    </justification>
  </clause>

  <clause id="8432">
    <literal><![CDATA[
      R(x,y,z) \ (u * a(x,w,v5)) = (R(x,y,z) \ u) * a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(8418(a,1),492(a,1,1))].">
      <j1 rule="para" parents="8418 492"/>
    </justification>
  </clause>

  <clause id="8433">
    <literal><![CDATA[
      a(x,y,z) * (R(x,u,w) \ (a(x,y,z) \ v5)) = R(x,u,w) \ v5
    ]]></literal>
    <justification jstring="[para(8418(a,1),4891(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8418 4891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8434">
    <literal><![CDATA[
      (x \ a(x,y,z)) * L(u,a(x,y,z),x \ 1) = (x \ 1) * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(138,a,8419,a(flip),b,202,a)].">
      <j1 rule="hyper" parents="138 8419 202"/>
    </justification>
  </clause>

  <clause id="8435">
    <literal><![CDATA[
      ((((a(x,y,z) / x) / a(x,y,z)) / u) * (u * a(x,y,z))) \ (a(x,y,z) / x) = a(u \ (1 / x),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(8427(a,1),3326(a,2,1,2))].">
      <j1 rule="para" parents="8427 3326"/>
    </justification>
  </clause>

  <clause id="8436">
    <literal><![CDATA[
      (x * L(y,z,x)) * a(z,x,L(y,z,x)) = z \ (x * (T(z,x) * y))
    ]]></literal>
    <justification jstring="[hyper(133,a,3285,a(flip),b,8416,a),flip(a)].">
      <j1 rule="hyper" parents="133 3285 8416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8437">
    <literal><![CDATA[
      ((x \ y) * z) * a(x,x \ y,z) = x \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,158,a(flip),b,8416,a),flip(a)].">
      <j1 rule="hyper" parents="133 158 8416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8438">
    <literal><![CDATA[
      ((x \ 1) * y) * a(x,x \ 1,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(133,a,71,a(flip),b,8416,a),flip(a)].">
      <j1 rule="hyper" parents="133 71 8416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8439">
    <literal><![CDATA[
      x * (a(x,y,z) * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,2293,a,b,8416,a)].">
      <j1 rule="hyper" parents="63 2293 8416"/>
    </justification>
  </clause>

  <clause id="8440">
    <literal><![CDATA[
      (x * y) * a(x,x,y) = R(x,x,y) * y
    ]]></literal>
    <justification jstring="[hyper(34,a,1163,a,b,8416,a),flip(a)].">
      <j1 rule="hyper" parents="34 1163 8416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8441">
    <literal><![CDATA[
      (x * L(y,x,z)) * a(z,x,L(y,x,z)) = x * y
    ]]></literal>
    <justification jstring="[hyper(34,a,100,a(flip),b,8416,a),flip(a)].">
      <j1 rule="hyper" parents="34 100 8416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8442">
    <literal><![CDATA[
      x \ ((x * y) * z) = a(x,y,z) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,8416,a(flip),b,2293,a)].">
      <j1 rule="hyper" parents="133 8416 2293"/>
    </justification>
  </clause>

  <clause id="8443">
    <literal><![CDATA[
      x * (y * a(x,z,z \ y)) = (x * z) * (z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),8416(a,1,2,1))].">
      <j1 rule="para" parents="10 8416"/>
    </justification>
  </clause>

  <clause id="8444">
    <literal><![CDATA[
      a(x,y,z) = (y * z) \ (x \ ((x * y) * z))
    ]]></literal>
    <justification jstring="[para(8416(a,1),69(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8416 69"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8445">
    <literal><![CDATA[
      L(T(x,(y * z) * a(x,y,z)),(y * z) * a(x,y,z),u) = (u * ((y * z) * a(x,y,z))) \ (u * ((x * y) * z))
    ]]></literal>
    <justification jstring="[para(8416(a,1),247(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8416 247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8446">
    <literal><![CDATA[
      a(x,y,z * ((u * (w \ v5)) * ((v6 * v7) * a(u * (v5 / w),v6,v7)))) = a(x,y,z * (((u * (v5 / w)) * v6) * v7))
    ]]></literal>
    <justification jstring="[para(8416(a,1),6056(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="8416 6056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8447">
    <literal><![CDATA[
      x * (y * (y * a(x,y,y))) = (x * y) * y
    ]]></literal>
    <justification jstring="[para(6858(a,1),8416(a,1,2))].">
      <j1 rule="para" parents="6858 8416"/>
    </justification>
  </clause>

  <clause id="8448">
    <literal><![CDATA[
      x * (a(y,z,u) * (w * a(x,w,a(y,z,u)))) = (x * w) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(6856(a,1),8416(a,1,2))].">
      <j1 rule="para" parents="6856 8416"/>
    </justification>
  </clause>

  <clause id="8449">
    <literal><![CDATA[
      x \ ((x * y) * a(z,u,w)) = a(z,u,w) * (y * a(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,6856,a(flip),b,8422,a),flip(a)].">
      <j1 rule="hyper" parents="316 6856 8422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8450">
    <literal><![CDATA[
      x \ (y \ ((y * a(z,u,w)) * x)) = a(z,u,w) * a(y,a(z,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(133,a,8422,a,b,6857,a(flip))].">
      <j1 rule="hyper" parents="133 8422 6857"/>
    </justification>
  </clause>

  <clause id="8451">
    <literal><![CDATA[
      x \ (y \ ((y * z) * (z \ x))) = a(y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,8422,a,b,158,a(flip))].">
      <j1 rule="hyper" parents="133 8422 158"/>
    </justification>
  </clause>

  <clause id="8452">
    <literal><![CDATA[
      (x / y) \ (x * z) = (y * z) * a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3200,a(flip),b,8422,a)].">
      <j1 rule="hyper" parents="63 3200 8422"/>
    </justification>
  </clause>

  <clause id="8453">
    <literal><![CDATA[
      (x * y) \ ((z / x) \ (z * y)) = a(x \ z,x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,3200,a(flip),b,8422,a(flip))].">
      <j1 rule="hyper" parents="133 3200 8422"/>
    </justification>
  </clause>

  <clause id="8454">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) = (y * L(z,y,x)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,296,a(flip),b,8422,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 296 8422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8455">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),y * z) = (x \ ((x * y) * z)) \ ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(8422(a,2),102(a,2,1))].">
      <j1 rule="para" parents="8422 102"/>
    </justification>
  </clause>

  <clause id="8456">
    <literal><![CDATA[
      ((x \ 1) * y) \ (x \ y) = a(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,8438,a)].">
      <j1 rule="hyper" parents="144 8438"/>
    </justification>
  </clause>

  <clause id="8457">
    <literal><![CDATA[
      a(x,x \ 1,(x \ 1) \ y) * y = x \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2317,a(flip),b,8438,a)].">
      <j1 rule="hyper" parents="63 2317 8438"/>
    </justification>
  </clause>

  <clause id="8458">
    <literal><![CDATA[
      a(x,x \ y,z) * ((x \ y) * z) = x \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,158,a(flip),b,8439,a),flip(a)].">
      <j1 rule="hyper" parents="133 158 8439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8459">
    <literal><![CDATA[
      (((x * y) * z) / (y * z)) \ (x * a(x,y,z)) = a(x,a(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[para(8439(a,1),6925(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="8439 6925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8460">
    <literal><![CDATA[
      x \ ((x * a(y,z,u)) * w) = w * (a(x,a(y,z,u),w) * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,6894,a(flip),b,8442,a),flip(a)].">
      <j1 rule="hyper" parents="316 6894 8442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8461">
    <literal><![CDATA[
      (x \ ((x * y) * z)) / z = a(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(136,a,8442,a,b,6865,a)].">
      <j1 rule="hyper" parents="136 8442 6865"/>
    </justification>
  </clause>

  <clause id="8462">
    <literal><![CDATA[
      x \ ((x * L(y,y,z)) * a(z,y,y)) = a(x,L(y,y,z),a(z,y,y)) * y
    ]]></literal>
    <justification jstring="[para(7294(a,1),8442(a,2,2))].">
      <j1 rule="para" parents="7294 8442"/>
    </justification>
  </clause>

  <clause id="8463">
    <literal><![CDATA[
      (x * y) \ ((1 / x) \ y) = a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,3367,a(flip),b,8444,a)].">
      <j1 rule="hyper" parents="316 3367 8444"/>
    </justification>
  </clause>

  <clause id="8465">
    <literal><![CDATA[
      ((x \ y) * z) \ (x \ (y * z)) = a(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),8444(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 8444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8466">
    <literal><![CDATA[
      (x * L(L(x,y,z),u,w)) \ (v5 \ ((v5 * L(L(x,u,w),y,z)) * x)) = a(v5,L(L(x,u,w),y,z),x)
    ]]></literal>
    <justification jstring="[para(839(a,1),8444(a,2,1)),flip(a)].">
      <j1 rule="para" parents="839 8444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8467">
    <literal><![CDATA[
      (x * y) \ ((z * (1 / x)) \ (R(z,x \ 1,x) * y)) = a(z * (1 / x),x,y)
    ]]></literal>
    <justification jstring="[para(2569(a,1),8444(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2569 8444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8469">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * (w \ 1)) * (w \ z)))) = a(x,y,a(u,w \ 1,w \ z))
    ]]></literal>
    <justification jstring="[para(8444(a,2),6063(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8444 6063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8470">
    <literal><![CDATA[
      L(x * a(y,x,x),x,y) = x
    ]]></literal>
    <justification jstring="[hyper(463,a,8447,a(flip))].">
      <j1 rule="hyper" parents="463 8447"/>
    </justification>
  </clause>

  <clause id="8471">
    <literal><![CDATA[
      L(x * a(y,x,x),z,x * a(y,x,x)) = L(x * a(y,x,x),z,x)
    ]]></literal>
    <justification jstring="[para(8470(a,1),7995(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8470 7995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8472">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) \ (u \ z)) = a(x,y,a(u,u \ 1,z))
    ]]></literal>
    <justification jstring="[para(8456(a,1),5626(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8456 5626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8473">
    <literal><![CDATA[
      a(x,y,(z \ u) * (u * z)) = a(x,y,a(z,z \ 1,u))
    ]]></literal>
    <justification jstring="[para(8456(a,1),6395(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8456 6395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8474">
    <literal><![CDATA[
      (x \ ((x * y) * z)) / z = y * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2290,a(flip),b,8461,a),flip(a)].">
      <j1 rule="hyper" parents="316 2290 8461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8475">
    <literal><![CDATA[
      L(a(x,y \ 1,z),y,y) = y * ((x \ ((x * (y \ 1)) * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(139,a,8461,a,b,2460,a),flip(a)].">
      <j1 rule="hyper" parents="139 8461 2460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8476">
    <literal><![CDATA[
      a(x,y,z) = y \ ((x \ ((x * y) * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(133,a,8461,a,b,2290,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 8461 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8477">
    <literal><![CDATA[
      a(x,y,z) \ ((x \ ((x * y) * z)) / z) = y
    ]]></literal>
    <justification jstring="[hyper(133,a,8461,a,b,xx)].">
      <j1 rule="hyper" parents="133 8461"/>
    </justification>
  </clause>

  <clause id="8478">
    <literal><![CDATA[
      (x \ (y * (x * z))) / T(y,x * z) = a(x,z,y) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,3975,a,b,8461,a)].">
      <j1 rule="hyper" parents="63 3975 8461"/>
    </justification>
  </clause>

  <clause id="8479">
    <literal><![CDATA[
      a(a(x,y,z),y,y) \ (1 / (((x \ ((x * y) * z)) / z) \ a(x,y,z))) = y
    ]]></literal>
    <justification jstring="[para(8461(a,2),7340(a,1,2,2,1))].">
      <j1 rule="para" parents="8461 7340"/>
    </justification>
  </clause>

  <clause id="8480">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) \ ((1 / x) \ (y \ L(y,z,u))) = a(x \ 1,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5566,a(flip),b,8463,a),flip(a)].">
      <j1 rule="hyper" parents="316 5566 8463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8481">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) * a(x \ 1,x,y * R(y,z,u)) = (1 / x) \ (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,5567,a(flip),b,8463,a)].">
      <j1 rule="hyper" parents="139 5567 8463"/>
    </justification>
  </clause>

  <clause id="8482">
    <literal><![CDATA[
      R(x,y,(z * u) \ ((1 / u) \ z)) = R(x,y,a(u \ 1,u,z))
    ]]></literal>
    <justification jstring="[para(8463(a,1),4752(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8463 4752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8483">
    <literal><![CDATA[
      R(x,y,(y * x) \ ((1 / x) \ y)) \ ((1 / x) \ y) = y * a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(8463(a,1),4768(a,2,2))].">
      <j1 rule="para" parents="8463 4768"/>
    </justification>
  </clause>

  <clause id="8484">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ (((1 / u) \ 1) \ w))) = a(x,y,z * a(u \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(8463(a,1),7780(a,2,3,2))].">
      <j1 rule="para" parents="8463 7780"/>
    </justification>
  </clause>

  <clause id="8485">
    <literal><![CDATA[
      (x \ (y * z)) / z = (x \ y) * a(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),8474(a,1,1,2,1))].">
      <j1 rule="para" parents="10 8474"/>
    </justification>
  </clause>

  <clause id="8486">
    <literal><![CDATA[
      (x \ y) / y = (x \ 1) * a(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(71(a,1),8474(a,1,1,2))].">
      <j1 rule="para" parents="71 8474"/>
    </justification>
  </clause>

  <clause id="8487">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * w) * z))) = a(x,y,w * a(u,w,z))
    ]]></literal>
    <justification jstring="[para(8474(a,1),5477(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8474 5477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8488">
    <literal><![CDATA[
      x \ (((x \ 1) \ (((x \ 1) * x) * y)) / y) = L(y,x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,2408,a,b,8476,a),flip(a)].">
      <j1 rule="hyper" parents="63 2408 8476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8489">
    <literal><![CDATA[
      x \ ((R(y,y,x) \ ((y \ ((y * y) * x)) * z)) / z) = a(R(y,y,x),x,z)
    ]]></literal>
    <justification jstring="[para(1164(a,2),8476(a,2,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1164 8476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8490">
    <literal><![CDATA[
      a(x,y,((z \ ((z * x) * u)) / u) \ a(z,x,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(8476(a,2),7510(a,1,3,2))].">
      <j1 rule="para" parents="8476 7510"/>
    </justification>
  </clause>

  <clause id="8491">
    <literal><![CDATA[
      T(x * a((y \ ((y * x) * z)) / z,x,x),x * ((y \ ((y * x) * z)) / z)) = 1 / (((y \ ((y * x) * z)) / z) \ a(y,x,z))
    ]]></literal>
    <justification jstring="[para(8476(a,2),8190(a,2,2,2))].">
      <j1 rule="para" parents="8476 8190"/>
    </justification>
  </clause>

  <clause id="8492">
    <literal><![CDATA[
      x * ((x \ y) / y) = a(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,8486,a,b,8419,a(flip))].">
      <j1 rule="hyper" parents="139 8486 8419"/>
    </justification>
  </clause>

  <clause id="8493">
    <literal><![CDATA[
      a(x,x \ 1,x * y) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),8492(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 8492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8494">
    <literal><![CDATA[
      (x * ((x \ y) / y)) \ y = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(8492(a,2),1384(a,1,1))].">
      <j1 rule="para" parents="8492 1384"/>
    </justification>
  </clause>

  <clause id="8495">
    <literal><![CDATA[
      a(x,x \ 1,y * x) = x * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(3910(a,1),8492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3910 8492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8496">
    <literal><![CDATA[
      a(x,y,z * (((u \ w) / w) * u)) = a(x,y,a(u,u \ 1,w) * z)
    ]]></literal>
    <justification jstring="[para(8492(a,1),5623(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="8492 5623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8497">
    <literal><![CDATA[
      a(x,y,z \ (u * (((w \ v5) / v5) * w))) = a(x,y,z \ (a(w,w \ 1,v5) * u))
    ]]></literal>
    <justification jstring="[para(8492(a,1),6003(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="8492 6003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8498">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * (v5 \ (w \ v5))))) = a(x,y,z * (u \ a(w,w \ 1,v5)))
    ]]></literal>
    <justification jstring="[para(8492(a,1),6049(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="8492 6049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8499">
    <literal><![CDATA[
      a(x,y,(z \ (u * (w \ (u \ w)))) * v5) = a(x,y,(z \ a(u,u \ 1,w)) * v5)
    ]]></literal>
    <justification jstring="[para(8492(a,1),6069(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="8492 6069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8500">
    <literal><![CDATA[
      a(x,x \ 1,y * x) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,8493,a)].">
      <j1 rule="hyper" parents="63 5469 8493"/>
    </justification>
  </clause>

  <clause id="8501">
    <literal><![CDATA[
      (x * (a(y,z,u) * y)) \ (a(y,z,u) * (x * y)) = a(x,a(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(133,a,8401,a(flip),b,89,a)].">
      <j1 rule="hyper" parents="133 8401 89"/>
    </justification>
  </clause>

  <clause id="8502">
    <literal><![CDATA[
      R(a(x,y,z),u,x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,2348,a,b,8401,a(flip))].">
      <j1 rule="hyper" parents="35 2348 8401"/>
    </justification>
  </clause>

  <clause id="8503">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (1 / x) = L(a(x,y,z),u,w) / x
    ]]></literal>
    <justification jstring="[para(8502(a,1),535(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8502 535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8504">
    <literal><![CDATA[
      a(x,y,z) \ (x * u) = x * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,160,a(flip),b,8403,a)].">
      <j1 rule="hyper" parents="133 160 8403"/>
    </justification>
  </clause>

  <clause id="8505">
    <literal><![CDATA[
      x * (a(x,x,y) * y) = x \ ((x * x) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8442,a,b,8403,a),flip(a)].">
      <j1 rule="hyper" parents="63 8442 8403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8506">
    <literal><![CDATA[
      a(x,y,(z \ ((z * z) * u)) * w) = a(x,y,(z * L(u,z,z)) * w)
    ]]></literal>
    <justification jstring="[para(8505(a,1),7854(a,1,3,1))].">
      <j1 rule="para" parents="8505 7854"/>
    </justification>
  </clause>

  <clause id="8507">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * a(u,w,v5) = u * (a(u,w,v5) * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,6498,a,b,8412,a)].">
      <j1 rule="hyper" parents="63 6498 8412"/>
    </justification>
  </clause>

  <clause id="8508">
    <literal><![CDATA[
      (x * y) \ (x * (a(x,y,y) * (y * z))) = L(z,y,x) * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(8412(a,1),7395(a,1,2))].">
      <j1 rule="para" parents="8412 7395"/>
    </justification>
  </clause>

  <clause id="8510">
    <literal><![CDATA[
      L(a(x,y,z),u,x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,2307,a,b,8413,a)].">
      <j1 rule="hyper" parents="35 2307 8413"/>
    </justification>
  </clause>

  <clause id="8511">
    <literal><![CDATA[
      (a(x,y,z) * x) \ (x * (u * a(x,y,z))) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,8413,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="133 8413 100"/>
    </justification>
  </clause>

  <clause id="8512">
    <literal><![CDATA[
      (x * (y * a(x,z,u))) \ ((a(x,z,u) * x) * y) = a(a(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(8413(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8413 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8513">
    <literal><![CDATA[
      a(x,y,a(x,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,8510,a)].">
      <j1 rule="hyper" parents="53 8510"/>
    </justification>
  </clause>

  <clause id="8514">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),v5,x) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(8510(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8510 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8515">
    <literal><![CDATA[
      (x * y) * L(a(x,z,u),w,v5) = x * (y * L(a(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(8510(a,1),403(a,1,2,1))].">
      <j1 rule="para" parents="8510 403"/>
    </justification>
  </clause>

  <clause id="8516">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(x,u,w) = L(x,y,z) * (x \ a(x,u,w))
    ]]></literal>
    <justification jstring="[para(8510(a,1),1135(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8510 1135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8517">
    <literal><![CDATA[
      L(a(x,y,z) \ L(a(x,y,z),u,w),v5,x) = a(x,y,z) \ L(L(a(x,y,z),u,w),v5,x)
    ]]></literal>
    <justification jstring="[para(8510(a,1),2138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8510 2138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8518">
    <literal><![CDATA[
      a(x,y,a(x,z,u)) = w \ w
    ]]></literal>
    <justification jstring="[hyper(316,a,67,a,b,8513,a),flip(a)].">
      <j1 rule="hyper" parents="316 67 8513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8519">
    <literal><![CDATA[
      a(x,x,L(y,x,x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,7554,a,b,8518,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 7554 8518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8520">
    <literal><![CDATA[
      a(x,x,x \ y) = a(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5811,a(flip),b,8519,a),flip(a)].">
      <j1 rule="hyper" parents="63 5811 8519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8521">
    <literal><![CDATA[
      a(x,x,y) \ L(y,x,x) = L(L(y,x,x),x,x)
    ]]></literal>
    <justification jstring="[para(8519(a,1),4950(a,1,1))].">
      <j1 rule="para" parents="8519 4950"/>
    </justification>
  </clause>

  <clause id="8522">
    <literal><![CDATA[
      a(x,x,x \ y) = a(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,8520,a),flip(a)].">
      <j1 rule="hyper" parents="316 5469 8520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8523">
    <literal><![CDATA[
      L(a(x,x,x \ y),z,x * (x \ y)) = a(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7289,a,b,8522,a)].">
      <j1 rule="hyper" parents="63 7289 8522"/>
    </justification>
  </clause>

  <clause id="8524">
    <literal><![CDATA[
      x * ((y * z) * a(x,z,y)) = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5524,a(flip),b,8414,a),flip(a)].">
      <j1 rule="hyper" parents="63 5524 8414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8525">
    <literal><![CDATA[
      x \ (R(x,x,y) * y) = y * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,8440,a(flip),b,8414,a(flip))].">
      <j1 rule="hyper" parents="133 8440 8414"/>
    </justification>
  </clause>

  <clause id="8526">
    <literal><![CDATA[
      x \ ((x * y) * T(z,y)) = (z * y) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,5524,a(flip),b,8414,a(flip))].">
      <j1 rule="hyper" parents="133 5524 8414"/>
    </justification>
  </clause>

  <clause id="8527">
    <literal><![CDATA[
      R(x,x,y) * (x \ y) = y * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1167,a(flip),b,8525,a)].">
      <j1 rule="hyper" parents="63 1167 8525"/>
    </justification>
  </clause>

  <clause id="8529">
    <literal><![CDATA[
      a(x,x \ 1,a(y,z,u) * x) = x * L(1 / x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(5371(a,1),8495(a,2,2))].">
      <j1 rule="para" parents="5371 8495"/>
    </justification>
  </clause>

  <clause id="8530">
    <literal><![CDATA[
      (x * (y * z)) / z = x * (a(x,y,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6919,a(flip),b,8504,a)].">
      <j1 rule="hyper" parents="63 6919 8504"/>
    </justification>
  </clause>

  <clause id="8531">
    <literal><![CDATA[
      (x * (a(x,y,z) \ y)) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(138,a,8504,a(flip),b,6919,a(flip))].">
      <j1 rule="hyper" parents="138 8504 6919"/>
    </justification>
  </clause>

  <clause id="8532">
    <literal><![CDATA[
      a(x,y,z) \ y = x \ ((x * (y * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(133,a,6919,a(flip),b,8504,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 6919 8504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8533">
    <literal><![CDATA[
      a(x,y,z) \ (x \ u) = x \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,168,a(flip),b,8504,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 168 8504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8534">
    <literal><![CDATA[
      x * (y * (a(y,z,x) \ z)) = L(x,z,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(8504(a,1),6926(a,1,2))].">
      <j1 rule="para" parents="8504 6926"/>
    </justification>
  </clause>

  <clause id="8535">
    <literal><![CDATA[
      (x * (a(x,y,z) \ y)) * (z \ 1) = x * (y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(138,a,8530,a(flip),b,964,a)].">
      <j1 rule="hyper" parents="138 8530 964"/>
    </justification>
  </clause>

  <clause id="8536">
    <literal><![CDATA[
      R((x * (a(x,y,z) \ y)) / u,u,z) = (x * (y * z)) / (u * z)
    ]]></literal>
    <justification jstring="[para(8530(a,1),303(a,1,1,1))].">
      <j1 rule="para" parents="8530 303"/>
    </justification>
  </clause>

  <clause id="8537">
    <literal><![CDATA[
      (x * (a(x,T(y,x),z) \ T(y,x))) * z = (y * x) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,3285,a,b,8531,a),flip(a)].">
      <j1 rule="hyper" parents="316 3285 8531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8538">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) \ y,x,a(z,u,w)) = (a(z,u,w) * x) \ (x * (y * a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(133,a,8531,a(flip),b,2319,a),flip(a)].">
      <j1 rule="hyper" parents="133 8531 2319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8539">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ u,z,w)) = a(x,y,(w * z) \ (z * (u * w)))
    ]]></literal>
    <justification jstring="[para(8531(a,1),5504(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="8531 5504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8541">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z),y) = y \ (x \ ((x * (y * z)) / z))
    ]]></literal>
    <justification jstring="[hyper(133,a,8532,a(flip),b,4787,a),flip(a)].">
      <j1 rule="hyper" parents="133 8532 4787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8542">
    <literal><![CDATA[
      R(x,y,z) \ (((x * y) * z) / z) = a(R(x,y,z),y,z) \ y
    ]]></literal>
    <justification jstring="[para(109(a,1),8532(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="109 8532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8544">
    <literal><![CDATA[
      (x \ (y \ ((y * (x * z)) / z))) \ x = x * a(y,x,z)
    ]]></literal>
    <justification jstring="[para(8532(a,1),5207(a,1,1,2))].">
      <j1 rule="para" parents="8532 5207"/>
    </justification>
  </clause>

  <clause id="8546">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),a(z,u,w),u)) = a(x,y,u \ (z \ ((z * (u * w)) / w)))
    ]]></literal>
    <justification jstring="[para(8532(a,1),6745(a,2,3,2))].">
      <j1 rule="para" parents="8532 6745"/>
    </justification>
  </clause>

  <clause id="8547">
    <literal><![CDATA[
      a(x,x,y) \ (a(x,x,y) \ 1) = y \ L(L(y,x,x),x,x)
    ]]></literal>
    <justification jstring="[para(8521(a,1),6941(a,2,2))].">
      <j1 rule="para" parents="8521 6941"/>
    </justification>
  </clause>

  <clause id="8549">
    <literal><![CDATA[
      x \ (a(x,x \ 1,x \ y) \ y) = L(x \ y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1384,a(flip),b,8533,a),flip(a)].">
      <j1 rule="hyper" parents="63 1384 8533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8550">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ (a(w,v5,v6) \ 1)))) = a(x,y,z \ (u \ (a(w,v5,v6) \ w)))
    ]]></literal>
    <justification jstring="[para(8533(a,1),5834(a,1,3,2,2))].">
      <j1 rule="para" parents="8533 5834"/>
    </justification>
  </clause>

  <clause id="8551">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ (L(x,y,z) * (x \ u)) = a(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(133,a,1126,a(flip),b,8437,a)].">
      <j1 rule="hyper" parents="133 1126 8437"/>
    </justification>
  </clause>

  <clause id="8553">
    <literal><![CDATA[
      x * (y * a(x,x,x * y)) = (x * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(8520(a,1),8443(a,1,2,2))].">
      <j1 rule="para" parents="8520 8443"/>
    </justification>
  </clause>

  <clause id="8554">
    <literal><![CDATA[
      x \ ((y \ 1) \ (((y \ 1) * y) * (y \ x))) = L(y \ x,y,y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,2408,a,b,8451,a),flip(a)].">
      <j1 rule="hyper" parents="316 2408 8451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8556">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w \ z) * (u * w)))) = a(x,y,a(u,w,w \ z))
    ]]></literal>
    <justification jstring="[para(8451(a,1),5602(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8451 5602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8557">
    <literal><![CDATA[
      (x * (y \ z)) * a(x \ y,x,y \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,168,a(flip),b,8452,a),flip(a)].">
      <j1 rule="hyper" parents="63 168 8452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8558">
    <literal><![CDATA[
      (x * (y \ z)) \ ((y / x) \ z) = a(x \ y,x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(133,a,168,a(flip),b,8452,a(flip))].">
      <j1 rule="hyper" parents="133 168 8452"/>
    </justification>
  </clause>

  <clause id="8559">
    <literal><![CDATA[
      (x / y) \ (x * (1 / y)) = K(y,y \ 1) * a(y \ x,y,1 / y)
    ]]></literal>
    <justification jstring="[para(1085(a,2),8452(a,2,1))].">
      <j1 rule="para" parents="1085 8452"/>
    </justification>
  </clause>

  <clause id="8560">
    <literal><![CDATA[
      (L(x,y,y) * a(y,y,x)) * (((L(x,y,y) \ z) * x) \ (a(y,y,x) * ((L(x,y,y) \ z) * L(x,y,y)))) = (z / L(x,y,y)) \ (z * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(4960(a,2),8452(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4960 8452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8561">
    <literal><![CDATA[
      a(x,y,(z * u) \ (((u \ w) / z) \ w)) = a(x,y,a(z \ (u \ w),z,u))
    ]]></literal>
    <justification jstring="[para(8453(a,1),5607(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8453 5607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8562">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) = (L(z,y,x) * y) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,4336,a,b,8454,a),flip(a)].">
      <j1 rule="hyper" parents="316 4336 8454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8563">
    <literal><![CDATA[
      (L(x,y,z) * L(u,L(x,y,z),x)) \ (L(x,y,z) * u) = a(x,L(x,y,z),L(u,x,L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(1231(a,1),8454(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1231 8454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8564">
    <literal><![CDATA[
      (x * L(R(y,z,u),x,L(y,w,v5))) \ (x * R(y,z,u)) = a(L(y,w,v5),x,L(R(y,z,u),x,y))
    ]]></literal>
    <justification jstring="[para(8001(a,1),8454(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8001 8454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8565">
    <literal><![CDATA[
      a(x,y,z) \ (a(u,u \ w,a(x,y,z) \ 1) * ((u \ w) * a(x,y,z))) = (a(x,y,z) \ 1) \ (u \ (w * (a(x,y,z) \ 1)))
    ]]></literal>
    <justification jstring="[para(8458(a,1),7882(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8458 7882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8566">
    <literal><![CDATA[
      a(x,y,(z * (u \ w)) \ (u \ (w * z))) = a(x,y,a(u,u \ w,z))
    ]]></literal>
    <justification jstring="[para(8465(a,1),5626(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8465 5626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8567">
    <literal><![CDATA[
      a(x,y,((z * (u \ w)) \ (u \ (w * z))) * v5) = a(x,y,v5 * a(u,u \ w,z))
    ]]></literal>
    <justification jstring="[para(8465(a,1),6007(a,2,3,2))].">
      <j1 rule="para" parents="8465 6007"/>
    </justification>
  </clause>

  <clause id="8568">
    <literal><![CDATA[
      (1 / (x \ y)) * (y \ x) = y \ (x * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(138,a,7343,a(flip),b,8485,a)].">
      <j1 rule="hyper" parents="138 7343 8485"/>
    </justification>
  </clause>

  <clause id="8570">
    <literal><![CDATA[
      (x * (y \ z)) * a(y,y \ z,x) = y \ (z * T(x,y \ z))
    ]]></literal>
    <justification jstring="[hyper(133,a,158,a(flip),b,8524,a),flip(a)].">
      <j1 rule="hyper" parents="133 158 8524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8571">
    <literal><![CDATA[
      a(x,y,z) = (z * y) \ (x \ ((x * y) * T(z,y)))
    ]]></literal>
    <justification jstring="[para(8524(a,1),69(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8524 69"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8572">
    <literal><![CDATA[
      x * (y * (z * a(x,z,y))) = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(6858(a,1),8524(a,1,2))].">
      <j1 rule="para" parents="6858 8524"/>
    </justification>
  </clause>

  <clause id="8573">
    <literal><![CDATA[
      x \ (y \ ((y * z) * T(x,z))) = z * a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,8526,a,b,6858,a(flip))].">
      <j1 rule="hyper" parents="133 8526 6858"/>
    </justification>
  </clause>

  <clause id="8574">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z),z * y) = (x \ ((x * y) * T(z,y))) \ (z * y)
    ]]></literal>
    <justification jstring="[para(8526(a,2),232(a,2,1))].">
      <j1 rule="para" parents="8526 232"/>
    </justification>
  </clause>

  <clause id="8575">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) \ (z * y) = L(z,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,8562,a(flip))].">
      <j1 rule="hyper" parents="39 2301 8562"/>
    </justification>
  </clause>

  <clause id="8576">
    <literal><![CDATA[
      (x * y) \ (a(z,u,w) \ (x * (y * a(z,u,w)))) = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(5253(a,1),8571(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5253 8571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8577">
    <literal><![CDATA[
      (x * y) \ ((z \ L(z,u,w)) \ (x * (y * (z \ L(z,u,w))))) = a(z \ L(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(6649(a,1),8571(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6649 8571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8578">
    <literal><![CDATA[
      (x * y) \ ((x * z) * T(y,z)) = L(z * a(x,z,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,8572,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="133 8572 100"/>
    </justification>
  </clause>

  <clause id="8579">
    <literal><![CDATA[
      a(x,y \ z,L(y,y \ z,x)) \ z = L(y,y \ z,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,168,a(flip),b,8575,a)].">
      <j1 rule="hyper" parents="63 168 8575"/>
    </justification>
  </clause>

  <clause id="8580">
    <literal><![CDATA[
      (x * y) \ (L(x,z,y) * (y * z)) = L(a(y,z,x) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,8534,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="133 8534 100"/>
    </justification>
  </clause>

  <clause id="8581">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * v5) * (v6 * (a(v6,v7,R(z,u,w) * v5) \ v7))) = a(x,y,L(R(z,u,w) * v5,v7,v6) * (v6 * v7))
    ]]></literal>
    <justification jstring="[para(8534(a,1),7425(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8534 7425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8582">
    <literal><![CDATA[
      a(x,y,(z \ u) \ ((1 / z) * u)) = a(x,y,a(z,z \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7441,a,b,8473,a)].">
      <j1 rule="hyper" parents="63 7441 8473"/>
    </justification>
  </clause>

  <clause id="8583">
    <literal><![CDATA[
      a(x,y,z) \ (u \ (a(x,y,z) * (u * w))) = a(u,w,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(63,a,2332,a(flip),b,8478,a)].">
      <j1 rule="hyper" parents="63 2332 8478"/>
    </justification>
  </clause>

  <clause id="8584">
    <literal><![CDATA[
      L(a(x,x,y * x),z,x * (x \ y)) = a(x,x,y * x)
    ]]></literal>
    <justification jstring="[para(8522(a,1),8523(a,1,1))].">
      <j1 rule="para" parents="8522 8523"/>
    </justification>
  </clause>

  <clause id="8585">
    <literal><![CDATA[
      R((x * (a(x,y,z) \ y)) / u,u,z) = (x * (y * (z \ 1))) / (u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(8535(a,1),1036(a,2,1))].">
      <j1 rule="para" parents="8535 1036"/>
    </justification>
  </clause>

  <clause id="8586">
    <literal><![CDATA[
      L(x,y,z) \ (u \ ((u * (L(x,y,z) * x)) / x)) = a(u,L(x,y,z),x) \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,6970,a,b,8544,a),flip(a)].">
      <j1 rule="hyper" parents="39 6970 8544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8587">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * a(x \ L(y,z,u),x,y * L(y,z,u)) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[para(2652(a,1),8557(a,1,2))].">
      <j1 rule="para" parents="2652 8557"/>
    </justification>
  </clause>

  <clause id="8588">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) * a(x \ y,x,y * R(y,z,u)) = (y / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(5567(a,1),8557(a,1,2))].">
      <j1 rule="para" parents="5567 8557"/>
    </justification>
  </clause>

  <clause id="8589">
    <literal><![CDATA[
      L(a(x,x,y * x),z,y) = a(x,x,y * x)
    ]]></literal>
    <justification jstring="[para(10(a,1),8584(a,1,3))].">
      <j1 rule="para" parents="10 8584"/>
    </justification>
  </clause>

  <clause id="8590">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,x) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,5010,a,b,8415,a)].">
      <j1 rule="hyper" parents="35 5010 8415"/>
    </justification>
  </clause>

  <clause id="8591">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * x) \ (x * (u * (a(x,y,z) \ 1))) = L(u,x,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,8415,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="133 8415 100"/>
    </justification>
  </clause>

  <clause id="8592">
    <literal><![CDATA[
      a(x,x,L(y,z,x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,5124,a(flip),b,8590,a(flip))].">
      <j1 rule="hyper" parents="39 5124 8590"/>
    </justification>
  </clause>

  <clause id="8593">
    <literal><![CDATA[
      a(x,x,L(y,z,x)) = x \ R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,7329,a,b,8592,a),flip(a)].">
      <j1 rule="hyper" parents="316 7329 8592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8594">
    <literal><![CDATA[
      a(x * y,x * y,L(y,x,x)) = a(x * y,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5887,a(flip),b,8592,a)].">
      <j1 rule="hyper" parents="63 5887 8592"/>
    </justification>
  </clause>

  <clause id="8596">
    <literal><![CDATA[
      R(x,x,L(y,z,x)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(38,a,7329,a,b,8593,a(flip))].">
      <j1 rule="hyper" parents="38 7329 8593"/>
    </justification>
  </clause>

  <clause id="8597">
    <literal><![CDATA[
      a(x,y,L(L(z,z,L(u,w,z)),v5,v6)) = a(x,y,L(R(z,z,u),v5,v6))
    ]]></literal>
    <justification jstring="[para(8596(a,1),5953(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="8596 5953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8598">
    <literal><![CDATA[
      a(x * y,x * y,x * (x * y)) = a(x * y,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5810,a,b,8594,a)].">
      <j1 rule="hyper" parents="63 5810 8594"/>
    </justification>
  </clause>

  <clause id="8599">
    <literal><![CDATA[
      L(L(x,y,y),y,y) * (a(y,y,x) * a(y,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(39,a,445,a,b,8547,a(flip))].">
      <j1 rule="hyper" parents="39 445 8547"/>
    </justification>
  </clause>

  <clause id="8601">
    <literal><![CDATA[
      L(L(x,y,y) * (a(y,y,x) * a(y,y,x)),y,y) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,1058,a,b,8599,a)].">
      <j1 rule="hyper" parents="63 1058 8599"/>
    </justification>
  </clause>

  <clause id="8602">
    <literal><![CDATA[
      a(x,y,L(L(z,u,u),u,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(8599(a,1),5804(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8599 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8603">
    <literal><![CDATA[
      a(x,y,L(z * (u \ 1),u,u)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6778,a(flip),b,8602,a)].">
      <j1 rule="hyper" parents="63 6778 8602"/>
    </justification>
  </clause>

  <clause id="8604">
    <literal><![CDATA[
      a(x,y,L(L(z * u,w,v5),z,z)) = a(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,6042,a(flip),b,8602,a)].">
      <j1 rule="hyper" parents="63 6042 8602"/>
    </justification>
  </clause>

  <clause id="8605">
    <literal><![CDATA[
      a(x,y,L(z * u,z,z)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5999,a(flip),b,8603,a)].">
      <j1 rule="hyper" parents="63 5999 8603"/>
    </justification>
  </clause>

  <clause id="8606">
    <literal><![CDATA[
      a(x,y,L(z * u,u,u)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5888,a(flip),b,8603,a)].">
      <j1 rule="hyper" parents="63 5888 8603"/>
    </justification>
  </clause>

  <clause id="8607">
    <literal><![CDATA[
      R(x,L(y * z,y,y),L(y * z,y,y)) = a(x,L(y * z,y,y),y \ z) * x
    ]]></literal>
    <justification jstring="[hyper(138,a,8605,a(flip),b,2376,a),flip(a)].">
      <j1 rule="hyper" parents="138 8605 2376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8608">
    <literal><![CDATA[
      a(x,y,z \ (z \ u)) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),8605(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 8605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8609">
    <literal><![CDATA[
      a(x,y,L(z \ u,u,u)) = a(x,y,R(z,u,u) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,7233,a(flip),b,8608,a),flip(a)].">
      <j1 rule="hyper" parents="63 7233 8608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8611">
    <literal><![CDATA[
      L(a(x,x,y) * (L(y,x,x) * a(x,x,y)),x,x) = y
    ]]></literal>
    <justification jstring="[para(6883(a,1),8601(a,1,1))].">
      <j1 rule="para" parents="6883 8601"/>
    </justification>
  </clause>

  <clause id="8612">
    <literal><![CDATA[
      a(x,y,L(z \ u,u,u)) = a(x,y,L(z,u,u) \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,6066,a(flip),b,8609,a),flip(a)].">
      <j1 rule="hyper" parents="316 6066 8609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8615">
    <literal><![CDATA[
      L(a(x,x,y) * y,x,x) = y
    ]]></literal>
    <justification jstring="[para(4953(a,1),8611(a,1,1,2))].">
      <j1 rule="para" parents="4953 8611"/>
    </justification>
  </clause>

  <clause id="8616">
    <literal><![CDATA[
      L(a(x,x,(R(y,z,u) \ y) \ 1) * ((R(y,z,u) \ y) \ 1),x,x) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,7651,a(flip),b,8615,a),flip(a)].">
      <j1 rule="hyper" parents="316 7651 8615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8617">
    <literal><![CDATA[
      L(x * a(y,y,x),y,y) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,2314,a(flip),b,8615,a)].">
      <j1 rule="hyper" parents="63 2314 8615"/>
    </justification>
  </clause>

  <clause id="8618">
    <literal><![CDATA[
      L(x * a(y,y,x),y,y) = z * (u * (u \ (z \ x)))
    ]]></literal>
    <justification jstring="[hyper(316,a,76,a,b,8617,a),flip(a)].">
      <j1 rule="hyper" parents="316 76 8617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8619">
    <literal><![CDATA[
      L(L(1 / x,y,y) \ 1,y,y) = x
    ]]></literal>
    <justification jstring="[para(6584(a,2),8617(a,1,1))].">
      <j1 rule="para" parents="6584 8617"/>
    </justification>
  </clause>

  <clause id="8620">
    <literal><![CDATA[
      (x * x) * (x \ (x \ y)) = y * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,1114,a,b,8618,a)].">
      <j1 rule="hyper" parents="41 1114 8618"/>
    </justification>
  </clause>

  <clause id="8621">
    <literal><![CDATA[
      (x * x) * (x \ (x \ y)) = L(1 / y,x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,6584,a,b,8620,a),flip(a)].">
      <j1 rule="hyper" parents="316 6584 8620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8622">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (a(x,y,z) \ u) = u * a(a(x,y,z),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6305,a(flip),b,8620,a)].">
      <j1 rule="hyper" parents="63 6305 8620"/>
    </justification>
  </clause>

  <clause id="8623">
    <literal><![CDATA[
      L(x,y,(z \ (z \ u)) * (z * z)) = L(x,y,u * a(z,z,u))
    ]]></literal>
    <justification jstring="[para(8620(a,1),1668(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8620 1668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8624">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w \ (w \ v5)) * (w * w)))) = a(x,y,z \ (u \ (v5 * a(w,w,v5))))
    ]]></literal>
    <justification jstring="[para(8620(a,1),5602(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="8620 5602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8625">
    <literal><![CDATA[
      a(x,y,(z \ (u * a(w,w,u))) * v5) = a(x,y,v5 * (z \ ((w \ (w \ u)) * (w * w))))
    ]]></literal>
    <justification jstring="[para(8620(a,1),5665(a,1,3,1,2))].">
      <j1 rule="para" parents="8620 5665"/>
    </justification>
  </clause>

  <clause id="8627">
    <literal><![CDATA[
      a(x,x \ 1,x \ y) \ y = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(38,a,1362,a,b,8549,a),flip(a)].">
      <j1 rule="hyper" parents="38 1362 8549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8628">
    <literal><![CDATA[
      (a(x,y,z) * u) \ ((u * w) * T(a(x,y,z),w)) = L(w * a(u,w,a(x,y,z)),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2324,a,b,8578,a)].">
      <j1 rule="hyper" parents="63 2324 8578"/>
    </justification>
  </clause>

  <clause id="8629">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) \ (((y \ L(y,z,u)) * w) * T(x,w)) = L(w * a(y \ L(y,z,u),w,x),x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5066,a(flip),b,8578,a)].">
      <j1 rule="hyper" parents="63 5066 8578"/>
    </justification>
  </clause>

  <clause id="8630">
    <literal><![CDATA[
      L(x,y,L(z * a(u,z,w),w,u)) = L(x,y,(u * w) \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(8578(a,1),4034(a,1,3))].">
      <j1 rule="para" parents="8578 4034"/>
    </justification>
  </clause>

  <clause id="8631">
    <literal><![CDATA[
      a(L(x * a(y,x,z),z,y),u,w) = a((y * z) \ ((y * x) * z),u,w)
    ]]></literal>
    <justification jstring="[para(8578(a,1),4035(a,1,1))].">
      <j1 rule="para" parents="8578 4035"/>
    </justification>
  </clause>

  <clause id="8632">
    <literal><![CDATA[
      L(L(x,y,z) * a(u,L(x,y,z),w),w,u) = (u * w) \ ((u * L(x,y,z)) * T(w,x))
    ]]></literal>
    <justification jstring="[para(4304(a,1),8578(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4304 8578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8633">
    <literal><![CDATA[
      L(x * a(y,x,L(z,u,w) \ z),L(z,u,w) \ z,y) = (y * (L(z,u,w) \ z)) \ ((y * x) * (L(z,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(6484(a,1),8578(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6484 8578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8634">
    <literal><![CDATA[
      L(a(x * y,x * y,y),z,x) = a(x * y,x * y,x * (x * y))
    ]]></literal>
    <justification jstring="[para(8598(a,1),8589(a,1,1))].">
      <j1 rule="para" parents="8598 8589"/>
    </justification>
  </clause>

  <clause id="8635">
    <literal><![CDATA[
      a(x,y,a(z \ u,(z \ u) \ 1,u)) = a(x,y,(u * ((z \ u) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5493,a(flip),b,8472,a),flip(a)].">
      <j1 rule="hyper" parents="63 5493 8472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8636">
    <literal><![CDATA[
      R(x,y,(z * u) \ ((1 / u) \ z)) = L(x,y,a(u \ 1,u,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5371,a(flip),b,8482,a),flip(a)].">
      <j1 rule="hyper" parents="316 5371 8482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8637">
    <literal><![CDATA[
      a(x,y,z \ (u \ (z * (u * w)))) = a(x,y,w * a(u,w,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5602,a,b,8487,a)].">
      <j1 rule="hyper" parents="63 5602 8487"/>
    </justification>
  </clause>

  <clause id="8638">
    <literal><![CDATA[
      a(x,y,(z \ (u \ ((u * x) * z))) \ a(u,x,z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5546,a(flip),b,8490,a)].">
      <j1 rule="hyper" parents="63 5546 8490"/>
    </justification>
  </clause>

  <clause id="8639">
    <literal><![CDATA[
      R(x,y,z) \ (((x * y) * z) / z) = a(L(x,y,z),y,z) \ y
    ]]></literal>
    <justification jstring="[para(4643(a,1),8542(a,2,1))].">
      <j1 rule="para" parents="4643 8542"/>
    </justification>
  </clause>

  <clause id="8640">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (L(u,w,a(x,y,z)) * (a(x,y,z) * w)) = L(a(a(x,y,z),w,u) \ w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2324,a,b,8580,a)].">
      <j1 rule="hyper" parents="63 2324 8580"/>
    </justification>
  </clause>

  <clause id="8641">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) \ (L(y \ R(y,z,u),w,x) * (x * w)) = L(a(x,w,y \ R(y,z,u)) \ w,x,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2264,a(flip),b,8580,a)].">
      <j1 rule="hyper" parents="63 2264 8580"/>
    </justification>
  </clause>

  <clause id="8642">
    <literal><![CDATA[
      L(a(x,y,z * K(x * y,z)) \ y,x,z * K(x * y,z)) = ((z * K(x * y,z)) * x) \ (((x * (y * z)) / (x * y)) * (x * y))
    ]]></literal>
    <justification jstring="[para(2749(a,1),8580(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2749 8580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8643">
    <literal><![CDATA[
      a(L(a(x,y,z) \ y,x,z),u,w) = a(L(y,z,x),u,w)
    ]]></literal>
    <justification jstring="[para(8580(a,1),4642(a,1,1))].">
      <j1 rule="para" parents="8580 4642"/>
    </justification>
  </clause>

  <clause id="8644">
    <literal><![CDATA[
      L(a(x,y,z \ L(z,u,w)) \ y,x,z \ L(z,u,w)) = ((z \ L(z,u,w)) * x) \ (x * (y * (z \ L(z,u,w))))
    ]]></literal>
    <justification jstring="[para(5031(a,1),8580(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5031 8580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8645">
    <literal><![CDATA[
      a(L(a(x,y,z) \ y,x,z * (u * u)),w,v5) = a(L(y,z * (u * u),x),w,v5)
    ]]></literal>
    <justification jstring="[para(5804(a,1),8643(a,1,1,1,1))].">
      <j1 rule="para" parents="5804 8643"/>
    </justification>
  </clause>

  <clause id="8646">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (z * u)) = a(x,y,a(z,z \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6685,a(flip),b,8582,a)].">
      <j1 rule="hyper" parents="63 6685 8582"/>
    </justification>
  </clause>

  <clause id="8647">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,u)) = a(x,y,a(z,z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8118,a,b,8646,a),flip(a)].">
      <j1 rule="hyper" parents="63 8118 8646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8648">
    <literal><![CDATA[
      R(x,y,(z * u) \ ((1 / u) \ z)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,7848,a(flip),b,8636,a),flip(a)].">
      <j1 rule="hyper" parents="316 7848 8636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8649">
    <literal><![CDATA[
      R(x,y,z) \ (x * y) = a(L(x,y,z),y,z) \ y
    ]]></literal>
    <justification jstring="[para(11(a,1),8639(a,1,2))].">
      <j1 rule="para" parents="11 8639"/>
    </justification>
  </clause>

  <clause id="8650">
    <literal><![CDATA[
      a(L(x,y,z),y,z) \ y = x * (R(x,y,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1169,a(flip),b,8649,a),flip(a)].">
      <j1 rule="hyper" parents="63 1169 8649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8652">
    <literal><![CDATA[
      (x * (a(y,z,u) * L(y,w,v5))) \ (a(y,z,u) * (x * L(y,w,v5))) = a(x,a(y,z,u),L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(8409(a,1),2352(a,1,2))].">
      <j1 rule="para" parents="8409 2352"/>
    </justification>
  </clause>

  <clause id="8653">
    <literal><![CDATA[
      (L(x,y,z) \ x) * a(x,u,w) = x * (L(x,y,z) \ a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,1129,a(flip),b,8423,a),flip(a)].">
      <j1 rule="hyper" parents="63 1129 8423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8655">
    <literal><![CDATA[
      R(x,y,z) \ (u * a(x,w,v5)) = a(x,w,v5) * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,2290,a,b,8432,a),flip(a)].">
      <j1 rule="hyper" parents="316 2290 8432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8657">
    <literal><![CDATA[
      R(x,y,z) \ (a(x,u,w) * v5) = a(x,u,w) * (R(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),8433(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8658">
    <literal><![CDATA[
      a(x,y,z) * (R(x,u,w) \ 1) = R(x,u,w) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(67(a,1),8433(a,1,2,2))].">
      <j1 rule="para" parents="67 8433"/>
    </justification>
  </clause>

  <clause id="8659">
    <literal><![CDATA[
      a(x,y,z) * ((R(x,u,w) \ 1) * x) = (R(x,u,w) \ a(x,y,z)) * x
    ]]></literal>
    <justification jstring="[para(8658(a,1),8402(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8658 8402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8660">
    <literal><![CDATA[
      L(x,a(y,z,u),y) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2496,a(flip),b,8511,a)].">
      <j1 rule="hyper" parents="63 2496 8511"/>
    </justification>
  </clause>

  <clause id="8662">
    <literal><![CDATA[
      L(x,a(y,a(z,u,y),w),a(z,u,y)) = L(x,a(z,u,y),a(a(z,u,y),y,w))
    ]]></literal>
    <justification jstring="[para(7009(a,1),8660(a,1,2))].">
      <j1 rule="para" parents="7009 8660"/>
    </justification>
  </clause>

  <clause id="8663">
    <literal><![CDATA[
      R(x,x,y) * L(z,x,a(x,x,y)) = x * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(8660(a,1),7337(a,1,2))].">
      <j1 rule="para" parents="8660 7337"/>
    </justification>
  </clause>

  <clause id="8664">
    <literal><![CDATA[
      ((x * y) \ (x * (y * z))) * L(((x * y) \ (x * (y * z))) \ z,u,w) = (x * y) \ (x * ((y * z) * L(a(x,y,z),u,w)))
    ]]></literal>
    <justification jstring="[para(8515(a,1),1515(a,2,2))].">
      <j1 rule="para" parents="8515 1515"/>
    </justification>
  </clause>

  <clause id="8665">
    <literal><![CDATA[
      (x * (a(x,y,z) \ T(y,x))) * z = (y * x) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(3465(a,1),8537(a,1,1,2,1))].">
      <j1 rule="para" parents="3465 8537"/>
    </justification>
  </clause>

  <clause id="8666">
    <literal><![CDATA[
      ((a(x,y,z) \ y) * x) * z = (y * x) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(5329(a,1),8665(a,1,1))].">
      <j1 rule="para" parents="5329 8665"/>
    </justification>
  </clause>

  <clause id="8667">
    <literal><![CDATA[
      ((a(x,y,z) \ y) * x) * z = x * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,3285,a(flip),b,8666,a),flip(a)].">
      <j1 rule="hyper" parents="316 3285 8666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8670">
    <literal><![CDATA[
      a(x,y,z) * (L(x,u,w) \ x) = x * (L(x,u,w) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a,b,8653,a)].">
      <j1 rule="hyper" parents="63 2290 8653"/>
    </justification>
  </clause>

  <clause id="8671">
    <literal><![CDATA[
      a(x,y,z) * (R(x,u,w) \ x) = x * (R(x,u,w) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1169,a(flip),b,8655,a),flip(a)].">
      <j1 rule="hyper" parents="63 1169 8655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8672">
    <literal><![CDATA[
      L(x \ y,x,a(x,z,z)) = a(x,z,z) * (R(x,z,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2382,a,b,8657,a)].">
      <j1 rule="hyper" parents="63 2382 8657"/>
    </justification>
  </clause>

  <clause id="8674">
    <literal><![CDATA[
      (((x \ L(x,y,z)) * u) * w) \ ((x \ L(x,y,z)) * (u * w)) = a(w,u,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(8388(a,1),5784(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8388 5784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8675">
    <literal><![CDATA[
      R(x,y,z) * (L(x \ L(x,u,w),y,z) \ 1) = L(1 / R(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,8395,a(flip),b,6591,a)].">
      <j1 rule="hyper" parents="139 8395 6591"/>
    </justification>
  </clause>

  <clause id="8676">
    <literal><![CDATA[
      (L(a(x,y,z) \ 1,u,w) * w) * a(u,w,L(a(x,y,z) \ 1,u,w)) = u \ (w * (T(u,w) * (a(x,y,z) \ 1)))
    ]]></literal>
    <justification jstring="[para(5005(a,2),8436(a,1,1))].">
      <j1 rule="para" parents="5005 8436"/>
    </justification>
  </clause>

  <clause id="8677">
    <literal><![CDATA[
      x \ (((x \ 1) \ (K(x \ 1,x) * y)) / y) = L(y,x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(272(a,2),8488(a,1,2,1,2,1))].">
      <j1 rule="para" parents="272 8488"/>
    </justification>
  </clause>

  <clause id="8678">
    <literal><![CDATA[
      a(x,y,z * (((u \ w) / w) * u)) = a(x,y,a(u,u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,7579,a(flip),b,8496,a),flip(a)].">
      <j1 rule="hyper" parents="316 7579 8496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8679">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w \ u)) * w)) = a(x,y,a(w,w,u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5642,a(flip),b,8678,a)].">
      <j1 rule="hyper" parents="63 5642 8678"/>
    </justification>
  </clause>

  <clause id="8680">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * w) = a(x,y,a(u,u,z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8189,a(flip),b,8679,a)].">
      <j1 rule="hyper" parents="63 8189 8679"/>
    </justification>
  </clause>

  <clause id="8681">
    <literal><![CDATA[
      a(x,y,(z * L(u,z,z)) * w) = a(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6372,a(flip),b,8506,a),flip(a)].">
      <j1 rule="hyper" parents="63 6372 8506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8683">
    <literal><![CDATA[
      a(x,y,(L(z,u,u) * u) * w) = a(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5542,a,b,8681,a)].">
      <j1 rule="hyper" parents="63 5542 8681"/>
    </justification>
  </clause>

  <clause id="8684">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,u,u))) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,8681,a)].">
      <j1 rule="hyper" parents="63 5469 8681"/>
    </justification>
  </clause>

  <clause id="8685">
    <literal><![CDATA[
      a(x,y,(z \ (z \ u)) * w) = a(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,7458,a(flip),b,8681,a),flip(a)].">
      <j1 rule="hyper" parents="63 7458 8681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8686">
    <literal><![CDATA[
      a(x,y,z * (L(u,w,w) * w)) = a(x,y,(w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5623,a(flip),b,8681,a)].">
      <j1 rule="hyper" parents="63 5623 8681"/>
    </justification>
  </clause>

  <clause id="8687">
    <literal><![CDATA[
      a(x,y,z * (((u \ w) * (u * u)) * L(v5,(u \ w) * (u * u),(u \ 1) \ w))) = a(x,y,(((u \ w) * (u * u)) \ v5) * z)
    ]]></literal>
    <justification jstring="[para(1653(a,1),8684(a,1,3,2,2))].">
      <j1 rule="para" parents="1653 8684"/>
    </justification>
  </clause>

  <clause id="8688">
    <literal><![CDATA[
      a(x,y,z * (R(u,w,v5) * L(v6,R(u,w,v5),R(u,w,v5)))) = a(x,y,T(v6 / R(u,w,v5),u) * z)
    ]]></literal>
    <justification jstring="[para(2838(a,2),8684(a,2,3,1))].">
      <j1 rule="para" parents="2838 8684"/>
    </justification>
  </clause>

  <clause id="8689">
    <literal><![CDATA[
      a(x,y,z * ((L(u * (w * w),v5,v6) \ (w * w)) * L(v7,L(u * (w * w),v5,v6) \ (w * w),L(u,v5,v6) \ 1))) = a(x,y,((L(u * (w * w),v5,v6) \ (w * w)) \ v7) * z)
    ]]></literal>
    <justification jstring="[para(7872(a,1),8684(a,1,3,2,2))].">
      <j1 rule="para" parents="7872 8684"/>
    </justification>
  </clause>

  <clause id="8690">
    <literal><![CDATA[
      a(x,y,L(z * u,z,z) * w) = a(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),8685(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8691">
    <literal><![CDATA[
      a(x,y,z * L(u * w,u,u)) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,8690,a)].">
      <j1 rule="hyper" parents="63 5469 8690"/>
    </justification>
  </clause>

  <clause id="8692">
    <literal><![CDATA[
      a(x,y,z * L(u * w,w,w)) = a(x,y,(w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5654,a(flip),b,8690,a)].">
      <j1 rule="hyper" parents="63 5654 8690"/>
    </justification>
  </clause>

  <clause id="8693">
    <literal><![CDATA[
      a(x,y,(z \ u) * R(w / L(z * u,z,z),z * u,z * u)) = a(x,y,(z * u) * (w * ((z * u) \ 1)))
    ]]></literal>
    <justification jstring="[para(6824(a,1),8690(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6824 8690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8694">
    <literal><![CDATA[
      a(x,y,(z \ u) * (w * (a(w,v5,L(z * u,z,z)) \ v5))) = a(x,y,w * (v5 * L(z * u,z,z)))
    ]]></literal>
    <justification jstring="[para(8531(a,1),8691(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8531 8691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8695">
    <literal><![CDATA[
      a(x,y,(z \ u) * (w * (a(w,v5,L(u * z,z,z)) \ v5))) = a(x,y,w * (v5 * L(u * z,z,z)))
    ]]></literal>
    <justification jstring="[para(8531(a,1),8692(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8531 8692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8696">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(x,y,y)))) = L(z,y,x) * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(6855(a,1),8508(a,1,2,2))].">
      <j1 rule="para" parents="6855 8508"/>
    </justification>
  </clause>

  <clause id="8698">
    <literal><![CDATA[
      x \ (y \ ((L(L(z,u,w) \ z,x,y) * (y * x)) / (L(z,u,w) \ z))) = L(a(y,x,L(z,u,w) \ z) \ 1,a(y,x,L(z,u,w) \ z),x)
    ]]></literal>
    <justification jstring="[para(6503(a,2),8541(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6503 8541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8699">
    <literal><![CDATA[
      a(x,y,z * L(a(u \ 1,w,v5) \ 1,a(u \ 1,w,v5),w)) = a(x,y,z * (w \ (u \ (((u \ 1) * (w * v5)) / v5))))
    ]]></literal>
    <justification jstring="[para(8541(a,2),7780(a,1,3,2))].">
      <j1 rule="para" parents="8541 7780"/>
    </justification>
  </clause>

  <clause id="8700">
    <literal><![CDATA[
      (x / y) \ (x * (1 / y)) = K(y,y \ 1) * a(y \ x,y,y)
    ]]></literal>
    <justification jstring="[para(2535(a,1),8559(a,2,2))].">
      <j1 rule="para" parents="2535 8559"/>
    </justification>
  </clause>

  <clause id="8701">
    <literal><![CDATA[
      (x / y) \ (x * (1 / y)) = y * (a(y \ x,y,y) / y)
    ]]></literal>
    <justification jstring="[hyper(316,a,5301,a(flip),b,8700,a),flip(a)].">
      <j1 rule="hyper" parents="316 5301 8700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8702">
    <literal><![CDATA[
      a(x,y,(z * (u \ (L(w,z,u) * u))) \ (z * R(T(w,u * z),u,z))) = a(x,y,a(u,u \ (L(w,z,u) * u),z))
    ]]></literal>
    <justification jstring="[para(1430(a,1),8566(a,1,3,2))].">
      <j1 rule="para" parents="1430 8566"/>
    </justification>
  </clause>

  <clause id="8703">
    <literal><![CDATA[
      a(x,y,L(L(z,z,L(u,w,z)),v5,v6)) = a(x,y,L(L(z,z,u),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,5953,a(flip),b,8597,a),flip(a)].">
      <j1 rule="hyper" parents="316 5953 8597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8704">
    <literal><![CDATA[
      L(a(x * y,x * y,y),z,x) = a(x * y,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,8598,a(flip),b,8634,a),flip(a)].">
      <j1 rule="hyper" parents="316 8598 8634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8705">
    <literal><![CDATA[
      x \ (((1 / x) \ y) / y) = L(y,x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(666(a,1),8677(a,1,2,1))].">
      <j1 rule="para" parents="666 8677"/>
    </justification>
  </clause>

  <clause id="8706">
    <literal><![CDATA[
      x \ (((1 / x) \ y) / y) = a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2408,a(flip),b,8705,a),flip(a)].">
      <j1 rule="hyper" parents="316 2408 8705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8707">
    <literal><![CDATA[
      L(x * a(y,z,z),z,y) = L(x,z,y) * a(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,18,a,b,8696,a)].">
      <j1 rule="hyper" parents="63 18 8696"/>
    </justification>
  </clause>

  <clause id="8708">
    <literal><![CDATA[
      L(x * a(y,z,z),z,y) = a(y,z,z) * L(x,z,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2290,a,b,8707,a),flip(a)].">
      <j1 rule="hyper" parents="316 2290 8707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8709">
    <literal><![CDATA[
      x * (a(y,z,z) * L(a(y,z,z) \ (x \ 1),z,y)) = (x * a(y,z,z)) \ (L(x,z,y) * a(y,z,z))
    ]]></literal>
    <justification jstring="[para(8707(a,1),1494(a,2,2))].">
      <j1 rule="para" parents="8707 1494"/>
    </justification>
  </clause>

  <clause id="8710">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,(w \ 1) \ v5) = L(x \ L(x,y,z),u,w \ v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,8380,a(flip),b,8382,a),flip(a)].">
      <j1 rule="hyper" parents="316 8380 8382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8712">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,a(x,w,v5)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8408(a,1),8411(a,2,2))].">
      <j1 rule="para" parents="8408 8411"/>
    </justification>
  </clause>

  <clause id="8713">
    <literal><![CDATA[
      (a(x,y,z) / x) * L(x,u,w) = a(x,y,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,8712,a(flip),b,7101,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 8712 7101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8714">
    <literal><![CDATA[
      a(x,y,z) * (T(u,a(x,y,z)) * L(x \ L(x,w,v5),v6,v7)) = (u * a(x,y,z)) * L(x \ L(x,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(8712(a,1),782(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8712 782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8715">
    <literal><![CDATA[
      a(x,y,z) * (u * L(x \ L(x,w,v5),a(x,y,z),u)) = u * (a(x,y,z) * (x \ L(x,w,v5)))
    ]]></literal>
    <justification jstring="[para(8712(a,1),3332(a,2,2,2))].">
      <j1 rule="para" parents="8712 3332"/>
    </justification>
  </clause>

  <clause id="8717">
    <literal><![CDATA[
      R(a(x,y,z) / x,L(x,u,w),a(x,y,z) / x) \ L(x,u,w) = L(x,u,w) * ((a(x,y,z) * (x \ L(x,u,w))) \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(8713(a,1),4779(a,2,2,1))].">
      <j1 rule="para" parents="8713 4779"/>
    </justification>
  </clause>

  <clause id="8718">
    <literal><![CDATA[
      a(x,y,z) * (z * a(y,z,a(x,y,z))) = y \ (x \ ((x * y) * z))
    ]]></literal>
    <justification jstring="[hyper(133,a,8422,a,b,8448,a),flip(a)].">
      <j1 rule="hyper" parents="133 8422 8448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8719">
    <literal><![CDATA[
      R(x,y,z) = a(x,y,z) * (x * a(z * y,x,a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(34,a,3429,a(flip),b,8448,a)].">
      <j1 rule="hyper" parents="34 3429 8448"/>
    </justification>
  </clause>

  <clause id="8720">
    <literal><![CDATA[
      R(x,y,z) = a(x,y,z) * (x * a(y * z,x,a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(34,a,3416,a(flip),b,8448,a)].">
      <j1 rule="hyper" parents="34 3416 8448"/>
    </justification>
  </clause>

  <clause id="8721">
    <literal><![CDATA[
      R(x,y,z) = x * (a(x,y,z) * a(z * y,x,a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(316,a,8403,a(flip),b,8719,a),flip(a)].">
      <j1 rule="hyper" parents="316 8403 8719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8722">
    <literal><![CDATA[
      a(x,y,z) * a(z * y,x,a(x,y,z)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,8719,a,b,8403,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 8719 8403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8723">
    <literal><![CDATA[
      x * a(y * z,x,a(x,z,y)) = a(x,z,y) \ R(x,z,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,8719,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="133 8719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8724">
    <literal><![CDATA[
      R(x,y,z) = x * (a(x,y,z) * a(y * z,x,a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(316,a,8403,a(flip),b,8720,a),flip(a)].">
      <j1 rule="hyper" parents="316 8403 8720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8725">
    <literal><![CDATA[
      (x * a(x,y,z)) \ R(x,y,z) = a(y * z,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,8720,a,b,6856,a)].">
      <j1 rule="hyper" parents="133 8720 6856"/>
    </justification>
  </clause>

  <clause id="8726">
    <literal><![CDATA[
      a(x * y,z,a(z,x,y)) * a(z,x,y) = z \ R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,8720,a,b,8413,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 8720 8413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8727">
    <literal><![CDATA[
      a(x,y,z) * a(y * z,x,a(x,y,z)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,8720,a,b,8403,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 8720 8403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8728">
    <literal><![CDATA[
      x * a(y * z,x,a(x,y,z)) = a(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,8720,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="133 8720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8729">
    <literal><![CDATA[
      (x \ 1) * (a(x \ 1,x,y) * a(y * x,x \ 1,a(y,x,x))) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(6406(a,1),8721(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6406 8721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8730">
    <literal><![CDATA[
      (x * (a(y,z,u) * a(u * z,y,a(y,z,u)))) / x = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(8722(a,2),2197(a,1,1,2))].">
      <j1 rule="para" parents="8722 2197"/>
    </justification>
  </clause>

  <clause id="8731">
    <literal><![CDATA[
      a(R(x,y,z),u,w) * a(u * w,R(x,y,z),a(R(x,y,z),u,w)) = R(x,y,z) \ R(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,31,a,b,8724,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 31 8724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8732">
    <literal><![CDATA[
      a(x * y,z,a(z,x,y)) \ R(z,x,y) = z * a(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,8725,a)].">
      <j1 rule="hyper" parents="39 2301 8725"/>
    </justification>
  </clause>

  <clause id="8734">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (R(x,y,z) * T(u,x * a(y * z,x,a(x,y,z)))) = L(u,R(x,y,z),a(x,y,z) \ 1) * ((a(x,y,z) \ 1) * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(8728(a,2),3492(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8728 3492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8735">
    <literal><![CDATA[
      x * (a(y,x,a(z,y,x)) * a(z,y,x)) = y \ (z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,6855,a(flip),b,8718,a)].">
      <j1 rule="hyper" parents="63 6855 8718"/>
    </justification>
  </clause>

  <clause id="8737">
    <literal><![CDATA[
      x \ (y \ ((y * x) * a(z,u,x))) = a(z,u,x) * a(y,x,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(133,a,8449,a,b,6854,a(flip))].">
      <j1 rule="hyper" parents="133 8449 6854"/>
    </justification>
  </clause>

  <clause id="8738">
    <literal><![CDATA[
      x \ (y \ ((y * a(z,u,w)) * v5)) = x \ (v5 * (a(y,a(z,u,w),v5) * a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(133,a,8460,a,b,10,a)].">
      <j1 rule="hyper" parents="133 8460 10"/>
    </justification>
  </clause>

  <clause id="8739">
    <literal><![CDATA[
      a(x,a(y,z,u),y) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2544,a(flip),b,8501,a),flip(a)].">
      <j1 rule="hyper" parents="63 2544 8501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8741">
    <literal><![CDATA[
      x \ (a(y,x,a(x,z,u)) \ x) = a(y,a(x,z,u),x) \ 1
    ]]></literal>
    <justification jstring="[para(8739(a,1),6880(a,1,2,1))].">
      <j1 rule="para" parents="8739 6880"/>
    </justification>
  </clause>

  <clause id="8743">
    <literal><![CDATA[
      x \ (a(y,x,a(x,z,u)) \ x) = a(y,x,a(x,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(8739(a,1),8741(a,2,1))].">
      <j1 rule="para" parents="8739 8741"/>
    </justification>
  </clause>

  <clause id="8744">
    <literal><![CDATA[
      a(a(x,y,z),x,u) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2545,a(flip),b,8512,a),flip(a)].">
      <j1 rule="hyper" parents="63 2545 8512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8745">
    <literal><![CDATA[
      L(x,a(y,a(y,z,u),w),a(y,z,u)) = L(x,a(y,z,u),a(a(y,z,u),y,w))
    ]]></literal>
    <justification jstring="[para(8744(a,1),8660(a,1,2))].">
      <j1 rule="para" parents="8744 8660"/>
    </justification>
  </clause>

  <clause id="8746">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ u,z,w)) = a(x,y,L(u,w,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,6028,a(flip),b,8539,a),flip(a)].">
      <j1 rule="hyper" parents="316 6028 8539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8747">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w * v5) \ u,z,v5 * w)) = a(x,y,L(u,w * v5,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5557,a,b,8746,a)].">
      <j1 rule="hyper" parents="63 5557 8746"/>
    </justification>
  </clause>

  <clause id="8748">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w * ((v5 * v5) \ v6)) \ u,z,w * v6)) = a(x,y,L(u,w * ((v5 * v5) \ v6),z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6074,a(flip),b,8746,a)].">
      <j1 rule="hyper" parents="63 6074 8746"/>
    </justification>
  </clause>

  <clause id="8749">
    <literal><![CDATA[
      a(x,y,L(a(z,u,L(w,v5,v6)) \ u,z,L(w \ 1,v5,v6))) = a(x,y,L(u,L(w \ 1,v5,v6),z))
    ]]></literal>
    <justification jstring="[para(2655(a,1),8746(a,1,3,1,1))].">
      <j1 rule="para" parents="2655 8746"/>
    </justification>
  </clause>

  <clause id="8750">
    <literal><![CDATA[
      a(x,y,L(a(z,u,(w * v5) * v6) \ u,z,v6 * (w * ((v7 * v7) \ v5)))) = a(x,y,L(u,v6 * (w * ((v7 * v7) \ v5)),z))
    ]]></literal>
    <justification jstring="[para(5985(a,1),8746(a,1,3,1,1))].">
      <j1 rule="para" parents="5985 8746"/>
    </justification>
  </clause>

  <clause id="8751">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w * R(v5,v6,v7)) \ u,z,w * L(v5,v6,v7))) = a(x,y,L(u,w * R(v5,v6,v7),z))
    ]]></literal>
    <justification jstring="[para(7496(a,1),8746(a,1,3))].">
      <j1 rule="para" parents="7496 8746"/>
    </justification>
  </clause>

  <clause id="8752">
    <literal><![CDATA[
      R(a(x,y,a(z,u,w)) \ 1,a(x,y,a(z,u,w)),y) = y / (a(z,u,w) \ (x \ (a(z,u,w) * (x * y))))
    ]]></literal>
    <justification jstring="[para(8583(a,2),2284(a,2,2))].">
      <j1 rule="para" parents="8583 2284"/>
    </justification>
  </clause>

  <clause id="8753">
    <literal><![CDATA[
      ((x \ 1) \ y) / (a(z,u,w) \ (v5 \ (a(z,u,w) * (v5 * ((x \ 1) \ y))))) = (x \ y) / (a(v5,(x \ 1) \ y,a(z,u,w)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(8583(a,2),8038(a,1,2))].">
      <j1 rule="para" parents="8583 8038"/>
    </justification>
  </clause>

  <clause id="8754">
    <literal><![CDATA[
      L(x,y,L(z * a(u,z,w),w,u)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,4190,a(flip),b,8630,a),flip(a)].">
      <j1 rule="hyper" parents="316 4190 8630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8755">
    <literal><![CDATA[
      a(L(x * a(y,x,z),z,y),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,4563,a(flip),b,8631,a),flip(a)].">
      <j1 rule="hyper" parents="316 4563 8631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8756">
    <literal><![CDATA[
      a(L(a(x,y,z) * y,z,x),u,w) = a(L(y,x,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2791,a,b,8755,a)].">
      <j1 rule="hyper" parents="63 2791 8755"/>
    </justification>
  </clause>

  <clause id="8757">
    <literal><![CDATA[
      (x * (a(L(y,z,u),w,v5) * a(v5 * w,R(y,z,u),a(R(y,z,u),w,v5)))) / x = R(y,z,u) \ R(R(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(4643(a,1),8730(a,1,1,2,1))].">
      <j1 rule="para" parents="4643 8730"/>
    </justification>
  </clause>

  <clause id="8759">
    <literal><![CDATA[
      R(x,y,z) \ (x * a(x,y,z)) = a(x,a(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[para(20(a,2),8459(a,1,1))].">
      <j1 rule="para" parents="20 8459"/>
    </justification>
  </clause>

  <clause id="8760">
    <literal><![CDATA[
      a(x,y,z) * (R(x,y,z) \ x) = a(x,a(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8655,a(flip),b,8759,a)].">
      <j1 rule="hyper" parents="63 8655 8759"/>
    </justification>
  </clause>

  <clause id="8761">
    <literal><![CDATA[
      x * (R(x,y,z) \ a(x,y,z)) = a(x,a(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1169,a(flip),b,8759,a)].">
      <j1 rule="hyper" parents="63 1169 8759"/>
    </justification>
  </clause>

  <clause id="8762">
    <literal><![CDATA[
      x \ a(x,a(x,y,z),y * z) = R(x,y,z) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,8759,a(flip),b,1169,a(flip))].">
      <j1 rule="hyper" parents="133 8759 1169"/>
    </justification>
  </clause>

  <clause id="8763">
    <literal><![CDATA[
      x * ((R(x,y,z) \ a(x,y,z)) * (x \ L(x,u,w))) = (x \ L(x,u,w)) * a(x,a(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,8761,a(flip),b,5067,a),flip(a)].">
      <j1 rule="hyper" parents="139 8761 5067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8764">
    <literal><![CDATA[
      x * ((R(x,y,z) \ a(x,y,z)) * (x \ L(x,u,w))) = a(x,a(x,y,z),y * z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(8761(a,1),5132(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8761 5132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8765">
    <literal><![CDATA[
      x \ (a(y,z,z) * (x * L(z,z,y))) = a(x,L(z,z,y),a(y,z,z)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,2296,a,b,8462,a)].">
      <j1 rule="hyper" parents="63 2296 8462"/>
    </justification>
  </clause>

  <clause id="8766">
    <literal><![CDATA[
      a(a(x,y,z),y,y) \ ((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1) = y
    ]]></literal>
    <justification jstring="[para(5298(a,1),8479(a,1,2))].">
      <j1 rule="para" parents="5298 8479"/>
    </justification>
  </clause>

  <clause id="8767">
    <literal><![CDATA[
      x \ ((R(y,y,x) \ ((y \ ((y * y) * x)) * z)) / z) = a(L(y,y,x),x,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,4643,a(flip),b,8489,a),flip(a)].">
      <j1 rule="hyper" parents="316 4643 8489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8772">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((z \ (u \ w)) \ w)) = a(x,y,a(z \ (u \ w),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5629,a(flip),b,8561,a)].">
      <j1 rule="hyper" parents="63 5629 8561"/>
    </justification>
  </clause>

  <clause id="8773">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ (a(x,y,z) \ u)) \ 1 = L(u \ 1,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(8622(a,2),4965(a,1,1))].">
      <j1 rule="para" parents="8622 4965"/>
    </justification>
  </clause>

  <clause id="8777">
    <literal><![CDATA[
      a(x,y,a(z \ u,(z \ u) \ 1,u)) = a(x,y,(z \ u) * (u \ z))
    ]]></literal>
    <justification jstring="[para(7690(a,1),8635(a,2,3))].">
      <j1 rule="para" parents="7690 8635"/>
    </justification>
  </clause>

  <clause id="8778">
    <literal><![CDATA[
      a(x,y,(z \ x) * (x \ z)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,6902,a(flip),b,8777,a),flip(a)].">
      <j1 rule="hyper" parents="63 6902 8777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8779">
    <literal><![CDATA[
      L((x \ y) * (y \ x),z,y) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(52,a,8778,a)].">
      <j1 rule="hyper" parents="52 8778"/>
    </justification>
  </clause>

  <clause id="8781">
    <literal><![CDATA[
      ((((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1) * (((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1) / a(a(x,y,z),y,y))) / ((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1)) * a(a(x,y,z),y,y) = T((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(8766(a,1),2983(a,2,2))].">
      <j1 rule="para" parents="8766 2983"/>
    </justification>
  </clause>

  <clause id="8782">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ (((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1) * u)) / u = y * a(a(a(x,y,z),y,y),a(a(x,y,z),y,y) \ ((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1),u)
    ]]></literal>
    <justification jstring="[para(8766(a,1),8485(a,2,1))].">
      <j1 rule="para" parents="8766 8485"/>
    </justification>
  </clause>

  <clause id="8783">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w * ((v5 * v5) * v6)) = L(x \ L(x,y,z),u,w * v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,8380,a(flip),b,8384,a),flip(a)].">
      <j1 rule="hyper" parents="316 8380 8384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8784">
    <literal><![CDATA[
      a(R(x,y,z),u,u * L(u,w,v5)) = L(a(x,u,u * L(u,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[para(8241(a,1),8394(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8241 8394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8785">
    <literal><![CDATA[
      a(L(x,y,z),u,u * L(u,w,v5)) = L(a(x,u,u * L(u,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4643,a(flip),b,8784,a)].">
      <j1 rule="hyper" parents="63 4643 8784"/>
    </justification>
  </clause>

  <clause id="8786">
    <literal><![CDATA[
      a(L(x,y,z),z,z * L(z,u,w)) = a(x,z,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,8245,a(flip),b,8785,a),flip(a)].">
      <j1 rule="hyper" parents="316 8245 8785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8787">
    <literal><![CDATA[
      (x * y) \ ((z * (1 / x)) \ (R(z,x \ 1,x) * y)) = a(z * (x \ 1),x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,3150,a(flip),b,8467,a),flip(a)].">
      <j1 rule="hyper" parents="316 3150 8467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8788">
    <literal><![CDATA[
      L(x,y,a(x,x,y)) \ ((1 / x) \ y) = y * a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(8648(a,1),8483(a,1,1))].">
      <j1 rule="para" parents="8648 8483"/>
    </justification>
  </clause>

  <clause id="8789">
    <literal><![CDATA[
      x * a(y \ 1,y,x) = y \ ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(8397(a,1),8788(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8397 8788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8790">
    <literal><![CDATA[
      a(x,y,z) * a(u,u,a(x,y,z)) = u \ ((1 / u) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(7226(a,1),8789(a,1,2))].">
      <j1 rule="para" parents="7226 8789"/>
    </justification>
  </clause>

  <clause id="8791">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * a(y,z,u) = x \ ((1 / x) \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a,b,8790,a)].">
      <j1 rule="hyper" parents="63 2290 8790"/>
    </justification>
  </clause>

  <clause id="8792">
    <literal><![CDATA[
      L(x \ ((1 / x) \ a(y,z,u)),x,x) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(8790(a,1),8617(a,1,1))].">
      <j1 rule="para" parents="8790 8617"/>
    </justification>
  </clause>

  <clause id="8793">
    <literal><![CDATA[
      L(a(x,y,z),u,u) / (u \ 1) = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(8792(a,1),5328(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8792 5328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8794">
    <literal><![CDATA[
      (a(x,y,z) * u) \ L(a(x,y,z),u,u) = u \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,2345,a,b,8793,a)].">
      <j1 rule="hyper" parents="36 2345 8793"/>
    </justification>
  </clause>

  <clause id="8795">
    <literal><![CDATA[
      L(x \ 1,a(y,z,u),x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,2553,a(flip),b,8794,a)].">
      <j1 rule="hyper" parents="63 2553 8794"/>
    </justification>
  </clause>

  <clause id="8797">
    <literal><![CDATA[
      (x * a(y,z,u)) * L(x \ 1,w,v5) = x * (a(y,z,u) * L(x \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(8795(a,1),403(a,1,2,1))].">
      <j1 rule="para" parents="8795 403"/>
    </justification>
  </clause>

  <clause id="8798">
    <literal><![CDATA[
      a(x,x \ L(x,y,z),x \ u) = a(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1500,a(flip),b,8551,a)].">
      <j1 rule="hyper" parents="63 1500 8551"/>
    </justification>
  </clause>

  <clause id="8799">
    <literal><![CDATA[
      x \ ((y \ L(y,z,u)) \ ((x / y) * L(y,z,u))) = a(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7770,a,b,8798,a)].">
      <j1 rule="hyper" parents="63 7770 8798"/>
    </justification>
  </clause>

  <clause id="8800">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ ((u / x) * L(x,y,z)) = u * a(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(139,a,8798,a(flip),b,7770,a),flip(a)].">
      <j1 rule="hyper" parents="139 8798 7770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8801">
    <literal><![CDATA[
      (x * (y * (z \ 1))) / (u * (z \ 1)) = (x * (y * z)) / (u * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8536,a(flip),b,8585,a),flip(a)].">
      <j1 rule="hyper" parents="63 8536 8585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8802">
    <literal><![CDATA[
      (x * (y * (z \ 1))) / ((L(z,u,w) \ z) * (z \ 1)) = (x * (y * z)) / (L(1 / z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,6607,a,b,8801,a),flip(a)].">
      <j1 rule="hyper" parents="316 6607 8801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8803">
    <literal><![CDATA[
      (x * ((y \ R(y,z,u)) * w)) / (x * w) = L(y \ R(y,z,u),w \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2517,a(flip),b,8801,a),flip(a)].">
      <j1 rule="hyper" parents="63 2517 8801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8804">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) / (x * w) = L(a(y,z,u),w \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2454,a(flip),b,8801,a),flip(a)].">
      <j1 rule="hyper" parents="63 2454 8801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8805">
    <literal><![CDATA[
      (x * ((y * (a(y,z,u) \ z)) * u)) / (w * u) = (x * (y * (z * (u \ 1)))) / (w * (u \ 1))
    ]]></literal>
    <justification jstring="[para(8535(a,1),8801(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8535 8801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8806">
    <literal><![CDATA[
      L(a(x,y,z),u \ 1,w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2454,a(flip),b,8804,a),flip(a)].">
      <j1 rule="hyper" parents="63 2454 8804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8807">
    <literal><![CDATA[
      L(x \ R(x,y,z),u \ 1,w) = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2517,a(flip),b,8803,a),flip(a)].">
      <j1 rule="hyper" parents="63 2517 8803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8808">
    <literal><![CDATA[
      L((x \ 1) \ R(x \ 1,y,z),u,w) = L(x * R(x \ 1,y,z),u \ 1,w)
    ]]></literal>
    <justification jstring="[para(1511(a,1),8807(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1511 8807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8809">
    <literal><![CDATA[
      L(x,y,z) \ (u \ ((u * (L(x,y,z) * x)) / x)) = a(u,x,L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(2548(a,1),8586(a,2,1))].">
      <j1 rule="para" parents="2548 8586"/>
    </justification>
  </clause>

  <clause id="8810">
    <literal><![CDATA[
      L(x,a(y,a(z,u,y),w),a(z,u,y)) = L(x,a(z,u,y),a(y,a(z,u,y),w))
    ]]></literal>
    <justification jstring="[para(7009(a,1),8662(a,2,3))].">
      <j1 rule="para" parents="7009 8662"/>
    </justification>
  </clause>

  <clause id="8813">
    <literal><![CDATA[
      L(x,a(y,a(y,z,u),w),a(y,z,u)) = L(x,a(y,z,u),a(y,a(y,z,u),w))
    ]]></literal>
    <justification jstring="[para(8744(a,1),8745(a,2,3))].">
      <j1 rule="para" parents="8744 8745"/>
    </justification>
  </clause>

  <clause id="8814">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w * (L(v5,v6,v7) \ v5)) = L(x \ L(x,y,z),u,w * (v5 * L(v5,v6,v7)))
    ]]></literal>
    <justification jstring="[para(7463(a,1),8783(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="7463 8783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8815">
    <literal><![CDATA[
      (a(x,y,z) * u) * L(u \ 1,w,v5) = u * (a(x,y,z) * L(u \ 1,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,2292,a,b,8797,a)].">
      <j1 rule="hyper" parents="63 2292 8797"/>
    </justification>
  </clause>

  <clause id="8816">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ (u / x)) * L(x,y,z) = u * a(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6163,a(flip),b,8800,a)].">
      <j1 rule="hyper" parents="63 6163 8800"/>
    </justification>
  </clause>

  <clause id="8817">
    <literal><![CDATA[
      L(x,y,z) \ (u * a(x,x \ L(x,y,z),u)) = T((x \ L(x,y,z)) \ (u / x),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(390,a,8800,a(flip),b,6163,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="390 8800 6163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8818">
    <literal><![CDATA[
      L(x * R(x \ 1,y,z),u \ 1,w) = L(x * R(x \ 1,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1511(a,1),8808(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1511 8808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8819">
    <literal><![CDATA[
      L(x,y,z) \ (u \ ((u * (x * L(x,y,z))) / x)) = a(u,x,L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(257(a,1),8809(a,1,2,2,1,2))].">
      <j1 rule="para" parents="257 8809"/>
    </justification>
  </clause>

  <clause id="8820">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) \ (z / y)) * L(y,x,x) = z * a(y,y \ L(y,x,x),z)
    ]]></literal>
    <justification jstring="[para(5088(a,2),8816(a,1,1,1))].">
      <j1 rule="para" parents="5088 8816"/>
    </justification>
  </clause>

  <clause id="8821">
    <literal><![CDATA[
      R(x,x,y * L(y,z,u)) = L(x,x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,4663,a,b,8391,a)].">
      <j1 rule="hyper" parents="35 4663 8391"/>
    </justification>
  </clause>

  <clause id="8823">
    <literal><![CDATA[
      L(x,x,L(y,z,u) \ y) = L(x,x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8367,a(flip),b,8821,a)].">
      <j1 rule="hyper" parents="63 8367 8821"/>
    </justification>
  </clause>

  <clause id="8824">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),z * y) = (x \ ((x * y) * z)) \ ((y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1668,a,b,8455,a)].">
      <j1 rule="hyper" parents="63 1668 8455"/>
    </justification>
  </clause>

  <clause id="8825">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w \ z) * (u * w)))) = a(x,y,a(u,w \ 1,w \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8271,a(flip),b,8469,a)].">
      <j1 rule="hyper" parents="63 8271 8469"/>
    </justification>
  </clause>

  <clause id="8826">
    <literal><![CDATA[
      a(x,y,a(z,u \ 1,u \ w)) = a(x,y,a(z,u,u \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8556,a(flip),b,8825,a),flip(a)].">
      <j1 rule="hyper" parents="63 8556 8825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8827">
    <literal><![CDATA[
      a(x,y,a(z,z,z \ u)) = a(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8221,a(flip),b,8826,a),flip(a)].">
      <j1 rule="hyper" parents="63 8221 8826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8828">
    <literal><![CDATA[
      a(x,y,a(z,u \ 1,u \ 1)) = a(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(2383(a,1),8826(a,2,3))].">
      <j1 rule="para" parents="2383 8826"/>
    </justification>
  </clause>

  <clause id="8829">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,u)) = a(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8647,a,b,8827,a)].">
      <j1 rule="hyper" parents="63 8647 8827"/>
    </justification>
  </clause>

  <clause id="8830">
    <literal><![CDATA[
      a(x,y,a(z,z,u * z)) = a(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[para(8522(a,1),8827(a,1,3))].">
      <j1 rule="para" parents="8522 8827"/>
    </justification>
  </clause>

  <clause id="8831">
    <literal><![CDATA[
      a(x,y,a(z * u,z * u,u)) = a(x,y,a(z,z * u,z * u))
    ]]></literal>
    <justification jstring="[para(8598(a,1),8830(a,1,3))].">
      <j1 rule="para" parents="8598 8830"/>
    </justification>
  </clause>

  <clause id="8832">
    <literal><![CDATA[
      a(x,y,a(z,u \ 1,u)) = a(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(2534(a,1),8828(a,1,3))].">
      <j1 rule="para" parents="2534 8828"/>
    </justification>
  </clause>

  <clause id="8833">
    <literal><![CDATA[
      a(x,y,a(z,u * z,u * z)) = a(x,y,a(u,u * z,u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7280,a,b,8831,a)].">
      <j1 rule="hyper" parents="63 7280 8831"/>
    </justification>
  </clause>

  <clause id="8834">
    <literal><![CDATA[
      a(x,y,a(R(z,u,u),R(z,u,u) * L(u,u,z),R(z,u,u) * L(u,u,z))) = a(x,y,a(z * u,R(z,u,u) * L(u,u,z),L(u,u,z)))
    ]]></literal>
    <justification jstring="[para(7155(a,1),8831(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="7155 8831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8835">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ (u \ w))) = a(x,y,z * a(u \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(83(a,1),8484(a,1,3,2,2,1))].">
      <j1 rule="para" parents="83 8484"/>
    </justification>
  </clause>

  <clause id="8837">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w \ (v5 \ w)) * v5))) = a(x,y,z \ (a(v5,v5 \ 1,w) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5780,a(flip),b,8497,a)].">
      <j1 rule="hyper" parents="63 5780 8497"/>
    </justification>
  </clause>

  <clause id="8838">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ (v5 \ (w \ v5))))) = a(x,y,z * (u \ a(w,w \ 1,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7783,a,b,8498,a)].">
      <j1 rule="hyper" parents="63 7783 8498"/>
    </justification>
  </clause>

  <clause id="8839">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),a(z,u,w),u)) = a(x,y,u \ (z \ (w \ (z * (u * w)))))
    ]]></literal>
    <justification jstring="[hyper(316,a,5606,a(flip),b,8546,a),flip(a)].">
      <j1 rule="hyper" parents="316 5606 8546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8840">
    <literal><![CDATA[
      x \ ((y \ 1) \ (K(y \ 1,y) * (y \ x))) = L(y \ x,y,y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(272(a,2),8554(a,1,2,2,1))].">
      <j1 rule="para" parents="272 8554"/>
    </justification>
  </clause>

  <clause id="8841">
    <literal><![CDATA[
      a(L(a(x,y,z) \ y,x,z),u,w) = a(L(y,z * (v5 * v5),x),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,4652,a(flip),b,8645,a)].">
      <j1 rule="hyper" parents="63 4652 8645"/>
    </justification>
  </clause>

  <clause id="8843">
    <literal><![CDATA[
      a(L(x,y * (z * z),u),w,v5) = a(L(x,y,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,8643,a(flip),b,8841,a),flip(a)].">
      <j1 rule="hyper" parents="63 8643 8841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8844">
    <literal><![CDATA[
      a(L(x,y \ 1,z),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(229(a,1),8843(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="229 8843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8846">
    <literal><![CDATA[
      L((a(x,y,z) * u) \ 1,a(x,y,z),a(x,y,z)) = ((a(x,y,z) \ 1) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),8773(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8847">
    <literal><![CDATA[
      (x \ ((x * y) * T(z,y))) \ (z * y) = (x \ ((x * y) * z)) \ ((y * z) * 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,8574,a(flip),b,8824,a)].">
      <j1 rule="hyper" parents="63 8574 8824"/>
    </justification>
  </clause>

  <clause id="8848">
    <literal><![CDATA[
      (x \ ((x * y) * T(z,y))) \ (z * y) = (x \ ((x * y) * z)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,169,a(flip),b,8847,a),flip(a)].">
      <j1 rule="hyper" parents="316 169 8847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8849">
    <literal><![CDATA[
      (a(x,x,y) \ ((a(x,x,y) * x) * z)) \ (x * z) = (a(x,x,y) \ (R(x,x,y) * T(z,x))) \ (z * x)
    ]]></literal>
    <justification jstring="[para(7333(a,1),8848(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7333 8848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8850">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) \ (x \ y) = y \ ((x \ 1) \ (T(x,x \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(3002(a,1),8840(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3002 8840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8851">
    <literal><![CDATA[
      x \ ((y \ 1) \ (T(y,y \ 1) \ x)) = ((1 / y) * x) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(887(a,1),8850(a,1,1)),flip(a)].">
      <j1 rule="para" parents="887 8850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8852">
    <literal><![CDATA[
      ((1 / x) * y) \ (x \ y) = y \ ((1 / x) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3368,a(flip),b,8851,a),flip(a)].">
      <j1 rule="hyper" parents="63 3368 8851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8853">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,((w \ 1) * v5) * v6) = L(x \ L(x,y,z),u,v6 * (v5 * w))
    ]]></literal>
    <justification jstring="[hyper(316,a,8380,a(flip),b,8383,a),flip(a)].">
      <j1 rule="hyper" parents="316 8380 8383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8854">
    <literal><![CDATA[
      a(x,y,z \ (u \ (a(w,v5,v6) \ w))) = a(x,y,z \ (u \ (w \ a(w,v5,v6))))
    ]]></literal>
    <justification jstring="[hyper(63,a,5834,a(flip),b,8550,a),flip(a)].">
      <j1 rule="hyper" parents="63 5834 8550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8855">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) * a(x \ y,x,y * L(y,z,u)) = (y / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(7272(a,1),8588(a,1,2))].">
      <j1 rule="para" parents="7272 8588"/>
    </justification>
  </clause>

  <clause id="8856">
    <literal><![CDATA[
      (a(x,y,z) \ x) \ (x * (u * (a(x,y,z) \ 1))) = L(u,x,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(8405(a,1),8591(a,1,1))].">
      <j1 rule="para" parents="8405 8591"/>
    </justification>
  </clause>

  <clause id="8857">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) \ u,x,a(x,y,z) \ 1) = (a(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[para(4993(a,1),8856(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4993 8856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8858">
    <literal><![CDATA[
      (x \ 1) * (a(x \ 1,x,y) * 1) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(7283(a,1),8729(a,1,2,2))].">
      <j1 rule="para" parents="7283 8729"/>
    </justification>
  </clause>

  <clause id="8859">
    <literal><![CDATA[
      (x \ 1) * a(x \ 1,x,y) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(538,a,8858,a)].">
      <j1 rule="hyper" parents="538 8858"/>
    </justification>
  </clause>

  <clause id="8861">
    <literal><![CDATA[
      x \ a(x \ 1,x,y) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2502,a(flip),b,8859,a)].">
      <j1 rule="hyper" parents="63 2502 8859"/>
    </justification>
  </clause>

  <clause id="8862">
    <literal><![CDATA[
      x * R(x \ 1,x,y) = a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,1510,a,b,8859,a)].">
      <j1 rule="hyper" parents="34 1510 8859"/>
    </justification>
  </clause>

  <clause id="8863">
    <literal><![CDATA[
      a(x,y,(z \ (R(u \ 1,u,w) * u)) * v5) = a(x,y,v5 * (z \ a(u \ 1,u,w)))
    ]]></literal>
    <justification jstring="[para(8861(a,1),5670(a,1,3,1,2,1))].">
      <j1 rule="para" parents="8861 5670"/>
    </justification>
  </clause>

  <clause id="8864">
    <literal><![CDATA[
      a(x \ 1,x,x \ y) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,735,a,b,8862,a),flip(a)].">
      <j1 rule="hyper" parents="63 735 8862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8865">
    <literal><![CDATA[
      (x / (y * x)) * y = a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,623,a,b,8862,a)].">
      <j1 rule="hyper" parents="63 623 8862"/>
    </justification>
  </clause>

  <clause id="8866">
    <literal><![CDATA[
      R(1 / x,x,y) * x = a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,609,a,b,8862,a)].">
      <j1 rule="hyper" parents="63 609 8862"/>
    </justification>
  </clause>

  <clause id="8867">
    <literal><![CDATA[
      a(x,y,(z \ (u * (w / (u * w)))) * v5) = a(x,y,v5 * (z \ a(u \ 1,u,w)))
    ]]></literal>
    <justification jstring="[para(8865(a,1),5665(a,2,3,2,2))].">
      <j1 rule="para" parents="8865 5665"/>
    </justification>
  </clause>

  <clause id="8868">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w / (u * w),v5) * (v5 * (w / (u * w))))) = a(x,y,z \ (v5 * a(u \ 1,u,w)))
    ]]></literal>
    <justification jstring="[para(8865(a,1),5598(a,2,3,2,2))].">
      <j1 rule="para" parents="8865 5598"/>
    </justification>
  </clause>

  <clause id="8870">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w \ 1) * R(1 / w,w,v5)))) = a(x,y,z \ (u * a(w \ 1,w,v5)))
    ]]></literal>
    <justification jstring="[para(8866(a,1),6356(a,2,3,2,2))].">
      <j1 rule="para" parents="8866 6356"/>
    </justification>
  </clause>

  <clause id="8871">
    <literal><![CDATA[
      x \ ((y \ 1) \ (((y \ 1) * y) * (y \ x))) = ((y \ x) / x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,8451,a,b,8864,a)].">
      <j1 rule="hyper" parents="63 8451 8864"/>
    </justification>
  </clause>

  <clause id="8872">
    <literal><![CDATA[
      (x \ y) * (((x \ y) / y) * x) = x \ ((1 / x) \ (x \ y))
    ]]></literal>
    <justification jstring="[para(8864(a,1),8789(a,1,2))].">
      <j1 rule="para" parents="8864 8789"/>
    </justification>
  </clause>

  <clause id="8873">
    <literal><![CDATA[
      L(1 / (x \ y),x,y \ (x \ y)) = 1 / (x \ ((1 / x) \ (x \ y)))
    ]]></literal>
    <justification jstring="[para(8872(a,1),6616(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8872 6616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8874">
    <literal><![CDATA[
      x \ ((1 / y) \ (y \ x)) = ((y \ x) / x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,3367,a(flip),b,8871,a)].">
      <j1 rule="hyper" parents="63 3367 8871"/>
    </justification>
  </clause>

  <clause id="8875">
    <literal><![CDATA[
      ((1 / x) * y) \ (x \ y) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,8852,a,b,8874,a)].">
      <j1 rule="hyper" parents="63 8852 8874"/>
    </justification>
  </clause>

  <clause id="8876">
    <literal><![CDATA[
      L(x \ y,x,y \ (x \ y)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(39,a,1656,a,b,8875,a)].">
      <j1 rule="hyper" parents="39 1656 8875"/>
    </justification>
  </clause>

  <clause id="8877">
    <literal><![CDATA[
      a(x,y,(z \ (u * ((u * w) \ w))) * v5) = a(x,y,v5 * (z \ a(u \ 1,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6069,a(flip),b,8867,a)].">
      <j1 rule="hyper" parents="63 6069 8867"/>
    </justification>
  </clause>

  <clause id="8878">
    <literal><![CDATA[
      L(a(x,x,y \ R(y,z,u)) * ((R(y,z,u) \ y) \ 1),x,x) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(7651(a,1),8616(a,1,1,1,3))].">
      <j1 rule="para" parents="7651 8616"/>
    </justification>
  </clause>

  <clause id="8879">
    <literal><![CDATA[
      L(a(x,x,y \ L(y,z,u)) * ((R(y,z,u) \ y) \ 1),x,x) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(7390(a,1),8878(a,1,1,1))].">
      <j1 rule="para" parents="7390 8878"/>
    </justification>
  </clause>

  <clause id="8880">
    <literal><![CDATA[
      L(a(x,x,y * L(y,z,u)) * ((R(y,z,u) \ y) \ 1),x,x) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(5566(a,1),8879(a,1,1,1))].">
      <j1 rule="para" parents="5566 8879"/>
    </justification>
  </clause>

  <clause id="8881">
    <literal><![CDATA[
      L(a(x,x,y * L(y,z,u)) * (y \ R(y,z,u)),x,x) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(7651(a,1),8880(a,1,1,2))].">
      <j1 rule="para" parents="7651 8880"/>
    </justification>
  </clause>

  <clause id="8882">
    <literal><![CDATA[
      a(x,x,y * L(y,z,u)) * (y \ R(y,z,u)) = L(1 / (y \ R(y,z,u)),x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(41,a,8619,a,b,8881,a),flip(a)].">
      <j1 rule="hyper" parents="41 8619 8881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8883">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w \ (w \ v5)) * (w * w)))) = a(x,y,z \ (u \ L(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,7739,a(flip),b,8624,a),flip(a)].">
      <j1 rule="hyper" parents="316 7739 8624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8884">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (w \ (w \ v5))) * (w * w))) = a(x,y,z \ (u \ L(v5,w,w)))
    ]]></literal>
    <justification jstring="[para(388(a,1),8883(a,1,3,2))].">
      <j1 rule="para" parents="388 8883"/>
    </justification>
  </clause>

  <clause id="8885">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ (w \ v5)))) = a(x,y,z \ (u \ L(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5813,a(flip),b,8884,a)].">
      <j1 rule="hyper" parents="63 5813 8884"/>
    </justification>
  </clause>

  <clause id="8887">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ (w \ v5)) * (w * w)))) = a(x,y,z * (u \ L(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7052,a(flip),b,8625,a),flip(a)].">
      <j1 rule="hyper" parents="63 7052 8625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8888">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w \ (w \ v5))) * (w * w))) = a(x,y,z * (u \ L(v5,w,w)))
    ]]></literal>
    <justification jstring="[para(388(a,1),8887(a,1,3,2))].">
      <j1 rule="para" parents="388 8887"/>
    </justification>
  </clause>

  <clause id="8889">
    <literal><![CDATA[
      a(x,y,(z \ (u \ (u \ w))) * v5) = a(x,y,v5 * (z \ L(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5875,a(flip),b,8888,a)].">
      <j1 rule="hyper" parents="63 5875 8888"/>
    </justification>
  </clause>

  <clause id="8891">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ (w \ v5)))) = a(x,y,z * (u \ L(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,8889,a)].">
      <j1 rule="hyper" parents="63 5469 8889"/>
    </justification>
  </clause>

  <clause id="8892">
    <literal><![CDATA[
      a(x,y,z * (u \ L(w * v5,w,w))) = a(x,y,z * (u \ (w \ v5)))
    ]]></literal>
    <justification jstring="[para(9(a,1),8891(a,1,3,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8893">
    <literal><![CDATA[
      a(x,y,z * (a(u,u,u * w) \ 1)) = a(x,y,z * ((u * w) \ (u \ w)))
    ]]></literal>
    <justification jstring="[para(5088(a,2),8892(a,1,3,2))].">
      <j1 rule="para" parents="5088 8892"/>
    </justification>
  </clause>

  <clause id="8894">
    <literal><![CDATA[
      a(x,y,a(z,z,z * u) * w) = a(x,y,w * ((z * u) \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5529,a(flip),b,8893,a)].">
      <j1 rule="hyper" parents="63 5529 8893"/>
    </justification>
  </clause>

  <clause id="8895">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w) * a(R(x,u,w),L(x \ L(x,y,z),u,w),v5),v5,R(x,u,w)) = (R(x,u,w) * v5) \ (L(R(x,u,w),y,z) * T(v5,x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(8387(a,1),8632(a,2,2,1))].">
      <j1 rule="para" parents="8387 8632"/>
    </justification>
  </clause>

  <clause id="8897">
    <literal><![CDATA[
      a(x,x,y * L(y,z,u)) * (y \ R(y,z,u)) = L(R(y,z,u) \ y,x,x) \ 1
    ]]></literal>
    <justification jstring="[para(7652(a,1),8882(a,2,1,1))].">
      <j1 rule="para" parents="7652 8882"/>
    </justification>
  </clause>

  <clause id="8898">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) * a(x \ 1,x,y * L(y,z,u)) = (1 / x) \ (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(7272(a,1),8481(a,1,2))].">
      <j1 rule="para" parents="7272 8481"/>
    </justification>
  </clause>

  <clause id="8899">
    <literal><![CDATA[
      L(a(x,y,z) \ L(a(x,y,z),u,w),v5,x) = a(x,y,z) \ L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(8514(a,1),8517(a,2,2))].">
      <j1 rule="para" parents="8514 8517"/>
    </justification>
  </clause>

  <clause id="8902">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) \ y,x,a(z,u,w)) = L(y,a(z,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,2496,a(flip),b,8538,a),flip(a)].">
      <j1 rule="hyper" parents="316 2496 8538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8903">
    <literal><![CDATA[
      L(a(x,y,a(z,u,u)) \ y,x,a(u \ z,u,z)) = L(y,a(u \ z,u,z),x)
    ]]></literal>
    <justification jstring="[para(8222(a,1),8902(a,1,1,1))].">
      <j1 rule="para" parents="8222 8902"/>
    </justification>
  </clause>

  <clause id="8905">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ (((x \ L(x,y,z)) * (u * w)) / w) = a(w,u,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7126,a(flip),b,8674,a)].">
      <j1 rule="hyper" parents="63 7126 8674"/>
    </justification>
  </clause>

  <clause id="8906">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ R(w \ 1,w,v5)))) = a(x,y,z \ (u * a(w \ 1,w,v5)))
    ]]></literal>
    <justification jstring="[para(902(a,1),8870(a,1,3,2,2))].">
      <j1 rule="para" parents="902 8870"/>
    </justification>
  </clause>

  <clause id="8907">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ (((x \ L(x,y,z)) * (u * w)) / w) = a(w,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5566,a(flip),b,8905,a),flip(a)].">
      <j1 rule="hyper" parents="316 5566 8905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8908">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ (((x \ L(x,y,z)) * (u * w)) / w) = a(w \ 1,u,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(964(a,1),8905(a,1,2))].">
      <j1 rule="para" parents="964 8905"/>
    </justification>
  </clause>

  <clause id="8909">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (x \ (((x \ L(y,z,u)) \ (((x \ L(y,z,u)) * x) * (y * L(y,z,u)))) / (y * L(y,z,u)))) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[para(8476(a,1),8587(a,1,2))].">
      <j1 rule="para" parents="8476 8587"/>
    </justification>
  </clause>

  <clause id="8910">
    <literal><![CDATA[
      (x * (y * (z * (u \ 1)))) / (w * (u \ 1)) = (x * (y * (z * u))) / (w * u)
    ]]></literal>
    <justification jstring="[para(8531(a,1),8805(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8531 8805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8911">
    <literal><![CDATA[
      (L(x,y,z) \ u) * a(x,x \ L(x,y,z),u) = T((x \ L(x,y,z)) \ (u / x),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8423,a(flip),b,8817,a)].">
      <j1 rule="hyper" parents="63 8423 8817"/>
    </justification>
  </clause>

  <clause id="8912">
    <literal><![CDATA[
      (L(x,y,z) \ u) * a(x,x \ L(x,y,z),u) = T((x \ L(x,y,z)) \ (u / x),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,4304,a(flip),b,8911,a),flip(a)].">
      <j1 rule="hyper" parents="316 4304 8911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8914">
    <literal><![CDATA[
      L((T(x,y) \ z) \ L(T(x,y) \ z,u,w),v5,v6) = L(x \ (z * L(z \ x,u,w)),v5,v6 \ 1)
    ]]></literal>
    <justification jstring="[para(1252(a,1),8393(a,2,1))].">
      <j1 rule="para" parents="1252 8393"/>
    </justification>
  </clause>

  <clause id="8915">
    <literal><![CDATA[
      (L(x,y,z) * L(u,x,L(x,y,z))) \ (L(x,y,z) * u) = a(x,L(x,y,z),L(u,x,L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(1231(a,1),8563(a,1,1,2))].">
      <j1 rule="para" parents="1231 8563"/>
    </justification>
  </clause>

  <clause id="8916">
    <literal><![CDATA[
      (x * L(R(y,z,u),x,L(y,w,v5))) \ (x * R(y,z,u)) = a(L(y,w,v5),x,L(L(y,z,u),x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,5953,a(flip),b,8564,a),flip(a)].">
      <j1 rule="hyper" parents="316 5953 8564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8917">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),a(z,u,w),y) = (a(z,u,w) * y) \ ((y * x) * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(2286(a,1),8628(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2286 8628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8919">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),a(z,u,w),y) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,2349,a(flip),b,8917,a),flip(a)].">
      <j1 rule="hyper" parents="316 2349 8917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8920">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) * y,a(z,u,w),x) = L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,2314,a,b,8919,a)].">
      <j1 rule="hyper" parents="63 2314 8919"/>
    </justification>
  </clause>

  <clause id="8921">
    <literal><![CDATA[
      L(x * a(x,L(x,y,z),a(u,w,v5)),a(u,w,v5),L(x,y,z)) = L(x,L(x,y,z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(1529(a,1),8919(a,1,1,2))].">
      <j1 rule="para" parents="1529 8919"/>
    </justification>
  </clause>

  <clause id="8922">
    <literal><![CDATA[
      L(x * a(y,x,a(z * u,w,v5)),a(u * z,w,v5),y) = L(x,y,a(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(2771(a,1),8919(a,1,1,2,3))].">
      <j1 rule="para" parents="2771 8919"/>
    </justification>
  </clause>

  <clause id="8923">
    <literal><![CDATA[
      L(x * 1,a(y,z,L(u,w,v5)),u) = L(x,u,a(y,z,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(6988(a,1),8919(a,1,1,2))].">
      <j1 rule="para" parents="6988 8919"/>
    </justification>
  </clause>

  <clause id="8924">
    <literal><![CDATA[
      L(x,a(y,z,L(u,w,v5)),u) = L(x,u,a(y,z,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(8(a,1),8923(a,1,1))].">
      <j1 rule="para" parents="8 8923"/>
    </justification>
  </clause>

  <clause id="8926">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) * y = y * a(x,y,a(u * z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(41,a,8920,a,b,8922,a)].">
      <j1 rule="hyper" parents="41 8920 8922"/>
    </justification>
  </clause>

  <clause id="8927">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) = a(x,y,a(u * z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(35,a,2290,a,b,8926,a)].">
      <j1 rule="hyper" parents="35 2290 8926"/>
    </justification>
  </clause>

  <clause id="8929">
    <literal><![CDATA[
      a(x,y,L(a(z,u,L(w,v5,v6)) \ u,z,L(w,v5,v6))) = a(x,y,L(u,L(w \ 1,v5,v6),z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6377,a(flip),b,8749,a)].">
      <j1 rule="hyper" parents="63 6377 8749"/>
    </justification>
  </clause>

  <clause id="8930">
    <literal><![CDATA[
      a(x,y,L(z,L(u \ 1,w,v5),v6)) = a(x,y,L(z,L(u,w,v5),v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,8746,a(flip),b,8929,a),flip(a)].">
      <j1 rule="hyper" parents="63 8746 8929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8931">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * (u * x)) / (L(1 / x,y,z) \ 1) = L(u,x \ 1,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8366,a(flip),b,8802,a),flip(a)].">
      <j1 rule="hyper" parents="63 8366 8802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8932">
    <literal><![CDATA[
      L(x,y \ 1,L(y,z,u) \ y) = L(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7789,a(flip),b,8931,a),flip(a)].">
      <j1 rule="hyper" parents="63 7789 8931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8934">
    <literal><![CDATA[
      a(x \ 1,y,z \ L(z,u,w)) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8907,a(flip),b,8908,a),flip(a)].">
      <j1 rule="hyper" parents="63 8907 8908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8935">
    <literal><![CDATA[
      a(x \ 1,y,z * L(z,u,w)) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5566,a(flip),b,8934,a)].">
      <j1 rule="hyper" parents="63 5566 8934"/>
    </justification>
  </clause>

  <clause id="8936">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) * a(x,x,y * L(y,z,u)) = (1 / x) \ (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(8935(a,1),8898(a,1,2))].">
      <j1 rule="para" parents="8935 8898"/>
    </justification>
  </clause>

  <clause id="8937">
    <literal><![CDATA[
      L(T(x,y) \ (z * L(z \ T(x,y),u,w)),v5,v6) = L(x \ (z * L(z \ x,u,w)),v5,v6 \ 1)
    ]]></literal>
    <justification jstring="[para(1252(a,1),8914(a,1,1))].">
      <j1 rule="para" parents="1252 8914"/>
    </justification>
  </clause>

  <clause id="8938">
    <literal><![CDATA[
      (x * L(R(y,z,u),x,L(y,w,v5))) \ (x * R(y,z,u)) = a(L(y,w,v5),x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,8004,a(flip),b,8916,a),flip(a)].">
      <j1 rule="hyper" parents="316 8004 8916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8940">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,w,v5)) = (u * L(R(x,w,v5),u,x)) \ (u * R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(8001(a,1),8938(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8001 8938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8942">
    <literal><![CDATA[
      L(x \ (y * L(y \ x,z,u)),w,v5 \ 1) = L(x \ (y * L(y \ x,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(6444(a,1),8937(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6444 8937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8943">
    <literal><![CDATA[
      (x * (y * (L(x,z,u) \ x))) * a(x,L(x,z,u) \ x,y) = x * (y * R(L(x,z,u) \ x,x,y))
    ]]></literal>
    <justification jstring="[para(7925(a,1),5162(a,1,2))].">
      <j1 rule="para" parents="7925 5162"/>
    </justification>
  </clause>

  <clause id="8944">
    <literal><![CDATA[
      T(T(x * K(x * (y \ z),x),u),y \ z) = R(T(x,u),y \ (a(w,v5,v6) \ z),x)
    ]]></literal>
    <justification jstring="[para(6756(a,1),5308(a,1,1,1,2))].">
      <j1 rule="para" parents="6756 5308"/>
    </justification>
  </clause>

  <clause id="8945">
    <literal><![CDATA[
      R(T(x,y),z \ (a(u,w,v5) \ v6),x) = R(T(x,y),z \ v6,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3257,a(flip),b,8944,a),flip(a)].">
      <j1 rule="hyper" parents="63 3257 8944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8947">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = (x \ (a(z,u,w) \ y)) \ (a(z,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5269,a(flip),b,8945,a),flip(a)].">
      <j1 rule="hyper" parents="63 5269 8945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8949">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ w)) \ (a(y,z,u) \ w) = (x \ w) \ w
    ]]></literal>
    <justification jstring="[hyper(63,a,1651,a(flip),b,8947,a),flip(a)].">
      <j1 rule="hyper" parents="63 1651 8947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8950">
    <literal><![CDATA[
      x / (y \ (a(z,u,w) \ x)) = ((a(z,u,w) \ x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(209,a,206,a(flip),b,8949,a(flip))].">
      <j1 rule="hyper" parents="209 206 8949"/>
    </justification>
  </clause>

  <clause id="8951">
    <literal><![CDATA[
      R(x,y,(z * (u * (w * (v5 * v5)))) \ (u * (z * w))) = L(x,y,a(z,w * (v5 * v5),u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1701,a(flip),b,5444,a)].">
      <j1 rule="hyper" parents="63 1701 5444"/>
    </justification>
  </clause>

  <clause id="8953">
    <literal><![CDATA[
      R(x,y,(z * (u * w)) \ (u * (z * w))) = L(x,y,a(z,w * (v5 * v5),u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4831,a(flip),b,8951,a)].">
      <j1 rule="hyper" parents="63 4831 8951"/>
    </justification>
  </clause>

  <clause id="8955">
    <literal><![CDATA[
      L(x,y,a(z,u * (w * w),v5)) = L(x,y,a(z,u,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5443,a(flip),b,8953,a),flip(a)].">
      <j1 rule="hyper" parents="63 5443 8953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8956">
    <literal><![CDATA[
      L(x,y,a(z,u \ 1,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(229(a,1),8955(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="229 8955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8957">
    <literal><![CDATA[
      L(x,y,a(z,u \ 1,u \ 1)) = L(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(2383(a,1),8956(a,2,3))].">
      <j1 rule="para" parents="2383 8956"/>
    </justification>
  </clause>

  <clause id="8959">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * L((u * z) \ u,w,v5)) = a(x,y,(u \ ((u / z) * L(z,w,v5))) \ 1)
    ]]></literal>
    <justification jstring="[para(7118(a,1),5912(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7118 5912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8960">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * L((u * z) \ u,w,v5)) = a(x,y,u \ ((u / z) * L(z,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,2534,a(flip),b,8959,a),flip(a)].">
      <j1 rule="hyper" parents="316 2534 8959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8961">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * L((u * z) \ u,w,v5)) = a(x,y,u \ ((z \ u) * L(z,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5627,a(flip),b,8960,a),flip(a)].">
      <j1 rule="hyper" parents="316 5627 8960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8962">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * L((z * u) \ z,w,v5)) = a(x,y,z \ ((u \ z) * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7775,a(flip),b,8961,a)].">
      <j1 rule="hyper" parents="63 7775 8961"/>
    </justification>
  </clause>

  <clause id="8963">
    <literal><![CDATA[
      ((x / y) * z) \ L((x / y) * u,w,v5) = ((y \ x) * z) \ L((y \ x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,1364,a(flip),b,6296,a),flip(a)].">
      <j1 rule="hyper" parents="63 1364 6296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8965">
    <literal><![CDATA[
      (((x * y) \ 1) * x) \ L(((x * y) \ 1) * x,z,u) = (1 / (x * y)) * (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1743,a(flip),b,8963,a),flip(a)].">
      <j1 rule="hyper" parents="63 1743 8963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8966">
    <literal><![CDATA[
      ((x \ y) * z) \ L((x \ y) * x,u,w) = ((y / x) * z) \ L(y,u,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),8963(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 8963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8967">
    <literal><![CDATA[
      (((x \ y) * z) \ L((x \ y) * z,u,w)) \ 1 = L((y / x) * z,u,w) \ ((y / x) * z)
    ]]></literal>
    <justification jstring="[para(8963(a,1),1894(a,1,1))].">
      <j1 rule="para" parents="8963 1894"/>
    </justification>
  </clause>

  <clause id="8968">
    <literal><![CDATA[
      ((x \ y) * x) \ L((x \ y) * x,z,u) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),8966(a,2,1))].">
      <j1 rule="para" parents="12 8966"/>
    </justification>
  </clause>

  <clause id="8969">
    <literal><![CDATA[
      L((x / y) * z,u,w) \ ((x / y) * z) = L((y \ x) * z,u,w) \ ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1894,a(flip),b,8967,a),flip(a)].">
      <j1 rule="hyper" parents="63 1894 8967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8970">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,(L(y,z,u) \ y) \ 1) = (y \ L(y,z,u)) * (x * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(1895(a,1),6501(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1895 6501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8971">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * (L(x,y,z) \ x)) = L(u,L(x,y,z) \ x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5076(a,1),8970(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5076 8970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8983">
    <literal><![CDATA[
      ((L(R(x,y,z),u,w) * (x * v5)) / v5) \ (x * L(R(x,y,z),u,w)) = a(L(L(x,y,z),u,w),x,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,4653,a(flip),b,6935,a),flip(a)].">
      <j1 rule="hyper" parents="316 4653 6935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8984">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,y)) = a(x,a(w,v5,y),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2544,a(flip),b,6986,a)].">
      <j1 rule="hyper" parents="63 2544 6986"/>
    </justification>
  </clause>

  <clause id="8985">
    <literal><![CDATA[
      (((x / L(y,z,u)) * (L(y,z,u) * a(w,v5,y))) / a(w,v5,y)) \ x = a(L(y,z,u) \ x,a(w,v5,y),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6948,a,b,8984,a)].">
      <j1 rule="hyper" parents="63 6948 8984"/>
    </justification>
  </clause>

  <clause id="8986">
    <literal><![CDATA[
      L(K(a(x,y,y),L(y,y,x)) * z,L(y,y,x),a(x,y,y)) = (y \ (L(y,y,x) * z)) * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,6896,a(flip),b,7312,a),flip(a)].">
      <j1 rule="hyper" parents="316 6896 7312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8987">
    <literal><![CDATA[
      (x \ y) \ L(y * (x \ 1),x * (y \ (x \ y)),a(y,x,x)) = (x * (y \ (x \ y))) \ 1
    ]]></literal>
    <justification jstring="[para(8213(a,1),7698(a,1,2))].">
      <j1 rule="para" parents="8213 7698"/>
    </justification>
  </clause>

  <clause id="8988">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u) \ (u \ L(z,z,u)),w,v5)) = a(x,y,L(((z \ 1) \ u) \ L(z,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,5718,a(flip),b,7756,a),flip(a)].">
      <j1 rule="hyper" parents="316 5718 7756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8989">
    <literal><![CDATA[
      L(x,y,(z * u) \ (w \ T(z * (u * w),v5 * v5))) = L(x,y,a(w * (v5 * v5),u,z))
    ]]></literal>
    <justification jstring="[para(833(a,1),7835(a,1,3,2,2))].">
      <j1 rule="para" parents="833 7835"/>
    </justification>
  </clause>

  <clause id="8990">
    <literal><![CDATA[
      L(x,y,a(z * (u * u),w,v5)) = L(x,y,(v5 * w) \ (z \ (v5 * (w * z))))
    ]]></literal>
    <justification jstring="[hyper(63,a,4032,a(flip),b,8989,a),flip(a)].">
      <j1 rule="hyper" parents="63 4032 8989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8992">
    <literal><![CDATA[
      L(x,y,a(z * (u * u),w,v5)) = L(x,y,a(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,7833,a(flip),b,8990,a),flip(a)].">
      <j1 rule="hyper" parents="316 7833 8990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8993">
    <literal><![CDATA[
      L(x,y,a((z * z) * u,w,v5)) = L(x,y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(2771(a,1),8992(a,1,3))].">
      <j1 rule="para" parents="2771 8992"/>
    </justification>
  </clause>

  <clause id="8994">
    <literal><![CDATA[
      L(x,y,a(z \ L(z,u,w),v5,v6)) = L(x,y,a(z * L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(5137(a,1),8993(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5137 8993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8995">
    <literal><![CDATA[
      (x / (L(y,x,y) * x)) * L(L(y,x,y) * x,z,u) = ((y \ x) / x) \ L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,8248,a(flip),b,8170,a),flip(a)].">
      <j1 rule="hyper" parents="316 8248 8170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8996">
    <literal><![CDATA[
      (K(x,y) * (z * u)) / (z * (T(K(x,y),z) * u)) = a(z,K((z \ (x \ z)) \ 1,y),u)
    ]]></literal>
    <justification jstring="[para(3625(a,1),8353(a,1,2,2,1))].">
      <j1 rule="para" parents="3625 8353"/>
    </justification>
  </clause>

  <clause id="8997">
    <literal><![CDATA[
      K(x,y) * ((z * u) / (z * (T(K(x,y),z) * u))) = a(z,K((z \ (x \ z)) \ 1,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,660,a(flip),b,8996,a)].">
      <j1 rule="hyper" parents="63 660 8996"/>
    </justification>
  </clause>

  <clause id="8998">
    <literal><![CDATA[
      K(x,y) * ((z * u) / (z * (T(K(x,y),z) * u))) = a(z,T(K(x,y),z),u)
    ]]></literal>
    <justification jstring="[para(3625(a,1),8997(a,2,2))].">
      <j1 rule="para" parents="3625 8997"/>
    </justification>
  </clause>

  <clause id="8999">
    <literal><![CDATA[
      K(x,y) * ((z * u) / (z * (T(K(x,y),z) * u))) = a(z,K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,3465,a(flip),b,8998,a),flip(a)].">
      <j1 rule="hyper" parents="316 3465 8998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9000">
    <literal><![CDATA[
      L(x,L(L(y,z,u),w,v5),y) = L(x,y,L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,4372,a(flip),b,8354,a)].">
      <j1 rule="hyper" parents="63 4372 8354"/>
    </justification>
  </clause>

  <clause id="9001">
    <literal><![CDATA[
      (x * L(L(x,y,z),u,w)) * L(v5,x,L(L(x,y,z),u,w)) = x * (L(L(x,y,z),u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(139,a,9000,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="139 9000 18"/>
    </justification>
  </clause>

  <clause id="9003">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (a(x,y,z) * u) = ((x \ R(x,y,z)) \ u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(3424(a,2),8355(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3424 8355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9004">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) * a(x,y,z) = (x \ R(x,y,z)) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(327,a,9003,a),flip(a)].">
      <j1 rule="hyper" parents="327 9003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9005">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ a(x,y,z) = (R(x,y,z) \ x) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7653,a(flip),b,9004,a),flip(a)].">
      <j1 rule="hyper" parents="63 7653 9004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9006">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ a(x,y,z) = a(x,y,z) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,2290,a,b,9005,a),flip(a)].">
      <j1 rule="hyper" parents="316 2290 9005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9007">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ a(x,y,z) = a(x,a(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,8760,a(flip),b,9006,a),flip(a)].">
      <j1 rule="hyper" parents="316 8760 9006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9012">
    <literal><![CDATA[
      a(x,L(y,z,u),a(y,w,v5)) = a(x,a(y,w,v5),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2544,a(flip),b,8652,a)].">
      <j1 rule="hyper" parents="63 2544 8652"/>
    </justification>
  </clause>

  <clause id="9013">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,y,y)) = a(x,a(y,y,w),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7280,a,b,9012,a)].">
      <j1 rule="hyper" parents="63 7280 9012"/>
    </justification>
  </clause>

  <clause id="9015">
    <literal><![CDATA[
      x \ (a(y,z,z) * (x * L(z,z,y))) = a(x,a(z,z,y),L(z,z,y)) * z
    ]]></literal>
    <justification jstring="[para(9013(a,1),8765(a,2,1))].">
      <j1 rule="para" parents="9013 8765"/>
    </justification>
  </clause>

  <clause id="9016">
    <literal><![CDATA[
      a(x,y,z * (R(u,w,v5) * L(v6,R(u,w,v5),L(u,w,v5)))) = a(x,y,T(v6 / R(u,w,v5),u) * z)
    ]]></literal>
    <justification jstring="[para(4628(a,1),8688(a,1,3,2,2))].">
      <j1 rule="para" parents="4628 8688"/>
    </justification>
  </clause>

  <clause id="9017">
    <literal><![CDATA[
      a(x,y,(z \ u) * (w * (a(w,v5,z \ u) \ v5))) = a(x,y,w * (v5 * L(z * u,z,z)))
    ]]></literal>
    <justification jstring="[para(8605(a,1),8694(a,1,3,2,2,1))].">
      <j1 rule="para" parents="8605 8694"/>
    </justification>
  </clause>

  <clause id="9018">
    <literal><![CDATA[
      a(x,y,L(z \ u,w,v5) * (v5 * w)) = a(x,y,v5 * (w * L(z * u,z,z)))
    ]]></literal>
    <justification jstring="[para(8534(a,1),9017(a,1,3))].">
      <j1 rule="para" parents="8534 9017"/>
    </justification>
  </clause>

  <clause id="9019">
    <literal><![CDATA[
      a(x,y,z * (u * L(w * v5,w,w))) = a(x,y,z * (u * (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5472,a(flip),b,9018,a),flip(a)].">
      <j1 rule="hyper" parents="63 5472 9018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9020">
    <literal><![CDATA[
      a(x,y,(z \ u) * (w * (a(w,v5,z \ u) \ v5))) = a(x,y,w * (v5 * L(u * z,z,z)))
    ]]></literal>
    <justification jstring="[para(8606(a,1),8695(a,1,3,2,2,1))].">
      <j1 rule="para" parents="8606 8695"/>
    </justification>
  </clause>

  <clause id="9021">
    <literal><![CDATA[
      a(x,y,L(z \ u,w,v5) * (v5 * w)) = a(x,y,v5 * (w * L(u * z,z,z)))
    ]]></literal>
    <justification jstring="[para(8534(a,1),9020(a,1,3))].">
      <j1 rule="para" parents="8534 9020"/>
    </justification>
  </clause>

  <clause id="9022">
    <literal><![CDATA[
      a(x,y,z * (u * L(w * v5,v5,v5))) = a(x,y,z * (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5472,a(flip),b,9021,a),flip(a)].">
      <j1 rule="hyper" parents="63 5472 9021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9023">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w * v5) \ u,z,v5 * w)) = a(x,y,L(u,v5 * ((v6 * v6) \ w),z))
    ]]></literal>
    <justification jstring="[para(5835(a,1),8748(a,1,3,1,1))].">
      <j1 rule="para" parents="5835 8748"/>
    </justification>
  </clause>

  <clause id="9024">
    <literal><![CDATA[
      a(x,y,L(z,u * ((w * w) \ v5),v6)) = a(x,y,L(z,v5 * u,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,8747,a(flip),b,9023,a),flip(a)].">
      <j1 rule="hyper" parents="63 8747 9023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9026">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * T(u,L(x,y,z) \ x) = x * (u * R(L(x,y,z) \ x,x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5524,a(flip),b,8943,a)].">
      <j1 rule="hyper" parents="63 5524 8943"/>
    </justification>
  </clause>

  <clause id="9027">
    <literal><![CDATA[
      x * (y * R(L(x,z,u) \ x,x,y)) = (x * (L(x,z,u) \ x)) * y
    ]]></literal>
    <justification jstring="[para(6477(a,1),9026(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6477 9026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9031">
    <literal><![CDATA[
      L(K(a(x,y,y),L(y,y,x)) * z,L(y,y,x),a(x,y,y)) = ((z / y) * L(y,y,x)) * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(4382(a,1),8986(a,2,1))].">
      <j1 rule="para" parents="4382 8986"/>
    </justification>
  </clause>

  <clause id="9032">
    <literal><![CDATA[
      a(x,y,L(L(z,z,L(u,u,z)),w,v5)) = a(x,y,L(((u \ 1) \ z) \ L(u,u,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,7750,a,b,8988,a)].">
      <j1 rule="hyper" parents="63 7750 8988"/>
    </justification>
  </clause>

  <clause id="9033">
    <literal><![CDATA[
      a(x,y,L(((z \ 1) \ u) \ L(z,z,u),w,v5)) = a(x,y,L(L(u,u,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,8703,a(flip),b,9032,a),flip(a)].">
      <j1 rule="hyper" parents="63 8703 9032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9035">
    <literal><![CDATA[
      L(K(a(x,y,y),L(y,y,x)) * z,L(y,y,x),a(x,y,y)) = a(x,y,y) * ((z / y) * L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,2290,a,b,9031,a),flip(a)].">
      <j1 rule="hyper" parents="316 2290 9031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9036">
    <literal><![CDATA[
      a(x,y,y) * ((z / y) * L(y,y,x)) = L(z,L(y,y,x),a(x,y,y))
    ]]></literal>
    <justification jstring="[para(2312(a,1),9035(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2312 9035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9038">
    <literal><![CDATA[
      T(K(x,L(T(y,y \ z),y \ z,u)),u * z) = T(K(x,(u * (y \ z)) \ (u * z)),u * (y \ z))
    ]]></literal>
    <justification jstring="[para(336(a,1),3909(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="336 3909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9039">
    <literal><![CDATA[
      T(K(x,(y * (z \ u)) \ (y * u)),y * (z \ u)) = T(K(x,L(T(z,u),z \ u,y)),y * u)
    ]]></literal>
    <justification jstring="[para(1958(a,1),9038(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1958 9038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9041">
    <literal><![CDATA[
      K(x,T((y * (z \ u)) \ (y * u),y * (z \ u))) = T(K(x,L(T(z,u),z \ u,y)),y * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3865,a,b,9039,a)].">
      <j1 rule="hyper" parents="63 3865 9039"/>
    </justification>
  </clause>

  <clause id="9043">
    <literal><![CDATA[
      T(K(x,L(T(y,z),y \ z,u)),u * z) = K(x,(u * z) / (u * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,4146,a(flip),b,9041,a),flip(a)].">
      <j1 rule="hyper" parents="63 4146 9041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9044">
    <literal><![CDATA[
      T(K(x,L(T(y,z),y \ z,u)),u * z) = K(x,u / ((u * (y \ z)) / z))
    ]]></literal>
    <justification jstring="[hyper(316,a,1943,a(flip),b,9043,a),flip(a)].">
      <j1 rule="hyper" parents="316 1943 9043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9045">
    <literal><![CDATA[
      T(L(K(x,T(y,z)),u,w),v5 * z) = K(x,v5 / ((v5 * (y \ z)) / z))
    ]]></literal>
    <justification jstring="[para(4292(a,2),9044(a,1,1))].">
      <j1 rule="para" parents="4292 9044"/>
    </justification>
  </clause>

  <clause id="9046">
    <literal><![CDATA[
      L(T(K(x,T(y,z)),u * z),w,v5) = K(x,u / ((u * (y \ z)) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a,b,9045,a)].">
      <j1 rule="hyper" parents="63 25 9045"/>
    </justification>
  </clause>

  <clause id="9048">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),w,v5) = K(x,u / ((u * (y \ z)) / z))
    ]]></literal>
    <justification jstring="[para(3865(a,2),9046(a,1,1))].">
      <j1 rule="para" parents="3865 9046"/>
    </justification>
  </clause>

  <clause id="9049">
    <literal><![CDATA[
      (K(x,y) * (z \ 1)) \ R(K(x,y) * (z \ 1),u,w) = (z \ K(x,y)) \ R(z \ K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(4158(a,1),4189(a,1,2,1))].">
      <j1 rule="para" parents="4158 4189"/>
    </justification>
  </clause>

  <clause id="9050">
    <literal><![CDATA[
      (x \ 1) \ (K(y,z) * R(K(z,y) * (x \ 1),u,w)) = (x \ K(z,y)) \ R(x \ K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3009,a(flip),b,9049,a)].">
      <j1 rule="hyper" parents="63 3009 9049"/>
    </justification>
  </clause>

  <clause id="9051">
    <literal><![CDATA[
      (x \ K(y,z)) \ R(x \ K(y,z),u,w) = (x \ 1) \ R(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(3000(a,1),9050(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3000 9050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9052">
    <literal><![CDATA[
      (x \ K(y,z)) \ R(x \ K(y,z),u,w) = x * R(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,1511,a(flip),b,9051,a),flip(a)].">
      <j1 rule="hyper" parents="316 1511 9051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9054">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) / ((x \ L(x,y,z)) * x) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,1279,a(flip),b,4358,a),flip(a)].">
      <j1 rule="hyper" parents="316 1279 4358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9055">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) / L(x,y,z) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1273(a,1),9054(a,1,2))].">
      <j1 rule="para" parents="1273 9054"/>
    </justification>
  </clause>

  <clause id="9056">
    <literal><![CDATA[
      (((x * a(y,x,x)) \ x) * (z * (x * a(y,x,x)))) / L(x * a(y,x,x),x,y) = L(z,x * a(y,x,x),(x * a(y,x,x)) \ L(x * a(y,x,x),x,y))
    ]]></literal>
    <justification jstring="[para(8470(a,1),9055(a,1,1,1,2))].">
      <j1 rule="para" parents="8470 9055"/>
    </justification>
  </clause>

  <clause id="9057">
    <literal><![CDATA[
      (x * (L(R(x,y,z),u,w) * (R(T(x,v5),y,z) \ v5))) / x = (v5 * L(R(x,y,z),u,w)) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(27(a,2),4467(a,1,1,2,2,1))].">
      <j1 rule="para" parents="27 4467"/>
    </justification>
  </clause>

  <clause id="9058">
    <literal><![CDATA[
      L(R(x,y,L(L(x,z,u) \ x,L(x,z,u),y)),z,u) \ (x * y) = y * ((L(x,z,u) * y) \ (x * y))
    ]]></literal>
    <justification jstring="[para(29(a,1),4929(a,1,1))].">
      <j1 rule="para" parents="29 4929"/>
    </justification>
  </clause>

  <clause id="9059">
    <literal><![CDATA[
      L(x \ ((a(y,z,u) \ 1) \ w),x,a(y,z,u)) = ((a(y,z,u) * x) \ w) * (a(y,z,u) * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,388,a(flip),b,5052,a),flip(a)].">
      <j1 rule="hyper" parents="316 388 5052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9060">
    <literal><![CDATA[
      (x \ (L(y,z,u) \ y)) / ((y \ L(y,z,u)) \ 1) = (y \ L(y,z,u)) \ (x \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(1894(a,1),5071(a,1,1,2))].">
      <j1 rule="para" parents="1894 5071"/>
    </justification>
  </clause>

  <clause id="9061">
    <literal><![CDATA[
      (x \ (L(y,z,u) \ y)) / (L(y,z,u) \ y) = (y \ L(y,z,u)) \ (x \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(1894(a,1),9060(a,1,2))].">
      <j1 rule="para" parents="1894 9060"/>
    </justification>
  </clause>

  <clause id="9062">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (u \ (L(x,y,z) \ x)) = (x \ L(x,y,z)) \ (u \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6483,a(flip),b,9061,a)].">
      <j1 rule="hyper" parents="63 6483 9061"/>
    </justification>
  </clause>

  <clause id="9063">
    <literal><![CDATA[
      x * ((y \ L(y,z,u)) \ (x \ (y \ L(y,z,u)))) = a(x,x \ 1,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(9061(a,1),8492(a,1,2))].">
      <j1 rule="para" parents="9061 8492"/>
    </justification>
  </clause>

  <clause id="9064">
    <literal><![CDATA[
      K(x,y / a(z,u,w)) * (((y * (a(z,u,w) \ 1)) * x) / (x * y)) = L(a(z,u,w) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1941(a,1),5224(a,1,1))].">
      <j1 rule="para" parents="1941 5224"/>
    </justification>
  </clause>

  <clause id="9065">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) * (((w * (a(y,z,u) \ 1)) * x) / (x * w)) = L(a(y,z,u) \ 1,w,x)
    ]]></literal>
    <justification jstring="[para(2276(a,1),9064(a,1,1,2))].">
      <j1 rule="para" parents="2276 9064"/>
    </justification>
  </clause>

  <clause id="9066">
    <literal><![CDATA[
      a(x,y,L((L(z,u,w) * (z \ v5)) * z,v6,v7)) = a(x,y,L(v5 * L(z \ 1,u,w),v6,v7))
    ]]></literal>
    <justification jstring="[para(7075(a,1),6001(a,1,3,1,1))].">
      <j1 rule="para" parents="7075 6001"/>
    </justification>
  </clause>

  <clause id="9067">
    <literal><![CDATA[
      a(x,y,L(z * L(u \ 1,w,v5),v6,v7)) = a(x,y,L(z * L(u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(4380(a,1),9066(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4380 9066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9068">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 * (v6 * (v7 \ 1)))))) = a(x,y,z \ (u * (w * (v5 * (v6 * v7)))))
    ]]></literal>
    <justification jstring="[hyper(63,a,7522,a(flip),b,6048,a),flip(a)].">
      <j1 rule="hyper" parents="63 7522 6048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9070">
    <literal><![CDATA[
      (((x * x) \ x) \ y) \ L(((x * x) \ x) \ z,u,w) = ((x \ 1) \ y) \ L((x \ 1) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(283(a,1),6229(a,1,2,1,1))].">
      <j1 rule="para" parents="283 6229"/>
    </justification>
  </clause>

  <clause id="9073">
    <literal><![CDATA[
      a(x,y,z \ (((L(u,w,v5) \ 1) * u) * v6)) = a(x,y,z \ (v6 * (u \ L(u \ 1,w,v5))))
    ]]></literal>
    <justification jstring="[para(6614(a,1),6357(a,1,3,2,1))].">
      <j1 rule="para" parents="6614 6357"/>
    </justification>
  </clause>

  <clause id="9074">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ L(w \ 1,v5,v6)))) = a(x,y,z \ (u * (w * L(w,v5,v6))))
    ]]></literal>
    <justification jstring="[hyper(63,a,6352,a(flip),b,9073,a),flip(a)].">
      <j1 rule="hyper" parents="63 6352 9073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9077">
    <literal><![CDATA[
      T(R(x * K(y,x),y,z * L(z,u,w)),y) = (y * (z \ L(z,u,w))) \ ((y * x) * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(1718(a,1),6644(a,1,1))].">
      <j1 rule="para" parents="1718 6644"/>
    </justification>
  </clause>

  <clause id="9078">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ (((L(x,y,z) \ x) * u) * w) = w * (u * K(x * (L(x,y,z) \ u),w))
    ]]></literal>
    <justification jstring="[para(3567(a,1),6663(a,2,2,2))].">
      <j1 rule="para" parents="3567 6663"/>
    </justification>
  </clause>

  <clause id="9079">
    <literal><![CDATA[
      a(x,y,L(L(z * K(u,w),v5,v6),v7,v8 \ v9)) = a(x,y,L(L(z,v7,(v8 \ K(v10,v11)) \ v9),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5767,a(flip),b,6704,a)].">
      <j1 rule="hyper" parents="63 5767 6704"/>
    </justification>
  </clause>

  <clause id="9080">
    <literal><![CDATA[
      a(x,y,L(L(z,u,(w \ K(v5,v6)) \ v7),v8,v9)) = a(x,y,L(L(z,u,w \ v7),v8,v9))
    ]]></literal>
    <justification jstring="[hyper(63,a,6367,a(flip),b,9079,a),flip(a)].">
      <j1 rule="hyper" parents="63 6367 9079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9081">
    <literal><![CDATA[
      a(x,y,L(L(z,u,(w \ 1) \ v5),v6,v7)) = a(x,y,L(L(z,u,w \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(180(a,1),9080(a,1,3,1,3,1,2))].">
      <j1 rule="para" parents="180 9080"/>
    </justification>
  </clause>

  <clause id="9082">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ (L(x,y,z) \ x) = L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,6613,a,b,6728,a),flip(a)].">
      <j1 rule="hyper" parents="35 6613 6728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9084">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z)) = L(x * L(x,y,z),u,w) \ (x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2017,a(flip),b,9082,a),flip(a)].">
      <j1 rule="hyper" parents="63 2017 9082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9085">
    <literal><![CDATA[
      (((x * (y * L(y,z,u))) / y) \ (x * L(y,z,u))) \ (x * L(y,z,u)) = (x * (y * L(y,z,u))) / y
    ]]></literal>
    <justification jstring="[para(257(a,1),6797(a,2,1,2))].">
      <j1 rule="para" parents="257 6797"/>
    </justification>
  </clause>

  <clause id="9087">
    <literal><![CDATA[
      (L(x \ 1,y,z) * u) * a(w,v5,L(x,y,z)) = L(x \ 1,y,z) * (u * a(w,v5,L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(2655(a,1),6908(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2655 6908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9089">
    <literal><![CDATA[
      ((a(x,y,z) \ (a(x,y,z) \ 1)) * (u * w)) / w = (w * ((a(x,y,z) * a(x,y,z)) \ u)) / T(w,u)
    ]]></literal>
    <justification jstring="[para(7034(a,1),7028(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7034 7028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9090">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (L(x \ 1,u,w) * v5) = x * (L(x,y,z) \ (L(x,u,w) * (x \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7154,a(flip),b,7081,a),flip(a)].">
      <j1 rule="hyper" parents="63 7154 7081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9091">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (L(x \ 1,u,w) * v5) = L(x,y,z) \ (L(x,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,1139,a(flip),b,9090,a),flip(a)].">
      <j1 rule="hyper" parents="316 1139 9090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9092">
    <literal><![CDATA[
      T(L(x \ L(x,y,z),x,L(x,y,z) * u),w) = L(T(u \ ((u / x) * L(x,y,z)),w),u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(4382(a,1),7103(a,2,1,1,2))].">
      <j1 rule="para" parents="4382 7103"/>
    </justification>
  </clause>

  <clause id="9093">
    <literal><![CDATA[
      L(x / L(x,y,z),x,x \ u) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1283,a(flip),b,7113,a),flip(a)].">
      <j1 rule="hyper" parents="63 1283 7113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9094">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,x \ u) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[para(1378(a,1),9093(a,1,1))].">
      <j1 rule="para" parents="1378 9093"/>
    </justification>
  </clause>

  <clause id="9095">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(u,u,x)) = L(L(x,y,z) \ x,x,(u \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3254,a,b,9094,a)].">
      <j1 rule="hyper" parents="63 3254 9094"/>
    </justification>
  </clause>

  <clause id="9096">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u * x) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1584,a(flip),b,9094,a),flip(a)].">
      <j1 rule="hyper" parents="63 1584 9094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9097">
    <literal><![CDATA[
      (x / y) * (y * (L(y,z,u) \ y)) = x * L(L(y,z,u) \ y,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,9094,a(flip),b,1598,a),flip(a)].">
      <j1 rule="hyper" parents="139 9094 1598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9098">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,x * u) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),9094(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 9094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9099">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,x,u),L(x,y,z),z * y) = L((z * (y * x)) \ ((z * y) * x),x,x \ u)
    ]]></literal>
    <justification jstring="[para(9094(a,1),897(a,1,1))].">
      <j1 rule="para" parents="9094 897"/>
    </justification>
  </clause>

  <clause id="9100">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,(u / x) * L(x,w,v5)) = L(L(x,y,z) \ x,x,L(x,w,v5) * u)
    ]]></literal>
    <justification jstring="[para(4382(a,1),9094(a,1,3))].">
      <j1 rule="para" parents="4382 9094"/>
    </justification>
  </clause>

  <clause id="9101">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) * u = (u / x) * (x * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(9094(a,1),6642(a,1,1))].">
      <j1 rule="para" parents="9094 6642"/>
    </justification>
  </clause>

  <clause id="9103">
    <literal><![CDATA[
      (x / y) * (L(1 / y,z,u) \ 1) = x * L(L(y,z,u) \ y,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6595,a,b,9097,a)].">
      <j1 rule="hyper" parents="63 6595 9097"/>
    </justification>
  </clause>

  <clause id="9107">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) * u = (u / x) * (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,6595,a,b,9101,a),flip(a)].">
      <j1 rule="hyper" parents="316 6595 9101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9108">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) \ ((x / y) * (L(1 / y,z,u) \ 1)) = x \ ((x / (L(y,z,u) \ y)) * L(L(y,z,u) \ y,y,x))
    ]]></literal>
    <justification jstring="[para(9103(a,2),7109(a,1,2))].">
      <j1 rule="para" parents="9103 7109"/>
    </justification>
  </clause>

  <clause id="9109">
    <literal><![CDATA[
      a(x \ (L(L(y,z,u) \ y,y,w) * w),v5,v6) = a(x \ ((y \ w) * (L(1 / y,z,u) \ 1)),v5,v6)
    ]]></literal>
    <justification jstring="[para(9107(a,2),4177(a,1,1,2))].">
      <j1 rule="para" parents="9107 4177"/>
    </justification>
  </clause>

  <clause id="9110">
    <literal><![CDATA[
      a(x,y,z * (L(L(u,w,v5) \ u,u,v6) * v6)) = a(x,y,z * ((v6 / u) * L(1 / u,w,v5)))
    ]]></literal>
    <justification jstring="[para(9107(a,2),5895(a,1,3,2))].">
      <j1 rule="para" parents="9107 5895"/>
    </justification>
  </clause>

  <clause id="9111">
    <literal><![CDATA[
      a(x,y,L(L(L(z,u,w) \ z,z,v5) * v5,v6,v7)) = a(x,y,L((z \ v5) * (L(1 / z,u,w) \ 1),v6,v7))
    ]]></literal>
    <justification jstring="[para(9107(a,2),5717(a,1,3,1))].">
      <j1 rule="para" parents="9107 5717"/>
    </justification>
  </clause>

  <clause id="9112">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,(x \ u) * L(x,w,v5)) = L(L(x,y,z) \ x,x,L(x,w,v5) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1664,a(flip),b,9100,a)].">
      <j1 rule="hyper" parents="63 1664 9100"/>
    </justification>
  </clause>

  <clause id="9113">
    <literal><![CDATA[
      a(x,y,z * (L(L(u,w,v5) \ u,u,v6) * v6)) = a(x,y,z * ((v6 / u) * L(u \ 1,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5705,a(flip),b,9110,a),flip(a)].">
      <j1 rule="hyper" parents="316 5705 9110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9114">
    <literal><![CDATA[
      a(x,y,z * (L(L(u,w,v5) \ u,u,v6) * v6)) = a(x,y,z * ((u \ v6) * L(u \ 1,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5642,a(flip),b,9113,a),flip(a)].">
      <j1 rule="hyper" parents="316 5642 9113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9115">
    <literal><![CDATA[
      a(x,y,z * (L(L(u,w,v5) \ u,u,v6) * v6)) = a(x,y,z * ((u \ v6) * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,8283,a(flip),b,9114,a),flip(a)].">
      <j1 rule="hyper" parents="316 8283 9114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9116">
    <literal><![CDATA[
      L((x * (y * z)) \ ((x * y) * z),z,z \ u) = L((x * (y * z)) \ ((x * y) * z),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,897,a(flip),b,9099,a),flip(a)].">
      <j1 rule="hyper" parents="63 897 9099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9117">
    <literal><![CDATA[
      L((x * (y * z)) \ ((x * y) * z),z,z \ u) = L(a(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[para(14(a,2),9116(a,2,1))].">
      <j1 rule="para" parents="14 9116"/>
    </justification>
  </clause>

  <clause id="9118">
    <literal><![CDATA[
      L(a(x,y,z),z,z \ u) = L(a(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[para(14(a,2),9117(a,1,1))].">
      <j1 rule="para" parents="14 9117"/>
    </justification>
  </clause>

  <clause id="9119">
    <literal><![CDATA[
      L(a(x,y,z \ u),z \ u,u \ (z \ u)) = L(a(x,y,z \ u),z \ u,z \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4815,a(flip),b,9118,a)].">
      <j1 rule="hyper" parents="63 4815 9118"/>
    </justification>
  </clause>

  <clause id="9120">
    <literal><![CDATA[
      L(a(x,y,z \ u),z \ u,u) = L(a(x,y,z \ u),z \ u,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1588,a(flip),b,9118,a),flip(a)].">
      <j1 rule="hyper" parents="63 1588 9118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9122">
    <literal><![CDATA[
      L(a(x,y,z),z,u) * u = (u / z) * (z * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(138,a,9118,a(flip),b,2437,a)].">
      <j1 rule="hyper" parents="138 9118 2437"/>
    </justification>
  </clause>

  <clause id="9123">
    <literal><![CDATA[
      L(a(x,y,z),z,L(u \ 1,u,u \ z)) = L(a(x,y,z),z,z / u)
    ]]></literal>
    <justification jstring="[para(1603(a,2),9118(a,1,3))].">
      <j1 rule="para" parents="1603 9118"/>
    </justification>
  </clause>

  <clause id="9124">
    <literal><![CDATA[
      1 / (a(x,y,z) * (L(a(x,y,z),z,u) \ a(x,y,z))) = L(1 / a(x,y,z),z,z \ u)
    ]]></literal>
    <justification jstring="[para(9118(a,1),6594(a,1,2,2,1))].">
      <j1 rule="para" parents="9118 6594"/>
    </justification>
  </clause>

  <clause id="9126">
    <literal><![CDATA[
      a(x,y,z) \ ((u / z) * (z * a(x,y,z))) = L(a(x,y,z),z,u) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,9122,a(flip),b,1127,a)].">
      <j1 rule="hyper" parents="133 9122 1127"/>
    </justification>
  </clause>

  <clause id="9127">
    <literal><![CDATA[
      L(a(x,y,z),z,L(u \ 1,u,z)) = L(a(x,y,z),z,z / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,7191,a(flip),b,9123,a)].">
      <j1 rule="hyper" parents="63 7191 9123"/>
    </justification>
  </clause>

  <clause id="9128">
    <literal><![CDATA[
      L(1 / a(x,y,z),z,z \ u) = 1 / (L(a(x,y,z) \ 1,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(5185(a,1),9124(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5185 9124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9130">
    <literal><![CDATA[
      L(1 / a(x,y,z),z,z \ u) = L(a(x,y,z) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,80,a(flip),b,9128,a),flip(a)].">
      <j1 rule="hyper" parents="316 80 9128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9131">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,z,z \ u) = L(a(x,y,z) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(2276(a,1),9130(a,1,1))].">
      <j1 rule="para" parents="2276 9130"/>
    </justification>
  </clause>

  <clause id="9132">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,z,u * z) = L(a(x,y,z) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1584,a(flip),b,9131,a),flip(a)].">
      <j1 rule="hyper" parents="63 1584 9131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9133">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,z,z * u) = L(a(x,y,z) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),9131(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 9131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9134">
    <literal><![CDATA[
      x \ (L(a(y,z,x \ u) \ 1,x \ u,x * (x \ u)) * u) = (x \ u) * T(a(y,z,x \ u) \ 1,u)
    ]]></literal>
    <justification jstring="[para(9132(a,2),714(a,1,2,1))].">
      <j1 rule="para" parents="9132 714"/>
    </justification>
  </clause>

  <clause id="9138">
    <literal><![CDATA[
      (x \ (x \ 1)) * (L(x \ 1,y,z) \ (1 / L(x \ 1,y,z))) = L(x,y,z) \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(6568(a,1),7188(a,2,2))].">
      <j1 rule="para" parents="6568 7188"/>
    </justification>
  </clause>

  <clause id="9139">
    <literal><![CDATA[
      ((1 / x) * (x * ((y * x) \ y))) \ ((y * x) \ y) = a((y * x) \ y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1759(a,1),7245(a,1,1,1))].">
      <j1 rule="para" parents="1759 7245"/>
    </justification>
  </clause>

  <clause id="9140">
    <literal><![CDATA[
      L((x * y) \ x,y,y \ 1) \ ((x * y) \ x) = a((x * y) \ x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(890(a,1),9139(a,1,1))].">
      <j1 rule="para" parents="890 9139"/>
    </justification>
  </clause>

  <clause id="9142">
    <literal><![CDATA[
      L(x,y,L(z \ u,z,u \ R(w,v5,v6)) \ L(w,v5,v6)) = L(x,y,(u \ R(w,v5,v6)) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1666,a(flip),b,7485,a),flip(a)].">
      <j1 rule="hyper" parents="316 1666 7485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9144">
    <literal><![CDATA[
      L(x,y,L(z \ u,z,u \ L(w,v5,v6)) \ L(w,v5,v6)) = L(x,y,(u \ R(w,v5,v6)) * z)
    ]]></literal>
    <justification jstring="[para(7482(a,1),9142(a,1,3,1))].">
      <j1 rule="para" parents="7482 9142"/>
    </justification>
  </clause>

  <clause id="9145">
    <literal><![CDATA[
      L(x,y,T((L(z,u,w) / v5) * v6,v6 \ v5)) = L(x,y,(v5 \ R(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[para(3740(a,1),9144(a,1,3))].">
      <j1 rule="para" parents="3740 9144"/>
    </justification>
  </clause>

  <clause id="9146">
    <literal><![CDATA[
      L(x,y,(z \ R(u,w,v5)) * v6) = L(x,y,(z \ L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,1666,a(flip),b,9145,a),flip(a)].">
      <j1 rule="hyper" parents="63 1666 9145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9148">
    <literal><![CDATA[
      x * ((x * L(T(y,x),z,u)) \ L(T(y,x),z,u)) = R(L(y,z,u),x,x) \ L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(565(a,1),7686(a,1,1)),flip(a)].">
      <j1 rule="para" parents="565 7686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9149">
    <literal><![CDATA[
      x * ((x * L(T(y,x),z,u)) \ L(T(y,x),z,u)) = L(R(y,x,x),z,u) \ L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(29(a,1),9148(a,2,1))].">
      <j1 rule="para" parents="29 9148"/>
    </justification>
  </clause>

  <clause id="9150">
    <literal><![CDATA[
      x * ((L(y,z,u) * x) \ L(T(y,x),z,u)) = L(R(y,x,x),z,u) \ L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(251(a,1),9149(a,1,2,1))].">
      <j1 rule="para" parents="251 9149"/>
    </justification>
  </clause>

  <clause id="9151">
    <literal><![CDATA[
      L(R(x,y,y),z,u) \ L(T(x,y),z,u) = y * ((y * L(x,z,u)) \ L(x,z,u))
    ]]></literal>
    <justification jstring="[para(2920(a,1),9150(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2920 9150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9152">
    <literal><![CDATA[
      x * ((x * R(T(y,x),z,u)) \ R(T(y,x),z,u)) = R(R(y,z,u),x,x) \ R(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(565(a,1),7687(a,1,1)),flip(a)].">
      <j1 rule="para" parents="565 7687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9153">
    <literal><![CDATA[
      x * L((a(y,z,z) \ (x \ 1)) * a(y,z,z),z,y) = (x * a(y,z,z)) \ (L(x,z,y) * a(y,z,z))
    ]]></literal>
    <justification jstring="[para(8708(a,2),8709(a,1,2))].">
      <j1 rule="para" parents="8708 8709"/>
    </justification>
  </clause>

  <clause id="9154">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w * L(v5,v6,v7)) \ u,z,w * L(v5,v6,v7))) = a(x,y,L(u,w * R(v5,v6,v7),z))
    ]]></literal>
    <justification jstring="[para(7272(a,1),8751(a,1,3,1,1))].">
      <j1 rule="para" parents="7272 8751"/>
    </justification>
  </clause>

  <clause id="9155">
    <literal><![CDATA[
      x * ((R(x,y,z) \ a(x,y,z)) * (x \ L(x,u,w))) = L(x,u,w) * (x \ a(x,a(x,y,z),y * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,8516,a(flip),b,8763,a),flip(a)].">
      <j1 rule="hyper" parents="316 8516 8763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9156">
    <literal><![CDATA[
      (a(x,x,y) \ ((a(x,x,y) * x) * z)) \ (x * z) = (a(x,x,y) \ (z * R(x,x,y))) \ (z * x)
    ]]></literal>
    <justification jstring="[para(2842(a,1),8849(a,2,1,2))].">
      <j1 rule="para" parents="2842 8849"/>
    </justification>
  </clause>

  <clause id="9157">
    <literal><![CDATA[
      (a(x,x,y) \ ((a(x,x,y) * x) * z)) \ (x * z) = a(z,x,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,7338,a(flip),b,9156,a),flip(a)].">
      <j1 rule="hyper" parents="316 7338 9156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9158">
    <literal><![CDATA[
      (a(x,x,y) \ (R(x,x,y) * z)) \ (x * z) = a(z,x,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(7333(a,1),9157(a,1,1,2,1))].">
      <j1 rule="para" parents="7333 9157"/>
    </justification>
  </clause>

  <clause id="9159">
    <literal><![CDATA[
      x * ((L(y,z,u) * x) \ (y * x)) = L(y,z,u) \ (y * x)
    ]]></literal>
    <justification jstring="[para(6850(a,1),9058(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6850 9058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9160">
    <literal><![CDATA[
      x * ((L(y,z,u) * x) \ (y * x)) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,1129,a(flip),b,9159,a),flip(a)].">
      <j1 rule="hyper" parents="316 1129 9159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9161">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (x * u) = u \ (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(133,a,1129,a(flip),b,9159,a),flip(a)].">
      <j1 rule="hyper" parents="133 1129 9159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9165">
    <literal><![CDATA[
      x * (L(x,y,y \ z) \ z) = z * a(y \ z,y,x)
    ]]></literal>
    <justification jstring="[para(6639(a,1),9160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6639 9160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9166">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z),z,u) \ u) = u * a(z \ u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(9118(a,1),9165(a,1,2,1))].">
      <j1 rule="para" parents="9118 9165"/>
    </justification>
  </clause>

  <clause id="9167">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) = y \ (z * (L(z,y,x) \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8562,a,b,9161,a)].">
      <j1 rule="hyper" parents="63 8562 9161"/>
    </justification>
  </clause>

  <clause id="9168">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,y,z),u) = u \ (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4586,a,b,9161,a)].">
      <j1 rule="hyper" parents="63 4586 9161"/>
    </justification>
  </clause>

  <clause id="9169">
    <literal><![CDATA[
      x \ ((x \ y) * (L(x \ y,z,u) \ x)) = (x * L(x \ y,z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,4376,a(flip),b,9161,a),flip(a)].">
      <j1 rule="hyper" parents="63 4376 9161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9170">
    <literal><![CDATA[
      (x * L(y,z,u)) \ (x * y) = x \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,4336,a(flip),b,9161,a)].">
      <j1 rule="hyper" parents="63 4336 9161"/>
    </justification>
  </clause>

  <clause id="9171">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) * y = z * (L(z,y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,9167,a(flip))].">
      <j1 rule="hyper" parents="38 2295 9167"/>
    </justification>
  </clause>

  <clause id="9172">
    <literal><![CDATA[
      a(x,y,L(y \ z,y,x)) = y \ (L(z / y,y,x) \ z)
    ]]></literal>
    <justification jstring="[para(6574(a,1),9167(a,2,2))].">
      <j1 rule="para" parents="6574 9167"/>
    </justification>
  </clause>

  <clause id="9173">
    <literal><![CDATA[
      a(x,y,a(z,u,L(u \ w,u,z))) = a(x,y,u \ (L(u \ w,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(9167(a,2),5641(a,1,3))].">
      <j1 rule="para" parents="9167 5641"/>
    </justification>
  </clause>

  <clause id="9175">
    <literal><![CDATA[
      T(a(x,y,L(z,y,x)) * y,z) = L(z,y,x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(9171(a,2),4434(a,1,1))].">
      <j1 rule="para" parents="9171 4434"/>
    </justification>
  </clause>

  <clause id="9177">
    <literal><![CDATA[
      T(a(x,L(y,z,z),L(a(z,z,y),L(y,z,z),x)) * L(y,z,z),a(z,z,y)) = L(a(z,z,y),L(y,z,z),x) \ y
    ]]></literal>
    <justification jstring="[para(4953(a,1),9175(a,2,2))].">
      <j1 rule="para" parents="4953 9175"/>
    </justification>
  </clause>

  <clause id="9178">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,w,v5)) = u \ (R(x,w,v5) * (L(R(x,w,v5),u,x) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8940,a,b,9170,a)].">
      <j1 rule="hyper" parents="63 8940 9170"/>
    </justification>
  </clause>

  <clause id="9179">
    <literal><![CDATA[
      L(x,y,z) \ (u * (L(u,x,L(x,y,z)) \ L(x,y,z))) = a(x,L(x,y,z),L(u,x,L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8915,a(flip),b,9170,a),flip(a)].">
      <j1 rule="hyper" parents="63 8915 9170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9185">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) \ y = x \ (L(y / x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(6574(a,1),9169(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6574 9169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9186">
    <literal><![CDATA[
      (x \ 1) \ (L(y / (x \ 1),x \ 1,x) \ y) = ((x \ 1) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(474(a,1),9185(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="474 9185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9187">
    <literal><![CDATA[
      x \ (L((y / x) / x,z,u) \ (y / x)) = (L(y,z,u) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(1352(a,1),9185(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1352 9185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9188">
    <literal><![CDATA[
      x \ (L((x \ y) / x,z,u) \ (x \ y)) = (x \ L(y,z,u)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(1363(a,1),9185(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1363 9185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9189">
    <literal><![CDATA[
      (x * y) \ (L((z * y) / (x * y),u,w) \ (z * y)) = ((x * L(x \ z,u,w)) * y) \ (z * y)
    ]]></literal>
    <justification jstring="[para(1528(a,1),9185(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1528 9185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9190">
    <literal><![CDATA[
      ((x / T(y,z)) * L((x / T(y,z)) \ T(z,y),u,w)) \ T(z,y) = (x / T(y,z)) \ (L(z / (x / y),u,w) \ T(z,y))
    ]]></literal>
    <justification jstring="[para(3848(a,1),9185(a,2,2,1,1))].">
      <j1 rule="para" parents="3848 9185"/>
    </justification>
  </clause>

  <clause id="9191">
    <literal><![CDATA[
      T(x,y) \ (L(T(z,u) / T(x,y),w,v5) \ T(z,u)) = T(x * L(x \ z,w,v5),u) \ T(z,u)
    ]]></literal>
    <justification jstring="[para(4887(a,1),9185(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4887 9185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9192">
    <literal><![CDATA[
      (x \ (L(y / x,z,u) \ y)) \ y = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(9185(a,1),6489(a,1,1))].">
      <j1 rule="para" parents="9185 6489"/>
    </justification>
  </clause>

  <clause id="9193">
    <literal><![CDATA[
      (x * y) \ (L((z * x) / (x * y),u,w) \ (z * x)) = ((y * L(y \ z,u,w)) * x) \ (z * x)
    ]]></literal>
    <justification jstring="[para(6300(a,1),9185(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6300 9185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9194">
    <literal><![CDATA[
      x \ (L((x \ y) / x,z,u) \ (x \ y)) = (L(y,z,u) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(7234(a,1),9187(a,1,2))].">
      <j1 rule="para" parents="7234 9187"/>
    </justification>
  </clause>

  <clause id="9195">
    <literal><![CDATA[
      (L(x,y,z) / u) \ (x / u) = (u \ L(x,y,z)) \ (u \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9188,a(flip),b,9194,a),flip(a)].">
      <j1 rule="hyper" parents="63 9188 9194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9196">
    <literal><![CDATA[
      (x \ 1) \ (y / (1 \ (x * y))) = ((x \ 1) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(6578(a,1),9186(a,1,2))].">
      <j1 rule="para" parents="6578 9186"/>
    </justification>
  </clause>

  <clause id="9197">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ y = (x \ 1) \ (y / (x * y))
    ]]></literal>
    <justification jstring="[para(66(a,1),9196(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="66 9196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9198">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ y = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(316,a,3351,a(flip),b,9197,a),flip(a)].">
      <j1 rule="hyper" parents="316 3351 9197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9199">
    <literal><![CDATA[
      (x * y) * (x * (y / (x * y))) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(9198(a,1),7821(a,1,2))].">
      <j1 rule="para" parents="9198 7821"/>
    </justification>
  </clause>

  <clause id="9200">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,w,v5)) = u \ (u * a(x,u,x))
    ]]></literal>
    <justification jstring="[para(8012(a,1),9178(a,2,2))].">
      <j1 rule="para" parents="8012 9178"/>
    </justification>
  </clause>

  <clause id="9201">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,w,v5)) = a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,9,a(flip),b,9200,a),flip(a)].">
      <j1 rule="hyper" parents="316 9 9200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9204">
    <literal><![CDATA[
      T(x * y,z) \ (L(T(u,w) / T(x * y,z),v5,v6) \ T(u,w)) = T(x * (y * L(y \ (x \ u),v5,v6)),w) \ T(u,w)
    ]]></literal>
    <justification jstring="[para(879(a,1),9191(a,2,1,1))].">
      <j1 rule="para" parents="879 9191"/>
    </justification>
  </clause>

  <clause id="9205">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) \ ((x * w) * (y \ L(y,z,u))) = R(w,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2735,a(flip),b,9077,a),flip(a)].">
      <j1 rule="hyper" parents="63 2735 9077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9207">
    <literal><![CDATA[
      R(x,y,z * L(z,u,w)) = L(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7732,a(flip),b,9205,a),flip(a)].">
      <j1 rule="hyper" parents="63 7732 9205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9210">
    <literal><![CDATA[
      R(x,y,L(z,u,w) \ z) = L(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,1721,a,b,9207,a)].">
      <j1 rule="hyper" parents="63 1721 9207"/>
    </justification>
  </clause>

  <clause id="9211">
    <literal><![CDATA[
      R(x,y,z \ L(z,u,w)) = L(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,1718,a,b,9207,a)].">
      <j1 rule="hyper" parents="63 1718 9207"/>
    </justification>
  </clause>

  <clause id="9212">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ z) = L(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8367,a(flip),b,9207,a)].">
      <j1 rule="hyper" parents="63 8367 9207"/>
    </justification>
  </clause>

  <clause id="9213">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),x \ L(x,y,z)) = x \ (u * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,4324,a(flip),b,9210,a),flip(a)].">
      <j1 rule="hyper" parents="63 4324 9210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9214">
    <literal><![CDATA[
      L(x,L(y,z,u),y \ L(y,z,u)) * y = (x * L(y,z,u)) * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(138,a,9210,a(flip),b,108,a)].">
      <j1 rule="hyper" parents="138 9210 108"/>
    </justification>
  </clause>

  <clause id="9215">
    <literal><![CDATA[
      L((x \ L(x,y,z)) / u,u,x \ L(x,y,z)) = 1 / (u * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,1898,a(flip),b,9211,a),flip(a)].">
      <j1 rule="hyper" parents="63 1898 9211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9216">
    <literal><![CDATA[
      L(x,y \ 1,y \ L(y,z,u)) = L(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8932,a(flip),b,9212,a),flip(a)].">
      <j1 rule="hyper" parents="63 8932 9212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9217">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,x,x \ L(x,y,z)) = (L(1 / x,y,z) \ 1) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,7761,a(flip),b,9212,a),flip(a)].">
      <j1 rule="hyper" parents="63 7761 9212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9218">
    <literal><![CDATA[
      L((1 / x) \ y,1 / x,x \ L(x,z,u)) = (1 / L(x,z,u)) \ ((L(x,z,u) \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7095,a(flip),b,9212,a),flip(a)].">
      <j1 rule="hyper" parents="63 7095 9212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9219">
    <literal><![CDATA[
      L(x,y,z \ L(z,u,u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(4952(a,1),9212(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4952 9212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9220">
    <literal><![CDATA[
      L(x,y,a(z,u,u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7484,a(flip),b,9219,a)].">
      <j1 rule="hyper" parents="63 7484 9219"/>
    </justification>
  </clause>

  <clause id="9221">
    <literal><![CDATA[
      R(x,y,a(z,u,u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5371,a,b,9220,a)].">
      <j1 rule="hyper" parents="63 5371 9220"/>
    </justification>
  </clause>

  <clause id="9222">
    <literal><![CDATA[
      L(x \ y,x,a(z,z,x)) = a(x,z,z) * (R(x,z,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8672,a(flip),b,9220,a),flip(a)].">
      <j1 rule="hyper" parents="63 8672 9220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9223">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),u,a(w,w,v5)) = L(x \ L(x,u,a(v5,w,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,9220,a(flip),b,2137,a)].">
      <j1 rule="hyper" parents="133 9220 2137"/>
    </justification>
  </clause>

  <clause id="9224">
    <literal><![CDATA[
      L(x,y,a(L(z,u,w),w,w)) = L(x,y,a(w,w,z))
    ]]></literal>
    <justification jstring="[para(8592(a,1),9220(a,2,3))].">
      <j1 rule="para" parents="8592 9220"/>
    </justification>
  </clause>

  <clause id="9225">
    <literal><![CDATA[
      R(x,y,z * R(z,u,u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4487,a,b,9221,a)].">
      <j1 rule="hyper" parents="63 4487 9221"/>
    </justification>
  </clause>

  <clause id="9226">
    <literal><![CDATA[
      L(x,y,a(z * u,z,u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7266,a(flip),b,9225,a)].">
      <j1 rule="hyper" parents="63 7266 9225"/>
    </justification>
  </clause>

  <clause id="9227">
    <literal><![CDATA[
      L(x,y,a(z,u,z * u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5377,a(flip),b,9225,a)].">
      <j1 rule="hyper" parents="63 5377 9225"/>
    </justification>
  </clause>

  <clause id="9228">
    <literal><![CDATA[
      L(x,y,a(z * u,u,z)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(2771(a,1),9226(a,1,3))].">
      <j1 rule="para" parents="2771 9226"/>
    </justification>
  </clause>

  <clause id="9229">
    <literal><![CDATA[
      L(x * y,z,a(y,y,x)) = x * y
    ]]></literal>
    <justification jstring="[hyper(63,a,6853,a(flip),b,9227,a),flip(a)].">
      <j1 rule="hyper" parents="63 6853 9227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9230">
    <literal><![CDATA[
      ((x * y) * (x * y)) / L(y * (x * y),x,a(y,y,x)) = a(x,y,x * y) * x
    ]]></literal>
    <justification jstring="[para(9227(a,1),2375(a,1,2))].">
      <j1 rule="para" parents="9227 2375"/>
    </justification>
  </clause>

  <clause id="9232">
    <literal><![CDATA[
      L(x * y,z,a(x,y,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(63,a,9220,a,b,9229,a)].">
      <j1 rule="hyper" parents="63 9220 9229"/>
    </justification>
  </clause>

  <clause id="9233">
    <literal><![CDATA[
      L(x * (y \ 1),z,a(x,y,y)) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,8957,a(flip),b,9232,a)].">
      <j1 rule="hyper" parents="63 8957 9232"/>
    </justification>
  </clause>

  <clause id="9234">
    <literal><![CDATA[
      (a(x,y,y) * z) * (x * y) = a(x,y,y) * (z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(139,a,9232,a(flip),b,7635,a(flip))].">
      <j1 rule="hyper" parents="139 9232 7635"/>
    </justification>
  </clause>

  <clause id="9235">
    <literal><![CDATA[
      x \ L(x,y * z,a(z,z,y)) = a(x,y * z,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(9228(a,1),8247(a,1,2))].">
      <j1 rule="para" parents="9228 8247"/>
    </justification>
  </clause>

  <clause id="9236">
    <literal><![CDATA[
      (x * (y \ (x \ y))) \ 1 = (x \ y) \ (y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(9233(a,1),8987(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9233 8987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9238">
    <literal><![CDATA[
      (a(x,y,y) * (z * (x * y))) \ (((a(x,y,y) * z) * x) * y) = a(a(x,y,y) * z,x,y)
    ]]></literal>
    <justification jstring="[para(9234(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9234 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9239">
    <literal><![CDATA[
      ((a(x,y,y) * (z * (x * y))) / y) \ ((a(x,y,y) * z) * x) = a(a(x,y,y) * z,x,y)
    ]]></literal>
    <justification jstring="[para(9234(a,1),6925(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9234 6925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9240">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),x \ L(x,y,z)) = (x \ u) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,5152,a(flip),b,9213,a),flip(a)].">
      <j1 rule="hyper" parents="316 5152 9213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9241">
    <literal><![CDATA[
      ((x * y) * (x * y)) / (y * (x * y)) = a(x,y,x * y) * x
    ]]></literal>
    <justification jstring="[para(6872(a,1),9230(a,1,2))].">
      <j1 rule="para" parents="6872 9230"/>
    </justification>
  </clause>

  <clause id="9242">
    <literal><![CDATA[
      R((x * y) / y,y,y * x) = a(x,y,x * y) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,4709,a,b,9241,a)].">
      <j1 rule="hyper" parents="63 4709 9241"/>
    </justification>
  </clause>

  <clause id="9244">
    <literal><![CDATA[
      a(x,y,x * y) * x = R(x,y,y * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),9242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 9242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9245">
    <literal><![CDATA[
      x * a(x,y,x * y) = R(x,y,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a(flip),b,9244,a)].">
      <j1 rule="hyper" parents="63 2290 9244"/>
    </justification>
  </clause>

  <clause id="9246">
    <literal><![CDATA[
      L((1 / x) \ y,x \ 1,x \ L(x,z,u)) = (1 / L(x,z,u)) \ ((L(x,z,u) \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7641,a(flip),b,9218,a)].">
      <j1 rule="hyper" parents="63 7641 9218"/>
    </justification>
  </clause>

  <clause id="9247">
    <literal><![CDATA[
      (a(x,y,y) * (z * (x * y))) \ ((a(x,y,y) * (z * x)) * y) = a(a(x,y,y) * z,x,y)
    ]]></literal>
    <justification jstring="[para(8402(a,1),9238(a,1,2,1))].">
      <j1 rule="para" parents="8402 9238"/>
    </justification>
  </clause>

  <clause id="9248">
    <literal><![CDATA[
      (((x * (y * z)) / z) * a(y,z,z)) \ ((a(y,z,z) * x) * y) = a(a(y,z,z) * x,y,z)
    ]]></literal>
    <justification jstring="[para(6942(a,1),9239(a,1,1))].">
      <j1 rule="para" parents="6942 9239"/>
    </justification>
  </clause>

  <clause id="9249">
    <literal><![CDATA[
      L((1 / x) \ y,x,x \ L(x,z,u)) = (1 / L(x,z,u)) \ ((L(x,z,u) \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9216,a(flip),b,9246,a)].">
      <j1 rule="hyper" parents="63 9216 9246"/>
    </justification>
  </clause>

  <clause id="9250">
    <literal><![CDATA[
      (a(x,y,y) * (z * (x * y))) \ (a(x,y,y) * ((z * x) * y)) = a(a(x,y,y) * z,x,y)
    ]]></literal>
    <justification jstring="[para(6865(a,1),9247(a,1,2))].">
      <j1 rule="para" parents="6865 9247"/>
    </justification>
  </clause>

  <clause id="9251">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),a(y,z,z)) = a(a(y,z,z) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,482,a(flip),b,9250,a)].">
      <j1 rule="hyper" parents="63 482 9250"/>
    </justification>
  </clause>

  <clause id="9259">
    <literal><![CDATA[
      ((a(x,y,z) \ (a(x,y,z) \ 1)) * (u * w)) / w = (a(x,y,z) * a(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(316,a,5313,a(flip),b,9089,a),flip(a)].">
      <j1 rule="hyper" parents="316 5313 9089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9261">
    <literal><![CDATA[
      ((a(x,y,z) * a(x,y,z)) \ (u * w)) / w = (a(x,y,z) * a(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(7027(a,1),9259(a,1,1))].">
      <j1 rule="para" parents="7027 9259"/>
    </justification>
  </clause>

  <clause id="9262">
    <literal><![CDATA[
      (x * ((a(y,z,u) * a(y,z,u)) \ w)) / w = (a(y,z,u) * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(7034(a,1),9261(a,1,1))].">
      <j1 rule="para" parents="7034 9261"/>
    </justification>
  </clause>

  <clause id="9263">
    <literal><![CDATA[
      ((a(x,y,z) * a(x,y,z)) \ u) * w = u * ((a(x,y,z) * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(151,a,9262,a)].">
      <j1 rule="hyper" parents="151 9262"/>
    </justification>
  </clause>

  <clause id="9264">
    <literal><![CDATA[
      (x * ((a(y,z,u) * a(y,z,u)) \ w)) * v5 = (x * w) * ((a(y,z,u) * a(y,z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(138,a,7034,a(flip),b,9262,a)].">
      <j1 rule="hyper" parents="138 7034 9262"/>
    </justification>
  </clause>

  <clause id="9265">
    <literal><![CDATA[
      R(x,a(y,z,u) * a(y,z,u),w) = (a(y,z,u) * a(y,z,u)) \ (x * (a(y,z,u) * a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,4730,a(flip),b,9262,a)].">
      <j1 rule="hyper" parents="63 4730 9262"/>
    </justification>
  </clause>

  <clause id="9266">
    <literal><![CDATA[
      (x * (y * ((a(z,u,w) * a(z,u,w)) \ v5))) \ ((x * ((a(z,u,w) * a(z,u,w)) \ y)) * v5) = a(x,(a(z,u,w) * a(z,u,w)) \ y,v5)
    ]]></literal>
    <justification jstring="[para(9263(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9263 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9267">
    <literal><![CDATA[
      (x * ((a(y,z,u) * a(y,z,u)) \ (w * v5))) \ ((((a(y,z,u) * a(y,z,u)) \ x) * w) * v5) = a((a(y,z,u) * a(y,z,u)) \ x,w,v5)
    ]]></literal>
    <justification jstring="[para(9263(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9263 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9268">
    <literal><![CDATA[
      R(x,a(y,z,u) * a(y,z,u),w) = T(x,a(y,z,u) * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,22,a,b,9265,a),flip(a)].">
      <j1 rule="hyper" parents="316 22 9265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9269">
    <literal><![CDATA[
      R(x,a(y,z,u) * a(y,z,u),w) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5243,a(flip),b,9268,a),flip(a)].">
      <j1 rule="hyper" parents="316 5243 9268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9272">
    <literal><![CDATA[
      R(x,a(y,z,u) * a(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,2273,a(flip),b,9269,a),flip(a)].">
      <j1 rule="hyper" parents="316 2273 9269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9274">
    <literal><![CDATA[
      (x * (a(y,z,u) * a(y,z,u))) * ((a(y,z,u) * a(y,z,u)) \ T(w,x)) = w * x
    ]]></literal>
    <justification jstring="[para(9272(a,1),4673(a,2,2))].">
      <j1 rule="para" parents="9272 4673"/>
    </justification>
  </clause>

  <clause id="9275">
    <literal><![CDATA[
      T(L(x \ L(x,y,z),x,L(x,y,z) * u),w) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,8140,a(flip),b,9092,a),flip(a)].">
      <j1 rule="hyper" parents="316 8140 9092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9276">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,L(x,y,z) * u) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(6499,a,9275,a)].">
      <j1 rule="hyper" parents="6499 9275"/>
    </justification>
  </clause>

  <clause id="9278">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,L(x,y,z) \ u) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),9276(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 9276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9279">
    <literal><![CDATA[
      T((x / L(y,z,u)) * y,y \ L(y,z,u)) = L(y \ L(y,z,u),y,x) \ x
    ]]></literal>
    <justification jstring="[para(9278(a,1),3740(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9278 3740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9280">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ u),x \ L(x,y,z)) = L(x \ L(x,y,z),x,u) \ u
    ]]></literal>
    <justification jstring="[para(4327(a,1),9279(a,1,1))].">
      <j1 rule="para" parents="4327 9279"/>
    </justification>
  </clause>

  <clause id="9281">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) \ u = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(5024,a,9280,a),flip(a)].">
      <j1 rule="hyper" parents="5024 9280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9283">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ a(x,y,z),x \ R(x,y,z),u) \ u = (x \ R(x,y,z)) * (L(x \ R(x,y,z),x,z * y) \ u)
    ]]></literal>
    <justification jstring="[para(3424(a,2),9281(a,1,1,1,2))].">
      <j1 rule="para" parents="3424 9281"/>
    </justification>
  </clause>

  <clause id="9284">
    <literal><![CDATA[
      L((x * y) \ L(x * y,z,u),y * x,w) \ w = (y * x) * (L(y * x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(4877(a,1),9281(a,1,1,1))].">
      <j1 rule="para" parents="4877 9281"/>
    </justification>
  </clause>

  <clause id="9288">
    <literal><![CDATA[
      (x * a(y,z,z)) \ (L(x,z,y) * a(y,z,z)) = x * L(x \ 1,z,y)
    ]]></literal>
    <justification jstring="[para(2274(a,1),9153(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2274 9153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9289">
    <literal><![CDATA[
      (x * a(y,z,z)) \ (L(x,z,y) * a(y,z,z)) = x \ L(x,z,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1064,a(flip),b,9288,a),flip(a)].">
      <j1 rule="hyper" parents="316 1064 9288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9291">
    <literal><![CDATA[
      (x * a(y,z,z)) \ L(x * a(y,z,z),z,y) = x \ L(x,z,y)
    ]]></literal>
    <justification jstring="[para(8707(a,2),9289(a,1,2))].">
      <j1 rule="para" parents="8707 9289"/>
    </justification>
  </clause>

  <clause id="9292">
    <literal><![CDATA[
      a(x,y,L(z,u * R(w,v5,v6),v7)) = a(x,y,L(z,u * L(w,v5,v6),v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,8746,a(flip),b,9154,a),flip(a)].">
      <j1 rule="hyper" parents="63 8746 9154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9293">
    <literal><![CDATA[
      a(x,y,L(z * (u * R(w,v5,v6)),u * L(w,v5,v6),u * R(w,v5,v6))) = a(x,y,(u * R(w,v5,v6)) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8606,a(flip),b,9292,a),flip(a)].">
      <j1 rule="hyper" parents="63 8606 9292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9294">
    <literal><![CDATA[
      x * ((R(x,y,z) \ a(x,y,z)) * (x \ L(x,u,w))) = L(x,u,w) * (R(x,y,z) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(8762(a,1),9155(a,2,2))].">
      <j1 rule="para" parents="8762 9155"/>
    </justification>
  </clause>

  <clause id="9295">
    <literal><![CDATA[
      a(x,a(x,y,z),y * z) * (x \ L(x,u,w)) = L(x,u,w) * (R(x,y,z) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8764,a(flip),b,9294,a)].">
      <j1 rule="hyper" parents="63 8764 9294"/>
    </justification>
  </clause>

  <clause id="9296">
    <literal><![CDATA[
      (R(x,y,z) * u) \ R(T(x,(u / x) * x),w,v5) = (((u / x) * R(x,y,z)) * x) \ R(x,w,v5)
    ]]></literal>
    <justification jstring="[para(3483(a,1),3318(a,1,2,1))].">
      <j1 rule="para" parents="3483 3318"/>
    </justification>
  </clause>

  <clause id="9297">
    <literal><![CDATA[
      (R(x,y,z) * u) \ R(T(x,u),w,v5) = (((u / x) * R(x,y,z)) * x) \ R(x,w,v5)
    ]]></literal>
    <justification jstring="[para(12(a,1),9296(a,1,2,1,2))].">
      <j1 rule="para" parents="12 9296"/>
    </justification>
  </clause>

  <clause id="9299">
    <literal><![CDATA[
      (R(x,y,z) * u) \ R(T(x,u),w,v5) = (((u / x) * x) * R(x,y,z)) \ R(x,w,v5)
    ]]></literal>
    <justification jstring="[para(1550(a,1),9297(a,2,1))].">
      <j1 rule="para" parents="1550 9297"/>
    </justification>
  </clause>

  <clause id="9300">
    <literal><![CDATA[
      (R(x,y,z) * u) \ R(T(x,u),w,v5) = (u * R(x,y,z)) \ R(x,w,v5)
    ]]></literal>
    <justification jstring="[para(12(a,1),9299(a,2,1,1))].">
      <j1 rule="para" parents="12 9299"/>
    </justification>
  </clause>

  <clause id="9302">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,y,z) * ((a(x,x,y) \ 1) \ z) = ((z / y) * L(y,x,x)) / (a(x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(7111(a,1),5102(a,1,1))].">
      <j1 rule="para" parents="7111 5102"/>
    </justification>
  </clause>

  <clause id="9303">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,y,z) * ((a(x,x,y) \ 1) \ z) = (a(x,x,y) \ 1) \ ((z / y) * L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,4994,a(flip),b,9302,a),flip(a)].">
      <j1 rule="hyper" parents="316 4994 9302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9304">
    <literal><![CDATA[
      (a(x,x,y) \ 1) \ ((z / y) * L(y,x,x)) = L(a(x,x,y),y,z) * (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7075,a(flip),b,9303,a),flip(a)].">
      <j1 rule="hyper" parents="63 7075 9303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9305">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ (u * (w * (x \ L(x,y,z)))) = L(w,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(4992(a,1),5111(a,2,1))].">
      <j1 rule="para" parents="4992 5111"/>
    </justification>
  </clause>

  <clause id="9306">
    <literal><![CDATA[
      (x * (y / (x * x))) \ L((x * y) / (x * x),z,u) = L(x \ y,x,x) \ L((x * x) \ (x * y),z,u)
    ]]></literal>
    <justification jstring="[para(683(a,1),5191(a,2,1)),flip(a)].">
      <j1 rule="para" parents="683 5191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9307">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ L(L(z \ 1,u,w),v5,v5 \ 1)) = a(x,y,a(v5 \ 1,v5,L(z,u,w)) \ 1)
    ]]></literal>
    <justification jstring="[para(2655(a,1),6018(a,2,3,1))].">
      <j1 rule="para" parents="2655 6018"/>
    </justification>
  </clause>

  <clause id="9308">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ L(L(z \ 1,u,w),v5,v5 \ 1)) = a(x,y,L(a(v5 \ 1,v5,z) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(5188(a,2),9307(a,2,3))].">
      <j1 rule="para" parents="5188 9307"/>
    </justification>
  </clause>

  <clause id="9309">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ L(L(z \ 1,u,w),v5,v5 \ 1)) = a(x,y,L(a(v5 \ 1,v5,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,2655,a(flip),b,9308,a),flip(a)].">
      <j1 rule="hyper" parents="316 2655 9308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9310">
    <literal><![CDATA[
      a(x,y,((z * u) * (w \ 1)) \ ((u * (w \ 1)) * z)) = a(x,y,a(w \ K(u,w \ 1),u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5686,a(flip),b,6135,a)].">
      <j1 rule="hyper" parents="63 5686 6135"/>
    </justification>
  </clause>

  <clause id="9312">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((w \ 1) \ (z * (u * (w \ 1))))) = a(x,y,a(w \ K(u,w \ 1),u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7626,a(flip),b,9310,a)].">
      <j1 rule="hyper" parents="63 7626 9310"/>
    </justification>
  </clause>

  <clause id="9313">
    <literal><![CDATA[
      a(x,y,(z * u) \ (w \ (z * (u * w)))) = a(x,y,a(w \ K(u,w \ 1),u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7559,a(flip),b,9312,a)].">
      <j1 rule="hyper" parents="63 7559 9312"/>
    </justification>
  </clause>

  <clause id="9320">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) \ (u * (w * (L(x,y,z) \ x))) = L(w,L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(6477(a,1),6547(a,2,1))].">
      <j1 rule="para" parents="6477 6547"/>
    </justification>
  </clause>

  <clause id="9321">
    <literal><![CDATA[
      a(x,y,z \ (((u * (1 / (w / v5))) * (v5 \ w)) * v6)) = a(x,y,z \ (R(u,(w / v5) \ 1,v5 \ w) * v6))
    ]]></literal>
    <justification jstring="[para(4680(a,1),6753(a,2,3,2,1))].">
      <j1 rule="para" parents="4680 6753"/>
    </justification>
  </clause>

  <clause id="9322">
    <literal><![CDATA[
      R(x,y,(y * x) \ (z \ (x * (y * z)))) \ ((x * (y * z)) / z) = y * (((x * (y * z)) / z) / (x * y))
    ]]></literal>
    <justification jstring="[para(4695(a,1),6793(a,1,1))].">
      <j1 rule="para" parents="4695 6793"/>
    </justification>
  </clause>

  <clause id="9323">
    <literal><![CDATA[
      a(x,y,L((z / (u \ 1)) \ L(u,u,z),w,v5)) = a(x,y,L((((u \ 1) \ z) * z) \ ((u \ 1) \ z),w,v5))
    ]]></literal>
    <justification jstring="[para(3363(a,1),7755(a,2,3,1))].">
      <j1 rule="para" parents="3363 7755"/>
    </justification>
  </clause>

  <clause id="9325">
    <literal><![CDATA[
      L(x,y,z) * (T(u,x) * (x \ L(x,w,v5))) = (x \ L(x,w,v5)) * (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5017(a,1),8097(a,1,2,2))].">
      <j1 rule="para" parents="5017 8097"/>
    </justification>
  </clause>

  <clause id="9327">
    <literal><![CDATA[
      ((x \ y) \ (y * L(y \ (x \ y),z,u))) * y = (L(x,y,x) * y) * L(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[para(7108(a,1),8173(a,1,1))].">
      <j1 rule="para" parents="7108 8173"/>
    </justification>
  </clause>

  <clause id="9328">
    <literal><![CDATA[
      (L(x,y,x) * y) * L(y \ (x \ y),z,u) = (x \ L(x,z,u)) * y
    ]]></literal>
    <justification jstring="[para(5109(a,1),9327(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5109 9327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9329">
    <literal><![CDATA[
      (x / (x \ (y \ x))) * L(x \ (y \ x),z,u) = (y \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,8168,a,b,9328,a)].">
      <j1 rule="hyper" parents="63 8168 9328"/>
    </justification>
  </clause>

  <clause id="9331">
    <literal><![CDATA[
      (x * (x \ y)) \ ((x * ((x \ y) * (x \ y))) / (x \ y)) = L((x \ y) * (y \ x),x \ y,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),8296(a,2,3))].">
      <j1 rule="para" parents="10 8296"/>
    </justification>
  </clause>

  <clause id="9332">
    <literal><![CDATA[
      x \ ((y * ((y \ x) * (y \ x))) / (y \ x)) = L((y \ x) * (x \ y),y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(332,a,9331,a)].">
      <j1 rule="hyper" parents="332 9331"/>
    </justification>
  </clause>

  <clause id="9334">
    <literal><![CDATA[
      L((x \ y) * (y \ x),x \ y,y) = y \ (x / ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(567(a,1),9332(a,1,2)),flip(a)].">
      <j1 rule="para" parents="567 9332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9335">
    <literal><![CDATA[
      x * ((y \ x) * (x \ y)) = y / ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,8779,a(flip),b,9334,a(flip))].">
      <j1 rule="hyper" parents="139 8779 9334"/>
    </justification>
  </clause>

  <clause id="9336">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) * y = x / ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3519,a,b,9335,a)].">
      <j1 rule="hyper" parents="63 3519 9335"/>
    </justification>
  </clause>

  <clause id="9337">
    <literal><![CDATA[
      a(L(x,y,z),u,w) * a(u * w,R(x,y,z),a(R(x,y,z),u,w)) = R(x,y,z) \ R(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(4643(a,1),8731(a,1,1))].">
      <j1 rule="para" parents="4643 8731"/>
    </justification>
  </clause>

  <clause id="9338">
    <literal><![CDATA[
      a(x,y,L(L(L(z,u,w) \ z,z,v5) * v5,v6,v7)) = a(x,y,L((z \ v5) * L(1 / z,u,w),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(316,a,5888,a(flip),b,9111,a),flip(a)].">
      <j1 rule="hyper" parents="316 5888 9111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9339">
    <literal><![CDATA[
      a(x,y,L(L(L(z,u,w) \ z,z,v5) * v5,v6,v7)) = a(x,y,L((z \ v5) * L(z \ 1,u,w),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(316,a,5782,a(flip),b,9338,a),flip(a)].">
      <j1 rule="hyper" parents="316 5782 9338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9340">
    <literal><![CDATA[
      a(x,y,L(L(L(z,u,w) \ z,z,v5) * v5,v6,v7)) = a(x,y,L((z \ v5) * L(z,u,w),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(316,a,9067,a(flip),b,9339,a),flip(a)].">
      <j1 rule="hyper" parents="316 9067 9339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9341">
    <literal><![CDATA[
      x \ (L(a(y,z,x \ u) \ 1,x \ u,u) * u) = (x \ u) * T(a(y,z,x \ u) \ 1,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),9134(a,1,2,1,3))].">
      <j1 rule="para" parents="10 9134"/>
    </justification>
  </clause>

  <clause id="9342">
    <literal><![CDATA[
      x \ (L(a(y,z,x \ u) \ 1,x \ u,u) * u) = (x \ u) * (a(y,z,x \ u) \ 1)
    ]]></literal>
    <justification jstring="[para(4997(a,1),9341(a,2,2))].">
      <j1 rule="para" parents="4997 9341"/>
    </justification>
  </clause>

  <clause id="9343">
    <literal><![CDATA[
      x \ (L(a(y,z,x \ u) \ 1,x \ u,u) * u) = a(y,z,x \ u) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,6859,a(flip),b,9342,a),flip(a)].">
      <j1 rule="hyper" parents="316 6859 9342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9345">
    <literal><![CDATA[
      a(x,y,L(z * (u * R(w,v5,v6)),u * L(w,v5,v6),u * L(w,v5,v6))) = a(x,y,(u * R(w,v5,v6)) \ z)
    ]]></literal>
    <justification jstring="[para(7496(a,1),9293(a,1,3))].">
      <j1 rule="para" parents="7496 9293"/>
    </justification>
  </clause>

  <clause id="9346">
    <literal><![CDATA[
      (x * (y / (x * x))) \ L(x * (y / (x * x)),z,u) = L(x \ y,x,x) \ L((x * x) \ (x * y),z,u)
    ]]></literal>
    <justification jstring="[para(683(a,1),9306(a,1,2,1))].">
      <j1 rule="para" parents="683 9306"/>
    </justification>
  </clause>

  <clause id="9347">
    <literal><![CDATA[
      L(x,y,a(z,y,x)) \ ((x * (y * z)) / z) = y * (((x * (y * z)) / z) / (x * y))
    ]]></literal>
    <justification jstring="[para(7767(a,1),9322(a,1,1))].">
      <j1 rule="para" parents="7767 9322"/>
    </justification>
  </clause>

  <clause id="9348">
    <literal><![CDATA[
      x * (((y * (x * z)) / z) / (y * x)) = y \ ((y * (x * z)) / z)
    ]]></literal>
    <justification jstring="[para(6853(a,1),9347(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6853 9347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9349">
    <literal><![CDATA[
      x * ((y * x) \ ((y * (x * z)) / z)) = y \ ((y * (x * z)) / z)
    ]]></literal>
    <justification jstring="[para(6792(a,1),9348(a,1,2))].">
      <j1 rule="para" parents="6792 9348"/>
    </justification>
  </clause>

  <clause id="9350">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) / z) = y \ (x \ ((x * (y * z)) / z))
    ]]></literal>
    <justification jstring="[hyper(144,a,9349,a),flip(a)].">
      <j1 rule="hyper" parents="144 9349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9351">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (y * z)) = y \ (x \ ((x * (y * z)) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7126,a,b,9350,a)].">
      <j1 rule="hyper" parents="63 7126 9350"/>
    </justification>
  </clause>

  <clause id="9352">
    <literal><![CDATA[
      R(x,y,(z * u) \ (w \ (z * (u * w)))) = R(x,y,u \ (z \ ((z * (u * w)) / w)))
    ]]></literal>
    <justification jstring="[para(9350(a,1),4695(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9350 4695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9354">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),x,z * y) = L(y \ (z \ ((z * (y * x)) / x)),u,w)
    ]]></literal>
    <justification jstring="[para(9350(a,1),7127(a,2,1))].">
      <j1 rule="para" parents="9350 7127"/>
    </justification>
  </clause>

  <clause id="9355">
    <literal><![CDATA[
      L(K(x,y) * (z \ L(z,u,w)),z,w * u) = K(x,y) * (u \ (w \ ((w * (u * z)) / z)))
    ]]></literal>
    <justification jstring="[para(9350(a,1),7130(a,2,2))].">
      <j1 rule="para" parents="9350 7130"/>
    </justification>
  </clause>

  <clause id="9356">
    <literal><![CDATA[
      (x * ((y \ (z \ ((z * (y * x)) / x))) \ 1)) \ x = L(x \ L(x,y,z),x,z * y)
    ]]></literal>
    <justification jstring="[para(9350(a,1),8142(a,1,1,2,1))].">
      <j1 rule="para" parents="9350 8142"/>
    </justification>
  </clause>

  <clause id="9357">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * (z * w)) / w))) = a(x,y,a(1 / w,z,u))
    ]]></literal>
    <justification jstring="[para(9351(a,1),7452(a,1,3))].">
      <j1 rule="para" parents="9351 7452"/>
    </justification>
  </clause>

  <clause id="9358">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * L(w \ (u * z),z,u)))) = a(x,y,a(1 / (w \ (u * z)),z,u))
    ]]></literal>
    <justification jstring="[para(1468(a,1),9357(a,1,3,2,2))].">
      <j1 rule="para" parents="1468 9357"/>
    </justification>
  </clause>

  <clause id="9359">
    <literal><![CDATA[
      R(x,y,(z * u) \ (w \ (z * (u * w)))) = R(x,y,u \ (z \ (w \ (z * (u * w)))))
    ]]></literal>
    <justification jstring="[hyper(316,a,4774,a(flip),b,9352,a),flip(a)].">
      <j1 rule="hyper" parents="316 4774 9352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9360">
    <literal><![CDATA[
      R(x,x,y \ (z \ ((z * (y * u)) / u))) \ (y \ (z \ ((z * (y * u)) / u))) = x \ L(L(u \ L(u,y,z),x,x),u,z * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,9354,a,b,4658,a),flip(a)].">
      <j1 rule="hyper" parents="133 9354 4658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9361">
    <literal><![CDATA[
      x \ L(L(y \ L(y,z,u),x \ 1,x),y,u * z) = (x \ 1) * (z \ (u \ ((u * (z * y)) / y)))
    ]]></literal>
    <justification jstring="[hyper(133,a,9354,a,b,271,a)].">
      <j1 rule="hyper" parents="133 9354 271"/>
    </justification>
  </clause>

  <clause id="9363">
    <literal><![CDATA[
      a(x,y,(z * ((u \ (w \ ((w * (u * z)) / z))) \ 1)) \ z) = a(x,y,(w * u) \ ((w * (u * z)) / z))
    ]]></literal>
    <justification jstring="[para(9356(a,2),7133(a,1,3))].">
      <j1 rule="para" parents="9356 7133"/>
    </justification>
  </clause>

  <clause id="9364">
    <literal><![CDATA[
      R(x,y,z \ (u \ (w \ (u * (z * w))))) = L(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7765,a(flip),b,9359,a),flip(a)].">
      <j1 rule="hyper" parents="63 7765 9359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9366">
    <literal><![CDATA[
      L(K(x,y) * (z \ L(z,y,u)),z,u * y) = T(y,x) \ (u \ ((u * (y * z)) / z))
    ]]></literal>
    <justification jstring="[hyper(316,a,3002,a(flip),b,9355,a),flip(a)].">
      <j1 rule="hyper" parents="316 3002 9355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9367">
    <literal><![CDATA[
      a(x,y,z \ ((u \ w) * L((u \ w) \ z,z,u))) = a(x,y,a(1 / (w \ (u * z)),z,u))
    ]]></literal>
    <justification jstring="[para(1020(a,1),9358(a,1,3,2))].">
      <j1 rule="para" parents="1020 9358"/>
    </justification>
  </clause>

  <clause id="9368">
    <literal><![CDATA[
      a(x,y,(z \ (u \ w)) \ ((u * z) \ w)) = a(x,y,a(1 / (w \ (u * z)),z,u))
    ]]></literal>
    <justification jstring="[para(1259(a,1),9367(a,1,3))].">
      <j1 rule="para" parents="1259 9367"/>
    </justification>
  </clause>

  <clause id="9369">
    <literal><![CDATA[
      a(x,y,(z \ (u \ w)) * ((u * z) \ w)) = a(x,y,a(1 / (w \ (u * z)),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5568,a(flip),b,9368,a)].">
      <j1 rule="hyper" parents="63 5568 9368"/>
    </justification>
  </clause>

  <clause id="9370">
    <literal><![CDATA[
      a(x,y,(z \ (u \ w)) * ((u * z) \ w)) = a(x,y,a((w \ (u * z)) \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(1808(a,1),9369(a,2,3))].">
      <j1 rule="para" parents="1808 9369"/>
    </justification>
  </clause>

  <clause id="9371">
    <literal><![CDATA[
      x \ L(L(y \ L(y,z,u),x,x),y,u * z) = (x \ 1) * (z \ (u \ ((u * (z * y)) / y)))
    ]]></literal>
    <justification jstring="[para(7804(a,1),9361(a,1,2,1))].">
      <j1 rule="para" parents="7804 9361"/>
    </justification>
  </clause>

  <clause id="9372">
    <literal><![CDATA[
      a(x,y,(z * ((u \ (w \ ((w * (u * z)) / z))) \ 1)) \ z) = a(x,y,u \ (w \ ((w * (u * z)) / z)))
    ]]></literal>
    <justification jstring="[para(9350(a,1),9363(a,2,3))].">
      <j1 rule="para" parents="9350 9363"/>
    </justification>
  </clause>

  <clause id="9373">
    <literal><![CDATA[
      a(x,y,(z * ((u \ (w \ ((w * (u * z)) / z))) \ 1)) \ z) = a(x,y,u \ (w \ (z \ (w * (u * z)))))
    ]]></literal>
    <justification jstring="[hyper(316,a,5606,a(flip),b,9372,a),flip(a)].">
      <j1 rule="hyper" parents="316 5606 9372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9374">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,w),z,w * u)) = a(x,y,u \ (w \ (z \ (w * (u * z)))))
    ]]></literal>
    <justification jstring="[para(9356(a,1),9373(a,1,3))].">
      <j1 rule="para" parents="9356 9373"/>
    </justification>
  </clause>

  <clause id="9375">
    <literal><![CDATA[
      a(x,y,L(L(z \ 1,z,(u \ 1) \ z),w,v5)) = a(x,y,L((z / (u \ 1)) \ L(u,u,z),w,v5))
    ]]></literal>
    <justification jstring="[para(232(a,2),9323(a,2,3,1)),flip(a)].">
      <j1 rule="para" parents="232 9323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9376">
    <literal><![CDATA[
      a(x,y,L(L(z \ 1,z,u \ z),w,v5)) = a(x,y,L((z / (u \ 1)) \ L(u,u,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,9081,a(flip),b,9375,a)].">
      <j1 rule="hyper" parents="63 9081 9375"/>
    </justification>
  </clause>

  <clause id="9377">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u \ z),w,v5)) = a(x,y,L((z / (u \ 1)) \ L(u,u,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5891,a(flip),b,9376,a)].">
      <j1 rule="hyper" parents="63 5891 9376"/>
    </justification>
  </clause>

  <clause id="9378">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u \ z),w,v5)) = a(x,y,L(((u \ 1) \ z) \ L(u,u,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,5718,a(flip),b,9377,a),flip(a)].">
      <j1 rule="hyper" parents="316 5718 9377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9379">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u \ z),w,v5)) = a(x,y,L(L(z,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,9033,a(flip),b,9378,a),flip(a)].">
      <j1 rule="hyper" parents="316 9033 9378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9380">
    <literal><![CDATA[
      a(L(x,y,z),u,w) * a(u * w,R(x,y,z),a(L(x,y,z),u,w)) = R(x,y,z) \ R(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(4643(a,1),9337(a,1,2,3))].">
      <j1 rule="para" parents="4643 9337"/>
    </justification>
  </clause>

  <clause id="9381">
    <literal><![CDATA[
      (x * (y / (x * x))) \ L(x * (y / (x * x)),z,u) = L(x \ y,x,x) \ L(L(x \ y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(102(a,2),9346(a,2,2,1))].">
      <j1 rule="para" parents="102 9346"/>
    </justification>
  </clause>

  <clause id="9382">
    <literal><![CDATA[
      (x * (y / (x * x))) \ L(x * (y / (x * x)),z,u) = L((x \ y) \ L(x \ y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,2136,a(flip),b,9381,a),flip(a)].">
      <j1 rule="hyper" parents="316 2136 9381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9383">
    <literal><![CDATA[
      (x * (y / (x * x))) \ L(x * (y / (x * x)),z,u) = L(x \ (y * L(y \ x,z,u)),x,x)
    ]]></literal>
    <justification jstring="[para(1252(a,1),9382(a,2,1))].">
      <j1 rule="para" parents="1252 9382"/>
    </justification>
  </clause>

  <clause id="9386">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (R(T(x,v5),y,z) \ v5) = K(x,v6) * (R(T(x,v6),y,z) \ (v5 * L(R(x,y,z),u,w)))
    ]]></literal>
    <justification jstring="[para(27(a,2),4466(a,1,2,1))].">
      <j1 rule="para" parents="27 4466"/>
    </justification>
  </clause>

  <clause id="9400">
    <literal><![CDATA[
      R(x / (y \ L(y,z,u)),y \ L(y,z,u),y) = (x * ((y \ w) \ w)) / L((y \ w) \ w,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4681,a(flip),b,5158,a)].">
      <j1 rule="hyper" parents="63 4681 5158"/>
    </justification>
  </clause>

  <clause id="9402">
    <literal><![CDATA[
      (x * T(y,y \ L(y,z,u))) / L(y,z,u) = (x * ((y \ w) \ w)) / L((y \ w) \ w,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4062,a(flip),b,9400,a)].">
      <j1 rule="hyper" parents="63 4062 9400"/>
    </justification>
  </clause>

  <clause id="9403">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) / L((y \ z) \ z,u,w) = (x * y) / L(y,u,w)
    ]]></literal>
    <justification jstring="[para(1269(a,1),9402(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1269 9402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9404">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) / L((y \ z) \ z,u,w) = y * (L(y,u,w) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,4390,a(flip),b,9403,a),flip(a)].">
      <j1 rule="hyper" parents="316 4390 9403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9405">
    <literal><![CDATA[
      ((x \ y) \ y) * (L((x \ y) \ y,z,u) \ w) = x * (L(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,4390,a(flip),b,9404,a)].">
      <j1 rule="hyper" parents="63 4390 9404"/>
    </justification>
  </clause>

  <clause id="9406">
    <literal><![CDATA[
      (x * (L(x,y,z) \ ((x \ 1) * u))) * L((x \ 1) \ 1,y,z) = ((1 / x) * u) * x
    ]]></literal>
    <justification jstring="[para(9405(a,1),4436(a,1,1))].">
      <j1 rule="para" parents="9405 4436"/>
    </justification>
  </clause>

  <clause id="9407">
    <literal><![CDATA[
      (L(x,y,z) \ L(u,x \ 1,x)) * L((x \ 1) \ 1,y,z) = ((1 / x) * u) * x
    ]]></literal>
    <justification jstring="[para(1141(a,1),9406(a,1,1))].">
      <j1 rule="para" parents="1141 9406"/>
    </justification>
  </clause>

  <clause id="9409">
    <literal><![CDATA[
      (x / (y / (z * z))) \ L((x * (z * z)) / y,u,w) = ((y \ x) * (z * z)) \ L(y \ (x * (z * z)),u,w)
    ]]></literal>
    <justification jstring="[para(676(a,1),5192(a,1,1))].">
      <j1 rule="para" parents="676 5192"/>
    </justification>
  </clause>

  <clause id="9410">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ L(L(z \ 1,u,w),v5,v6)) = a(x,y,L((z \ 1) * L(z \ 1,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7442,a(flip),b,6017,a),flip(a)].">
      <j1 rule="hyper" parents="63 7442 6017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9411">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ L(L(z \ 1,u,w),v5,v6)) = a(x,y,L((z \ 1) * L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,9067,a(flip),b,9410,a),flip(a)].">
      <j1 rule="hyper" parents="316 9067 9410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9412">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ L(L(z \ 1,u,w),v5,v6)) = a(x,y,L(z * L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,6027,a(flip),b,9411,a),flip(a)].">
      <j1 rule="hyper" parents="316 6027 9411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9413">
    <literal><![CDATA[
      L(L(x \ L(x,x,a(y,z,u)),w,v5),L(x,w,v5),x * a(y,z,u)) = a(x,L(x,w,v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(2136(a,1),6325(a,1,1))].">
      <j1 rule="para" parents="2136 6325"/>
    </justification>
  </clause>

  <clause id="9414">
    <literal><![CDATA[
      L(L(a(x,x,a(y,z,u)),w,v5),L(x,w,v5),x * a(y,z,u)) = a(x,L(x,w,v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(7328(a,1),9413(a,1,1,1))].">
      <j1 rule="para" parents="7328 9413"/>
    </justification>
  </clause>

  <clause id="9415">
    <literal><![CDATA[
      ((x / y) * (y * (L(y,z,u) \ y))) / (L(y,z,u) \ y) = ((L(y,z,u) \ y) \ x) * L(L(y,z,u) \ y,y,x)
    ]]></literal>
    <justification jstring="[para(9097(a,2),6541(a,1,1))].">
      <j1 rule="para" parents="9097 6541"/>
    </justification>
  </clause>

  <clause id="9416">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ ((x * (L(x,y,z) \ x)) \ 1) = L(x \ 1,y,z) * L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(4459(a,1),6615(a,2,1))].">
      <j1 rule="para" parents="4459 6615"/>
    </justification>
  </clause>

  <clause id="9417">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ L(x \ 1,y,z) = L(x \ 1,y,z) * L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(4459(a,1),9416(a,1,2))].">
      <j1 rule="para" parents="4459 9416"/>
    </justification>
  </clause>

  <clause id="9418">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ L(x \ 1,y,z) = L(x \ 1,y,z) * L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(6585(a,2),9417(a,1,1))].">
      <j1 rule="para" parents="6585 9417"/>
    </justification>
  </clause>

  <clause id="9419">
    <literal><![CDATA[
      x * (L(y \ 1,z,u) \ (1 / L(y \ 1,z,u))) = x / (L(y \ 1,z,u) * L(1 / y,z,u))
    ]]></literal>
    <justification jstring="[para(9418(a,1),6579(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9418 6579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9420">
    <literal><![CDATA[
      (x \ (x \ 1)) / (L(x \ 1,y,z) * L(1 / x,y,z)) = L(x,y,z) \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,9138,a(flip),b,9419,a),flip(a)].">
      <j1 rule="hyper" parents="63 9138 9419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9421">
    <literal><![CDATA[
      1 / ((L(x \ 1,y,z) * L(1 / x,y,z)) * (x * x)) = L(x,y,z) \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,638,a(flip),b,9420,a)].">
      <j1 rule="hyper" parents="63 638 9420"/>
    </justification>
  </clause>

  <clause id="9422">
    <literal><![CDATA[
      1 / (L(x \ 1,y,z) * (L(1 / x,y,z) * (x * x))) = L(x,y,z) \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(32(a,1),9421(a,1,2))].">
      <j1 rule="para" parents="32 9421"/>
    </justification>
  </clause>

  <clause id="9423">
    <literal><![CDATA[
      1 / (L(x \ 1,y,z) * L((1 / x) * (x * x),y,z)) = L(x,y,z) \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1058(a,2),9422(a,1,2,2))].">
      <j1 rule="para" parents="1058 9422"/>
    </justification>
  </clause>

  <clause id="9424">
    <literal><![CDATA[
      1 / (L(x \ 1,y,z) * L(T(x,x \ 1),y,z)) = L(x,y,z) \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1243(a,1),9423(a,1,2,2,1))].">
      <j1 rule="para" parents="1243 9423"/>
    </justification>
  </clause>

  <clause id="9425">
    <literal><![CDATA[
      1 / (L(x,y,z) * L(x \ 1,y,z)) = L(x,y,z) \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(4315(a,1),9424(a,1,2))].">
      <j1 rule="para" parents="4315 9424"/>
    </justification>
  </clause>

  <clause id="9426">
    <literal><![CDATA[
      a(x,y,(z * ((u * (L(u,w,v5) \ u)) * K(v6,v7))) \ v8) = a(x,y,(z * (L(u \ K(v7,v6),w,v5) \ 1)) \ v8)
    ]]></literal>
    <justification jstring="[hyper(316,a,5684,a(flip),b,6656,a),flip(a)].">
      <j1 rule="hyper" parents="316 5684 6656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9427">
    <literal><![CDATA[
      L(L(x,y,z) \ L(L(x,y,z),u,w),v5,a(v6,v7,x)) = L(x,y,z) \ L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(6871(a,1),6885(a,2,2))].">
      <j1 rule="para" parents="6871 6885"/>
    </justification>
  </clause>

  <clause id="9429">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ (1 / w)) * (a(w,v5,v6) \ (a(w,v5,v6) / w)) = (((a(w,v5,v6) / w) / a(w,v5,v6)) / u) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(8427(a,1),7538(a,1,1,3,2))].">
      <j1 rule="para" parents="8427 7538"/>
    </justification>
  </clause>

  <clause id="9433">
    <literal><![CDATA[
      L(x,a(y,z,u) \ w,a(v5,v6,v7) * a(y,z,u)) * ((a(v5,v6,v7) * a(y,z,u)) * (a(y,z,u) \ w)) = (a(v5,v6,v7) * a(y,z,u)) * (x * (a(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(5268(a,1),7793(a,2,2))].">
      <j1 rule="para" parents="5268 7793"/>
    </justification>
  </clause>

  <clause id="9434">
    <literal><![CDATA[
      L(((L(x,y,z) \ x) * (L(x,y,z) \ x)) \ u,w,v5) = L(u,w,v5) * (L(x,y,z) * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,8377,a(flip),b,7893,a),flip(a)].">
      <j1 rule="hyper" parents="316 8377 7893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9435">
    <literal><![CDATA[
      L((x * (L(x,y,z) \ (L(x,y,z) \ x))) \ u,w,v5) = L(u,w,v5) * (L(x,y,z) * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(7892(a,1),9434(a,1,1,1))].">
      <j1 rule="para" parents="7892 9434"/>
    </justification>
  </clause>

  <clause id="9436">
    <literal><![CDATA[
      L(x * (L(y,z,u) * L(y \ 1,z,u)),w,v5) = L(x,w,v5) * (L(y,z,u) * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(8377(a,1),9435(a,1,1))].">
      <j1 rule="para" parents="8377 9435"/>
    </justification>
  </clause>

  <clause id="9439">
    <literal><![CDATA[
      L(a(a(x,y,z),u,w) \ u,a(x,y,z),w) = (a(x,y,z) * w) \ ((w * u) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(5276(a,1),8640(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5276 8640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9440">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ u = u * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(41,a,8917,a,b,9439,a),flip(a)].">
      <j1 rule="hyper" parents="41 8917 9439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9441">
    <literal><![CDATA[
      x \ (y \ ((y * (x * a(z,u,w))) / a(z,u,w))) = a(a(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,8544,a,b,9440,a)].">
      <j1 rule="hyper" parents="39 8544 9440"/>
    </justification>
  </clause>

  <clause id="9442">
    <literal><![CDATA[
      x \ (a(y,x,a(z,u,w)) \ x) = a(a(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,5207,a,b,9440,a)].">
      <j1 rule="hyper" parents="39 5207 9440"/>
    </justification>
  </clause>

  <clause id="9443">
    <literal><![CDATA[
      a(x,a(y,z,x),u) \ x = x * a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(7009(a,1),9440(a,1,1))].">
      <j1 rule="para" parents="7009 9440"/>
    </justification>
  </clause>

  <clause id="9444">
    <literal><![CDATA[
      x \ (a(y,x,a(x,z,u)) \ x) = a(x,a(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(316,a,8744,a(flip),b,9442,a),flip(a)].">
      <j1 rule="hyper" parents="316 8744 9442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9445">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ y = y * a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(152,a,9442,a),flip(a)].">
      <j1 rule="hyper" parents="152 9442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9446">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ y = a(a(z,u,w),y,x) * y
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,9442,a),flip(a)].">
      <j1 rule="hyper" parents="38 2295 9442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9447">
    <literal><![CDATA[
      a(x,a(y,z,x),u) \ 1 = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(34,a,8404,a,b,9443,a(flip))].">
      <j1 rule="hyper" parents="34 8404 9443"/>
    </justification>
  </clause>

  <clause id="9448">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) \ 1 = a(y,a(z,u,y),x)
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,9447,a)].">
      <j1 rule="hyper" parents="39 2301 9447"/>
    </justification>
  </clause>

  <clause id="9449">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * a(y,a(z,u,y),x) = 1
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,9447,a)].">
      <j1 rule="hyper" parents="38 2295 9447"/>
    </justification>
  </clause>

  <clause id="9450">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) \ w) * a(y,a(z,u,y),x) = w * (a(y,a(z,u,y),x) * a(y,a(z,u,y),x))
    ]]></literal>
    <justification jstring="[para(9447(a,1),5047(a,1,1,1))].">
      <j1 rule="para" parents="9447 5047"/>
    </justification>
  </clause>

  <clause id="9451">
    <literal><![CDATA[
      a(x * y,a(x,y,x * y),z) = a(z,x * y,a(x,y,y)) \ 1
    ]]></literal>
    <justification jstring="[para(7284(a,1),9448(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7284 9448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9452">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) \ x = a(y,a(z,u,y),x) * x
    ]]></literal>
    <justification jstring="[para(9448(a,1),8405(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9448 8405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9453">
    <literal><![CDATA[
      a(x * y,a(y,y,x * y),z) = a(z,x * y,a(x,y,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8830(a,1),9448(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8830 9448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9454">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) \ 1 = a(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8743,a(flip),b,9444,a)].">
      <j1 rule="hyper" parents="63 8743 9444"/>
    </justification>
  </clause>

  <clause id="9455">
    <literal><![CDATA[
      a(x,a(x,y,z),u) \ 1 = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,9454,a)].">
      <j1 rule="hyper" parents="39 2301 9454"/>
    </justification>
  </clause>

  <clause id="9456">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,w),w,a(y,z,u)) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(9445(a,1),8902(a,1,1))].">
      <j1 rule="para" parents="9445 8902"/>
    </justification>
  </clause>

  <clause id="9457">
    <literal><![CDATA[
      a(x,a(y,z,u),L(u,w,v5)) \ L(u,w,v5) = L(u,w,v5) * a(a(y,z,u),L(u,w,v5),x)
    ]]></literal>
    <justification jstring="[para(8984(a,1),9445(a,1,1))].">
      <j1 rule="para" parents="8984 9445"/>
    </justification>
  </clause>

  <clause id="9458">
    <literal><![CDATA[
      L(a(a(x,y,z),u,w) * u,w,a(x,y,z)) = L(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(9446(a,1),8902(a,1,1))].">
      <j1 rule="para" parents="9446 8902"/>
    </justification>
  </clause>

  <clause id="9459">
    <literal><![CDATA[
      x * a(a(x,y,z),x,u) = L(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(41,a,8408,a,b,9456,a),flip(a)].">
      <j1 rule="hyper" parents="41 8408 9456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9460">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * a(a(z,u,w),L(x,y,a(z,u,w)),y) = L(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(41,a,30,a,b,9456,a),flip(a)].">
      <j1 rule="hyper" parents="41 30 9456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9462">
    <literal><![CDATA[
      x \ L(x,a(x,y,z),u) = a(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,9459,a)].">
      <j1 rule="hyper" parents="144 9459"/>
    </justification>
  </clause>

  <clause id="9463">
    <literal><![CDATA[
      x \ L(x,a(x,y,z),u) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,8744,a(flip),b,9462,a),flip(a)].">
      <j1 rule="hyper" parents="316 8744 9462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9464">
    <literal><![CDATA[
      a(a(x,y,z),L(z,u,w),v5) * L(z,u,w) = L(L(z,u,w),a(x,y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(41,a,6871,a,b,9458,a),flip(a)].">
      <j1 rule="hyper" parents="41 6871 9458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9465">
    <literal><![CDATA[
      a(a(x,y,z),z,u) * z = L(z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(41,a,6868,a,b,9458,a),flip(a)].">
      <j1 rule="hyper" parents="41 6868 9458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9466">
    <literal><![CDATA[
      x * a(x,a(y,z,x),u) = L(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,7010,a(flip),b,9465,a)].">
      <j1 rule="hyper" parents="63 7010 9465"/>
    </justification>
  </clause>

  <clause id="9467">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * L(y,a(z,u,y),x) = y
    ]]></literal>
    <justification jstring="[hyper(139,a,9465,a(flip),b,9446,a)].">
      <j1 rule="hyper" parents="139 9465 9446"/>
    </justification>
  </clause>

  <clause id="9468">
    <literal><![CDATA[
      x \ L(x,a(y,z,x),u) = a(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[hyper(133,a,9465,a(flip),b,7010,a(flip))].">
      <j1 rule="hyper" parents="133 9465 7010"/>
    </justification>
  </clause>

  <clause id="9469">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * x = L(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[para(7009(a,1),9465(a,1,1))].">
      <j1 rule="para" parents="7009 9465"/>
    </justification>
  </clause>

  <clause id="9470">
    <literal><![CDATA[
      x * (L(x,y,z) \ a(x,a(u,w,x),v5)) = L(x,y,z) \ L(x,a(u,w,x),v5)
    ]]></literal>
    <justification jstring="[hyper(133,a,9466,a(flip),b,1128,a),flip(a)].">
      <j1 rule="hyper" parents="133 9466 1128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9471">
    <literal><![CDATA[
      ((1 / x) * a(1 / x,a(y,z,1 / x),u)) \ 1 = (L(x,a(y,z,1 / x),u) \ x) * x
    ]]></literal>
    <justification jstring="[para(9466(a,2),6592(a,1,1))].">
      <j1 rule="para" parents="9466 6592"/>
    </justification>
  </clause>

  <clause id="9472">
    <literal><![CDATA[
      L(x,a(y,z,x),u) \ x = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(35,a,1375,a,b,9467,a)].">
      <j1 rule="hyper" parents="35 1375 9467"/>
    </justification>
  </clause>

  <clause id="9473">
    <literal><![CDATA[
      x \ (L(x,a(y,z,x),u) * (w * a(u,x,a(y,z,x)))) = L(w,a(u,x,a(y,z,x)),L(x,a(y,z,x),u))
    ]]></literal>
    <justification jstring="[para(9467(a,1),2496(a,1,1))].">
      <j1 rule="para" parents="9467 2496"/>
    </justification>
  </clause>

  <clause id="9474">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * (y \ L(y,w,v5)) = L(y,a(z,u,y),x) \ L(y,w,v5)
    ]]></literal>
    <justification jstring="[para(9472(a,1),6842(a,1,1))].">
      <j1 rule="para" parents="9472 6842"/>
    </justification>
  </clause>

  <clause id="9475">
    <literal><![CDATA[
      a(x,a(y,z,u),L(u,w,v5)) \ 1 = a(a(y,z,u),L(u,w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(34,a,6944,a,b,9457,a(flip))].">
      <j1 rule="hyper" parents="34 6944 9457"/>
    </justification>
  </clause>

  <clause id="9477">
    <literal><![CDATA[
      ((1 / x) * a(1 / x,a(y,z,x),u)) \ 1 = (L(x,a(y,z,1 / x),u) \ x) * x
    ]]></literal>
    <justification jstring="[para(2535(a,1),9471(a,1,1,2,2))].">
      <j1 rule="para" parents="2535 9471"/>
    </justification>
  </clause>

  <clause id="9478">
    <literal><![CDATA[
      ((1 / x) * a(x \ 1,a(y,z,x),u)) \ 1 = (L(x,a(y,z,1 / x),u) \ x) * x
    ]]></literal>
    <justification jstring="[para(1808(a,1),9477(a,1,1,2))].">
      <j1 rule="para" parents="1808 9477"/>
    </justification>
  </clause>

  <clause id="9479">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) \ L(w,a(y,a(z,u,y),x),a(y,a(z,u,y),x)) = w * a(y,a(z,u,y),x)
    ]]></literal>
    <justification jstring="[hyper(35,a,5383,a(flip),b,9450,a),flip(a)].">
      <j1 rule="hyper" parents="35 5383 9450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9480">
    <literal><![CDATA[
      ((x * a(y,z,a(u,w,z))) / z) * L(z,a(u,w,z),y) = L(x,a(y,z,a(u,w,z)),L(z,a(u,w,z),y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4382,a(flip),b,9473,a)].">
      <j1 rule="hyper" parents="63 4382 9473"/>
    </justification>
  </clause>

  <clause id="9481">
    <literal><![CDATA[
      a(x,y,(z \ u) * R(w / L(z * u,z,z),z * u,z * u)) = a(x,y,(w * (z * u)) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5836,a(flip),b,8693,a),flip(a)].">
      <j1 rule="hyper" parents="316 5836 8693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9482">
    <literal><![CDATA[
      a(x,y,(z \ u) * R(w / L(z * u,z,z),z * u,z * u)) = a(x,y,L(w,z * u,z * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5808,a(flip),b,9481,a),flip(a)].">
      <j1 rule="hyper" parents="316 5808 9481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9483">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(w / L(z * u,z,z),z * u,z * u)) = a(x,y,L(w,z * u,z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7272,a(flip),b,9482,a)].">
      <j1 rule="hyper" parents="63 7272 9482"/>
    </justification>
  </clause>

  <clause id="9484">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(L(z * u,z,z) \ w,z * u,z * u)) = a(x,y,L(w,z * u,z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5560,a(flip),b,9483,a)].">
      <j1 rule="hyper" parents="63 5560 9483"/>
    </justification>
  </clause>

  <clause id="9485">
    <literal><![CDATA[
      (x / (y / (z * z))) \ L(x / (y / (z * z)),u,w) = ((y \ x) * (z * z)) \ L(y \ (x * (z * z)),u,w)
    ]]></literal>
    <justification jstring="[para(676(a,1),9409(a,1,2,1))].">
      <j1 rule="para" parents="676 9409"/>
    </justification>
  </clause>

  <clause id="9486">
    <literal><![CDATA[
      a(x,y,(z * ((u * (L(u,w,v5) \ u)) * K(v6,v7))) \ v8) = a(x,y,(z * L(u \ K(v7,v6),w,v5)) \ v8)
    ]]></literal>
    <justification jstring="[hyper(316,a,5970,a(flip),b,9426,a),flip(a)].">
      <j1 rule="hyper" parents="316 5970 9426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9487">
    <literal><![CDATA[
      ((x / (y * y)) \ z) \ L((x / (y * y)) \ z,u,w) = ((x \ z) * (y * y)) \ L(x \ (z * (y * y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5190,a(flip),b,9485,a)].">
      <j1 rule="hyper" parents="63 5190 9485"/>
    </justification>
  </clause>

  <clause id="9488">
    <literal><![CDATA[
      (((x * x) \ y) \ z) \ L(((x * x) \ y) \ z,u,w) = ((y \ z) * (x * x)) \ L(y \ (z * (x * x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,7911,a(flip),b,9487,a)].">
      <j1 rule="hyper" parents="63 7911 9487"/>
    </justification>
  </clause>

  <clause id="9489">
    <literal><![CDATA[
      (((x * x) \ y) \ z) \ L(((x * x) \ y) \ z,u,w) = ((y \ z) * (x * x)) \ L((y \ z) * (x * x),u,w)
    ]]></literal>
    <justification jstring="[para(388(a,1),9488(a,2,2,1))].">
      <j1 rule="para" parents="388 9488"/>
    </justification>
  </clause>

  <clause id="9490">
    <literal><![CDATA[
      (((x * x) \ y) \ z) \ L(((x * x) \ y) \ z,u,w) = (((y \ z) * (x * x)) \ L(y \ z,u,w)) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(316,a,1060,a(flip),b,9489,a),flip(a)].">
      <j1 rule="hyper" parents="316 1060 9489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9491">
    <literal><![CDATA[
      (((x * x) \ y) \ z) \ L(((x * x) \ y) \ z,u,w) = (y \ z) \ L(y \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,7621,a(flip),b,9490,a),flip(a)].">
      <j1 rule="hyper" parents="316 7621 9490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9493">
    <literal><![CDATA[
      ((x \ 1) \ y) \ L((x \ 1) \ y,z,u) = (x \ y) \ L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9070,a(flip),b,9491,a)].">
      <j1 rule="hyper" parents="63 9070 9491"/>
    </justification>
  </clause>

  <clause id="9494">
    <literal><![CDATA[
      (x \ 1) \ (y * L(y \ (x \ 1),z,u)) = (x \ y) \ L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1252,a(flip),b,9493,a)].">
      <j1 rule="hyper" parents="63 1252 9493"/>
    </justification>
  </clause>

  <clause id="9495">
    <literal><![CDATA[
      (x \ 1) \ (y * L(y \ (x \ 1),z,u)) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,1252,a(flip),b,9494,a),flip(a)].">
      <j1 rule="hyper" parents="316 1252 9494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9496">
    <literal><![CDATA[
      R(L(x,y,z) \ L(R(x,u,w),y,z),L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * R(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(29(a,1),4511(a,1,1,2))].">
      <j1 rule="para" parents="29 4511"/>
    </justification>
  </clause>

  <clause id="9497">
    <literal><![CDATA[
      (x \ L(x,y,z)) * R(a(u,w,v5),L(x,y,z),x) = (a(u,w,v5) * L(x,y,z)) * T(1 / x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1038(a,1),4623(a,1,2))].">
      <j1 rule="para" parents="1038 4623"/>
    </justification>
  </clause>

  <clause id="9498">
    <literal><![CDATA[
      (x \ L(x,y,z)) * R(a(u,w,v5),x,L(x,y,z)) = (a(u,w,v5) * L(x,y,z)) * T(1 / x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1471(a,1),9497(a,1,2))].">
      <j1 rule="para" parents="1471 9497"/>
    </justification>
  </clause>

  <clause id="9499">
    <literal><![CDATA[
      K(x,y) * ((z / L(x,u,w)) * L(L(x,u,w),v5,v6)) = L(L(T(x,y),u,w),v5,v6) * (L(x,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(4279(a,1),4923(a,1,1))].">
      <j1 rule="para" parents="4279 4923"/>
    </justification>
  </clause>

  <clause id="9501">
    <literal><![CDATA[
      K(x,y) * ((z / R(x,u,w)) * L(R(x,u,w),v5,v6)) = L(R(T(x,y),u,w),v5,v6) * (R(x,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(3387(a,1),4924(a,1,1))].">
      <j1 rule="para" parents="3387 4924"/>
    </justification>
  </clause>

  <clause id="9503">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * u) \ (u * (w * (a(x,y,z) \ 1))) = L(1 * w,a(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(5003(a,1),5058(a,2,1,1))].">
      <j1 rule="para" parents="5003 5058"/>
    </justification>
  </clause>

  <clause id="9504">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * u) \ (u * (w * (a(x,y,z) \ 1))) = L(w,a(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),9503(a,2,1))].">
      <j1 rule="para" parents="7 9503"/>
    </justification>
  </clause>

  <clause id="9506">
    <literal><![CDATA[
      R((x \ L(x,y,z)) \ u,(L(x,y,z) \ 1) \ (x \ 1),L(x,y,z) \ 1) = (u * (L(x,y,z) \ 1)) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(5015(a,1),5121(a,1,1))].">
      <j1 rule="para" parents="5015 5121"/>
    </justification>
  </clause>

  <clause id="9507">
    <literal><![CDATA[
      K(x,y) * ((L(y,z,z \ 1) \ y) * (L(y,z,z \ 1) * x)) = L(x,L(y,z,z \ 1),a(z \ 1,z,y)) * y
    ]]></literal>
    <justification jstring="[para(1378(a,1),5217(a,1,2,1))].">
      <j1 rule="para" parents="1378 5217"/>
    </justification>
  </clause>

  <clause id="9508">
    <literal><![CDATA[
      (x * (a(y,z,u) * a(y,z,u))) * T(w,x / (a(y,z,u) \ 1)) = w * (x * (a(y,z,u) * a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(2288(a,1),5346(a,1,1))].">
      <j1 rule="para" parents="2288 5346"/>
    </justification>
  </clause>

  <clause id="9509">
    <literal><![CDATA[
      (x * (a(y,z,u) * a(y,z,u))) * T(w,(a(y,z,u) \ 1) \ x) = w * (x * (a(y,z,u) * a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(4994(a,1),9508(a,1,2,2))].">
      <j1 rule="para" parents="4994 9508"/>
    </justification>
  </clause>

  <clause id="9510">
    <literal><![CDATA[
      (x / ((a(y,z,u) \ 1) \ w)) * (w * (a(y,z,u) * a(y,z,u))) = (w * (a(y,z,u) * a(y,z,u))) * (((a(y,z,u) \ 1) \ w) \ x)
    ]]></literal>
    <justification jstring="[para(116(a,1),9509(a,1,2)),flip(a)].">
      <j1 rule="para" parents="116 9509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9511">
    <literal><![CDATA[
      (x * (a(y,z,u) * a(y,z,u))) * T(w,a(y,z,u) * x) = w * (x * (a(y,z,u) * a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(3525(a,1),9509(a,1,2))].">
      <j1 rule="para" parents="3525 9509"/>
    </justification>
  </clause>

  <clause id="9512">
    <literal><![CDATA[
      (x * (a(y,z,u) * a(y,z,u))) * T(w,x) = w * (x * (a(y,z,u) * a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(5239(a,1),9511(a,1,2))].">
      <j1 rule="para" parents="5239 9511"/>
    </justification>
  </clause>

  <clause id="9514">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (1 / u)) * (w * (v5 * v6)))) = a(x,y,z \ (w * (v5 * (v6 * (u \ (1 / u))))))
    ]]></literal>
    <justification jstring="[para(717(a,1),6129(a,1,3,2,1))].">
      <j1 rule="para" parents="717 6129"/>
    </justification>
  </clause>

  <clause id="9516">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) \ ((x * w) * (L(y,z,u) \ y)) = L(1 * w,x,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(6485(a,1),6549(a,2,1,1))].">
      <j1 rule="para" parents="6485 6549"/>
    </justification>
  </clause>

  <clause id="9517">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) \ ((x * w) * (L(y,z,u) \ y)) = L(w,x,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(7(a,1),9516(a,2,1))].">
      <j1 rule="para" parents="7 9516"/>
    </justification>
  </clause>

  <clause id="9519">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * L(w,x,y \ L(y,z,u)) = (x * w) * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,9212,a(flip),b,9517,a)].">
      <j1 rule="hyper" parents="139 9212 9517"/>
    </justification>
  </clause>

  <clause id="9520">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * y = (x * y) * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(6156(a,1),9519(a,1,2))].">
      <j1 rule="para" parents="6156 9519"/>
    </justification>
  </clause>

  <clause id="9521">
    <literal><![CDATA[
      L(x \ R(x,y * (L(y,z,u) \ y),L(y,z,u)),x,1) = a(x,L(1 / y,z,u) \ 1,L(1 / y,z,u))
    ]]></literal>
    <justification jstring="[para(1714(a,1),6602(a,1,1,2))].">
      <j1 rule="para" parents="1714 6602"/>
    </justification>
  </clause>

  <clause id="9522">
    <literal><![CDATA[
      a(x,L(1 / y,z,u) \ 1,L(1 / y,z,u)) = x \ R(x,y * (L(y,z,u) \ y),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(228,a,9521,a),flip(a)].">
      <j1 rule="hyper" parents="228 9521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9524">
    <literal><![CDATA[
      x \ R(x,y * (L(y,z,u) \ y),L(y,z,u)) = a(x,L(1 / y,z,u) \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2650,a(flip),b,9522,a),flip(a)].">
      <j1 rule="hyper" parents="63 2650 9522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9525">
    <literal><![CDATA[
      (x * (a(y \ z,y,y) \ y)) / (a(y \ z,y,y) \ 1) = (x * (1 / (z \ (z / y)))) / a(y \ z,y,y)
    ]]></literal>
    <justification jstring="[para(6859(a,1),7354(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6859 7354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9526">
    <literal><![CDATA[
      (x * L(y,y,y \ z)) / (a(y \ z,y,y) \ 1) = (x * (1 / (z \ (z / y)))) / a(y \ z,y,y)
    ]]></literal>
    <justification jstring="[para(7297(a,1),9525(a,1,1,2))].">
      <j1 rule="para" parents="7297 9525"/>
    </justification>
  </clause>

  <clause id="9527">
    <literal><![CDATA[
      (a(x \ y,x,x) \ 1) \ (z * L(x,x,x \ y)) = (z * (1 / (y \ (y / x)))) / a(x \ y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4994,a(flip),b,9526,a)].">
      <j1 rule="hyper" parents="63 4994 9526"/>
    </justification>
  </clause>

  <clause id="9528">
    <literal><![CDATA[
      a(x \ y,x,x) \ (z * (1 / (y \ (y / x)))) = (a(x \ y,x,x) \ 1) \ (z * L(x,x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(316,a,2276,a(flip),b,9527,a)].">
      <j1 rule="hyper" parents="316 2276 9527"/>
    </justification>
  </clause>

  <clause id="9529">
    <literal><![CDATA[
      a(x,y,(z * (u * L(w,v5,v6))) * a(v7,v7,z * (u * L(w,v5,v6)))) = a(x,y,L(z * (u * R(w,v5,v6)),v7,v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,7823,a(flip),b,7435,a)].">
      <j1 rule="hyper" parents="63 7823 7435"/>
    </justification>
  </clause>

  <clause id="9530">
    <literal><![CDATA[
      a(x,y,z * ((u * (w \ v5)) * ((v6 * v7) * a(u * (w \ v5),v6,v7)))) = a(x,y,z * (((u * (v5 / w)) * v6) * v7))
    ]]></literal>
    <justification jstring="[para(3150(a,1),8446(a,1,3,2,2,2))].">
      <j1 rule="para" parents="3150 8446"/>
    </justification>
  </clause>

  <clause id="9531">
    <literal><![CDATA[
      (x * a(y,z,u)) * L(y \ L(y,w,v5),v6,v7) = a(y,z,u) * (x * L(y \ L(y,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(2273(a,1),8714(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2273 8714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9532">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),L(x \ L(x,u,w),v5,v6) \ (L(x \ L(x,u,w),v5,v6) \ v7)) \ v7) = ((L(x \ L(x,u,w),v5,v6) \ (L(x \ L(x,u,w),v5,v6) \ v7)) * a(x,y,z)) * L(x \ L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(2899(a,2),9531(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2899 9531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9533">
    <literal><![CDATA[
      R((x \ L(x,y,z)) \ u,x \ L(x,y,z),L(x,y,z) \ 1) = (u * (L(x,y,z) \ 1)) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(2095(a,1),9506(a,1,2))].">
      <j1 rule="para" parents="2095 9506"/>
    </justification>
  </clause>

  <clause id="9534">
    <literal><![CDATA[
      R((x \ L(x,y,z)) \ u,x \ L(x,y,z),L(x,y,z)) = (u * (L(x,y,z) \ 1)) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1033,a(flip),b,9533,a)].">
      <j1 rule="hyper" parents="63 1033 9533"/>
    </justification>
  </clause>

  <clause id="9535">
    <literal><![CDATA[
      K(x,y) * (a(z \ 1,z,y) * (L(y,z,z \ 1) * x)) = L(x,L(y,z,z \ 1),a(z \ 1,z,y)) * y
    ]]></literal>
    <justification jstring="[para(2408(a,1),9507(a,1,2,1))].">
      <j1 rule="para" parents="2408 9507"/>
    </justification>
  </clause>

  <clause id="9536">
    <literal><![CDATA[
      T(a(x \ 1,x,y) * (z * L(y,x,x \ 1)),K(z,y)) = L(z,L(y,x,x \ 1),a(x \ 1,x,y)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,4562,a,b,9535,a)].">
      <j1 rule="hyper" parents="63 4562 9535"/>
    </justification>
  </clause>

  <clause id="9537">
    <literal><![CDATA[
      a(x,y,L(z * (u * R(w,v5,v6)),v7,v7)) = a(x,y,L(z * (u * L(w,v5,v6)),v7,v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,5100,a(flip),b,9529,a),flip(a)].">
      <j1 rule="hyper" parents="63 5100 9529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9538">
    <literal><![CDATA[
      a(x,y,L(z * (u * L(w,v5,v6)),u * L(w,v5,v6),u * L(w,v5,v6))) = a(x,y,(u * R(w,v5,v6)) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9345,a(flip),b,9537,a),flip(a)].">
      <j1 rule="hyper" parents="63 9345 9537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9539">
    <literal><![CDATA[
      a(x,y,(z * R(u,w,v5)) \ v6) = a(x,y,(z * L(u,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,8606,a(flip),b,9538,a),flip(a)].">
      <j1 rule="hyper" parents="63 8606 9538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9540">
    <literal><![CDATA[
      a(x,y,((R(z,u,w) \ v5) * L(z,u,w)) \ v6) = a(x,y,v5 \ v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5628,a(flip),b,9539,a),flip(a)].">
      <j1 rule="hyper" parents="63 5628 9539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9541">
    <literal><![CDATA[
      a(x,y,R(z,u,w) \ v5) = a(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(182(a,1),9540(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="182 9540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9542">
    <literal><![CDATA[
      a(x,y,L(z,u,w \ 1) \ v5) = a(x,y,R(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(1033(a,1),9541(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1033 9541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9543">
    <literal><![CDATA[
      a(x,y,L(z,u,L(w \ 1,v5,v6)) \ v7) = a(x,y,R(z,u,L(w,v5,v6)) \ v7)
    ]]></literal>
    <justification jstring="[para(1713(a,1),9541(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1713 9541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9544">
    <literal><![CDATA[
      a(x,y,L(z,u,w \ 1) \ v5) = a(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,9541,a(flip),b,9542,a),flip(a)].">
      <j1 rule="hyper" parents="316 9541 9542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9545">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w \ 1),v5,v6) \ v7) = a(x,y,L(L(z,v5,v6),u,w) \ v7)
    ]]></literal>
    <justification jstring="[para(30(a,1),9544(a,1,3,1))].">
      <j1 rule="para" parents="30 9544"/>
    </justification>
  </clause>

  <clause id="9547">
    <literal><![CDATA[
      a(x,y,L(z,u,L(w \ 1,v5,v6)) \ v7) = a(x,y,L(z,u,L(w,v5,v6)) \ v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,9541,a(flip),b,9543,a),flip(a)].">
      <j1 rule="hyper" parents="316 9541 9543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9550">
    <literal><![CDATA[
      a(x,y,z * (((u * (w / v5)) * v6) * v7)) = a(x,y,z * (((u * (v5 \ w)) * v6) * v7))
    ]]></literal>
    <justification jstring="[para(8416(a,1),9530(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="8416 9530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9551">
    <literal><![CDATA[
      a(x,y,((((z * (u / w)) * v5) * v6) \ v7) * (((z * (w \ u)) * v5) * v6)) = a(x,y,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,5470,a(flip),b,9550,a),flip(a)].">
      <j1 rule="hyper" parents="63 5470 9550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9552">
    <literal><![CDATA[
      a(x,y,z * (((u * (w \ v5)) * a(u * (v5 / w),v6,v6)) * v7)) = a(x,y,z * (R(u * (v5 / w),v6,v6) * v7))
    ]]></literal>
    <justification jstring="[para(2381(a,1),9550(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="2381 9550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9553">
    <literal><![CDATA[
      a(x,y,(((z * (u \ w)) * v5) * (v6 \ v7)) * a(v6,v6 \ v7,(z * (w / u)) * v5)) = a(x,y,v6 \ (v7 * ((z * (w / u)) * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8567,a(flip),b,9551,a)].">
      <j1 rule="hyper" parents="63 8567 9551"/>
    </justification>
  </clause>

  <clause id="9554">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * T(((x \ L(x,y,z)) \ 1) \ u,w)) * (x \ L(x,y,z)) = T((x \ L(x,y,z)) * u,w)
    ]]></literal>
    <justification jstring="[para(1894(a,1),5063(a,1,1,1))].">
      <j1 rule="para" parents="1894 5063"/>
    </justification>
  </clause>

  <clause id="9555">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * T((L(x,y,z) \ x) \ u,w)) * (x \ L(x,y,z)) = T((x \ L(x,y,z)) * u,w)
    ]]></literal>
    <justification jstring="[para(1894(a,1),9554(a,1,1,2,1,1))].">
      <j1 rule="para" parents="1894 9554"/>
    </justification>
  </clause>

  <clause id="9556">
    <literal><![CDATA[
      (x * (L(x,y,z) \ T(L(x,y,z) * (x \ u),w))) * (x \ L(x,y,z)) = T((x \ L(x,y,z)) * u,w)
    ]]></literal>
    <justification jstring="[para(2113(a,1),9555(a,1,1))].">
      <j1 rule="para" parents="2113 9555"/>
    </justification>
  </clause>

  <clause id="9557">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ T((x \ L(x,y,z)) * u,w) = x * (L(x,y,z) \ T(L(x,y,z) * (x \ u),w))
    ]]></literal>
    <justification jstring="[hyper(35,a,5013,a,b,9556,a)].">
      <j1 rule="hyper" parents="35 5013 9556"/>
    </justification>
  </clause>

  <clause id="9558">
    <literal><![CDATA[
      x * K(x * (y \ L(y,z,u)),w) = y * (L(y,z,u) \ T(L(y,z,u) * (y \ x),w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5117,a(flip),b,9557,a)].">
      <j1 rule="hyper" parents="63 5117 9557"/>
    </justification>
  </clause>

  <clause id="9559">
    <literal><![CDATA[
      (x * (y * (L(z,u,w) \ z))) / ((z \ L(z,u,w)) \ 1) = (z \ L(z,u,w)) \ (x * (y * (z \ L(z,u,w))))
    ]]></literal>
    <justification jstring="[para(1894(a,1),5070(a,1,1,2,2))].">
      <j1 rule="para" parents="1894 5070"/>
    </justification>
  </clause>

  <clause id="9560">
    <literal><![CDATA[
      (x * (y * (L(z,u,w) \ z))) / (L(z,u,w) \ z) = (z \ L(z,u,w)) \ (x * (y * (z \ L(z,u,w))))
    ]]></literal>
    <justification jstring="[para(1894(a,1),9559(a,1,2))].">
      <j1 rule="para" parents="1894 9559"/>
    </justification>
  </clause>

  <clause id="9561">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ ((u / x) * (x * (x \ L(x,y,z)))) = ((L(x,y,z) \ x) \ u) * L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9415,a(flip),b,9560,a),flip(a)].">
      <j1 rule="hyper" parents="63 9415 9560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9562">
    <literal><![CDATA[
      (x * y) \ ((z \ L(z,u,w)) \ (x * (y * (z \ L(z,u,w))))) = y \ (x \ ((x * (y * (L(z,u,w) \ z))) / (L(z,u,w) \ z)))
    ]]></literal>
    <justification jstring="[para(9560(a,1),9350(a,1,2))].">
      <j1 rule="para" parents="9560 9350"/>
    </justification>
  </clause>

  <clause id="9563">
    <literal><![CDATA[
      ((L(x,y,z) \ x) \ u) * L(L(x,y,z) \ x,x,u) = (x \ L(x,y,z)) \ ((u / x) * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),9561(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9566">
    <literal><![CDATA[
      T(x * K(y * (a(z,u,w) * x),v5),y * a(z,u,w)) = (y * a(z,u,w)) \ T((a(z,u,w) * y) * T(x,y),v5)
    ]]></literal>
    <justification jstring="[para(3552(a,1),5350(a,1,1,2))].">
      <j1 rule="para" parents="3552 5350"/>
    </justification>
  </clause>

  <clause id="9567">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((L(x \ L(x,y,z),u,w) \ 1) * x) = (L(x * L(x,y,z),u,w) \ (x * L(x,y,z))) * x
    ]]></literal>
    <justification jstring="[para(9084(a,1),6157(a,2,1))].">
      <j1 rule="para" parents="9084 6157"/>
    </justification>
  </clause>

  <clause id="9568">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * R(x,x \ L(x,y,z),u)) = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7764,a(flip),b,6162,a),flip(a)].">
      <j1 rule="hyper" parents="63 7764 6162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9569">
    <literal><![CDATA[
      ((x * ((x * y) \ y)) \ x) \ T(x,x * ((x * y) \ y)) = T((x * (x * ((x * y) \ y))) / x,y \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3670,a(flip),b,6278,a),flip(a)].">
      <j1 rule="hyper" parents="63 3670 6278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9570">
    <literal><![CDATA[
      ((x * ((x * y) \ y)) \ x) \ T(x,x * ((x * y) \ y)) = T((x * (x * ((x * y) \ y))) / x,T(x,y))
    ]]></literal>
    <justification jstring="[para(22(a,2),9569(a,2,2))].">
      <j1 rule="para" parents="22 9569"/>
    </justification>
  </clause>

  <clause id="9571">
    <literal><![CDATA[
      ((x * ((x * y) \ y)) \ x) \ T(x,x * ((x * y) \ y)) = T(x * ((x * y) \ y),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,4021,a(flip),b,9570,a),flip(a)].">
      <j1 rule="hyper" parents="316 4021 9570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9572">
    <literal><![CDATA[
      ((x * y) / (z * z)) \ L(x * (y / (z * z)),u,w) = x * (y * L(y \ (x \ 1),u,w))
    ]]></literal>
    <justification jstring="[para(7602(a,1),6297(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7602 6297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9573">
    <literal><![CDATA[
      ((x * y) / (z * z)) \ L(x * (y / (z * z)),u,w) = (x * y) \ L(x * y,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,1494,a(flip),b,9572,a),flip(a)].">
      <j1 rule="hyper" parents="316 1494 9572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9575">
    <literal><![CDATA[
      (x * (y / (z * z))) \ L(x * (y / (z * z)),u,w) = (x * y) \ L(x * y,u,w)
    ]]></literal>
    <justification jstring="[para(683(a,1),9573(a,1,1))].">
      <j1 rule="para" parents="683 9573"/>
    </justification>
  </clause>

  <clause id="9576">
    <literal><![CDATA[
      L(x \ (y * L(y \ x,z,u)),x,x) = (x * y) \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9383,a(flip),b,9575,a)].">
      <j1 rule="hyper" parents="63 9383 9575"/>
    </justification>
  </clause>

  <clause id="9578">
    <literal><![CDATA[
      L(x \ (y * L(y \ x,z,u)),x,x) = (y * x) \ L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4877,a,b,9576,a),flip(a)].">
      <j1 rule="hyper" parents="316 4877 9576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9579">
    <literal><![CDATA[
      (L(x * (y \ 1),z,u) * ((x * (y \ 1)) \ (x * y))) \ (x * y) = (x * y) / ((y * L(y \ x,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(992(a,1),6626(a,2,2))].">
      <j1 rule="para" parents="992 6626"/>
    </justification>
  </clause>

  <clause id="9580">
    <literal><![CDATA[
      (L(x * (y \ 1),z,u) * (y * y)) \ (x * y) = (x * y) / ((y * L(y \ x,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(561(a,1),9579(a,1,1,2))].">
      <j1 rule="para" parents="561 9579"/>
    </justification>
  </clause>

  <clause id="9582">
    <literal><![CDATA[
      (x * y) / ((y * L(y \ x,z,u)) * y) = ((y * L(y \ x,z,u)) * y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(992(a,1),9580(a,1,1)),flip(a)].">
      <j1 rule="para" parents="992 9580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9583">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) \ (x * (y \ 1)) = ((y * L(y \ x,z,u)) * y) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1878,a,b,9582,a)].">
      <j1 rule="hyper" parents="63 1878 9582"/>
    </justification>
  </clause>

  <clause id="9584">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) \ (x * (y \ 1)) = L(x * y,z,u) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1348(a,1),9583(a,2,1))].">
      <j1 rule="para" parents="1348 9583"/>
    </justification>
  </clause>

  <clause id="9585">
    <literal><![CDATA[
      L((x \ 1) * y,z,u) \ ((x \ 1) * y) = L(y * x,z,u) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6408,a,b,9584,a)].">
      <j1 rule="hyper" parents="63 6408 9584"/>
    </justification>
  </clause>

  <clause id="9586">
    <literal><![CDATA[
      L((1 / x) * y,z,u) \ ((1 / x) * y) = L(y * x,z,u) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8969,a,b,9585,a)].">
      <j1 rule="hyper" parents="63 8969 9585"/>
    </justification>
  </clause>

  <clause id="9587">
    <literal><![CDATA[
      a(x,y,((L(z * u,w,v5) \ (z * u)) * (z * u)) * v6) = a(x,y,L((u \ 1) * z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(9585(a,1),6106(a,1,3,1,1))].">
      <j1 rule="para" parents="9585 6106"/>
    </justification>
  </clause>

  <clause id="9588">
    <literal><![CDATA[
      L((1 / x) * y,z,u) \ ((1 / x) * y) = ((y * x) \ L(y * x,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,1894,a,b,9586,a),flip(a)].">
      <j1 rule="hyper" parents="316 1894 9586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9589">
    <literal><![CDATA[
      ((x \ 1) * y) \ L((x \ 1) * y,z,u) = (y * x) \ L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(39,a,8967,a,b,9588,a(flip))].">
      <j1 rule="hyper" parents="39 8967 9588"/>
    </justification>
  </clause>

  <clause id="9590">
    <literal><![CDATA[
      (x * (y \ 1)) \ L(x * (y \ 1),z,u) = (x * y) \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4877,a,b,9589,a)].">
      <j1 rule="hyper" parents="63 4877 9589"/>
    </justification>
  </clause>

  <clause id="9592">
    <literal><![CDATA[
      (x * (x * y)) \ L(x * (x * y),z,u) = (1 / (x * y)) * (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8965,a(flip),b,9589,a),flip(a)].">
      <j1 rule="hyper" parents="63 8965 9589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9593">
    <literal><![CDATA[
      (((x \ (y * ((x \ y) \ 1))) \ 1) * y) \ L(((x \ (y * ((x \ y) \ 1))) \ 1) * y,z,u) = (x * (1 / (y \ x))) \ L(y * (x \ (y * ((x \ y) \ 1))),z,u)
    ]]></literal>
    <justification jstring="[para(7438(a,1),9589(a,2,1))].">
      <j1 rule="para" parents="7438 9589"/>
    </justification>
  </clause>

  <clause id="9594">
    <literal><![CDATA[
      (((x * y) \ L(x * y,z,u)) * w) * a((y \ 1) * x,((y \ 1) * x) \ L((y \ 1) * x,z,u),w) = ((y \ 1) * x) \ (L((y \ 1) * x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(9589(a,1),8437(a,1,1,1))].">
      <j1 rule="para" parents="9589 8437"/>
    </justification>
  </clause>

  <clause id="9597">
    <literal><![CDATA[
      (((x \ 1) \ y) * x) \ L(((x \ 1) \ y) * x,z,u) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8968,a(flip),b,9590,a),flip(a)].">
      <j1 rule="hyper" parents="63 8968 9590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9598">
    <literal><![CDATA[
      a(x,y,(L(1 / (z * u),w,v5) \ 1) * v6) = a(x,y,L((u \ 1) * z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(6592(a,2),9587(a,1,3,1))].">
      <j1 rule="para" parents="6592 9587"/>
    </justification>
  </clause>

  <clause id="9599">
    <literal><![CDATA[
      a(x,y,L(1 / (z * u),w,v5) * v6) = a(x,y,L((u \ 1) * z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5564,a(flip),b,9598,a)].">
      <j1 rule="hyper" parents="63 5564 9598"/>
    </justification>
  </clause>

  <clause id="9600">
    <literal><![CDATA[
      a(x,y,L((z * u) \ 1,w,v5) * v6) = a(x,y,L((u \ 1) * z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5562,a(flip),b,9599,a)].">
      <j1 rule="hyper" parents="63 5562 9599"/>
    </justification>
  </clause>

  <clause id="9601">
    <literal><![CDATA[
      a(x,y,L((z \ 1) * u,w,v5) * v6) = a(x,y,L(u * z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5989,a(flip),b,9600,a),flip(a)].">
      <j1 rule="hyper" parents="63 5989 9600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9602">
    <literal><![CDATA[
      a(x,y,z * L(u * (w \ 1),v5,v6)) = a(x,y,L(u * w,v5,v6) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5654,a(flip),b,9601,a)].">
      <j1 rule="hyper" parents="63 5654 9601"/>
    </justification>
  </clause>

  <clause id="9603">
    <literal><![CDATA[
      a(x,y,L(z * (u \ 1),w,v5) * v6) = a(x,y,L(z * u,w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,9602,a)].">
      <j1 rule="hyper" parents="63 5469 9602"/>
    </justification>
  </clause>

  <clause id="9604">
    <literal><![CDATA[
      a(x,y,L(R(z,u,w) \ z,v5,v6) * v7) = a(x,y,L(z * R(z,u,w),v5,v6) * v7)
    ]]></literal>
    <justification jstring="[para(1171(a,1),9603(a,1,3,1,1))].">
      <j1 rule="para" parents="1171 9603"/>
    </justification>
  </clause>

  <clause id="9606">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * ((L(x,y,z) \ x) \ v5) = L(x \ L(x,y,z),u,w) * ((x \ L(x,y,z)) \ v5)
    ]]></literal>
    <justification jstring="[para(1894(a,1),7082(a,1,2,1))].">
      <j1 rule="para" parents="1894 7082"/>
    </justification>
  </clause>

  <clause id="9607">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * ((L(x,y,z) \ x) \ v5) = ((x \ L(x,y,z)) \ v5) * L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,5022,a(flip),b,9606,a),flip(a)].">
      <j1 rule="hyper" parents="316 5022 9606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9608">
    <literal><![CDATA[
      ((x * (L(y,z,u) \ y)) / (1 / L(y,z,u))) * (1 / y) = (1 / y) * L((1 / y) \ x,1 / y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9210(a,1),7094(a,2,2))].">
      <j1 rule="para" parents="9210 7094"/>
    </justification>
  </clause>

  <clause id="9609">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(L(x,y,z) \ x,u,w) \ v5) = (x \ L(x,y,z)) * (L(x \ L(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(5076(a,1),7190(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5076 7190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9615">
    <literal><![CDATA[
      (x * (L(x,y,y) \ z)) \ (a(y,y,x) * z) = x \ ((a(y,y,x) * z) / (L(x,y,y) \ z))
    ]]></literal>
    <justification jstring="[para(4951(a,1),7223(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4951 7223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9616">
    <literal><![CDATA[
      x \ (R(x,y,z) * L(R(x,y,z) \ x,u,w)) = x * (R(x,y,z) \ L(x \ R(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(34,a,7656,a,b,7659,a),flip(a)].">
      <j1 rule="hyper" parents="34 7656 7659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9617">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) * L(x \ R(x,y,z),u,w) = x * (R(x,y,z) \ L(x \ R(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,2664,a,b,9616,a)].">
      <j1 rule="hyper" parents="63 2664 9616"/>
    </justification>
  </clause>

  <clause id="9618">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x \ (R(x,y,z) * L(R(x,y,z) \ x,u,w))) = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(9616(a,2),1255(a,1,2))].">
      <j1 rule="para" parents="9616 1255"/>
    </justification>
  </clause>

  <clause id="9619">
    <literal><![CDATA[
      (R(x,y,z) \ x) * L(x \ R(x,y,z),u,w) = x * (R(x,y,z) \ L(x \ R(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7653,a(flip),b,9617,a)].">
      <j1 rule="hyper" parents="63 7653 9617"/>
    </justification>
  </clause>

  <clause id="9620">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * u) \ (x \ R(x,y,z)) = (x \ R(x,y,z)) \ (u \ (x \ R(x,y,z)))
    ]]></literal>
    <justification jstring="[para(6812(a,1),8167(a,1,1,2))].">
      <j1 rule="para" parents="6812 8167"/>
    </justification>
  </clause>

  <clause id="9621">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * (u \ K(u * (x \ R(x,y,z)),u \ 1))) \ (x \ R(x,y,z)) = (x \ R(x,y,z)) \ ((x \ R(x,y,z)) / (u \ 1))
    ]]></literal>
    <justification jstring="[para(4206(a,1),9620(a,2,2))].">
      <j1 rule="para" parents="4206 9620"/>
    </justification>
  </clause>

  <clause id="9622">
    <literal><![CDATA[
      (x * ((y * z) * a(u,y,z))) \ (x * ((u * y) * z)) = L(T(u,y * z),(y * z) * a(u,y,z),x)
    ]]></literal>
    <justification jstring="[para(5243(a,1),8445(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5243 8445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9624">
    <literal><![CDATA[
      L(x * a(y,x,L(z,u,w) \ z),L(z,u,w) \ z,y) = L(x,y,L(z,u,w) \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,9517,a(flip),b,8633,a),flip(a)].">
      <j1 rule="hyper" parents="316 9517 8633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9625">
    <literal><![CDATA[
      L(x * a(y,x,z * L(z,u,w)),L(z,u,w) \ z,y) = L(x,y,L(z,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(2652(a,1),9624(a,1,1,2))].">
      <j1 rule="para" parents="2652 9624"/>
    </justification>
  </clause>

  <clause id="9626">
    <literal><![CDATA[
      L(x * a(y,x,z * L(z,u,w)),L(z,u,w) \ z,y \ 1) = L(x,y \ 1,L(z,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(8935(a,1),9625(a,1,1,2))].">
      <j1 rule="para" parents="8935 9625"/>
    </justification>
  </clause>

  <clause id="9627">
    <literal><![CDATA[
      L(x * 1,L(y,z,u) \ y,y \ 1) = L(x,y \ 1,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(5720(a,1),9626(a,1,1,2))].">
      <j1 rule="para" parents="5720 9626"/>
    </justification>
  </clause>

  <clause id="9628">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,y \ 1) = L(x,y \ 1,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(8(a,1),9627(a,1,1))].">
      <j1 rule="para" parents="8 9627"/>
    </justification>
  </clause>

  <clause id="9629">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,x \ 1,L(x,y,z) \ x) = (L(x,y,z) \ 1) \ ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6735,a(flip),b,9628,a),flip(a)].">
      <j1 rule="hyper" parents="63 6735 9628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9630">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,x,x \ L(x,y,z)) = (L(x,y,z) \ 1) \ ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8932,a(flip),b,9629,a)].">
      <j1 rule="hyper" parents="63 8932 9629"/>
    </justification>
  </clause>

  <clause id="9631">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ (x * u) = (L(x,y,z) \ 1) \ ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9217,a(flip),b,9630,a)].">
      <j1 rule="hyper" parents="63 9217 9630"/>
    </justification>
  </clause>

  <clause id="9632">
    <literal><![CDATA[
      L(a(x,y,z \ L(z,u,w)) \ y,x,z \ L(z,u,w)) = L(y,z \ L(z,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,9305,a(flip),b,8644,a),flip(a)].">
      <j1 rule="hyper" parents="316 9305 8644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9633">
    <literal><![CDATA[
      L(a(x,y,z * L(z,u,w)) \ y,x,z \ L(z,u,w)) = L(y,z \ L(z,u,w),x)
    ]]></literal>
    <justification jstring="[para(5566(a,1),9632(a,1,1,1))].">
      <j1 rule="para" parents="5566 9632"/>
    </justification>
  </clause>

  <clause id="9634">
    <literal><![CDATA[
      (L(a(x,y,z) \ 1,u,w) * w) * a(u,w,L(a(x,y,z),u,w)) = u \ (w * (T(u,w) * (a(x,y,z) \ 1)))
    ]]></literal>
    <justification jstring="[para(2655(a,1),8676(a,1,2))].">
      <j1 rule="para" parents="2655 8676"/>
    </justification>
  </clause>

  <clause id="9635">
    <literal><![CDATA[
      (L(a(x,y,z) \ 1,u,w) * w) * a(u,w,L(a(x,y,z),u,w)) = u \ (w * T(u * (a(x,y,z) \ 1),w))
    ]]></literal>
    <justification jstring="[para(5340(a,2),9634(a,2,2,2))].">
      <j1 rule="para" parents="5340 9634"/>
    </justification>
  </clause>

  <clause id="9636">
    <literal><![CDATA[
      (L(a(x,y,z) \ 1,u,w) * w) * a(u,w,L(a(x,y,z),u,w)) = u \ ((u * (a(x,y,z) \ 1)) * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,237,a(flip),b,9635,a),flip(a)].">
      <j1 rule="hyper" parents="316 237 9635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9637">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * (w * a(u,w,L(a(x,y,z),u,w))) = u \ ((u * (a(x,y,z) \ 1)) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9087,a(flip),b,9636,a)].">
      <j1 rule="hyper" parents="63 9087 9636"/>
    </justification>
  </clause>

  <clause id="9638">
    <literal><![CDATA[
      a(x,y,(z * T(L(u,z,w),w)) \ (z * R(T(u,w * z),w,z))) = a(x,y,a(w,w \ (L(u,z,w) * w),z))
    ]]></literal>
    <justification jstring="[para(22(a,2),8702(a,1,3,1,2))].">
      <j1 rule="para" parents="22 8702"/>
    </justification>
  </clause>

  <clause id="9639">
    <literal><![CDATA[
      a(x,y,(z * L(T(u,w),z,w)) \ (z * R(T(u,w * z),w,z))) = a(x,y,a(w,w \ (L(u,z,w) * w),z))
    ]]></literal>
    <justification jstring="[para(25(a,2),9638(a,1,3,1,2))].">
      <j1 rule="para" parents="25 9638"/>
    </justification>
  </clause>

  <clause id="9640">
    <literal><![CDATA[
      a(L(x,y,y) \ z,a(y,y,x),L(x,y,y)) = (((z / L(x,y,y)) * x) / a(y,y,x)) \ z
    ]]></literal>
    <justification jstring="[para(4953(a,1),8985(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4953 8985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9641">
    <literal><![CDATA[
      a(L(x,y,y) \ z,a(y,y,x),L(x,y,y)) = ((x * (L(x,y,y) \ z)) / a(y,y,x)) \ z
    ]]></literal>
    <justification jstring="[para(4327(a,1),9640(a,2,1,1))].">
      <j1 rule="para" parents="4327 9640"/>
    </justification>
  </clause>

  <clause id="9642">
    <literal><![CDATA[
      a(L(x,y,y) \ z,a(y,y,x),L(x,y,y)) = (a(y,y,x) \ (x * (L(x,y,y) \ z))) \ z
    ]]></literal>
    <justification jstring="[para(2276(a,1),9641(a,2,1))].">
      <j1 rule="para" parents="2276 9641"/>
    </justification>
  </clause>

  <clause id="9643">
    <literal><![CDATA[
      a(L(x,y,y) \ z,a(y,y,x),L(x,y,y)) = (x * (a(y,y,x) \ (L(x,y,y) \ z))) \ z
    ]]></literal>
    <justification jstring="[para(6893(a,1),9642(a,2,1))].">
      <j1 rule="para" parents="6893 9642"/>
    </justification>
  </clause>

  <clause id="9644">
    <literal><![CDATA[
      T(x * K(y * x,z),y * a(u,w,v5)) = (y * a(u,w,v5)) \ T((a(u,w,v5) * y) * T(x,y),z)
    ]]></literal>
    <justification jstring="[para(6634(a,1),9566(a,1,1,2))].">
      <j1 rule="para" parents="6634 9566"/>
    </justification>
  </clause>

  <clause id="9645">
    <literal><![CDATA[
      T(x * K(y * x,z),y) = (y * a(u,w,v5)) \ T((a(u,w,v5) * y) * T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5243,a(flip),b,9644,a)].">
      <j1 rule="hyper" parents="63 5243 9644"/>
    </justification>
  </clause>

  <clause id="9648">
    <literal><![CDATA[
      (x * a(y,z,u)) \ T((a(y,z,u) * x) * T(w,x),v5) = x \ T(w * x,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3648,a(flip),b,9645,a),flip(a)].">
      <j1 rule="hyper" parents="63 3648 9645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9649">
    <literal><![CDATA[
      (x * a(y,z,u)) \ T(w * (x * a(y,z,u)),v5) = x \ T(w * x,v5)
    ]]></literal>
    <justification jstring="[para(5253(a,1),9648(a,1,2,1))].">
      <j1 rule="para" parents="5253 9648"/>
    </justification>
  </clause>

  <clause id="9650">
    <literal><![CDATA[
      (x * (a(y,z,u) * a(y,z,u))) * (a(y,z,u) \ T(w * a(y,z,u),x)) = (w * (a(y,z,u) * a(y,z,u))) * x
    ]]></literal>
    <justification jstring="[para(9649(a,1),9274(a,1,2))].">
      <j1 rule="para" parents="9649 9274"/>
    </justification>
  </clause>

  <clause id="9651">
    <literal><![CDATA[
      (L(x * L(x,y,z),u,w) \ (x * L(x,y,z))) * x = (x \ L(x,y,z)) * (L(x \ L(x,y,z),u,w) \ x)
    ]]></literal>
    <justification jstring="[para(7064(a,1),9567(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7064 9567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9652">
    <literal><![CDATA[
      x \ ((x \ L(x,y,z)) * (L(x \ L(x,y,z),u,w) \ x)) = L(x * L(x,y,z),u,w) \ (x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,6532,a,b,9651,a)].">
      <j1 rule="hyper" parents="35 6532 9651"/>
    </justification>
  </clause>

  <clause id="9653">
    <literal><![CDATA[
      (x * L(x \ L(x,y,z),u,w)) \ L(x,y,z) = L(x * L(x,y,z),u,w) \ (x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9169,a(flip),b,9652,a)].">
      <j1 rule="hyper" parents="63 9169 9652"/>
    </justification>
  </clause>

  <clause id="9658">
    <literal><![CDATA[
      ((x * (L(y,z,u) \ y)) / (1 / L(y,z,u))) * (1 / y) = (1 / y) * L((1 / y) \ x,y \ 1,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7641(a,1),9608(a,2,2))].">
      <j1 rule="para" parents="7641 9608"/>
    </justification>
  </clause>

  <clause id="9659">
    <literal><![CDATA[
      (x * (a(y,z,u) * a(y,z,u))) * T(w,x) = (w * (a(y,z,u) * a(y,z,u))) * x
    ]]></literal>
    <justification jstring="[para(5330(a,1),9650(a,1,2))].">
      <j1 rule="para" parents="5330 9650"/>
    </justification>
  </clause>

  <clause id="9660">
    <literal><![CDATA[
      (x * (a(y,z,u) * a(y,z,u))) * w = x * (w * (a(y,z,u) * a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9512,a(flip),b,9659,a),flip(a)].">
      <j1 rule="hyper" parents="63 9512 9659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9662">
    <literal><![CDATA[
      ((x * (L(y,z,u) \ y)) / (1 / L(y,z,u))) * (1 / y) = (1 / y) * L((1 / y) \ x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9216(a,1),9658(a,2,2))].">
      <j1 rule="para" parents="9216 9658"/>
    </justification>
  </clause>

  <clause id="9663">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,x,x \ L(x,z,u)) = ((y * (L(x,z,u) \ x)) / (1 / L(x,z,u))) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(316,a,4979,a(flip),b,9662,a)].">
      <j1 rule="hyper" parents="316 4979 9662"/>
    </justification>
  </clause>

  <clause id="9664">
    <literal><![CDATA[
      ((x * (L(y,z,u) \ y)) / (1 / L(y,z,u))) * (1 / y) = y * L(y \ x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1350,a(flip),b,9663,a),flip(a)].">
      <j1 rule="hyper" parents="63 1350 9663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9665">
    <literal><![CDATA[
      L(x * (x \ y),x,x \ L(x,z,u)) = ((y * (L(x,z,u) \ x)) / (1 / L(x,z,u))) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(316,a,1558,a,b,9664,a)].">
      <j1 rule="hyper" parents="316 1558 9664"/>
    </justification>
  </clause>

  <clause id="9666">
    <literal><![CDATA[
      ((x * (L(y,z,u) \ y)) / (1 / L(y,z,u))) * (1 / y) = L(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),9665(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 9665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9668">
    <literal><![CDATA[
      T(L(x,y,z) * (L(x \ L(x,y,z),u,w) \ 1),L(x,y,z)) = L(x,u,w) * (L(L(x,u,w),y,z) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2148(a,1),4460(a,1,1,2))].">
      <j1 rule="para" parents="2148 4460"/>
    </justification>
  </clause>

  <clause id="9669">
    <literal><![CDATA[
      T(L(x,y,z) * (L(x \ L(x,y,z),u,w) \ 1),x) = L(x,u,w) * (L(L(x,u,w),y,z) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(4305,a,9668,a)].">
      <j1 rule="hyper" parents="4305 9668"/>
    </justification>
  </clause>

  <clause id="9670">
    <literal><![CDATA[
      T(L(x,y,z) * (L(x \ L(x,y,z),u,w) \ 1),x) = L(x,u,w) * (L(x \ L(x,u,w),y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,2149,a(flip),b,9669,a),flip(a)].">
      <j1 rule="hyper" parents="316 2149 9669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9672">
    <literal><![CDATA[
      L(x,y,z) * (L(x \ L(x,y,z),u,w) \ 1) = L(x,u,w) * (L(x \ L(x,u,w),y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,7817,a(flip),b,9670,a)].">
      <j1 rule="hyper" parents="63 7817 9670"/>
    </justification>
  </clause>

  <clause id="9673">
    <literal><![CDATA[
      T(((x * y) / x) * L(L(x,z,u),w,v5),L(L(x,w,v5),z,u)) = y * L(R(L(x,w,v5),y,L(L(x,w,v5),z,u)),z,u)
    ]]></literal>
    <justification jstring="[para(29(a,1),4973(a,2,2))].">
      <j1 rule="para" parents="29 4973"/>
    </justification>
  </clause>

  <clause id="9674">
    <literal><![CDATA[
      a(x,y,(z \ (1 / u)) * (w * ((u * z) \ K(u,u \ 1)))) = a(x,y,((z \ (1 / u)) * w) * ((z * u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(316,a,7418,a(flip),b,6058,a),flip(a)].">
      <j1 rule="hyper" parents="316 7418 6058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9675">
    <literal><![CDATA[
      a(x,y,(z \ (1 / u)) * (w * ((u * z) \ K(u,u \ 1)))) = a(x,y,(z * u) * ((z \ (1 / u)) * w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5529,a(flip),b,9674,a),flip(a)].">
      <j1 rule="hyper" parents="316 5529 9674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9676">
    <literal><![CDATA[
      a(x,y,L(z,((u \ w) * u) * u,u \ w) * ((w * u) * (u \ w))) = a(x,y,(w / u) * ((((u \ w) * u) * u) * z))
    ]]></literal>
    <justification jstring="[para(1586(a,1),6288(a,1,3,1))].">
      <j1 rule="para" parents="1586 6288"/>
    </justification>
  </clause>

  <clause id="9677">
    <literal><![CDATA[
      L((1 / x) * y,z,a(a(u,w,u) / x,a(u,w,u) / x,a(u,w,u) \ y)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(5428(a,1),7403(a,1,1))].">
      <j1 rule="para" parents="5428 7403"/>
    </justification>
  </clause>

  <clause id="9679">
    <literal><![CDATA[
      L((1 / x) * y,z,a(a(u,w,u) / x,a(u,w,u) / x,y)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(8074(a,1),9677(a,1,3))].">
      <j1 rule="para" parents="8074 9677"/>
    </justification>
  </clause>

  <clause id="9681">
    <literal><![CDATA[
      (x * L(y,z,y)) \ (L(a(u,w,v5),y,x) \ (x * L(y,z,y))) = (x * (y * a(u,w,v5))) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,8321,a(flip),b,8317,a),flip(a)].">
      <j1 rule="hyper" parents="316 8321 8317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9683">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) \ w) * ((u / (z \ 1)) \ (u * w))) = a(x,y,((z \ u) \ (u * w)) \ (L(z,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(1449(a,1),8343(a,1,3,2))].">
      <j1 rule="para" parents="1449 8343"/>
    </justification>
  </clause>

  <clause id="9684">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) \ w) * (((z \ 1) \ u) \ (u * w))) = a(x,y,((z \ u) \ (u * w)) \ (L(z,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5643,a(flip),b,9683,a)].">
      <j1 rule="hyper" parents="63 5643 9683"/>
    </justification>
  </clause>

  <clause id="9685">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * v5) * (v6 * (a(v6,v7,R(z,u,w) * v5) \ v7))) = a(x,y,v6 * (v7 * (R(z,u,w) * v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5472,a(flip),b,8581,a),flip(a)].">
      <j1 rule="hyper" parents="316 5472 8581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9686">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * v5) * (v6 * (a(v6,v7,L(z,u,w) * v5) \ v7))) = a(x,y,v6 * (v7 * (R(z,u,w) * v5)))
    ]]></literal>
    <justification jstring="[para(7376(a,1),9685(a,1,3,2,2,1))].">
      <j1 rule="para" parents="7376 9685"/>
    </justification>
  </clause>

  <clause id="9687">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) * v5,v6,v7) * (v7 * v6)) = a(x,y,v7 * (v6 * (R(z,u,w) * v5)))
    ]]></literal>
    <justification jstring="[para(8534(a,1),9686(a,1,3))].">
      <j1 rule="para" parents="8534 9686"/>
    </justification>
  </clause>

  <clause id="9688">
    <literal><![CDATA[
      a(x,y,z * (u * (R(w,v5,v6) * v7))) = a(x,y,z * (u * (L(w,v5,v6) * v7)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5472,a(flip),b,9687,a),flip(a)].">
      <j1 rule="hyper" parents="63 5472 9687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9689">
    <literal><![CDATA[
      a(x,y,z * (u \ ((u * u) * (R(w,v5,v6) * v7)))) = a(x,y,z * (R(u,u,R(w,v5,v6) * v7) * (L(w,v5,v6) * v7)))
    ]]></literal>
    <justification jstring="[para(1164(a,2),9688(a,1,3,2))].">
      <j1 rule="para" parents="1164 9688"/>
    </justification>
  </clause>

  <clause id="9690">
    <literal><![CDATA[
      a(x,y,z * (u * (L(w,v5,v6) * T(v7,w)))) = a(x,y,z * (u * (v7 * R(w,v5,v6))))
    ]]></literal>
    <justification jstring="[para(2842(a,1),9688(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="2842 9688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9691">
    <literal><![CDATA[
      a(x,y,z * (u * (w * R(v5,v6,v7)))) = a(x,y,z * (u * (w * L(v5,v6,v7))))
    ]]></literal>
    <justification jstring="[para(4313(a,1),9690(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="4313 9690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9692">
    <literal><![CDATA[
      a(x,y,z * (u * (w * L(v5,v6,a(v7,v8,v8))))) = a(x,y,z * (u * (w * L(v5,v6,a(v8,v8,v7)))))
    ]]></literal>
    <justification jstring="[para(9221(a,1),9691(a,1,3,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9221 9691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9693">
    <literal><![CDATA[
      a(x,y,z * (R(u,u,R(w,v5,v6) * v7) * (L(w,v5,v6) * v7))) = a(x,y,(u \ (R(w,v5,v6) * v7)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6370,a(flip),b,9689,a),flip(a)].">
      <j1 rule="hyper" parents="63 6370 9689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9695">
    <literal><![CDATA[
      a(x,y,L(a(z,u,(w * v5) * v6) \ u,z,v6 * (w * v5))) = a(x,y,L(u,v6 * (w * ((v7 * v7) \ v5)),z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6218,a(flip),b,8750,a)].">
      <j1 rule="hyper" parents="63 6218 8750"/>
    </justification>
  </clause>

  <clause id="9697">
    <literal><![CDATA[
      a(x,y,L(z,u * (w * ((v5 * v5) \ v6)),v7)) = a(x,y,L(z,(w * v6) * u,v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,8747,a(flip),b,9695,a),flip(a)].">
      <j1 rule="hyper" parents="63 8747 9695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9698">
    <literal><![CDATA[
      (x * (a(L(y,z,u),w,v5) * a(v5 * w,R(y,z,u),a(L(y,z,u),w,v5)))) / x = R(y,z,u) \ R(R(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(4643(a,1),8757(a,1,1,2,2,3))].">
      <j1 rule="para" parents="4643 8757"/>
    </justification>
  </clause>

  <clause id="9699">
    <literal><![CDATA[
      T(((x * y) / x) * L(L(x,z,u),w,v5),L(L(x,w,v5),z,u)) = y * L(L(R(x,y,L(L(x,w,v5),z,u)),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(29(a,1),9673(a,2,2,1))].">
      <j1 rule="para" parents="29 9673"/>
    </justification>
  </clause>

  <clause id="9700">
    <literal><![CDATA[
      x * L(L(R(y,x,L(L(y,z,u),w,v5)),z,u),w,v5) = T(L(L(y,z,u),w,v5) * x,L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(4608(a,1),9699(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4608 9699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9701">
    <literal><![CDATA[
      x * L(L(R(y,x,L(L(y,z,u),w,v5)),z,u),w,v5) = T(L(L(y,z,u),w,v5) * x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,4308,a(flip),b,9700,a),flip(a)].">
      <j1 rule="hyper" parents="316 4308 9700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9703">
    <literal><![CDATA[
      x * L(L(R(y,x,y),z,u),w,v5) = T(L(L(y,z,u),w,v5) * x,y)
    ]]></literal>
    <justification jstring="[para(5214(a,1),9701(a,1,2,1))].">
      <j1 rule="para" parents="5214 9701"/>
    </justification>
  </clause>

  <clause id="9704">
    <literal><![CDATA[
      x * T(L(L(x,y,z),u,w) * v5,x) = (x * v5) * L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(9703(a,1),1620(a,1,2))].">
      <j1 rule="para" parents="9703 1620"/>
    </justification>
  </clause>

  <clause id="9706">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * L(L(x,y,z),w,v5) = x * (L(x,y,z) \ (u * L(L(x,y,z),w,v5)))
    ]]></literal>
    <justification jstring="[para(4414(a,1),9704(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4414 9704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9707">
    <literal><![CDATA[
      L(x,y,z) * (x * (L(x,y,z) \ (u * L(L(x,y,z),w,v5)))) = L(L(x,y,z),w,v5) * (u * x)
    ]]></literal>
    <justification jstring="[para(9706(a,1),4435(a,1,2))].">
      <j1 rule="para" parents="9706 4435"/>
    </justification>
  </clause>

  <clause id="9708">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (v5 * x) = x * (v5 * L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,1128,a(flip),b,9707,a),flip(a)].">
      <j1 rule="hyper" parents="63 1128 9707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9710">
    <literal><![CDATA[
      (((x \ y) * x) * (x \ 1)) \ ((((x \ y) * x) * (x \ 1)) / z) = T((x \ 1) * y,x) \ (T((x \ 1) * y,x) / z)
    ]]></literal>
    <justification jstring="[para(1386(a,1),3317(a,2,2,1))].">
      <j1 rule="para" parents="1386 3317"/>
    </justification>
  </clause>

  <clause id="9711">
    <literal><![CDATA[
      (((x \ y) * x) * (x \ 1)) \ ((((x \ y) * x) * (x \ 1)) / z) = ((x \ 1) * y) \ (((x \ 1) * y) / z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2879,a(flip),b,9710,a),flip(a)].">
      <j1 rule="hyper" parents="316 2879 9710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9713">
    <literal><![CDATA[
      R(x \ y,x,x) \ ((((x \ y) * x) * (x \ 1)) / z) = ((x \ 1) * y) \ (((x \ 1) * y) / z)
    ]]></literal>
    <justification jstring="[para(565(a,1),9711(a,1,1))].">
      <j1 rule="para" parents="565 9711"/>
    </justification>
  </clause>

  <clause id="9714">
    <literal><![CDATA[
      R(x \ y,x,x) \ (R(x \ y,x,x) / z) = ((x \ 1) * y) \ (((x \ 1) * y) / z)
    ]]></literal>
    <justification jstring="[para(565(a,1),9713(a,1,2,1))].">
      <j1 rule="para" parents="565 9713"/>
    </justification>
  </clause>

  <clause id="9717">
    <literal><![CDATA[
      ((x * x) \ (y \ z)) * L(((x * x) \ (y \ z)) \ u,w,v5) = (y \ (z / (x * x))) * L((y \ (z / (x * x))) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(675(a,1),6295(a,2,2,1,1))].">
      <j1 rule="para" parents="675 6295"/>
    </justification>
  </clause>

  <clause id="9718">
    <literal><![CDATA[
      a(x,y,z \ (T((u * (w \ 1)) \ ((u * (w \ 1)) / v5),v5) * (u * w))) = a(x,y,z \ (T(v5,v5 \ 1) \ (u * (w \ 1))))
    ]]></literal>
    <justification jstring="[hyper(316,a,5497,a(flip),b,6358,a),flip(a)].">
      <j1 rule="hyper" parents="316 5497 6358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9719">
    <literal><![CDATA[
      (L(a(x,y,z),u \ (a(x,y,z) \ w),u) * (a(x,y,z) \ w)) \ w = w / (u * (a(x,y,z) * (u \ (a(x,y,z) \ w))))
    ]]></literal>
    <justification jstring="[para(2290(a,2),6627(a,2,2,2))].">
      <j1 rule="para" parents="2290 6627"/>
    </justification>
  </clause>

  <clause id="9720">
    <literal><![CDATA[
      (x * y) / ((R(x,y,y) * (L(y,y,x) * z)) / z) = ((R(x,y,y) * (L(y,y,x) * z)) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[para(7155(a,1),7161(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7155 7161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9721">
    <literal><![CDATA[
      (x * y) / ((R(x,y,y) * (L(y,y,x) * z)) / z) = a(L(x,y,y),L(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(316,a,7475,a(flip),b,9720,a),flip(a)].">
      <j1 rule="hyper" parents="316 7475 9720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9722">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((L(x \ L(x,y,z),u,w) \ v5) * (x \ L(x,y,z))) = L((x \ L(x,y,z)) \ 1,u,w) \ v5
    ]]></literal>
    <justification jstring="[para(1894(a,1),7185(a,1,1))].">
      <j1 rule="para" parents="1894 7185"/>
    </justification>
  </clause>

  <clause id="9723">
    <literal><![CDATA[
      (L(x \ L(x,y,z),u,w) \ v5) * (L(x,y,z) * L(x \ 1,y,z)) = L((x \ L(x,y,z)) \ 1,u,w) \ v5
    ]]></literal>
    <justification jstring="[hyper(63,a,7987,a(flip),b,9722,a)].">
      <j1 rule="hyper" parents="63 7987 9722"/>
    </justification>
  </clause>

  <clause id="9724">
    <literal><![CDATA[
      (L(x \ L(x,y,z),u,w) \ v5) * (L(x,y,z) * L(x \ 1,y,z)) = L(L(x,y,z) \ x,u,w) \ v5
    ]]></literal>
    <justification jstring="[para(1894(a,1),9723(a,2,1,1))].">
      <j1 rule="para" parents="1894 9723"/>
    </justification>
  </clause>

  <clause id="9725">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ L(x \ L(x,y,z),u,w) = L(x,y,z) * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(218,a,9724,a),flip(a)].">
      <j1 rule="hyper" parents="218 9724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9726">
    <literal><![CDATA[
      (x * a(y \ 1,y,z)) \ ((x * z) / (a(y \ 1,y,z) \ z)) = (a(y \ 1,y,z) * (x * L(z,y,y \ 1))) \ (x * z)
    ]]></literal>
    <justification jstring="[para(6882(a,1),7222(a,2,1))].">
      <j1 rule="para" parents="6882 7222"/>
    </justification>
  </clause>

  <clause id="9731">
    <literal><![CDATA[
      L(R((x \ (y * x)) \ (y * x),z,u),w,v5) * (R(x,z,u) \ (y * x)) = L(R(x,z,u),w,v5) * (R(x,z,u) \ (x * y))
    ]]></literal>
    <justification jstring="[para(3653(a,2),7857(a,1,1,1))].">
      <j1 rule="para" parents="3653 7857"/>
    </justification>
  </clause>

  <clause id="9732">
    <literal><![CDATA[
      a(x,(y \ 1) * z,((y \ 1) * z) * L((y \ 1) * z,u,w)) = a(x,(z * y) \ L(z * y,u,w),y * z)
    ]]></literal>
    <justification jstring="[para(9589(a,1),8239(a,2,2))].">
      <j1 rule="para" parents="9589 8239"/>
    </justification>
  </clause>

  <clause id="9733">
    <literal><![CDATA[
      a(x,(y \ 1) * z,((y \ 1) * z) * L((y \ 1) * z,u,w)) = a(x,z * y,(z * y) * L(z * y,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,8237,a(flip),b,9732,a),flip(a)].">
      <j1 rule="hyper" parents="316 8237 9732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9734">
    <literal><![CDATA[
      a(x,y,(z * ((L(u * w,v5,v6) \ (u * w)) * (u * w))) * v7) = a(x,y,v7 * (z * L((w \ 1) * u,v5,v6)))
    ]]></literal>
    <justification jstring="[para(9585(a,1),8286(a,1,3,1,2,1))].">
      <j1 rule="para" parents="9585 8286"/>
    </justification>
  </clause>

  <clause id="9735">
    <literal><![CDATA[
      a(x,y,(z * (L(1 / (u * w),v5,v6) \ 1)) * v7) = a(x,y,v7 * (z * L((w \ 1) * u,v5,v6)))
    ]]></literal>
    <justification jstring="[para(6592(a,2),9734(a,1,3,1,2))].">
      <j1 rule="para" parents="6592 9734"/>
    </justification>
  </clause>

  <clause id="9736">
    <literal><![CDATA[
      a(x,y,z * (u * L(1 / (w * v5),v6,v7))) = a(x,y,z * (u * L((v5 \ 1) * w,v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5896,a(flip),b,9735,a)].">
      <j1 rule="hyper" parents="63 5896 9735"/>
    </justification>
  </clause>

  <clause id="9737">
    <literal><![CDATA[
      a(x,y,z * (u * L((w * v5) \ 1,v6,v7))) = a(x,y,z * (u * L((v5 \ 1) * w,v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5705,a(flip),b,9736,a)].">
      <j1 rule="hyper" parents="63 5705 9736"/>
    </justification>
  </clause>

  <clause id="9738">
    <literal><![CDATA[
      a(x,y,z * (u * L((w \ 1) * v5,v6,v7))) = a(x,y,z * (u * L(v5 * w,v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8283,a(flip),b,9737,a),flip(a)].">
      <j1 rule="hyper" parents="63 8283 9737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9739">
    <literal><![CDATA[
      L(x * a(y \ L(y,z,u),x,w),w,y \ L(y,z,u)) = (w * (y \ L(y,z,u))) \ (w * (x * (y \ L(y,z,u))))
    ]]></literal>
    <justification jstring="[para(6649(a,1),8629(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6649 8629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9740">
    <literal><![CDATA[
      L(x * a(y \ L(y,z,u),x,w),w,y \ L(y,z,u)) = L(T(x,y \ L(y,z,u)),y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,247,a(flip),b,9739,a),flip(a)].">
      <j1 rule="hyper" parents="316 247 9739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9741">
    <literal><![CDATA[
      L(x * a(y \ L(y,z,u),x,w),w,y \ L(y,z,u)) = L(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(4992(a,1),9740(a,2,1))].">
      <j1 rule="para" parents="4992 9740"/>
    </justification>
  </clause>

  <clause id="9742">
    <literal><![CDATA[
      (x \ (y / (z * z))) * L((x \ (y / (z * z))) \ u,w,v5) = (x \ y) * L((x \ y) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,7602,a(flip),b,9717,a),flip(a)].">
      <j1 rule="hyper" parents="63 7602 9717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9744">
    <literal><![CDATA[
      T(x / y,y \ 1) * L(((y \ 1) \ (x / (y * y))) \ z,u,w) = ((y \ 1) \ x) * L(((y \ 1) \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(579(a,1),9742(a,1,1))].">
      <j1 rule="para" parents="579 9742"/>
    </justification>
  </clause>

  <clause id="9745">
    <literal><![CDATA[
      T(x / y,y \ 1) * L(T(x / y,y \ 1) \ z,u,w) = ((y \ 1) \ x) * L(((y \ 1) \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(579(a,1),9744(a,1,2,1,1))].">
      <j1 rule="para" parents="579 9744"/>
    </justification>
  </clause>

  <clause id="9746">
    <literal><![CDATA[
      ((x \ 1) \ y) * L(((x \ 1) \ y) \ z,u,w) = (y / x) * L((y / x) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,4868,a(flip),b,9745,a),flip(a)].">
      <j1 rule="hyper" parents="63 4868 9745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9748">
    <literal><![CDATA[
      ((x \ 1) \ y) * L(((x \ 1) \ y) \ z,u,w) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,4979,a(flip),b,9746,a),flip(a)].">
      <j1 rule="hyper" parents="316 4979 9746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9749">
    <literal><![CDATA[
      ((x \ 1) \ y) * L(((x \ 1) \ y) \ x,z,u) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,6834,a(flip),b,9748,a),flip(a)].">
      <j1 rule="hyper" parents="316 6834 9748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9750">
    <literal><![CDATA[
      ((x \ 1) \ y) * L(((x \ 1) \ y) \ x,z,u) = (x \ (y \ L(y,z,u))) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(316,a,6839,a,b,9749,a),flip(a)].">
      <j1 rule="hyper" parents="316 6839 9749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9751">
    <literal><![CDATA[
      (x / (y \ 1)) \ L(x,z,u) = y \ (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,6294,a(flip),b,9750,a(flip))].">
      <j1 rule="hyper" parents="35 6294 9750"/>
    </justification>
  </clause>

  <clause id="9752">
    <literal><![CDATA[
      (1 / x) \ (y \ L(y,z,u)) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(83(a,1),9751(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="83 9751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9753">
    <literal><![CDATA[
      (x / T(y,y \ 1)) \ L(x,z,u) = (y \ 1) \ (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[para(115(a,2),9751(a,1,1,2))].">
      <j1 rule="para" parents="115 9751"/>
    </justification>
  </clause>

  <clause id="9754">
    <literal><![CDATA[
      x \ ((y \ (x \ 1)) \ L(y \ (x \ 1),z,u)) = ((y \ x) / x) \ L(y \ (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(590(a,1),9751(a,1,1)),flip(a)].">
      <j1 rule="para" parents="590 9751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9755">
    <literal><![CDATA[
      (x \ (y \ L(y,z,u))) \ L(y,z,u) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(9751(a,1),6835(a,1,1))].">
      <j1 rule="para" parents="9751 6835"/>
    </justification>
  </clause>

  <clause id="9756">
    <literal><![CDATA[
      L(x,x,y \ L(y,z,u)) * (y \ L(y,z,u)) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6841,a,b,9752,a)].">
      <j1 rule="hyper" parents="63 6841 9752"/>
    </justification>
  </clause>

  <clause id="9758">
    <literal><![CDATA[
      ((x / y) \ L(x,z,u)) * (y \ 1) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,9752,a(flip),b,6660,a)].">
      <j1 rule="hyper" parents="138 9752 6660"/>
    </justification>
  </clause>

  <clause id="9759">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) \ ((y / x) \ L(y,z,u)) = a(x \ 1,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9752(a,1),8480(a,1,2))].">
      <j1 rule="para" parents="9752 8480"/>
    </justification>
  </clause>

  <clause id="9760">
    <literal><![CDATA[
      (1 / x) * ((y \ L(y,z,u)) \ ((y / x) \ L(y,z,u))) = a(1 / x,(1 / x) \ 1,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(9752(a,1),9063(a,1,2,2))].">
      <j1 rule="para" parents="9752 9063"/>
    </justification>
  </clause>

  <clause id="9761">
    <literal><![CDATA[
      (x \ L(y,z,u)) * ((x \ y) \ 1) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(80(a,1),9758(a,1,1,1))].">
      <j1 rule="para" parents="80 9758"/>
    </justification>
  </clause>

  <clause id="9762">
    <literal><![CDATA[
      ((L(x,y,z) / u) \ x) \ 1 = u \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,9761,a),flip(a)].">
      <j1 rule="hyper" parents="335 9761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9763">
    <literal><![CDATA[
      ((x \ L(x,y,z)) / u) \ 1 = (L(x,y,z) / u) \ x
    ]]></literal>
    <justification jstring="[hyper(39,a,6659,a,b,9762,a)].">
      <j1 rule="hyper" parents="39 6659 9762"/>
    </justification>
  </clause>

  <clause id="9764">
    <literal><![CDATA[
      1 / ((L(x,y,z) / u) \ x) = (x \ L(x,y,z)) / u
    ]]></literal>
    <justification jstring="[hyper(210,a,9763,a)].">
      <j1 rule="hyper" parents="210 9763"/>
    </justification>
  </clause>

  <clause id="9765">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u \ L(u,w,v5)) = (a(x,y,z) \ u) \ L(u,w,v5)
    ]]></literal>
    <justification jstring="[para(2332(a,1),9753(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2332 9753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9766">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) \ ((y / x) \ L(y,z,u)) = a(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,8935,a(flip),b,9759,a),flip(a)].">
      <j1 rule="hyper" parents="316 8935 9759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9767">
    <literal><![CDATA[
      a(x \ y,x,y \ L(y,z,u)) = a(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8558,a(flip),b,9766,a)].">
      <j1 rule="hyper" parents="63 8558 9766"/>
    </justification>
  </clause>

  <clause id="9768">
    <literal><![CDATA[
      a(x \ y,x,y * L(y,z,u)) = a(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5566,a(flip),b,9767,a)].">
      <j1 rule="hyper" parents="63 5566 9767"/>
    </justification>
  </clause>

  <clause id="9769">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) * a(x,x,y * L(y,z,u)) = (y / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9768(a,1),8855(a,1,2))].">
      <j1 rule="para" parents="9768 8855"/>
    </justification>
  </clause>

  <clause id="9770">
    <literal><![CDATA[
      (1 / x) \ (y \ R(y,z,u)) = (y / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8936,a(flip),b,9769,a)].">
      <j1 rule="hyper" parents="63 8936 9769"/>
    </justification>
  </clause>

  <clause id="9771">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(u,u,x * L(x,y,z)) = u \ ((x / u) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,9769,a(flip),b,8414,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 9769 8414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9772">
    <literal><![CDATA[
      a(x,x,y * L(y,z,u)) * (y \ R(y,z,u)) = x \ ((y / x) \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,9769,a(flip),b,8412,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 9769 8412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9773">
    <literal><![CDATA[
      (x / (y \ 1)) \ R(x,z,u) = y \ (x \ R(x,z,u))
    ]]></literal>
    <justification jstring="[para(80(a,1),9770(a,1,1)),flip(a)].">
      <j1 rule="para" parents="80 9770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9774">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ u) \ R(u,w,v5) = a(x,y,z) \ (u \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(4994(a,1),9773(a,1,1))].">
      <j1 rule="para" parents="4994 9773"/>
    </justification>
  </clause>

  <clause id="9776">
    <literal><![CDATA[
      x * (L(R(y,z,u) \ y,x,x) \ 1) = (y / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,8897,a(flip),b,9772,a(flip))].">
      <j1 rule="hyper" parents="139 8897 9772"/>
    </justification>
  </clause>

  <clause id="9777">
    <literal><![CDATA[
      x * (L(L(R(y,z,u),w,v5) \ L(y,w,v5),x,x) \ 1) = (L(y,w,v5) / x) \ R(L(y,w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(29(a,1),9776(a,1,2,1,1,1))].">
      <j1 rule="para" parents="29 9776"/>
    </justification>
  </clause>

  <clause id="9778">
    <literal><![CDATA[
      x \ (y \ ((x \ 1) * L((x \ 1) \ y,z,u))) = ((y \ x) / x) \ L(y \ (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(1252(a,1),9754(a,1,2))].">
      <j1 rule="para" parents="1252 9754"/>
    </justification>
  </clause>

  <clause id="9779">
    <literal><![CDATA[
      ((x \ y) / y) \ L(x \ (y \ 1),z,u) = y \ (x \ (y * L(y \ x,z,u)))
    ]]></literal>
    <justification jstring="[para(1350(a,1),9778(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1350 9778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9780">
    <literal><![CDATA[
      x * (L(L(R(y,z,u),w,v5) \ L(y,w,v5),x,x) \ 1) = (L(y,w,v5) / x) \ L(R(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(29(a,1),9777(a,2,2))].">
      <j1 rule="para" parents="29 9777"/>
    </justification>
  </clause>

  <clause id="9781">
    <literal><![CDATA[
      (x * y) * (L(L(R(y,z,u),x,x \ 1) \ L(y,x,x \ 1),x * y,x * y) \ 1) = (1 / x) \ R(L(y,x,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(889(a,1),9777(a,2,1))].">
      <j1 rule="para" parents="889 9777"/>
    </justification>
  </clause>

  <clause id="9782">
    <literal><![CDATA[
      (1 / x) * ((y \ L(y,z,u)) \ ((y / x) \ L(y,z,u))) = a(1 / x,x,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(83(a,1),9760(a,2,2))].">
      <j1 rule="para" parents="83 9760"/>
    </justification>
  </clause>

  <clause id="9783">
    <literal><![CDATA[
      (1 / x) * ((y \ L(y,z,u)) \ ((y / x) \ L(y,z,u))) = a(1 / x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,2652,a(flip),b,9782,a),flip(a)].">
      <j1 rule="hyper" parents="316 2652 9782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9784">
    <literal><![CDATA[
      (1 / x) * ((y \ L(y,z,u)) \ ((y / x) \ L(y,z,u))) = a(x \ 1,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,1813,a(flip),b,9783,a),flip(a)].">
      <j1 rule="hyper" parents="316 1813 9783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9785">
    <literal><![CDATA[
      (1 / x) * ((y \ L(y,z,u)) \ ((y / x) \ L(y,z,u))) = a(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,8935,a(flip),b,9784,a),flip(a)].">
      <j1 rule="hyper" parents="316 8935 9784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9786">
    <literal><![CDATA[
      a(x,y,z \ (T((u * (w \ 1)) \ ((u * (w \ 1)) / v5),v5) * (u * w))) = a(x,y,z \ (T(v5,v5 \ 1) \ (u * w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,7737,a(flip),b,9718,a),flip(a)].">
      <j1 rule="hyper" parents="316 7737 9718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9787">
    <literal><![CDATA[
      a(x,y,z \ (T((u * (w \ 1)) \ ((u * (w \ 1)) / v5),v5) * (u * w))) = a(x,y,z \ (v5 \ (u * w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5603,a(flip),b,9786,a),flip(a)].">
      <j1 rule="hyper" parents="316 5603 9786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9789">
    <literal><![CDATA[
      x / (y * (a(z,u,w) * (y \ (a(z,u,w) \ x)))) = (y * ((y \ (a(z,u,w) \ x)) * a(z,u,w))) \ x
    ]]></literal>
    <justification jstring="[para(2308(a,1),9719(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2308 9719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9790">
    <literal><![CDATA[
      x / (y * (a(z,u,w) * (y \ (a(z,u,w) \ x)))) = a(y,y \ (a(z,u,w) \ x),a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,2321,a(flip),b,9789,a),flip(a)].">
      <j1 rule="hyper" parents="316 2321 9789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9791">
    <literal><![CDATA[
      L(R(T(x,y),z,u),w,v5) * (R(x,z,u) \ (y * x)) = L(R(x,z,u),w,v5) * (R(x,z,u) \ (x * y))
    ]]></literal>
    <justification jstring="[para(3167(a,2),9731(a,1,1,1,1))].">
      <j1 rule="para" parents="3167 9731"/>
    </justification>
  </clause>

  <clause id="9792">
    <literal><![CDATA[
      (K(x,y) * ((z * x) * (T(x,y) \ 1))) \ ((1 / (1 / T(x,y))) * T(z,x)) = L(T(x,y),T(x,y) \ 1,T(x,y) * T(z,x))
    ]]></literal>
    <justification jstring="[para(406(a,1),3115(a,1,1))].">
      <j1 rule="para" parents="406 3115"/>
    </justification>
  </clause>

  <clause id="9793">
    <literal><![CDATA[
      (x * L(a(y,z,u),w,v5)) \ ((x * v6) * L(a(y,z,u),w,v5)) = L(K(a(y,z,u),x) * v6,x,L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(4279(a,1),3301(a,2,1,1))].">
      <j1 rule="para" parents="4279 3301"/>
    </justification>
  </clause>

  <clause id="9794">
    <literal><![CDATA[
      (x * L(a(y,z,u),w,v5)) \ ((x * v6) * L(a(y,z,u),w,v5)) = L(v6,x,L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(2312(a,1),9793(a,2,1))].">
      <j1 rule="para" parents="2312 9793"/>
    </justification>
  </clause>

  <clause id="9796">
    <literal><![CDATA[
      L(a(x,y,L(a(z,u,w),v5,v6)) \ y,x,L(a(z,u,w),v5,v6)) = (x * L(a(z,u,w),v5,v6)) \ (x * (y * L(a(z,u,w),v5,v6)))
    ]]></literal>
    <justification jstring="[para(8531(a,1),9794(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8531 9794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9798">
    <literal><![CDATA[
      (x / R(y,z,(z * y) \ x)) * L(R(y,z,(z * y) \ x),u,w) = (L(y,u,w) * z) * ((y * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,4769,a(flip),b,4773,a),flip(a)].">
      <j1 rule="hyper" parents="316 4769 4773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9799">
    <literal><![CDATA[
      (x * L(x \ K(y,z),u,w)) * T(v5,x * L(x \ 1,u,w)) = K(y,z) * (v5 * (x * L(x \ 1,u,w)))
    ]]></literal>
    <justification jstring="[para(5181(a,1),5198(a,1,2,2))].">
      <j1 rule="para" parents="5181 5198"/>
    </justification>
  </clause>

  <clause id="9800">
    <literal><![CDATA[
      K(x,y) * (z * (u * L(u \ 1,w,v5))) = (u * L(u \ K(x,y),w,v5)) * z
    ]]></literal>
    <justification jstring="[para(4986(a,1),9799(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4986 9799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9802">
    <literal><![CDATA[
      (x * L(x \ K(y,z),u,w)) * v5 = K(y,z) * (v5 * (x \ L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(1064(a,1),9800(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1064 9800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9806">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ v5,L(z,u,w),L(z,v6,v7) \ 1) \ (v5 * (1 / L(z,v6,v7)))) = a(x,y,L(z,v6,v7) \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1577(a,1),5742(a,1,3,1))].">
      <j1 rule="para" parents="1577 5742"/>
    </justification>
  </clause>

  <clause id="9807">
    <literal><![CDATA[
      ((x * (K(y,z) * u)) * L(R(T(K(z,y),u),w,v5),u,x)) / (x * (K(y,z) * u)) = R((x * u) / (x * (K(y,z) * u)),w,v5)
    ]]></literal>
    <justification jstring="[para(29(a,1),6214(a,1,1,2))].">
      <j1 rule="para" parents="29 6214"/>
    </justification>
  </clause>

  <clause id="9808">
    <literal><![CDATA[
      R(x,y * (L(y,z,u) \ y),y * (L(y,z,u) \ y)) = ((y * (L(y,z,u) \ y)) * x) * L(y \ K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6655(a,1),6458(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6655 6458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9809">
    <literal><![CDATA[
      R(x,y * (L(y,z,u) \ y),y * (y * L(y,z,u))) = ((y * (L(y,z,u) \ y)) * x) * L(y \ K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1731,a(flip),b,9808,a)].">
      <j1 rule="hyper" parents="63 1731 9808"/>
    </justification>
  </clause>

  <clause id="9810">
    <literal><![CDATA[
      R(x,y * (L(y,z,u) \ y),L(y * (y * y),z,u)) = ((y * (L(y,z,u) \ y)) * x) * L(y \ K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(1367(a,2),9809(a,1,3))].">
      <j1 rule="para" parents="1367 9809"/>
    </justification>
  </clause>

  <clause id="9811">
    <literal><![CDATA[
      ((x * (L(x,y,z) \ x)) * u) * L(x \ K(u,x),y,z) = R(u,x * (L(x,y,z) \ x),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1710,a(flip),b,9810,a),flip(a)].">
      <j1 rule="hyper" parents="63 1710 9810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9813">
    <literal><![CDATA[
      x \ ((L(y,z,u) * L(y \ 1,z,u)) * T(w,y \ L(y,z,u))) = (x \ w) * ((y \ L(y,z,u)) * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(5133(a,1),6647(a,1,2,1))].">
      <j1 rule="para" parents="5133 6647"/>
    </justification>
  </clause>

  <clause id="9815">
    <literal><![CDATA[
      (x \ y) * ((z \ L(z,u,w)) * (z \ L(z,u,w))) = x \ ((L(z,u,w) * L(z \ 1,u,w)) * y)
    ]]></literal>
    <justification jstring="[para(4992(a,1),9813(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4992 9813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9816">
    <literal><![CDATA[
      L(x * ((y \ L(y,z,u)) * (y \ L(y,z,u))),w,v5) = (L(y,z,u) * L(y \ 1,z,u)) * L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(38,a,1060,a,b,9815,a(flip))].">
      <j1 rule="hyper" parents="38 1060 9815"/>
    </justification>
  </clause>

  <clause id="9817">
    <literal><![CDATA[
      x \ ((L(y,z,u) * L(y \ 1,z,u)) * w) = (x \ w) * (L(y,z,u) * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(5133(a,1),9815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 9815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9818">
    <literal><![CDATA[
      x / (L(y,z,u) * L(y \ 1,z,u)) = (L(y,z,u) * L(y \ 1,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(518,a,9817,a)].">
      <j1 rule="hyper" parents="518 9817"/>
    </justification>
  </clause>

  <clause id="9819">
    <literal><![CDATA[
      (x * (L(x,y,z) \ (L(x,y,z) \ x))) * u = (L(x,y,z) * L(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,8376,a,b,9818,a)].">
      <j1 rule="hyper" parents="63 8376 9818"/>
    </justification>
  </clause>

  <clause id="9820">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ u) * (L(x,y,z) \ x) = (L(x,y,z) * L(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,7884,a,b,9818,a)].">
      <j1 rule="hyper" parents="63 7884 9818"/>
    </justification>
  </clause>

  <clause id="9821">
    <literal><![CDATA[
      x * (y * (L(y,z,u) \ (L(y,z,u) \ y))) = (L(y,z,u) * L(y \ 1,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,6316,a,b,9818,a)].">
      <j1 rule="hyper" parents="63 6316 9818"/>
    </justification>
  </clause>

  <clause id="9822">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ 1 = L(x,y,z) \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,9425,a(flip),b,9818,a),flip(a)].">
      <j1 rule="hyper" parents="63 9425 9818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9824">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ (u * w) = u * (w / (L(x,y,z) * L(x \ 1,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7918,a(flip),b,9818,a),flip(a)].">
      <j1 rule="hyper" parents="63 7918 9818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9826">
    <literal><![CDATA[
      (L(x,y,z) \ (L(1 / x,y,z) \ 1)) * u = (L(x,y,z) * L(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(6598(a,2),9819(a,1,1))].">
      <j1 rule="para" parents="6598 9819"/>
    </justification>
  </clause>

  <clause id="9827">
    <literal><![CDATA[
      x * (L(y,z,u) \ (L(1 / y,z,u) \ 1)) = (L(y,z,u) * L(y \ 1,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(6598(a,2),9821(a,1,2))].">
      <j1 rule="para" parents="6598 9821"/>
    </justification>
  </clause>

  <clause id="9828">
    <literal><![CDATA[
      ((L(x,y,z) * L(x \ 1,y,z)) \ u) / u = L(x,y,z) \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(149,a,9826,a)].">
      <j1 rule="hyper" parents="149 9826"/>
    </justification>
  </clause>

  <clause id="9830">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ (u * w) = u * ((L(x,y,z) * L(x \ 1,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(9818(a,1),9824(a,2,2))].">
      <j1 rule="para" parents="9818 9824"/>
    </justification>
  </clause>

  <clause id="9832">
    <literal><![CDATA[
      (((L(x,y,z) * L(x \ 1,y,z)) \ u) * w) * a(L(x,y,z) * L(x \ 1,y,z),(L(x,y,z) * L(x \ 1,y,z)) \ u,w) = u * ((L(x,y,z) * L(x \ 1,y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8437,a,b,9830,a)].">
      <j1 rule="hyper" parents="63 8437 9830"/>
    </justification>
  </clause>

  <clause id="9833">
    <literal><![CDATA[
      L((x * ((L(y,z,u) * L(y \ 1,z,u)) \ w)) \ v5,(L(y,z,u) * L(y \ 1,z,u)) \ (x * w),L(y,z,u) * L(y \ 1,z,u)) = (x * w) \ ((L(y,z,u) * L(y \ 1,z,u)) * v5)
    ]]></literal>
    <justification jstring="[para(9830(a,1),475(a,1,1,1))].">
      <j1 rule="para" parents="9830 475"/>
    </justification>
  </clause>

  <clause id="9835">
    <literal><![CDATA[
      a(x,y,z * (((L(u,w,v5) * L(u \ 1,w,v5)) \ (v6 * v7)) * v8)) = a(x,y,z * (v8 * (((L(u,w,v5) * L(u \ 1,w,v5)) \ v7) * v6)))
    ]]></literal>
    <justification jstring="[para(9830(a,2),5796(a,1,3,2,1))].">
      <j1 rule="para" parents="9830 5796"/>
    </justification>
  </clause>

  <clause id="9836">
    <literal><![CDATA[
      L(a(x,(L(y,z,u) * L(y \ 1,z,u)) \ 1,w),L(y,z,u) * L(y \ 1,z,u),L(y,z,u) * L(y \ 1,z,u)) = (L(y,z,u) * L(y \ 1,z,u)) * ((x \ (((L(y,z,u) * L(y \ 1,z,u)) \ (x * 1)) * w)) / w)
    ]]></literal>
    <justification jstring="[para(9830(a,2),8475(a,2,2,1,2,1))].">
      <j1 rule="para" parents="9830 8475"/>
    </justification>
  </clause>

  <clause id="9838">
    <literal><![CDATA[
      L(x * (L(y,z,u) * L(y \ 1,z,u)),w,v5) = (L(y,z,u) * L(y \ 1,z,u)) * L(x,w,v5)
    ]]></literal>
    <justification jstring="[para(5133(a,1),9816(a,1,1,2))].">
      <j1 rule="para" parents="5133 9816"/>
    </justification>
  </clause>

  <clause id="9839">
    <literal><![CDATA[
      R(a(x,y,z) \ (u * (w * a(x,y,z))),a(x,y,z),a(x,y,z)) = 1 \ (a(x,y,z) * (u * (w * (a(x,y,z) \ 1))))
    ]]></literal>
    <justification jstring="[hyper(63,a,5378,a(flip),b,7964,a)].">
      <j1 rule="hyper" parents="63 5378 7964"/>
    </justification>
  </clause>

  <clause id="9840">
    <literal><![CDATA[
      1 \ (a(x,y,z) * (u * (w * (a(x,y,z) \ 1)))) = (u * (w * a(x,y,z))) * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2282,a(flip),b,9839,a),flip(a)].">
      <j1 rule="hyper" parents="63 2282 9839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9841">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) * (a(z,u,w) \ 1) = a(z,u,w) * (x * (y * (a(z,u,w) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(179,a,9840,a),flip(a)].">
      <j1 rule="hyper" parents="179 9840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9843">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u * (w * a(x,y,z))) = a(x,y,z) * (u * (w * (a(x,y,z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5006,a,b,9841,a)].">
      <j1 rule="hyper" parents="63 5006 9841"/>
    </justification>
  </clause>

  <clause id="9844">
    <literal><![CDATA[
      L(a(x,y,z \ R(z,u,w)) \ y,x,z \ R(z,u,w)) = (x * (z \ R(z,u,w))) \ (x * (y * (z \ R(z,u,w))))
    ]]></literal>
    <justification jstring="[para(2228(a,1),8641(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2228 8641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9845">
    <literal><![CDATA[
      L(a(x,y,z \ R(z,u,w)) \ y,x,z \ R(z,u,w)) = L(T(y,z \ R(z,u,w)),z \ R(z,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,247,a(flip),b,9844,a),flip(a)].">
      <j1 rule="hyper" parents="316 247 9844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9846">
    <literal><![CDATA[
      L(a(x,y,z \ R(z,u,w)) \ y,x,z \ R(z,u,w)) = L(y,z \ R(z,u,w),x)
    ]]></literal>
    <justification jstring="[para(2191(a,1),9845(a,2,1))].">
      <j1 rule="para" parents="2191 9845"/>
    </justification>
  </clause>

  <clause id="9847">
    <literal><![CDATA[
      L(a(x,y,z * R(z,u,w)) \ y,x,z \ R(z,u,w)) = L(y,z \ R(z,u,w),x)
    ]]></literal>
    <justification jstring="[para(5567(a,1),9846(a,1,1,1))].">
      <j1 rule="para" parents="5567 9846"/>
    </justification>
  </clause>

  <clause id="9848">
    <literal><![CDATA[
      L(a(x,y,z * R(z,u,w)) \ y,x,z \ L(z,u,w)) = L(y,z \ R(z,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7482,a(flip),b,9847,a)].">
      <j1 rule="hyper" parents="63 7482 9847"/>
    </justification>
  </clause>

  <clause id="9849">
    <literal><![CDATA[
      L(a(x,y,z * L(z,u,w)) \ y,x,z \ L(z,u,w)) = L(y,z \ R(z,u,w),x)
    ]]></literal>
    <justification jstring="[para(7272(a,1),9848(a,1,1,1))].">
      <j1 rule="para" parents="7272 9848"/>
    </justification>
  </clause>

  <clause id="9850">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),w) = L(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9633,a(flip),b,9849,a),flip(a)].">
      <j1 rule="hyper" parents="63 9633 9849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9851">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) * (u * (x \ R(x,y,z))) = L(u,x \ L(x,y,z),(x \ R(x,y,z)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2635,a,b,9850,a)].">
      <j1 rule="hyper" parents="63 2635 9850"/>
    </justification>
  </clause>

  <clause id="9852">
    <literal><![CDATA[
      L(x,y \ L(y,z,z),u) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(2380(a,1),9850(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2380 9850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9853">
    <literal><![CDATA[
      L(x,R(y,y,z) \ y,u) = L(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(7666(a,2),9852(a,1,2))].">
      <j1 rule="para" parents="7666 9852"/>
    </justification>
  </clause>

  <clause id="9854">
    <literal><![CDATA[
      L((x \ L(x,y,y)) \ z,a(x,y,y),L(y,y,x)) = y \ (R(y,y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7702,a(flip),b,9853,a),flip(a)].">
      <j1 rule="hyper" parents="63 7702 9853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9855">
    <literal><![CDATA[
      L((x \ L(x,y,y)) \ z,a(x,y,y),L(y,y,x)) = R(y,y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1167,a(flip),b,9854,a),flip(a)].">
      <j1 rule="hyper" parents="316 1167 9854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9856">
    <literal><![CDATA[
      L(x,y,z) * L(((z * y) \ (z * (y * x))) \ x,u,w) = (z * y) \ (z * ((y * x) * L(a(z,y,x),u,w)))
    ]]></literal>
    <justification jstring="[para(18(a,2),8664(a,1,1))].">
      <j1 rule="para" parents="18 8664"/>
    </justification>
  </clause>

  <clause id="9857">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L(a(x,y,z),u,w))) = L(z,y,x) * L(L(z,y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),9856(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="18 9856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9858">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * a(x,y,z))) = L(z,y,x) * L(L(z,y,x) \ z,u,x)
    ]]></literal>
    <justification jstring="[para(8510(a,1),9857(a,1,2,2,2))].">
      <j1 rule="para" parents="8510 9857"/>
    </justification>
  </clause>

  <clause id="9859">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,z) = (z * y) \ ((z * y) * x)
    ]]></literal>
    <justification jstring="[para(8416(a,1),9858(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8416 9858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9860">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,z) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,9,a(flip),b,9859,a),flip(a)].">
      <j1 rule="hyper" parents="316 9 9859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9861">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,9,a(flip),b,9859,a),flip(a)].">
      <j1 rule="hyper" parents="133 9 9859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9863">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ x),y,z) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,8335,a(flip),b,9860,a)].">
      <j1 rule="hyper" parents="63 8335 9860"/>
    </justification>
  </clause>

  <clause id="9864">
    <literal><![CDATA[
      L(x * L(x,y,z),u,z) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,9860,a(flip),b,1349,a),flip(a)].">
      <j1 rule="hyper" parents="138 9860 1349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9866">
    <literal><![CDATA[
      x \ (y \ ((y * x) * z)) = z * (L(z,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(41,a,454,a,b,9863,a)].">
      <j1 rule="hyper" parents="41 454 9863"/>
    </justification>
  </clause>

  <clause id="9867">
    <literal><![CDATA[
      L(L(x * (L(x,y,z) \ x),u,w),y,z) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(9863(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9863 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9868">
    <literal><![CDATA[
      R(x,y,L((z * (L(z,u,w) \ z)) \ 1,u,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(9863(a,1),1713(a,2,3))].">
      <j1 rule="para" parents="9863 1713"/>
    </justification>
  </clause>

  <clause id="9870">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((z * (w * (L(w,z,u) \ w))) * u)) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(9863(a,1),5737(a,2,3))].">
      <j1 rule="para" parents="9863 5737"/>
    </justification>
  </clause>

  <clause id="9872">
    <literal><![CDATA[
      L(1 / L(x,y,z),y,z) = 1 / x
    ]]></literal>
    <justification jstring="[para(6599(a,1),9863(a,1,1))].">
      <j1 rule="para" parents="6599 9863"/>
    </justification>
  </clause>

  <clause id="9873">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,y,z) = x \ 1
    ]]></literal>
    <justification jstring="[para(7088(a,1),9863(a,1,1))].">
      <j1 rule="para" parents="7088 9863"/>
    </justification>
  </clause>

  <clause id="9874">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w) \ 1,u,w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(5185(a,1),9863(a,1,1))].">
      <j1 rule="para" parents="5185 9863"/>
    </justification>
  </clause>

  <clause id="9880">
    <literal><![CDATA[
      a(x * (L(x,y,z) \ x),u,x * (L(x,y,z) \ x)) = a(x,u,L(x * (L(x,y,z) \ x),w,v5))
    ]]></literal>
    <justification jstring="[para(9863(a,1),9201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9863 9201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9881">
    <literal><![CDATA[
      (x \ y) * (L(z * (L(z,u,w) \ z),u,w) * L((z * (L(z,u,w) \ z)) \ 1,u,w)) = x \ ((z * L((z * (L(z,u,w) \ z)) \ 1,u,w)) * y)
    ]]></literal>
    <justification jstring="[para(9863(a,1),9817(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9863 9817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9882">
    <literal><![CDATA[
      L(L(1 / L(x,y,z),u,w),y,z) = L(1 / x,u,w)
    ]]></literal>
    <justification jstring="[para(9872(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9872 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9883">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w) \ 1,u,w) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,1894,a(flip),b,9873,a),flip(a)].">
      <j1 rule="hyper" parents="316 1894 9873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9884">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,y,z) \ x) = L(L(x,y,z),y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(41,a,1371,a,b,9873,a)].">
      <j1 rule="hyper" parents="41 1371 9873"/>
    </justification>
  </clause>

  <clause id="9885">
    <literal><![CDATA[
      L(x * y,y,x) \ 1 = y \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(41,a,298,a,b,9873,a),flip(a)].">
      <j1 rule="hyper" parents="41 298 9873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9886">
    <literal><![CDATA[
      x * (y * (L(z,y,x) \ 1)) = (x * y) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,9873,a(flip),b,18,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 9873 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9887">
    <literal><![CDATA[
      L(((x * y) \ z) \ 1,y,x) = (y \ (x \ z)) \ 1
    ]]></literal>
    <justification jstring="[para(298(a,1),9873(a,1,1,1))].">
      <j1 rule="para" parents="298 9873"/>
    </justification>
  </clause>

  <clause id="9888">
    <literal><![CDATA[
      (x \ (y \ ((y * x) * z))) \ 1 = L(z \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(454(a,1),9873(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="454 9873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9889">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,y * z) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(3422(a,2),9873(a,1,1,1))].">
      <j1 rule="para" parents="3422 9873"/>
    </justification>
  </clause>

  <clause id="9890">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,z * y) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(3424(a,2),9873(a,1,1,1))].">
      <j1 rule="para" parents="3424 9873"/>
    </justification>
  </clause>

  <clause id="9891">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w) \ 1,x,z * y) = L(x \ R(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(3431(a,1),9873(a,1,1,1))].">
      <j1 rule="para" parents="3431 9873"/>
    </justification>
  </clause>

  <clause id="9892">
    <literal><![CDATA[
      (x / (L(y,z,u) \ 1)) * L(L(y,z,u) \ 1,z,u) = (L(y,z,u) \ 1) \ ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[para(9873(a,1),4382(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9873 4382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9893">
    <literal><![CDATA[
      (x / L(y,z,u)) * L(L(y,z,u),z,u) = (x / (L(y,z,u) \ 1)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(9873(a,1),7083(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9873 7083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9894">
    <literal><![CDATA[
      L(x,y,z) * (L(L(x,y,z),y,z) \ u) = (L(x,y,z) \ 1) * ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(9873(a,1),7154(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9873 7154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9895">
    <literal><![CDATA[
      L(x * y,y,x) = 1 / (y \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(210,a,9885,a),flip(a)].">
      <j1 rule="hyper" parents="210 9885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9896">
    <literal><![CDATA[
      a(L(x * y,y,x),z,u) = a((y \ (x \ 1)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(9885(a,1),1809(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9885 1809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9897">
    <literal><![CDATA[
      a(x,y,L(z * u,u,z)) = a(x,y,u \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(9885(a,1),2534(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9885 2534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9898">
    <literal><![CDATA[
      (1 / L(x * y,y,x)) * L(L(x * y,y,x),z,u) = L(L(x * y,y,x),z,u) * (y \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(9885(a,1),4325(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9885 4325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9900">
    <literal><![CDATA[
      L(L(x * y,y,x),z,u) * (y \ (x \ 1)) = (y \ (x \ 1)) * L((y \ (x \ 1)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(9895(a,2),602(a,1,1,1))].">
      <j1 rule="para" parents="9895 602"/>
    </justification>
  </clause>

  <clause id="9901">
    <literal><![CDATA[
      (x * y) \ L(x * y,y,x) = a(x,y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[para(9895(a,2),7237(a,1,2))].">
      <j1 rule="para" parents="9895 7237"/>
    </justification>
  </clause>

  <clause id="9902">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,z) = (x \ L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,1894,a,b,9861,a),flip(a)].">
      <j1 rule="hyper" parents="316 1894 9861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9903">
    <literal><![CDATA[
      x \ (y * (L(y,z,x) \ x)) = L(y,z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,9168,a(flip),b,9861,a)].">
      <j1 rule="hyper" parents="63 9168 9861"/>
    </justification>
  </clause>

  <clause id="9904">
    <literal><![CDATA[
      x * (L(y,z,x) \ y) = y * (L(y,z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,9861,a(flip),b,9168,a(flip))].">
      <j1 rule="hyper" parents="139 9861 9168"/>
    </justification>
  </clause>

  <clause id="9909">
    <literal><![CDATA[
      a(x,L(x,y,z),L(u,x,L(x,y,z))) = L(u,x,L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,9179,a(flip),b,9903,a)].">
      <j1 rule="hyper" parents="63 9179 9903"/>
    </justification>
  </clause>

  <clause id="9912">
    <literal><![CDATA[
      L(a(x,y,z),z,u) \ a(x,y,z) = a(z \ u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,9166,a(flip),b,9904,a),flip(a)].">
      <j1 rule="hyper" parents="34 9166 9904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9916">
    <literal><![CDATA[
      (x * (L(y,z,x) \ y)) * y = y * (L(y,z,x) \ (x * y))
    ]]></literal>
    <justification jstring="[para(9904(a,2),4428(a,1,1))].">
      <j1 rule="para" parents="9904 4428"/>
    </justification>
  </clause>

  <clause id="9917">
    <literal><![CDATA[
      x \ (y \ (z \ ((z * y) * x))) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(517,a,9866,a)].">
      <j1 rule="hyper" parents="517 9866"/>
    </justification>
  </clause>

  <clause id="9918">
    <literal><![CDATA[
      x \ (y \ ((y * x) * z)) = L(1 / z,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,6585,a,b,9866,a),flip(a)].">
      <j1 rule="hyper" parents="316 6585 9866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9919">
    <literal><![CDATA[
      x \ (y \ ((y * x) * (z \ L(z,u,w)))) = L(L(z,u,w) \ z,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,6603,a(flip),b,9866,a),flip(a)].">
      <j1 rule="hyper" parents="316 6603 9866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9920">
    <literal><![CDATA[
      x \ (y \ ((y * x) * a(z,u,w))) = L(a(z,u,w) \ 1,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,5185,a(flip),b,9866,a),flip(a)].">
      <j1 rule="hyper" parents="316 5185 9866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9921">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * a(z,x,y) = L(y,x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(34,a,8735,a,b,9866,a(flip))].">
      <j1 rule="hyper" parents="34 8735 9866"/>
    </justification>
  </clause>

  <clause id="9922">
    <literal><![CDATA[
      L(a(x,y,z),z,u) \ a(x,y,z) = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,8737,a(flip),b,9866,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 8737 9866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9923">
    <literal><![CDATA[
      x * (y * (L(a(z,u,w),y,x) \ 1)) = (a(z,u,w) \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,5006,a,b,9886,a),flip(a)].">
      <j1 rule="hyper" parents="316 5006 9886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9924">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,y * x) = (x \ (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,8016,a,b,9887,a)].">
      <j1 rule="hyper" parents="63 8016 9887"/>
    </justification>
  </clause>

  <clause id="9926">
    <literal><![CDATA[
      a(x,y,L(z * u,u,z)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5805,a(flip),b,9897,a),flip(a)].">
      <j1 rule="hyper" parents="316 5805 9897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9927">
    <literal><![CDATA[
      a(x,y,L(z * u,z,u)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5535,a,b,9926,a)].">
      <j1 rule="hyper" parents="63 5535 9926"/>
    </justification>
  </clause>

  <clause id="9928">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,z) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(41,a,9873,a,b,9902,a)].">
      <j1 rule="hyper" parents="41 9873 9902"/>
    </justification>
  </clause>

  <clause id="9929">
    <literal><![CDATA[
      x \ (y \ (L(L(y,z,u),w,v5) \ ((y * L(L(y,w,v5),z,u)) * x))) = L(x,y,L(L(y,z,u),w,v5)) \ x
    ]]></literal>
    <justification jstring="[para(839(a,1),9917(a,1,2,2,2,1))].">
      <j1 rule="para" parents="839 9917"/>
    </justification>
  </clause>

  <clause id="9930">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,z * y) = a(z,y,y \ (z \ ((z * y) * x)))
    ]]></literal>
    <justification jstring="[para(9917(a,1),871(a,1,1))].">
      <j1 rule="para" parents="9917 871"/>
    </justification>
  </clause>

  <clause id="9931">
    <literal><![CDATA[
      L(1 / x,y,y \ 1) \ 1 = y \ ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3367,a(flip),b,9918,a),flip(a)].">
      <j1 rule="hyper" parents="63 3367 9918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9932">
    <literal><![CDATA[
      1 / (x \ ((1 / x) \ y)) = L(1 / y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(209,a,3367,a(flip),b,9918,a(flip))].">
      <j1 rule="hyper" parents="209 3367 9918"/>
    </justification>
  </clause>

  <clause id="9933">
    <literal><![CDATA[
      L(1 / x,y \ 1,y) \ 1 = (y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(71(a,1),9918(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="71 9918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9934">
    <literal><![CDATA[
      L(1 / L(x,y,z),z,y) \ 1 = z \ (y \ (z * (T(y,z) * x)))
    ]]></literal>
    <justification jstring="[para(3285(a,1),9918(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3285 9918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9935">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,1894,a,b,9928,a),flip(a)].">
      <j1 rule="hyper" parents="39 1894 9928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9936">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,u,z) \ x) = L(L(x,y,z),u,z) \ 1
    ]]></literal>
    <justification jstring="[para(9928(a,1),2147(a,1,2))].">
      <j1 rule="para" parents="9928 2147"/>
    </justification>
  </clause>

  <clause id="9937">
    <literal><![CDATA[
      (x * y) \ L(x * y,z,x) = y \ (x * L(x \ y,z,x))
    ]]></literal>
    <justification jstring="[hyper(41,a,1364,a,b,9935,a),flip(a)].">
      <j1 rule="hyper" parents="41 1364 9935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9938">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(x,u,z)) = L(L(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,9935,a(flip),b,2136,a)].">
      <j1 rule="hyper" parents="139 9935 2136"/>
    </justification>
  </clause>

  <clause id="9939">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (z * u) = z * (u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(9935(a,1),5031(a,1,1))].">
      <j1 rule="para" parents="9935 5031"/>
    </justification>
  </clause>

  <clause id="9940">
    <literal><![CDATA[
      L(1 / (x \ y),x,y \ (x \ y)) = L(1 / (x \ y),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,8873,a,b,9932,a)].">
      <j1 rule="hyper" parents="63 8873 9932"/>
    </justification>
  </clause>

  <clause id="9941">
    <literal><![CDATA[
      x * a(y,y \ 1,x) = (y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6601,a(flip),b,9933,a)].">
      <j1 rule="hyper" parents="63 6601 9933"/>
    </justification>
  </clause>

  <clause id="9942">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w \ 1) \ (w \ v5)))) = a(x,y,z \ (L(v5,w \ 1,w) * u))
    ]]></literal>
    <justification jstring="[para(9941(a,1),7945(a,1,3,2,2))].">
      <j1 rule="para" parents="9941 7945"/>
    </justification>
  </clause>

  <clause id="9943">
    <literal><![CDATA[
      L(a(x,x,L(y,z,u)),z,u) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(5099(a,1),9874(a,1,1))].">
      <j1 rule="para" parents="5099 9874"/>
    </justification>
  </clause>

  <clause id="9944">
    <literal><![CDATA[
      a(x * y,x * y,L(y,z,x)) = a(x * y,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,8704,a,b,9943,a),flip(a)].">
      <j1 rule="hyper" parents="41 8704 9943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9945">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ 1,u,w) = L(1 / L(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(9882(a,1),9873(a,1,1,1))].">
      <j1 rule="para" parents="9882 9873"/>
    </justification>
  </clause>

  <clause id="9946">
    <literal><![CDATA[
      a(x,y,y \ x) = a(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(39,a,2538,a(flip),b,9901,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 2538 9901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9947">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * (w \ u))) = a(x,y,z * a(u,w,u * w))
    ]]></literal>
    <justification jstring="[para(9946(a,1),5868(a,2,3,2))].">
      <j1 rule="para" parents="9946 5868"/>
    </justification>
  </clause>

  <clause id="9948">
    <literal><![CDATA[
      a(x,y,a(z,u,u \ z)) = a(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(9946(a,2),7284(a,1,3))].">
      <j1 rule="para" parents="9946 7284"/>
    </justification>
  </clause>

  <clause id="9951">
    <literal><![CDATA[
      a(x \ y,a(y,x,x \ y),z) = a(z,x \ y,a(y,x,x)) \ 1
    ]]></literal>
    <justification jstring="[para(9948(a,1),9448(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9948 9448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9952">
    <literal><![CDATA[
      a(x,y,z) * a(y,z,a(x,y,z)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a,b,9921,a)].">
      <j1 rule="hyper" parents="63 2290 9921"/>
    </justification>
  </clause>

  <clause id="9953">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,y,x) \ z) = a(y,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,2274,a,b,9921,a)].">
      <j1 rule="hyper" parents="35 2274 9921"/>
    </justification>
  </clause>

  <clause id="9954">
    <literal><![CDATA[
      a(x,y,z \ ((u \ ((w \ (v5 \ w)) \ 1)) * v6)) = a(x,y,z \ (v6 * (u \ (((w * v5) \ w) \ 1))))
    ]]></literal>
    <justification jstring="[para(9924(a,1),6076(a,1,3,2,1,2))].">
      <j1 rule="para" parents="9924 6076"/>
    </justification>
  </clause>

  <clause id="9956">
    <literal><![CDATA[
      L(x,y,z) * L(x,u,z) = x * L(L(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,9938,a(flip),b,1126,a),flip(a)].">
      <j1 rule="hyper" parents="139 9938 1126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9957">
    <literal><![CDATA[
      L(x,y,z) * L(x \ 1,u,z) = x \ L(L(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,9938,a(flip),b,1134,a),flip(a)].">
      <j1 rule="hyper" parents="133 9938 1134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9958">
    <literal><![CDATA[
      L(x,y,z) \ (a(z,y,x) \ x) = a(y,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,6996,a,b,9953,a)].">
      <j1 rule="hyper" parents="63 6996 9953"/>
    </justification>
  </clause>

  <clause id="9959">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y,w,u)) * (y * L(L(y,z,u),w,u)) = (x * L(y,z,u)) * L(y,w,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,9956,a(flip),b,199,a)].">
      <j1 rule="hyper" parents="139 9956 199"/>
    </justification>
  </clause>

  <clause id="9960">
    <literal><![CDATA[
      L((x * L(L(x,y,z),y,z)) * u,L(x,y,z),L(x,y,z)) = L(x,y,z) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(9956(a,1),1114(a,1,1,1))].">
      <j1 rule="para" parents="9956 1114"/>
    </justification>
  </clause>

  <clause id="9961">
    <literal><![CDATA[
      L((L(x,y,z) * L(x,y,z)) * u,w,v5) = (x * L(L(x,y,z),y,z)) * L(u,w,v5)
    ]]></literal>
    <justification jstring="[para(9956(a,1),1115(a,2,1))].">
      <j1 rule="para" parents="9956 1115"/>
    </justification>
  </clause>

  <clause id="9962">
    <literal><![CDATA[
      x \ (L(y,z,u) \ (L(y,w,u) \ ((y * L(L(y,w,u),z,u)) * x))) = L(x,L(y,z,u),L(y,w,u)) \ x
    ]]></literal>
    <justification jstring="[para(9956(a,1),9917(a,1,2,2,2,1))].">
      <j1 rule="para" parents="9956 9917"/>
    </justification>
  </clause>

  <clause id="9964">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,y * z) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,7650,a(flip),b,9889,a),flip(a)].">
      <j1 rule="hyper" parents="316 7650 9889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9965">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,z * y) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,1668,a,b,9964,a)].">
      <j1 rule="hyper" parents="63 1668 9964"/>
    </justification>
  </clause>

  <clause id="9966">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),x,z * y) = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(9965(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9965 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9967">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z),z,u) \ u) = u * a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,9922,a(flip),b,9903,a),flip(a)].">
      <j1 rule="hyper" parents="139 9922 9903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9968">
    <literal><![CDATA[
      a(x,y,z) \ a(u,z,a(x,y,z)) = L(a(x,y,z),z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,9922,a(flip),b,1002,a)].">
      <j1 rule="hyper" parents="133 9922 1002"/>
    </justification>
  </clause>

  <clause id="9969">
    <literal><![CDATA[
      a(x,y,z) * a(u,z,a(x,y,z)) = L(a(x,y,z) \ 1,z,u) \ 1
    ]]></literal>
    <justification jstring="[para(9922(a,1),5185(a,1,2))].">
      <j1 rule="para" parents="9922 5185"/>
    </justification>
  </clause>

  <clause id="9970">
    <literal><![CDATA[
      R(x,y,L(L(z \ 1,u,w),u,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(4459(a,1),9868(a,1,3,1))].">
      <j1 rule="para" parents="4459 9868"/>
    </justification>
  </clause>

  <clause id="9971">
    <literal><![CDATA[
      R(x,y,L(L(z,u,w),u,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8331,a(flip),b,9970,a)].">
      <j1 rule="hyper" parents="63 8331 9970"/>
    </justification>
  </clause>

  <clause id="9972">
    <literal><![CDATA[
      R(x,y,z) * (y * L(L(z,u,w),u,w)) = (x * y) * L(L(z,u,w),u,w)
    ]]></literal>
    <justification jstring="[hyper(138,a,9971,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="138 9971 20"/>
    </justification>
  </clause>

  <clause id="9973">
    <literal><![CDATA[
      a(x,y,L(z \ (L(L(u,w,v5),w,v5) \ 1),v6,v7)) = a(x,y,L(z \ u,v6,v7))
    ]]></literal>
    <justification jstring="[para(9884(a,1),6081(a,1,3,1,2))].">
      <j1 rule="para" parents="9884 6081"/>
    </justification>
  </clause>

  <clause id="9974">
    <literal><![CDATA[
      (x * (L(L(x,y,z),y,z) \ 1)) \ u = u * (L(x,y,z) * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(9884(a,1),8377(a,1,1,2))].">
      <j1 rule="para" parents="9884 8377"/>
    </justification>
  </clause>

  <clause id="9975">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ u = u * (x * (L(L(x,y,z),y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(9884(a,1),9821(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9884 9821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9977">
    <literal><![CDATA[
      (x * y) * (L(y,z,x) \ y) = y * (L(y,z,x) \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,9520,a(flip),b,9916,a)].">
      <j1 rule="hyper" parents="63 9520 9916"/>
    </justification>
  </clause>

  <clause id="9979">
    <literal><![CDATA[
      (L(L(x,y,z),u,z) \ 1) * L(x,y,z) = (L(x,u,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(9936(a,1),4424(a,1,1))].">
      <j1 rule="para" parents="9936 4424"/>
    </justification>
  </clause>

  <clause id="9981">
    <literal><![CDATA[
      x \ (y * L(y \ x,x,y)) = a(y,x,y * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,2538,a(flip),b,9937,a),flip(a)].">
      <j1 rule="hyper" parents="63 2538 9937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9982">
    <literal><![CDATA[
      (x * (y * (z \ L(z,u,x)))) \ (((z \ L(z,u,x)) * x) * y) = a(z \ L(z,u,x),x,y)
    ]]></literal>
    <justification jstring="[para(9939(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9939 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9983">
    <literal><![CDATA[
      x \ (L(y,z,u) * (y \ L(y,z,u))) = (x \ y) * (y \ L(L(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[para(9957(a,1),6315(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9957 6315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9984">
    <literal><![CDATA[
      (x \ y) * (L(z,u,w) * L(z \ 1,u,w)) = x \ (y * (z \ L(L(z,u,w),u,w)))
    ]]></literal>
    <justification jstring="[para(9957(a,1),7916(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9957 7916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9986">
    <literal><![CDATA[
      L(x * (L(y,z,u) * L(y \ 1,z,u)),w,v5) = L(x,w,v5) * (y \ L(L(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[para(9957(a,1),9436(a,2,2))].">
      <j1 rule="para" parents="9957 9436"/>
    </justification>
  </clause>

  <clause id="9987">
    <literal><![CDATA[
      L(x * (L(y,z,u) * L(y \ 1,z,u)),w,v5) = (y \ L(L(y,z,u),z,u)) * L(x,w,v5)
    ]]></literal>
    <justification jstring="[para(9957(a,1),9838(a,2,1))].">
      <j1 rule="para" parents="9957 9838"/>
    </justification>
  </clause>

  <clause id="9988">
    <literal><![CDATA[
      a(x \ y,x,a(z,u,x)) = a(y,x,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9922,a(flip),b,9912,a),flip(a)].">
      <j1 rule="hyper" parents="63 9922 9912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9989">
    <literal><![CDATA[
      a(x \ y,x,a(z,z,x)) = a(y,x,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,7280,a,b,9988,a),flip(a)].">
      <j1 rule="hyper" parents="316 7280 9988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9990">
    <literal><![CDATA[
      a(a(x,x,y) \ z,y,a(y,x,x)) \ z = ((z / a(x,x,y)) / y) * (y * a(x,x,y))
    ]]></literal>
    <justification jstring="[para(9989(a,1),2455(a,1,1))].">
      <j1 rule="para" parents="9989 2455"/>
    </justification>
  </clause>

  <clause id="9991">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ 1,z,y) = y \ (z \ (y * (T(z,y) * x)))
    ]]></literal>
    <justification jstring="[hyper(316,a,9934,a(flip),b,9945,a),flip(a)].">
      <j1 rule="hyper" parents="316 9934 9945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9992">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w) \ 1,w,u) = u \ (w \ (u * (T(w,u) * a(x,y,z))))
    ]]></literal>
    <justification jstring="[para(2276(a,1),9991(a,1,1,1,1))].">
      <j1 rule="para" parents="2276 9991"/>
    </justification>
  </clause>

  <clause id="9993">
    <literal><![CDATA[
      L(L(1 / (x \ L(x,y,z)),u,w) \ 1,w,u) = u \ (w \ (u * ((x \ L(x,y,z)) * T(w,u))))
    ]]></literal>
    <justification jstring="[para(5023(a,2),9991(a,2,2,2,2))].">
      <j1 rule="para" parents="5023 9991"/>
    </justification>
  </clause>

  <clause id="9994">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,y * z) = a(z,y,y \ (z \ ((z * y) * x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,1668,a,b,9930,a)].">
      <j1 rule="hyper" parents="63 1668 9930"/>
    </justification>
  </clause>

  <clause id="9995">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,z,y) \ 1 = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,9952,a(flip),b,9969,a),flip(a)].">
      <j1 rule="hyper" parents="63 9952 9969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9996">
    <literal><![CDATA[
      x * (L(a(y,z,x) \ 1,x,x * a(y,z,x)) \ 1) = R(x * a(y,z,x),a(y,z,x),x)
    ]]></literal>
    <justification jstring="[para(9969(a,1),7014(a,1,2))].">
      <j1 rule="para" parents="9969 7014"/>
    </justification>
  </clause>

  <clause id="9997">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,z,y) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,1894,a,b,9995,a),flip(a)].">
      <j1 rule="hyper" parents="39 1894 9995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9998">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,z,y)
    ]]></literal>
    <justification jstring="[para(9995(a,1),9874(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9995 9874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10000">
    <literal><![CDATA[
      L(L(L(L(x,y,z),u,w),x,v5) \ L(L(x,y,z),u,w),x,L(L(x,y,z),u,w)) = a(v5,x,L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,9000,a(flip),b,9998,a)].">
      <j1 rule="hyper" parents="316 9000 9998"/>
    </justification>
  </clause>

  <clause id="10003">
    <literal><![CDATA[
      L(x * L(x,y,z),x,u) \ (x * L(x,y,z)) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(41,a,8245,a,b,9998,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="41 8245 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10004">
    <literal><![CDATA[
      L(L(x,y,z),x,u) \ L(x,y,z) = a(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(41,a,6987,a,b,9998,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="41 6987 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10005">
    <literal><![CDATA[
      L(x,L(x,y,z),u) \ x = a(u,L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(41,a,6969,a,b,9998,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="41 6969 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10006">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),x,y) = L(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(9998(a,2),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9998 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10007">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),z,u)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(9998(a,2),6000(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9998 6000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10008">
    <literal><![CDATA[
      L(L(x,y,L(L(y,z,u),w,v5)) \ x,x,L(L(y,z,u),w,v5)) = a(y,L(L(y,z,u),w,v5),x)
    ]]></literal>
    <justification jstring="[para(9000(a,1),9998(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9000 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10010">
    <literal><![CDATA[
      R(a(x,a(y,z,u),w) \ 1,w,(y * (u * z)) \ (u * (y * z))) = w \ L(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5443,a,b,9997,a)].">
      <j1 rule="hyper" parents="63 5443 9997"/>
    </justification>
  </clause>

  <clause id="10011">
    <literal><![CDATA[
      L(a(x,y * z,z) \ 1,z,y) = z \ L(z,y * z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9132,a(flip),b,9997,a)].">
      <j1 rule="hyper" parents="63 9132 9997"/>
    </justification>
  </clause>

  <clause id="10012">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),a(u,w,x),v5) = a(v5,a(u,w,x),L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(41,a,9427,a,b,9997,a)].">
      <j1 rule="hyper" parents="41 9427 9997"/>
    </justification>
  </clause>

  <clause id="10014">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),y) \ 1 = y \ L(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(41,a,7583,a,b,9997,a),flip(a)].">
      <j1 rule="hyper" parents="41 7583 9997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10015">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),z,y) = L(z \ L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(9997(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9997 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10016">
    <literal><![CDATA[
      L(x,L(x,y,z),u) \ x = a(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,2548,a(flip),b,10005,a),flip(a)].">
      <j1 rule="hyper" parents="316 2548 10005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10017">
    <literal><![CDATA[
      L(R(x,y,z),R(x,y,z) * L(x \ L(x,u,w),y,z),v5) \ R(x,y,z) = a(v5,L(R(x,y,z),u,w),R(x,y,z))
    ]]></literal>
    <justification jstring="[para(8387(a,2),10005(a,1,1,2))].">
      <j1 rule="para" parents="8387 10005"/>
    </justification>
  </clause>

  <clause id="10018">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) \ y = L(y,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,10016,a)].">
      <j1 rule="hyper" parents="39 2301 10016"/>
    </justification>
  </clause>

  <clause id="10019">
    <literal><![CDATA[
      a(x,T(1 / (1 / y),z),L(T(1 / (1 / y),z),u,w)) \ T(1 / (1 / y),z) = L(1 / (K(z,y) / y),L(T(1 / (1 / y),z),u,w),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,6638,a(flip),b,10018,a),flip(a)].">
      <j1 rule="hyper" parents="316 6638 10018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10020">
    <literal><![CDATA[
      L(x * y,L(x * y,x,x),z) = a(z,x * y,x \ y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(8605(a,1),10018(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8605 10018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10021">
    <literal><![CDATA[
      a(x,y * z,y \ z) \ (y * z) = L(y * z,L(y * z,y,z),x)
    ]]></literal>
    <justification jstring="[para(9927(a,1),10018(a,1,1))].">
      <j1 rule="para" parents="9927 10018"/>
    </justification>
  </clause>

  <clause id="10023">
    <literal><![CDATA[
      L(1 / L(a(x,y,z),u,w),z,y) = 1 / L(L(z,y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(10006(a,1),9872(a,1,1,2))].">
      <j1 rule="para" parents="10006 9872"/>
    </justification>
  </clause>

  <clause id="10029">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) \ 1 = y \ L(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(8234(a,1),10014(a,1,1))].">
      <j1 rule="para" parents="8234 10014"/>
    </justification>
  </clause>

  <clause id="10030">
    <literal><![CDATA[
      L(1 / L(a(x,y,z),u,w),z,y) = L(L(z,y,x) \ z,u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,6486,a(flip),b,10023,a),flip(a)].">
      <j1 rule="hyper" parents="316 6486 10023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10032">
    <literal><![CDATA[
      x \ (x \ (y * L(y \ (x * x),z,u))) = L(L(y,z,u) \ y,x,x) \ 1
    ]]></literal>
    <justification jstring="[para(5108(a,1),9919(a,1,2,2))].">
      <j1 rule="para" parents="5108 9919"/>
    </justification>
  </clause>

  <clause id="10033">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) \ (x \ L(x,y,z)) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9084,a,b,10003,a)].">
      <j1 rule="hyper" parents="63 9084 10003"/>
    </justification>
  </clause>

  <clause id="10034">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) * L(L(y,z,u) \ y,y,x) = 1 * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(10003(a,1),2018(a,1,1))].">
      <j1 rule="para" parents="10003 2018"/>
    </justification>
  </clause>

  <clause id="10035">
    <literal><![CDATA[
      x * (L(x,y,z) \ L(x \ L(x,y,z),x,u)) = a(u,x,x * L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(10003(a,1),5080(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10003 5080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10036">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,u) \ 1 = u \ ((x / u) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(6838(a,1),10032(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6838 10032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10038">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) \ (y \ L(y,z,u)) = L(y \ L(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,10033,a)].">
      <j1 rule="hyper" parents="39 2301 10033"/>
    </justification>
  </clause>

  <clause id="10039">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ a(u,x,x * L(x,y,z)) = L(x \ L(x,y,z),x,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,10033,a(flip),b,1002,a)].">
      <j1 rule="hyper" parents="133 10033 1002"/>
    </justification>
  </clause>

  <clause id="10041">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) \ (y \ L(y,z,u)) = L(y \ L(y,z,u),y,L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,9278,a,b,10038,a),flip(a)].">
      <j1 rule="hyper" parents="316 9278 10038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10043">
    <literal><![CDATA[
      a(x,y,L(z \ L(L(u,w,v5),w,v5),v6,v7)) = a(x,y,L(z \ u,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,5889,a(flip),b,9973,a)].">
      <j1 rule="hyper" parents="63 5889 9973"/>
    </justification>
  </clause>

  <clause id="10044">
    <literal><![CDATA[
      x * (L(y,z,u) * L(y \ 1,z,u)) = (L(L(y,z,u),z,u) \ y) \ x
    ]]></literal>
    <justification jstring="[para(1847(a,1),9974(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1847 9974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10045">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) \ x) \ u = u * (x \ L(L(x,y,z),y,z))
    ]]></literal>
    <justification jstring="[para(9957(a,1),10044(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9957 10044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10046">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ u = u * (L(L(x,y,z),y,z) \ x)
    ]]></literal>
    <justification jstring="[para(1847(a,1),9975(a,2,2))].">
      <j1 rule="para" parents="1847 9975"/>
    </justification>
  </clause>

  <clause id="10047">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ u) * (L(x,y,z) \ x) = u * (L(L(x,y,z),y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9820,a,b,10046,a)].">
      <j1 rule="hyper" parents="63 9820 10046"/>
    </justification>
  </clause>

  <clause id="10048">
    <literal><![CDATA[
      x * ((L(y,z,u) * L(y \ 1,z,u)) \ w) = (x * w) * (L(L(y,z,u),z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9830,a(flip),b,10046,a)].">
      <j1 rule="hyper" parents="63 9830 10046"/>
    </justification>
  </clause>

  <clause id="10050">
    <literal><![CDATA[
      (x \ y) * (y \ L(L(y,z,u),z,u)) = x \ L(L(y,z,u),z,u)
    ]]></literal>
    <justification jstring="[para(9938(a,1),9983(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9938 9983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10051">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w \ 1,w) * v5)) = a(x,y,z \ (v5 * (w \ (w \ u))))
    ]]></literal>
    <justification jstring="[hyper(63,a,6690,a(flip),b,9942,a),flip(a)].">
      <j1 rule="hyper" parents="63 6690 9942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10052">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,x),u),w,v5) = a(u,a(y,z,x),L(x,w,v5)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,2136,a(flip),b,10012,a)].">
      <j1 rule="hyper" parents="63 2136 10012"/>
    </justification>
  </clause>

  <clause id="10053">
    <literal><![CDATA[
      a(x,a(y,z,u),L(u,w,v5)) \ 1 = L(a(u,a(y,z,u),x),w,v5)
    ]]></literal>
    <justification jstring="[para(9468(a,1),10052(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9468 10052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10054">
    <literal><![CDATA[
      a(a(x,y,z),L(z,u,w),v5) = L(a(z,a(x,y,z),v5),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9475,a(flip),b,10053,a)].">
      <j1 rule="hyper" parents="63 9475 10053"/>
    </justification>
  </clause>

  <clause id="10055">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) \ (L(y,z,u) \ y) = L(L(y,z,u) \ y,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,7,a(flip),b,10034,a)].">
      <j1 rule="hyper" parents="133 7 10034"/>
    </justification>
  </clause>

  <clause id="10056">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(u,w,x)) = a(u,x,x * L(x,y,z)) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(8786(a,1),10055(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8786 10055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10057">
    <literal><![CDATA[
      x * (L(x,y,z) \ a(u,x,x * L(x,y,z))) = L(x \ L(x,y,z),x,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,6992,a(flip),b,10039,a)].">
      <j1 rule="hyper" parents="63 6992 10039"/>
    </justification>
  </clause>

  <clause id="10058">
    <literal><![CDATA[
      L(x,y,z) * (L(x \ L(x,y,z),x,u) \ 1) = a(u,x,x * L(x,y,z)) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,10057,a(flip),b,2342,a)].">
      <j1 rule="hyper" parents="139 10057 2342"/>
    </justification>
  </clause>

  <clause id="10060">
    <literal><![CDATA[
      L((x * L(L(x,y,z),y,z)) * u,w,v5) = (x * L(L(x,y,z),y,z)) * L(u,w,v5)
    ]]></literal>
    <justification jstring="[para(9956(a,1),9961(a,1,1,1))].">
      <j1 rule="para" parents="9956 9961"/>
    </justification>
  </clause>

  <clause id="10061">
    <literal><![CDATA[
      x \ (y * (z \ L(L(z,u,w),u,w))) = (x \ y) * (z \ L(L(z,u,w),u,w))
    ]]></literal>
    <justification jstring="[para(9957(a,1),9984(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9957 9984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10062">
    <literal><![CDATA[
      (x * (y \ L(L(y,z,u),z,u))) / L(L(y,z,u),z,u) = x / y
    ]]></literal>
    <justification jstring="[hyper(209,a,333,a(flip),b,10061,a)].">
      <j1 rule="hyper" parents="209 333 10061"/>
    </justification>
  </clause>

  <clause id="10063">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ (u * (x \ L(L(x,y,z),y,z)))) = u
    ]]></literal>
    <justification jstring="[hyper(37,a,4402,a,b,10062,a(flip))].">
      <j1 rule="hyper" parents="37 4402 10062"/>
    </justification>
  </clause>

  <clause id="10064">
    <literal><![CDATA[
      x * (y * (x \ L(L(x,z,u),z,u))) = L(L(x,z,u),z,u) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,10063,a(flip),b,1845,a),flip(a)].">
      <j1 rule="hyper" parents="139 10063 1845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10065">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ ((L(L(x,y,z),y,z) \ x) \ u)) = u
    ]]></literal>
    <justification jstring="[para(10045(a,2),10063(a,1,2,2))].">
      <j1 rule="para" parents="10045 10063"/>
    </justification>
  </clause>

  <clause id="10066">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) \ u) * (x \ L(L(x,y,z),y,z)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(133,a,398,a(flip),b,10064,a),flip(a)].">
      <j1 rule="hyper" parents="133 398 10064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10068">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) \ x) * u = x * (L(L(x,y,z),y,z) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),10065(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 10065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10070">
    <literal><![CDATA[
      (x * y) * (L(L(z,u,w),u,w) \ z) = x * (y * (L(L(z,u,w),u,w) \ z))
    ]]></literal>
    <justification jstring="[para(10046(a,1),10048(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10046 10048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10071">
    <literal><![CDATA[
      x \ (y * (L(L(z,u,w),u,w) \ z)) = (x \ y) * (L(L(z,u,w),u,w) \ z)
    ]]></literal>
    <justification jstring="[hyper(133,a,158,a(flip),b,10070,a(flip))].">
      <j1 rule="hyper" parents="133 158 10070"/>
    </justification>
  </clause>

  <clause id="10072">
    <literal><![CDATA[
      (x \ L(L(y,z,u),z,u)) * (L(L(y,z,u),z,u) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,168,a(flip),b,10071,a),flip(a)].">
      <j1 rule="hyper" parents="63 168 10071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10073">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(u,w,x)) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,10055,a(flip),b,10056,a),flip(a)].">
      <j1 rule="hyper" parents="316 10055 10056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10074">
    <literal><![CDATA[
      a(a(x,x,y) \ z,y,a(y,x,x)) \ z = ((a(x,x,y) \ z) / y) * (y * a(x,x,y))
    ]]></literal>
    <justification jstring="[para(2276(a,1),9990(a,2,1,1))].">
      <j1 rule="para" parents="2276 9990"/>
    </justification>
  </clause>

  <clause id="10075">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ ((x \ 1) * u) = (u / (L(x,y,z) \ 1)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(9873(a,1),9892(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9873 9892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10077">
    <literal><![CDATA[
      L(x * (y \ L(L(y,z,u),z,u)),w,v5) = L(x,w,v5) * (y \ L(L(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[para(9957(a,1),9986(a,1,1,2))].">
      <j1 rule="para" parents="9957 9986"/>
    </justification>
  </clause>

  <clause id="10078">
    <literal><![CDATA[
      L(x \ L(L(x,y,z),y,z),u,w) = x \ L(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,452,a(flip),b,10077,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 452 10077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10080">
    <literal><![CDATA[
      L(x,y,z) \ L(L(L(x,y,z),u,w),u,w) = x \ L(L(x,u,w),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2171,a,b,10078,a)].">
      <j1 rule="hyper" parents="63 2171 10078"/>
    </justification>
  </clause>

  <clause id="10081">
    <literal><![CDATA[
      (x * y) * (z \ L(L(z,u,w),u,w)) = x * (y * (z \ L(L(z,u,w),u,w)))
    ]]></literal>
    <justification jstring="[hyper(139,a,10078,a(flip),b,7635,a(flip))].">
      <j1 rule="hyper" parents="139 10078 7635"/>
    </justification>
  </clause>

  <clause id="10084">
    <literal><![CDATA[
      x \ (y * (z * (u \ L(L(u,w,v5),w,v5)))) = (x \ (y * z)) * (u \ L(L(u,w,v5),w,v5))
    ]]></literal>
    <justification jstring="[para(10081(a,1),10061(a,1,2))].">
      <j1 rule="para" parents="10081 10061"/>
    </justification>
  </clause>

  <clause id="10086">
    <literal><![CDATA[
      L(x * (y \ L(L(y,z,u),z,u)),w,v5) = (y \ L(L(y,z,u),z,u)) * L(x,w,v5)
    ]]></literal>
    <justification jstring="[para(9957(a,1),9987(a,1,1,2))].">
      <j1 rule="para" parents="9957 9987"/>
    </justification>
  </clause>

  <clause id="10087">
    <literal><![CDATA[
      x * (L(a(y,z,x) \ 1,x,a(y,z,x)) \ 1) = R(x * a(y,z,x),a(y,z,x),x)
    ]]></literal>
    <justification jstring="[para(9133(a,1),9996(a,1,2,1))].">
      <j1 rule="para" parents="9133 9996"/>
    </justification>
  </clause>

  <clause id="10088">
    <literal><![CDATA[
      R(x * a(y,z,x),a(y,z,x),x) = x * ((a(y,z,x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2633(a,1),10087(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2633 10087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10089">
    <literal><![CDATA[
      R(x * a(y,z,x),a(y,z,x),x) = x * a(y,z,x)
    ]]></literal>
    <justification jstring="[para(2301(a,1),10088(a,2,2))].">
      <j1 rule="para" parents="2301 10088"/>
    </justification>
  </clause>

  <clause id="10092">
    <literal><![CDATA[
      a(L(x,y,z) \ u,x,x * L(x,y,z)) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(39,a,10038,a,b,10041,a)].">
      <j1 rule="hyper" parents="39 10038 10041"/>
    </justification>
  </clause>

  <clause id="10093">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) \ (L(y,z,u) \ y) = L(L(y,z,u) \ y,y,L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(10092(a,1),10055(a,1,1))].">
      <j1 rule="para" parents="10092 10055"/>
    </justification>
  </clause>

  <clause id="10094">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(x,y,z) \ u) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10055,a(flip),b,10093,a),flip(a)].">
      <j1 rule="hyper" parents="63 10055 10093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10095">
    <literal><![CDATA[
      L(L(x * y,y,x),z,u) * (y \ (x \ 1)) = y \ ((x \ 1) * L((x \ 1) \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,1216,a(flip),b,9900,a),flip(a)].">
      <j1 rule="hyper" parents="316 1216 9900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10096">
    <literal><![CDATA[
      L(L(x * y,y,x),z,u) * (y \ (x \ 1)) = y \ (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(1350(a,1),10095(a,2,2))].">
      <j1 rule="para" parents="1350 10095"/>
    </justification>
  </clause>

  <clause id="10097">
    <literal><![CDATA[
      L(x,y,L(L(y,z,u),w,v5)) \ x = a(y,L(L(y,z,u),w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9861,a(flip),b,10008,a)].">
      <j1 rule="hyper" parents="63 9861 10008"/>
    </justification>
  </clause>

  <clause id="10099">
    <literal><![CDATA[
      a(x,L(L(x,y,z),u,w),v5) \ v5 = L(v5,x,L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,10097,a)].">
      <j1 rule="hyper" parents="39 2301 10097"/>
    </justification>
  </clause>

  <clause id="10100">
    <literal><![CDATA[
      a(x * (L(x,y,z) \ x),u,x * (L(x,y,z) \ x)) = a(x,u,L(x * (x * L(x,y,z)),w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,7465,a(flip),b,9880,a),flip(a)].">
      <j1 rule="hyper" parents="316 7465 9880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10101">
    <literal><![CDATA[
      a(x * (L(x,y,z) \ x),u,x * (L(x,y,z) \ x)) = a(x,u,x)
    ]]></literal>
    <justification jstring="[para(9863(a,1),9880(a,2,3))].">
      <j1 rule="para" parents="9863 9880"/>
    </justification>
  </clause>

  <clause id="10102">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ (((v5 * v6) \ v5) \ 1)))) = a(x,y,z \ (u * (w \ (v5 \ (v6 \ v5)))))
    ]]></literal>
    <justification jstring="[hyper(63,a,6355,a(flip),b,9954,a),flip(a)].">
      <j1 rule="hyper" parents="63 6355 9954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10103">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ ((v5 * v6) \ v6)))) = a(x,y,z \ (u * (w \ (v6 \ (v5 \ v6)))))
    ]]></literal>
    <justification jstring="[hyper(63,a,8275,a(flip),b,10102,a)].">
      <j1 rule="hyper" parents="63 8275 10102"/>
    </justification>
  </clause>

  <clause id="10104">
    <literal><![CDATA[
      x \ (y \ (x * ((z \ L(z,u,w)) * T(y,x)))) = L(L(L(z,u,w) \ z,x,y) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(5069(a,1),9993(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5069 9993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10105">
    <literal><![CDATA[
      a(x * (L(x,y,z) \ x),u,x * (L(x,y,z) \ x)) = a(x,u,L(L(L(x,y,z),w,v5),x,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,5828,a(flip),b,10100,a),flip(a)].">
      <j1 rule="hyper" parents="316 5828 10100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10106">
    <literal><![CDATA[
      a(x * (L(x,y,z) \ x),u,x * (L(x,y,z) \ x)) = a(x,u,L(L(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,8010,a(flip),b,10105,a),flip(a)].">
      <j1 rule="hyper" parents="316 8010 10105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10108">
    <literal><![CDATA[
      a(x,y,L(L(x,z,u),w,v5)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10101,a(flip),b,10106,a),flip(a)].">
      <j1 rule="hyper" parents="63 10101 10106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10110">
    <literal><![CDATA[
      (1 / L(x * y,y,x)) * L(L(x * y,y,x),z,u) = y \ (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,10096,a(flip),b,9898,a),flip(a)].">
      <j1 rule="hyper" parents="316 10096 9898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10111">
    <literal><![CDATA[
      L(x * y,y,x) \ L(L(x * y,y,x),z,u) = y \ (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1458,a(flip),b,10110,a)].">
      <j1 rule="hyper" parents="63 1458 10110"/>
    </justification>
  </clause>

  <clause id="10112">
    <literal><![CDATA[
      L((x * y) \ L(x * y,z,u),y,x) = y \ (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2136,a(flip),b,10111,a)].">
      <j1 rule="hyper" parents="63 2136 10111"/>
    </justification>
  </clause>

  <clause id="10113">
    <literal><![CDATA[
      L((x * y) \ L(x * y,z,u),x,y) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5186,a,b,10112,a)].">
      <j1 rule="hyper" parents="63 5186 10112"/>
    </justification>
  </clause>

  <clause id="10114">
    <literal><![CDATA[
      (x / y) * (y * (((y \ x) * y) \ L((y \ x) * y,z,u))) = x * (y \ ((y \ x) * L((y \ x) \ y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(139,a,10112,a(flip),b,1598,a),flip(a)].">
      <j1 rule="hyper" parents="139 10112 1598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10115">
    <literal><![CDATA[
      L(a(x,y * z,y * z) \ 1,z,y) = z \ (y * L(y \ z,y * z,x))
    ]]></literal>
    <justification jstring="[para(7304(a,2),10112(a,1,1))].">
      <j1 rule="para" parents="7304 10112"/>
    </justification>
  </clause>

  <clause id="10116">
    <literal><![CDATA[
      x \ (y * L(y \ x,x * y,a(z,u,w))) = L(a(x * y,x * y,a(z,u,w)),x,y)
    ]]></literal>
    <justification jstring="[para(7328(a,1),10113(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7328 10113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10117">
    <literal><![CDATA[
      x \ (y \ (L(L(y,z,u),w,v5) \ ((y * L(L(y,w,v5),z,u)) * x))) = a(y,L(L(y,z,u),w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,10097,a(flip),b,9929,a),flip(a)].">
      <j1 rule="hyper" parents="316 10097 9929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10118">
    <literal><![CDATA[
      (x / y) * (y * (((y \ x) * y) \ L((y \ x) * y,z,u))) = x * (y \ ((x / y) \ L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(6834(a,1),10114(a,2,2,2))].">
      <j1 rule="para" parents="6834 10114"/>
    </justification>
  </clause>

  <clause id="10123">
    <literal><![CDATA[
      L(R(x,y,z),R(x,y,z) * L(x \ L(x,u,w),y,z),v5) \ R(x,y,z) = a(v5,L(R(x,y,z),u,w),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5746,a(flip),b,10017,a),flip(a)].">
      <j1 rule="hyper" parents="316 5746 10017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10128">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) \ ((x / y) * (L(1 / y,z,u) \ 1)) = x \ (((L(y,z,u) \ y) \ x) * L(L(y,z,u) \ y,y,x))
    ]]></literal>
    <justification jstring="[para(6483(a,1),9108(a,2,2,1))].">
      <j1 rule="para" parents="6483 9108"/>
    </justification>
  </clause>

  <clause id="10129">
    <literal><![CDATA[
      L(a(x,a(x,y,z),y * z),x \ R(x,y,z),u) \ u = (x \ R(x,y,z)) * (L(x \ R(x,y,z),x,z * y) \ u)
    ]]></literal>
    <justification jstring="[para(9007(a,1),9283(a,1,1,1))].">
      <j1 rule="para" parents="9007 9283"/>
    </justification>
  </clause>

  <clause id="10130">
    <literal><![CDATA[
      L(a(x,a(x,y,z),y * z),x \ L(x,y,z),u) \ u = (x \ R(x,y,z)) * (L(x \ R(x,y,z),x,z * y) \ u)
    ]]></literal>
    <justification jstring="[para(9850(a,1),10129(a,1,1))].">
      <j1 rule="para" parents="9850 10129"/>
    </justification>
  </clause>

  <clause id="10131">
    <literal><![CDATA[
      L(a(x,a(x,y,z),y * z),x \ L(x,y,z),u) \ u = (x \ R(x,y,z)) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(3424(a,2),10130(a,2,2,1))].">
      <j1 rule="para" parents="3424 10130"/>
    </justification>
  </clause>

  <clause id="10132">
    <literal><![CDATA[
      a(x,y,(((z * (u \ w)) * v5) * (v6 \ v7)) * a(v6,v6 \ v7,(z * (u \ w)) * v5)) = a(x,y,v6 \ (v7 * ((z * (w / u)) * v5)))
    ]]></literal>
    <justification jstring="[para(5689(a,1),9553(a,1,3,2))].">
      <j1 rule="para" parents="5689 9553"/>
    </justification>
  </clause>

  <clause id="10133">
    <literal><![CDATA[
      R((x * y) / (x * (K(z,u) * y)),w,v5) = ((x * (K(z,u) * y)) * L(T(K(u,z),y),y,x)) / (x * (K(z,u) * y))
    ]]></literal>
    <justification jstring="[para(658(a,1),9807(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="658 9807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10135">
    <literal><![CDATA[
      R((x * y) / (x * (K(z,u) * y)),w,v5) = (x * y) / (x * (K(z,u) * y))
    ]]></literal>
    <justification jstring="[para(6213(a,1),10133(a,2,1))].">
      <j1 rule="para" parents="6213 10133"/>
    </justification>
  </clause>

  <clause id="10136">
    <literal><![CDATA[
      (x * (y * T(K(z,u),y))) / (x * y) = (x * y) / (x * (K(u,z) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6215,a(flip),b,10135,a)].">
      <j1 rule="hyper" parents="63 6215 10135"/>
    </justification>
  </clause>

  <clause id="10139">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / (x * u) = (x * u) / (x * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[para(114(a,1),10136(a,1,1,2))].">
      <j1 rule="para" parents="114 10136"/>
    </justification>
  </clause>

  <clause id="10140">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * z) / (u * (K(y,x) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4625,a,b,10139,a)].">
      <j1 rule="hyper" parents="63 4625 10139"/>
    </justification>
  </clause>

  <clause id="10141">
    <literal><![CDATA[
      (x * y) / (x * (K(T(z \ 1,u) \ 1,w) * y)) = (x * (T(K(w,z),u) * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(4030(a,1),10139(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4030 10139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10143">
    <literal><![CDATA[
      K(x,y / ((y * (z \ u)) / u)) = (y * u) / (y * (K(z,x) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9048,a(flip),b,10140,a)].">
      <j1 rule="hyper" parents="63 9048 10140"/>
    </justification>
  </clause>

  <clause id="10144">
    <literal><![CDATA[
      (x * y) / (x * (K(T(z \ 1,u) \ 1,w) * y)) = T((x * (K(w,z) * y)) / (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,1569,a(flip),b,10141,a),flip(a)].">
      <j1 rule="hyper" parents="316 1569 10141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10145">
    <literal><![CDATA[
      (x * y) / (x * (K(T(z \ 1,u) \ 1,w) * y)) = T((x * y) / (x * (K(z,w) * y)),u)
    ]]></literal>
    <justification jstring="[para(10139(a,1),10144(a,2,1))].">
      <j1 rule="para" parents="10139 10144"/>
    </justification>
  </clause>

  <clause id="10146">
    <literal><![CDATA[
      (x * y) / (x * (T(K(z,u),w) * y)) = T((x * y) / (x * (K(z,u) * y)),w)
    ]]></literal>
    <justification jstring="[para(3191(a,1),10145(a,1,2,2,1))].">
      <j1 rule="para" parents="3191 10145"/>
    </justification>
  </clause>

  <clause id="10147">
    <literal><![CDATA[
      K(x,y) * T((z * u) / (z * (K(x,y) * u)),z) = a(z,K(x,y),u)
    ]]></literal>
    <justification jstring="[para(10146(a,1),8999(a,1,2))].">
      <j1 rule="para" parents="10146 8999"/>
    </justification>
  </clause>

  <clause id="10148">
    <literal><![CDATA[
      K(x,y) * T(K(y,z / ((z * (x \ u)) / u)),z) = a(z,K(x,y),u)
    ]]></literal>
    <justification jstring="[para(10143(a,2),10147(a,1,2,1))].">
      <j1 rule="para" parents="10143 10147"/>
    </justification>
  </clause>

  <clause id="10149">
    <literal><![CDATA[
      K(x,y) * K(y,((z * (x \ u)) / u) \ z) = a(z,K(x,y),u)
    ]]></literal>
    <justification jstring="[para(3878(a,1),10148(a,1,2))].">
      <j1 rule="para" parents="3878 10148"/>
    </justification>
  </clause>

  <clause id="10150">
    <literal><![CDATA[
      a(x,K(y,z),u) = K(y,z) * K(z,(x / y) \ x)
    ]]></literal>
    <justification jstring="[para(3580(a,1),10149(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3580 10149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10151">
    <literal><![CDATA[
      a(x,K(y,z),u) = K(y,z) * K(z,y)
    ]]></literal>
    <justification jstring="[para(83(a,1),10150(a,2,2,2))].">
      <j1 rule="para" parents="83 10150"/>
    </justification>
  </clause>

  <clause id="10153">
    <literal><![CDATA[
      a(x,K(y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(316,a,2959,a(flip),b,10151,a),flip(a)].">
      <j1 rule="hyper" parents="316 2959 10151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10154">
    <literal><![CDATA[
      x * a(y,K(z,u),w) = x
    ]]></literal>
    <justification jstring="[para(10151(a,2),2972(a,1,2))].">
      <j1 rule="para" parents="10151 2972"/>
    </justification>
  </clause>

  <clause id="10156">
    <literal><![CDATA[
      L(x,K(y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,10153,a)].">
      <j1 rule="hyper" parents="52 10153"/>
    </justification>
  </clause>

  <clause id="10158">
    <literal><![CDATA[
      T(T(x,y),K(z,u)) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4560,a(flip),b,10156,a),flip(a)].">
      <j1 rule="hyper" parents="63 4560 10156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10159">
    <literal><![CDATA[
      (x * K(y,z)) \ u = K(y,z) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,298,a(flip),b,10156,a)].">
      <j1 rule="hyper" parents="63 298 10156"/>
    </justification>
  </clause>

  <clause id="10160">
    <literal><![CDATA[
      (x / (K(y,z) * u)) * K(y,z) = x / u
    ]]></literal>
    <justification jstring="[hyper(209,a,10156,a(flip),b,1604,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="209 10156 1604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10161">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / u = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(209,a,10156,a(flip),b,1573,a(flip))].">
      <j1 rule="hyper" parents="209 10156 1573"/>
    </justification>
  </clause>

  <clause id="10162">
    <literal><![CDATA[
      x \ ((x * K(y,z)) * u) = K(y,z) * u
    ]]></literal>
    <justification jstring="[hyper(139,a,454,a(flip),b,10156,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 454 10156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10163">
    <literal><![CDATA[
      K(x,y) * ((z * K(x,y)) \ u) = z \ u
    ]]></literal>
    <justification jstring="[hyper(139,a,298,a(flip),b,10156,a(flip))].">
      <j1 rule="hyper" parents="139 298 10156"/>
    </justification>
  </clause>

  <clause id="10165">
    <literal><![CDATA[
      (x * K(y,z)) * u = x * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,10156,a(flip),b,1573,a(flip))].">
      <j1 rule="hyper" parents="139 10156 1573"/>
    </justification>
  </clause>

  <clause id="10167">
    <literal><![CDATA[
      R(x,K(y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(3419,a,10154,a)].">
      <j1 rule="hyper" parents="3419 10154"/>
    </justification>
  </clause>

  <clause id="10169">
    <literal><![CDATA[
      x \ (y * (K(z,u) * x)) = T(y * K(z,u),x)
    ]]></literal>
    <justification jstring="[hyper(390,a,10154,a(flip),b,89,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="390 10154 89"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10170">
    <literal><![CDATA[
      R(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(10167(a,1),51(a,2))].">
      <j1 rule="para" parents="10167 51"/>
    </justification>
  </clause>

  <clause id="10174">
    <literal><![CDATA[
      T(T(x,y),K(z,u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(4120,a,10158,a)].">
      <j1 rule="hyper" parents="4120 10158"/>
    </justification>
  </clause>

  <clause id="10176">
    <literal><![CDATA[
      (x * K(y,z)) \ u = K(z,y) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,2981,a(flip),b,10159,a),flip(a)].">
      <j1 rule="hyper" parents="316 2981 10159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10177">
    <literal><![CDATA[
      T(x,y) \ ((z * K(y,x)) \ u) = x \ (z \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,10159,a,b,2996,a)].">
      <j1 rule="hyper" parents="133 10159 2996"/>
    </justification>
  </clause>

  <clause id="10178">
    <literal><![CDATA[
      K(x,y) * (T(z,K(x,y)) \ u) = z \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,665,a(flip),b,10159,a(flip))].">
      <j1 rule="hyper" parents="139 665 10159"/>
    </justification>
  </clause>

  <clause id="10179">
    <literal><![CDATA[
      K(x,y) \ ((z * x) \ u) = (z * T(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(3832(a,1),10159(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3832 10159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10180">
    <literal><![CDATA[
      x / (K(y,z) * u) = (x / u) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(3837,a,10160,a),flip(a)].">
      <j1 rule="hyper" parents="3837 10160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10181">
    <literal><![CDATA[
      (x / (y \ z)) * K(y,u) = x / (T(y,u) \ z)
    ]]></literal>
    <justification jstring="[para(2859(a,1),10160(a,1,1,2))].">
      <j1 rule="para" parents="2859 10160"/>
    </justification>
  </clause>

  <clause id="10182">
    <literal><![CDATA[
      (x / (1 / y)) * K(z,u) = x / (K(u,z) / y)
    ]]></literal>
    <justification jstring="[para(2979(a,1),10160(a,1,1,2))].">
      <j1 rule="para" parents="2979 10160"/>
    </justification>
  </clause>

  <clause id="10183">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(3097(a,1),10160(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3097 10160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10184">
    <literal><![CDATA[
      L(x * K(y,z),u,w) * v5 = L(x,u,w) * (K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(138,a,4837,a,b,10161,a)].">
      <j1 rule="hyper" parents="138 4837 10161"/>
    </justification>
  </clause>

  <clause id="10185">
    <literal><![CDATA[
      R(x * K(y,z),u,w) * v5 = R(x,u,w) * (K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(138,a,4604,a,b,10161,a)].">
      <j1 rule="hyper" parents="138 4604 10161"/>
    </justification>
  </clause>

  <clause id="10186">
    <literal><![CDATA[
      (x / (K(y,z) * u)) * (K(y,z) * w) = (x / u) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,10160,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 10160 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10187">
    <literal><![CDATA[
      L(x \ 1,y,z) * (K(u,w) * v5) = L(x \ K(u,w),y,z) * v5
    ]]></literal>
    <justification jstring="[hyper(138,a,4846,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 4846 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10188">
    <literal><![CDATA[
      L(x \ y,z,u) * (K(x,x \ y) * w) = L(y / x,z,u) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,4844,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 4844 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10189">
    <literal><![CDATA[
      (x * (y * z)) * (K(z,u) * w) = (x * (y * T(z,u))) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,3942,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 3942 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10190">
    <literal><![CDATA[
      (x * y) * (K(z,T(u,y)) * w) = (x * (K(z,u) * y)) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,3941,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 3941 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10191">
    <literal><![CDATA[
      (x * (y \ 1)) * (K(z,u) * w) = (x * (y \ K(z,u))) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,3940,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 3940 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10192">
    <literal><![CDATA[
      (x \ (y \ z)) * (K(y,y \ z) * u) = (x \ (z / y)) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,3919,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 3919 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10193">
    <literal><![CDATA[
      (x \ y) * (K(z,z \ y) * u) = (x \ (z * (y / z))) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,3918,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 3918 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10194">
    <literal><![CDATA[
      (x \ y) * (K(z,T(u,y)) * w) = (x \ (K(z,u) * y)) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,3914,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 3914 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10195">
    <literal><![CDATA[
      (x \ y) * (K(y,z) * u) = (x \ T(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,3846,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 3846 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10196">
    <literal><![CDATA[
      (x / (y \ z)) * (K(y \ z,y) * u) = (x / (z / y)) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,3834,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 3834 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10197">
    <literal><![CDATA[
      (x / T(y,z)) * (K(y,z) * u) = (x / y) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,3833,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 3833 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10198">
    <literal><![CDATA[
      (x * y) * (K(y,z) * u) = (x * T(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,3832,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 3832 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10199">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * u) = x * u
    ]]></literal>
    <justification jstring="[hyper(138,a,3824,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 3824 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10200">
    <literal><![CDATA[
      (x \ 1) * (K(y,z) * u) = (x \ K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,3780,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 3780 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10201">
    <literal><![CDATA[
      (x * (y * K(z,u))) * w = (x * y) * (K(z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(138,a,3763,a(flip),b,10161,a)].">
      <j1 rule="hyper" parents="138 3763 10161"/>
    </justification>
  </clause>

  <clause id="10202">
    <literal><![CDATA[
      (x * T(y,z)) * (K(z,y) * u) = (x * y) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,3268,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 3268 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10203">
    <literal><![CDATA[
      (x / y) * (K(z,y) * u) = (x / T(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,3259,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 3259 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10204">
    <literal><![CDATA[
      (x * y) * (K(x,y) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,3084,a(flip),b,10161,a),flip(a)].">
      <j1 rule="hyper" parents="138 3084 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10205">
    <literal><![CDATA[
      (x * (y * z)) / (z * y) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(2728(a,1),10161(a,1,1,2))].">
      <j1 rule="para" parents="2728 10161"/>
    </justification>
  </clause>

  <clause id="10206">
    <literal><![CDATA[
      (x * y) / (K(z,u) * y) = x * K(u,z)
    ]]></literal>
    <justification jstring="[para(2995(a,1),10161(a,1,1,2))].">
      <j1 rule="para" parents="2995 10161"/>
    </justification>
  </clause>

  <clause id="10207">
    <literal><![CDATA[
      (x * K(y,z * u)) * u = x * (u * K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(139,a,4129,a(flip),b,10162,a),flip(a)].">
      <j1 rule="hyper" parents="139 4129 10162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10208">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ u) = x * (T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,3002,a(flip),b,10162,a),flip(a)].">
      <j1 rule="hyper" parents="139 3002 10162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10209">
    <literal><![CDATA[
      (x * K(y,z)) * (T(y,z) \ u) = x * (y \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,2859,a(flip),b,10162,a),flip(a)].">
      <j1 rule="hyper" parents="139 2859 10162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10211">
    <literal><![CDATA[
      (x \ 1) \ ((x \ K(y,z)) * u) = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(3780(a,1),10162(a,1,2,1))].">
      <j1 rule="para" parents="3780 10162"/>
    </justification>
  </clause>

  <clause id="10212">
    <literal><![CDATA[
      K(x \ y,x) * (y \ z) = (x * (y / x)) \ z
    ]]></literal>
    <justification jstring="[para(3091(a,1),10163(a,1,2,1))].">
      <j1 rule="para" parents="3091 10163"/>
    </justification>
  </clause>

  <clause id="10213">
    <literal><![CDATA[
      ((x * K(y,z)) \ u) * w = K(z,y) * ((x \ u) * w)
    ]]></literal>
    <justification jstring="[para(10163(a,1),3001(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10163 3001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10214">
    <literal><![CDATA[
      K(x,x \ y) * ((z * (y / x)) \ u) = (z * (x \ y)) \ u
    ]]></literal>
    <justification jstring="[para(3151(a,1),10163(a,1,2,1))].">
      <j1 rule="para" parents="3151 10163"/>
    </justification>
  </clause>

  <clause id="10215">
    <literal><![CDATA[
      (x \ y) * ((z * K(x \ y,x)) \ u) = (y / x) * (z \ u)
    ]]></literal>
    <justification jstring="[para(10163(a,1),3202(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10163 3202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10216">
    <literal><![CDATA[
      K(x,y) * ((z / T(y,x)) \ u) = (z / y) \ u
    ]]></literal>
    <justification jstring="[para(3259(a,1),10163(a,1,2,1))].">
      <j1 rule="para" parents="3259 10163"/>
    </justification>
  </clause>

  <clause id="10217">
    <literal><![CDATA[
      K(x,y) * ((z * y) \ u) = (z * T(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(3268(a,1),10163(a,1,2,1))].">
      <j1 rule="para" parents="3268 10163"/>
    </justification>
  </clause>

  <clause id="10218">
    <literal><![CDATA[
      K(x,y) * ((z \ K(x,y)) \ u) = (z \ 1) \ u
    ]]></literal>
    <justification jstring="[para(3780(a,1),10163(a,1,2,1))].">
      <j1 rule="para" parents="3780 10163"/>
    </justification>
  </clause>

  <clause id="10219">
    <literal><![CDATA[
      K(x,y) * ((z \ 1) \ u) = (z \ K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(3828(a,1),10163(a,1,2,1))].">
      <j1 rule="para" parents="3828 10163"/>
    </justification>
  </clause>

  <clause id="10220">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ u) = (K(y,x) * z) \ u
    ]]></literal>
    <justification jstring="[para(3829(a,1),10163(a,1,2,1))].">
      <j1 rule="para" parents="3829 10163"/>
    </justification>
  </clause>

  <clause id="10221">
    <literal><![CDATA[
      K(x,y) * ((z * T(x,y)) \ u) = (z * x) \ u
    ]]></literal>
    <justification jstring="[para(3832(a,1),10163(a,1,2,1))].">
      <j1 rule="para" parents="3832 10163"/>
    </justification>
  </clause>

  <clause id="10222">
    <literal><![CDATA[
      K(x,y) * ((z / x) \ u) = (z / T(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(3833(a,1),10163(a,1,2,1))].">
      <j1 rule="para" parents="3833 10163"/>
    </justification>
  </clause>

  <clause id="10223">
    <literal><![CDATA[
      K(x,y) * ((z \ T(x,y)) \ u) = (z \ x) \ u
    ]]></literal>
    <justification jstring="[para(3846(a,1),10163(a,1,2,1))].">
      <j1 rule="para" parents="3846 10163"/>
    </justification>
  </clause>

  <clause id="10224">
    <literal><![CDATA[
      K(x,y) * ((z \ y) \ u) = (z \ T(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(3849(a,1),10163(a,1,2,1))].">
      <j1 rule="para" parents="3849 10163"/>
    </justification>
  </clause>

  <clause id="10225">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ w = K(u,z) * ((x * y) \ w)
    ]]></literal>
    <justification jstring="[para(3927(a,1),10163(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3927 10163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10226">
    <literal><![CDATA[
      K(x,T(y,z)) * ((u \ (K(x,y) * z)) \ w) = (u \ z) \ w
    ]]></literal>
    <justification jstring="[para(3914(a,1),10163(a,1,2,1))].">
      <j1 rule="para" parents="3914 10163"/>
    </justification>
  </clause>

  <clause id="10227">
    <literal><![CDATA[
      K(x,y) * ((z * (u \ K(x,y))) \ w) = (z * (u \ 1)) \ w
    ]]></literal>
    <justification jstring="[para(3940(a,1),10163(a,1,2,1))].">
      <j1 rule="para" parents="3940 10163"/>
    </justification>
  </clause>

  <clause id="10228">
    <literal><![CDATA[
      K(x,y) * (L(z \ K(x,y),u,w) \ v5) = L(z \ 1,u,w) \ v5
    ]]></literal>
    <justification jstring="[para(4846(a,1),10163(a,1,2,1))].">
      <j1 rule="para" parents="4846 10163"/>
    </justification>
  </clause>

  <clause id="10229">
    <literal><![CDATA[
      (x * y) * K(z,T(u,y)) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(316,a,3941,a,b,10165,a)].">
      <j1 rule="hyper" parents="316 3941 10165"/>
    </justification>
  </clause>

  <clause id="10230">
    <literal><![CDATA[
      K(x,y) * (T(z,K(x,y)) * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,642,a,b,10165,a)].">
      <j1 rule="hyper" parents="63 642 10165"/>
    </justification>
  </clause>

  <clause id="10231">
    <literal><![CDATA[
      ((x * (y * K(z,u))) * w) / (y * (K(z,u) * w)) = R(x,y * K(z,u),w)
    ]]></literal>
    <justification jstring="[hyper(209,a,10165,a(flip),b,199,a)].">
      <j1 rule="hyper" parents="209 10165 199"/>
    </justification>
  </clause>

  <clause id="10232">
    <literal><![CDATA[
      (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y * K(z,u),w)
    ]]></literal>
    <justification jstring="[para(10165(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10165 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10234">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ ((x * K(y,z)) * (u * w)) = L(w,u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(10165(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10165 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10235">
    <literal><![CDATA[
      T(x,y * K(z,u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10158,a(flip),b,10174,a)].">
      <j1 rule="hyper" parents="63 10158 10174"/>
    </justification>
  </clause>

  <clause id="10236">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(94(a,1),10174(a,2,2))].">
      <j1 rule="para" parents="94 10174"/>
    </justification>
  </clause>

  <clause id="10237">
    <literal><![CDATA[
      (x \ y) \ (x \ (x \ y)) = K(y,x) * (y \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,8195,a,b,10176,a)].">
      <j1 rule="hyper" parents="63 8195 10176"/>
    </justification>
  </clause>

  <clause id="10238">
    <literal><![CDATA[
      x \ (K(y,T(z,x)) * u) = K(y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4150,a,b,10176,a)].">
      <j1 rule="hyper" parents="63 4150 10176"/>
    </justification>
  </clause>

  <clause id="10239">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ R(y,x \ 1,x)) = a(y * (1 / x),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7019,a(flip),b,10176,a),flip(a)].">
      <j1 rule="hyper" parents="63 7019 10176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10240">
    <literal><![CDATA[
      K(x,y) * (L(a(z,u,w),v5 \ K(y,x),v5) \ v6) = (v5 * ((v5 \ K(y,x)) * a(z,u,w))) \ v6
    ]]></literal>
    <justification jstring="[para(2308(a,1),10176(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2308 10176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10242">
    <literal><![CDATA[
      K(x,y) * ((z * (u * y)) \ w) = (z * (u * T(y,x))) \ w
    ]]></literal>
    <justification jstring="[para(3942(a,1),10176(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3942 10176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10243">
    <literal><![CDATA[
      R(x * K(y,z),u,w) \ v5 = K(z,y) * (R(x,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(4604(a,2),10176(a,1,1))].">
      <j1 rule="para" parents="4604 10176"/>
    </justification>
  </clause>

  <clause id="10244">
    <literal><![CDATA[
      L(x * K(y,z),u,w) \ v5 = K(z,y) * (L(x,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(4837(a,2),10176(a,1,1))].">
      <j1 rule="para" parents="4837 10176"/>
    </justification>
  </clause>

  <clause id="10245">
    <literal><![CDATA[
      K(x \ y,x) * (L(x \ y,z,u) \ w) = L(y / x,z,u) \ w
    ]]></literal>
    <justification jstring="[para(4844(a,1),10176(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4844 10176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10246">
    <literal><![CDATA[
      K(x,y) * (L(z * y,u,w) \ v5) = L(z * T(y,x),u,w) \ v5
    ]]></literal>
    <justification jstring="[para(4847(a,1),10176(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4847 10176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10249">
    <literal><![CDATA[
      (x * (y \ K(z,u))) * (K(u,z) * w) = (x * (y \ 1)) * w
    ]]></literal>
    <justification jstring="[para(3940(a,1),10199(a,1,1))].">
      <j1 rule="para" parents="3940 10199"/>
    </justification>
  </clause>

  <clause id="10250">
    <literal><![CDATA[
      L(T(x,y),z,u) * (K(y,x) * w) = L(x,z,u) * w
    ]]></literal>
    <justification jstring="[para(4449(a,1),10199(a,1,1))].">
      <j1 rule="para" parents="4449 10199"/>
    </justification>
  </clause>

  <clause id="10251">
    <literal><![CDATA[
      L(x * K(y,z),u,w) * (K(z,y) * v5) = L(x,u,w) * v5
    ]]></literal>
    <justification jstring="[para(4837(a,2),10199(a,1,1))].">
      <j1 rule="para" parents="4837 10199"/>
    </justification>
  </clause>

  <clause id="10252">
    <literal><![CDATA[
      L(x \ K(y,z),u,w) * (K(z,y) * v5) = L(x \ 1,u,w) * v5
    ]]></literal>
    <justification jstring="[para(4846(a,1),10199(a,1,1))].">
      <j1 rule="para" parents="4846 10199"/>
    </justification>
  </clause>

  <clause id="10253">
    <literal><![CDATA[
      (T(x,y) \ L(x,z,u)) * (x * y) = (x \ L(x,z,u)) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(138,a,4012,a(flip),b,10205,a)].">
      <j1 rule="hyper" parents="138 4012 10205"/>
    </justification>
  </clause>

  <clause id="10254">
    <literal><![CDATA[
      (K(x,y) / x) * (y * x) = (1 / x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(138,a,3263,a(flip),b,10205,a),flip(a)].">
      <j1 rule="hyper" parents="138 3263 10205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10255">
    <literal><![CDATA[
      x / T(x,y * K(z,u)) = K(y * K(u,z),x)
    ]]></literal>
    <justification jstring="[hyper(209,a,10235,a,b,2928,a(flip))].">
      <j1 rule="hyper" parents="209 10235 2928"/>
    </justification>
  </clause>

  <clause id="10256">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4108,a,b,10236,a)].">
      <j1 rule="hyper" parents="63 4108 10236"/>
    </justification>
  </clause>

  <clause id="10257">
    <literal><![CDATA[
      T(x,y) \ ((T(x,y) \ 1) \ z) = x \ ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2966(a,1),10177(a,1,2,1))].">
      <j1 rule="para" parents="2966 10177"/>
    </justification>
  </clause>

  <clause id="10258">
    <literal><![CDATA[
      T(x,y) * ((z * T(x,y)) \ u) = x * ((z * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,10179,a(flip),b,2898,a)].">
      <j1 rule="hyper" parents="139 10179 2898"/>
    </justification>
  </clause>

  <clause id="10259">
    <literal><![CDATA[
      K(x,y) * (((z * T(x,y)) \ u) * w) = ((z * x) \ u) * w
    ]]></literal>
    <justification jstring="[para(10179(a,1),640(a,1,2,1))].">
      <j1 rule="para" parents="10179 640"/>
    </justification>
  </clause>

  <clause id="10260">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = x / (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3371,a,b,10181,a)].">
      <j1 rule="hyper" parents="63 3371 10181"/>
    </justification>
  </clause>

  <clause id="10261">
    <literal><![CDATA[
      ((x * y) / (K(z,u) / w)) * L(K(z,u) / w,y,x) = ((x * (y * (K(z,u) / w))) / (1 / w)) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1465,a,b,10182,a)].">
      <j1 rule="hyper" parents="316 1465 10182"/>
    </justification>
  </clause>

  <clause id="10262">
    <literal><![CDATA[
      K(x,y) * (1 / (1 / x)) = 1 / (K(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3107,a,b,10182,a)].">
      <j1 rule="hyper" parents="63 3107 10182"/>
    </justification>
  </clause>

  <clause id="10263">
    <literal><![CDATA[
      (x / (y / (y / z))) / (y / z) = (x / z) / (z \ y)
    ]]></literal>
    <justification jstring="[hyper(136,a,10183,a,b,3227,a)].">
      <j1 rule="hyper" parents="136 10183 3227"/>
    </justification>
  </clause>

  <clause id="10264">
    <literal><![CDATA[
      a(x,y,L(z,u,w) / (1 / (1 / v5))) = a(x,y,v5 \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(10183(a,2),8310(a,1,3))].">
      <j1 rule="para" parents="10183 8310"/>
    </justification>
  </clause>

  <clause id="10265">
    <literal><![CDATA[
      (x \ T(y,z)) * L(T(u,K(y,z)),w,v5) = (x \ y) * (L(u,w,v5) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,412,a(flip),b,10195,a),flip(a)].">
      <j1 rule="hyper" parents="63 412 10195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10267">
    <literal><![CDATA[
      R(x,y,(z \ T(u,w)) * v5) = R(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[para(10195(a,1),4697(a,1,3))].">
      <j1 rule="para" parents="10195 4697"/>
    </justification>
  </clause>

  <clause id="10268">
    <literal><![CDATA[
      a(x,y,(z \ ((K(u,w) * v5) * (v6 \ u))) * v7) = a(x,y,v7 * (z \ ((v6 \ T(u,w)) * v5)))
    ]]></literal>
    <justification jstring="[para(10195(a,1),5665(a,2,3,2,2))].">
      <j1 rule="para" parents="10195 5665"/>
    </justification>
  </clause>

  <clause id="10269">
    <literal><![CDATA[
      (x / T(y,z)) * (K(y,z) * L((x / y) \ u,w,v5)) = L(u / (x / y),w,v5) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(316,a,602,a,b,10197,a),flip(a)].">
      <j1 rule="hyper" parents="316 602 10197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10270">
    <literal><![CDATA[
      (x / T(y,z)) * L(T(y,z),u,w) = (x / y) * L(y,u,w)
    ]]></literal>
    <justification jstring="[para(4289(a,1),10197(a,1,2))].">
      <j1 rule="para" parents="4289 10197"/>
    </justification>
  </clause>

  <clause id="10271">
    <literal><![CDATA[
      (x * T(y,z)) * (T(y,z) \ u) = (x * y) * (y \ u)
    ]]></literal>
    <justification jstring="[para(2859(a,1),10198(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2859 10198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10272">
    <literal><![CDATA[
      (x \ 1) * (y * K(y * z,u)) = (x \ K(z * y,u)) * y
    ]]></literal>
    <justification jstring="[para(4130(a,1),10200(a,1,2))].">
      <j1 rule="para" parents="4130 10200"/>
    </justification>
  </clause>

  <clause id="10273">
    <literal><![CDATA[
      (((x \ K(y,z)) * u) / (x \ 1)) * L(x \ 1,w,v5) = L(x \ 1,w,v5) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(10200(a,1),4334(a,1,1,1))].">
      <j1 rule="para" parents="10200 4334"/>
    </justification>
  </clause>

  <clause id="10275">
    <literal><![CDATA[
      (x * T(y,z)) \ ((y * x) * u) = K(z,y) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(133,a,6246,a(flip),b,10202,a)].">
      <j1 rule="hyper" parents="133 6246 10202"/>
    </justification>
  </clause>

  <clause id="10276">
    <literal><![CDATA[
      (x / T(y,z)) * L(T(u,K(z,y)),w,v5) = (x / y) * (L(u,w,v5) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,412,a(flip),b,10203,a),flip(a)].">
      <j1 rule="hyper" parents="63 412 10203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10277">
    <literal><![CDATA[
      ((T(x,y) * y) * z) \ (K(x,y) * (z * (x * y))) = K(K(x,y) * z,x * y)
    ]]></literal>
    <justification jstring="[para(10204(a,1),646(a,1,1))].">
      <j1 rule="para" parents="10204 646"/>
    </justification>
  </clause>

  <clause id="10278">
    <literal><![CDATA[
      K(x,y) * (z * (T(x,y) \ u)) = T(z,K(x,y)) * (x \ u)
    ]]></literal>
    <justification jstring="[para(10208(a,1),4157(a,1,2))].">
      <j1 rule="para" parents="10208 4157"/>
    </justification>
  </clause>

  <clause id="10279">
    <literal><![CDATA[
      (x * (y \ z)) * (T(z / y,y) \ u) = (x * (z / y)) * ((z / y) \ u)
    ]]></literal>
    <justification jstring="[para(3889(a,1),10209(a,1,1))].">
      <j1 rule="para" parents="3889 10209"/>
    </justification>
  </clause>

  <clause id="10280">
    <literal><![CDATA[
      (x \ L(T(y,z),u,w)) * (T(y,z) \ v5) = (x \ L(y,u,w)) * (y \ v5)
    ]]></literal>
    <justification jstring="[para(4452(a,1),10209(a,1,1))].">
      <j1 rule="para" parents="4452 10209"/>
    </justification>
  </clause>

  <clause id="10282">
    <literal><![CDATA[
      a(((x \ K(y,z)) * u) * (x * x),w,v5) = a((K(y,z) * u) * x,w,v5)
    ]]></literal>
    <justification jstring="[para(10211(a,1),3214(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10211 3214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10283">
    <literal><![CDATA[
      K(x \ y,x) * (y \ (y / x)) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(316,a,3198,a(flip),b,10212,a),flip(a)].">
      <j1 rule="hyper" parents="316 3198 10212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10284">
    <literal><![CDATA[
      (((x * (y / x)) \ L(y,z,u)) * w) / (K(x \ y,x) * w) = R(y \ L(y,z,u),K(x \ y,x),w)
    ]]></literal>
    <justification jstring="[para(10212(a,1),5103(a,1,1,1))].">
      <j1 rule="para" parents="10212 5103"/>
    </justification>
  </clause>

  <clause id="10285">
    <literal><![CDATA[
      K(x,y) * ((z / T(y,x)) \ (a(z / y,u,w) \ v5)) = a(z / y,u,w) \ ((z / y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,8533,a,b,10216,a),flip(a)].">
      <j1 rule="hyper" parents="316 8533 10216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10287">
    <literal><![CDATA[
      K(x,y) * (((z / x) \ u) * w) = ((z / T(x,y)) \ u) * w
    ]]></literal>
    <justification jstring="[para(10216(a,1),3001(a,1,2,1))].">
      <j1 rule="para" parents="10216 3001"/>
    </justification>
  </clause>

  <clause id="10288">
    <literal><![CDATA[
      L(x,y,((z * T(u,w)) \ v5) \ v6) = L(x,y,((z * u) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[para(10217(a,1),4172(a,1,3,1))].">
      <j1 rule="para" parents="10217 4172"/>
    </justification>
  </clause>

  <clause id="10289">
    <literal><![CDATA[
      a(x,y,L((z * T(u,w)) \ v5,v6,v7)) = a(x,y,L((z * u) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(10217(a,1),5554(a,1,3,1))].">
      <j1 rule="para" parents="10217 5554"/>
    </justification>
  </clause>

  <clause id="10290">
    <literal><![CDATA[
      K(x,y) * (((z \ K(x,y)) \ u) * w) = ((z \ 1) \ u) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,10218,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 10218 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10291">
    <literal><![CDATA[
      ((x \ 1) \ y) \ (K(z,u) * w) = ((x \ K(z,u)) \ y) \ w
    ]]></literal>
    <justification jstring="[para(10218(a,1),477(a,1,1))].">
      <j1 rule="para" parents="10218 477"/>
    </justification>
  </clause>

  <clause id="10292">
    <literal><![CDATA[
      K(x,y) * (((z \ 1) \ u) * w) = ((z \ K(y,x)) \ u) * w
    ]]></literal>
    <justification jstring="[para(10218(a,1),3001(a,1,2,1))].">
      <j1 rule="para" parents="10218 3001"/>
    </justification>
  </clause>

  <clause id="10293">
    <literal><![CDATA[
      a(x,y,((z \ K(u,w)) \ v5) * v6) = a(x,y,((z \ 1) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(10218(a,1),5541(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10218 5541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10294">
    <literal><![CDATA[
      (x \ 1) \ L(x \ K(y,z),u,w) = x * L(x \ K(y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(34,a,3354,a(flip),b,10219,a),flip(a)].">
      <j1 rule="hyper" parents="34 3354 10219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10295">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ u) = z \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(316,a,3009,a(flip),b,10220,a),flip(a)].">
      <j1 rule="hyper" parents="316 3009 10220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10296">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = z \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2975,a(flip),b,10220,a),flip(a)].">
      <j1 rule="hyper" parents="316 2975 10220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10297">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z \ 1) * u) = (z \ K(x,y)) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,10296,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 10296 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10298">
    <literal><![CDATA[
      (T(x,y) \ z) \ ((u * T(x,y)) \ w) = (x \ z) \ ((u * x) \ w)
    ]]></literal>
    <justification jstring="[para(10221(a,1),2906(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10221 2906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10299">
    <literal><![CDATA[
      T((x / y) \ z,K(y,z)) = (x / T(y,z)) \ T(z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4109,a(flip),b,10222,a)].">
      <j1 rule="hyper" parents="63 4109 10222"/>
    </justification>
  </clause>

  <clause id="10300">
    <literal><![CDATA[
      (x \ T(y,z)) * L(K(z,y) * ((x \ y) \ T(y,z)),u,w) = L(x,u,w) * (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(10224(a,2),604(a,1,2,1))].">
      <j1 rule="para" parents="10224 604"/>
    </justification>
  </clause>

  <clause id="10301">
    <literal><![CDATA[
      K(x,T(y,z)) / z = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(374,a,10229,a)].">
      <j1 rule="hyper" parents="374 10229"/>
    </justification>
  </clause>

  <clause id="10302">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,y)) = T(x * K(z,u),y)
    ]]></literal>
    <justification jstring="[hyper(253,a,10229,a(flip),b,3776,a),flip(a)].">
      <j1 rule="hyper" parents="253 10229 3776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10303">
    <literal><![CDATA[
      K(x,T(y,x \ z)) / (x \ z) = 1 / (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,10181,a(flip),b,10301,a),flip(a)].">
      <j1 rule="hyper" parents="316 10181 10301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10304">
    <literal><![CDATA[
      (1 / x) * K(y,z / x) = K(y,x \ z) / x
    ]]></literal>
    <justification jstring="[para(116(a,1),10301(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="116 10301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10305">
    <literal><![CDATA[
      (1 / x) * K(y,x * z) = K(y,z * x) / x
    ]]></literal>
    <justification jstring="[para(3535(a,1),10301(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3535 10301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10306">
    <literal><![CDATA[
      (1 / x) * K(y / x,z) = K(x \ y,z) / x
    ]]></literal>
    <justification jstring="[para(3869(a,1),10301(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3869 10301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10307">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,161,a(flip),b,10238,a),flip(a)].">
      <j1 rule="hyper" parents="139 161 10238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10308">
    <literal><![CDATA[
      (x * y) \ (K(z,T(u,x * y)) * T(x,y)) = K(z,u) * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[para(2875(a,1),10238(a,2,2))].">
      <j1 rule="para" parents="2875 10238"/>
    </justification>
  </clause>

  <clause id="10309">
    <literal><![CDATA[
      (K(x,y) / x) * (y * x) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,890,a(flip),b,10254,a),flip(a)].">
      <j1 rule="hyper" parents="316 890 10254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10310">
    <literal><![CDATA[
      (K(x,(((x \ 1) * x) \ y) \ 1) / x) * (((((x \ 1) * x) \ y) \ 1) * x) = (x \ ((x \ 1) \ y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,9887,a(flip),b,10309,a),flip(a)].">
      <j1 rule="hyper" parents="316 9887 10309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10311">
    <literal><![CDATA[
      (K(x,y \ 1) / x) * ((y \ K(z,x)) * x) = L(y \ K(z,x),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3989(a,1),10309(a,1,1,1))].">
      <j1 rule="para" parents="3989 10309"/>
    </justification>
  </clause>

  <clause id="10312">
    <literal><![CDATA[
      a(x,y,L(z * ((u * w) * (K(w,u) / w)),v5,v6)) = a(x,y,L(z * L(u,w,w \ 1),v5,v6))
    ]]></literal>
    <justification jstring="[para(10309(a,1),5709(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="10309 5709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10313">
    <literal><![CDATA[
      x / (T(y,x) \ 1) = L(y,y,x) * x
    ]]></literal>
    <justification jstring="[para(1447(a,2),10260(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1447 10260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10314">
    <literal><![CDATA[
      L(x,x,L(y,z,u) * w) * (L(y,z,u) * w) = (L(y,z,u) * w) / (T(x,y * w) \ 1)
    ]]></literal>
    <justification jstring="[para(6512(a,1),10313(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6512 10313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10315">
    <literal><![CDATA[
      x \ (K(y,z) * (x * u)) = K(y,T(z,x)) * u
    ]]></literal>
    <justification jstring="[hyper(539,a,10295,a),flip(a)].">
      <j1 rule="hyper" parents="539 10295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10316">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ u) = (z \ u) * K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,3914,a,b,10295,a),flip(a)].">
      <j1 rule="hyper" parents="316 3914 10295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10317">
    <literal><![CDATA[
      x * (K(y,T(z,x)) * u) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,161,a(flip),b,10295,a(flip))].">
      <j1 rule="hyper" parents="139 161 10295"/>
    </justification>
  </clause>

  <clause id="10318">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * L(z \ u,w,v5)) = z \ (K(x,y) * L(z * u,w,v5))
    ]]></literal>
    <justification jstring="[para(1355(a,1),10295(a,1,2))].">
      <j1 rule="para" parents="1355 10295"/>
    </justification>
  </clause>

  <clause id="10319">
    <literal><![CDATA[
      a(x * (y \ (K(z,u) * w)),v5,v6) = a((y \ w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(10295(a,1),4179(a,1,1,2))].">
      <j1 rule="para" parents="10295 4179"/>
    </justification>
  </clause>

  <clause id="10320">
    <literal><![CDATA[
      a(x,y,(z * (u \ (K(w,v5) * v6))) * v7) = a(x,y,(z * (u \ v6)) * v7)
    ]]></literal>
    <justification jstring="[para(10295(a,1),5695(a,1,3,1,2))].">
      <j1 rule="para" parents="10295 5695"/>
    </justification>
  </clause>

  <clause id="10321">
    <literal><![CDATA[
      ((x * y) \ K(x,x \ 1)) * (x * y) = x * (K(y \ (1 / x),y * x) / x)
    ]]></literal>
    <justification jstring="[para(10305(a,1),7534(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10305 7534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10322">
    <literal><![CDATA[
      (1 / x) * K(y * (1 / x),z) = K(x \ y,z) / x
    ]]></literal>
    <justification jstring="[para(3561(a,2),10306(a,1,2))].">
      <j1 rule="para" parents="3561 10306"/>
    </justification>
  </clause>

  <clause id="10323">
    <literal><![CDATA[
      L(K(x \ y,z) / x,x \ 1,y) = y \ T(y / x,z)
    ]]></literal>
    <justification jstring="[para(10306(a,1),7700(a,1,1))].">
      <j1 rule="para" parents="10306 7700"/>
    </justification>
  </clause>

  <clause id="10324">
    <literal><![CDATA[
      L(K(x \ y,x \ 1) / x,x \ 1,y) = (y * (x \ (x \ 1))) / (y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(10306(a,1),8229(a,1,1))].">
      <j1 rule="para" parents="10306 8229"/>
    </justification>
  </clause>

  <clause id="10325">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z * u) * w) = (z * (K(x,y) * u)) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,10307,a(flip),b,410,a),flip(a)].">
      <j1 rule="hyper" parents="138 10307 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10326">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) * (z \ L(z * u,w,v5)) = (z \ 1) * (K(x,y) * L((z \ 1) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(898(a,1),10307(a,1,2))].">
      <j1 rule="para" parents="898 10307"/>
    </justification>
  </clause>

  <clause id="10327">
    <literal><![CDATA[
      x * K(y,T(z,u * x)) = K(y,T(z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(34,a,3929,a,b,10317,a)].">
      <j1 rule="hyper" parents="34 3929 10317"/>
    </justification>
  </clause>

  <clause id="10328">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(34,a,3883,a,b,10327,a)].">
      <j1 rule="hyper" parents="34 3883 10327"/>
    </justification>
  </clause>

  <clause id="10329">
    <literal><![CDATA[
      K(x / y,T(z,u * x)) = K(y \ x,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(34,a,3619,a(flip),b,10327,a),flip(a)].">
      <j1 rule="hyper" parents="34 3619 10327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10330">
    <literal><![CDATA[
      K(x,T(y / (z / u),y)) * u = u * K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(1961(a,1),10327(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1961 10327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10331">
    <literal><![CDATA[
      T(x \ (K(y,z) * u),K(y,z)) = (T(x,K(y,z)) \ u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(10178(a,1),471(a,1,1))].">
      <j1 rule="para" parents="10178 471"/>
    </justification>
  </clause>

  <clause id="10332">
    <literal><![CDATA[
      T(x,K(y,z)) \ (K(y,z) * u) = K(y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(4107(a,1),10178(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4107 10178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10333">
    <literal><![CDATA[
      (x / (y * z)) * (K(y,z) * u) = (x / (z * y)) * u
    ]]></literal>
    <justification jstring="[para(2728(a,1),10186(a,1,1,2))].">
      <j1 rule="para" parents="2728 10186"/>
    </justification>
  </clause>

  <clause id="10334">
    <literal><![CDATA[
      ((x * (y * K(z,u))) * w) / (y * (K(z,u) * w)) = R(x,y,K(z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(136,a,10201,a,b,109,a)].">
      <j1 rule="hyper" parents="136 10201 109"/>
    </justification>
  </clause>

  <clause id="10335">
    <literal><![CDATA[
      (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y,K(z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(133,a,10201,a,b,89,a)].">
      <j1 rule="hyper" parents="133 10201 89"/>
    </justification>
  </clause>

  <clause id="10336">
    <literal><![CDATA[
      (x * ((y * z) * (K(u,w) * (v5 * v5)))) / v6 = (x * (y * (z * K(u,w)))) / (v6 / (v5 * v5))
    ]]></literal>
    <justification jstring="[para(10201(a,1),677(a,1,1,2))].">
      <j1 rule="para" parents="10201 677"/>
    </justification>
  </clause>

  <clause id="10337">
    <literal><![CDATA[
      (x * (y * (z * K(u,w)))) * v5 = (x * (y * z)) * (K(u,w) * v5)
    ]]></literal>
    <justification jstring="[para(3763(a,1),10201(a,1,1,2))].">
      <j1 rule="para" parents="3763 10201"/>
    </justification>
  </clause>

  <clause id="10338">
    <literal><![CDATA[
      ((x * (y * K(z,u))) \ w) * v5 = K(u,z) * (((x * y) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(3763(a,1),10213(a,1,1,1))].">
      <j1 rule="para" parents="3763 10213"/>
    </justification>
  </clause>

  <clause id="10339">
    <literal><![CDATA[
      (x * (y / (y / z))) \ u = K(z,z \ y) * ((x * z) \ u)
    ]]></literal>
    <justification jstring="[para(3090(a,2),10225(a,1,1,2))].">
      <j1 rule="para" parents="3090 10225"/>
    </justification>
  </clause>

  <clause id="10340">
    <literal><![CDATA[
      K(x,y) * (z * (K(y,x) * u)) = T(z,K(y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(3006,a,10230,a)].">
      <j1 rule="hyper" parents="3006 10230"/>
    </justification>
  </clause>

  <clause id="10341">
    <literal><![CDATA[
      x \ (T(y,K(z,u)) * x) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(253,a,10230,a(flip),b,479,a),flip(a)].">
      <j1 rule="hyper" parents="253 10230 479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10343">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (K(y,z) * w) = (T(x,K(y,z)) * u) \ w
    ]]></literal>
    <justification jstring="[para(10230(a,1),477(a,1,1))].">
      <j1 rule="para" parents="10230 477"/>
    </justification>
  </clause>

  <clause id="10346">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(325,a,10341,a)].">
      <j1 rule="hyper" parents="325 10341"/>
    </justification>
  </clause>

  <clause id="10347">
    <literal><![CDATA[
      T(T(x,y),K(z,u)) = T(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,118,a(flip),b,10341,a)].">
      <j1 rule="hyper" parents="63 118 10341"/>
    </justification>
  </clause>

  <clause id="10348">
    <literal><![CDATA[
      T(x * y,K(y,x) * z) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(2756(a,1),10346(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2756 10346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10350">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(4106(a,1),10346(a,1,1))].">
      <j1 rule="para" parents="4106 10346"/>
    </justification>
  </clause>

  <clause id="10351">
    <literal><![CDATA[
      T(T(x,K(y,z * x)),u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(4163(a,2),10346(a,1,1))].">
      <j1 rule="para" parents="4163 10346"/>
    </justification>
  </clause>

  <clause id="10352">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10158,a(flip),b,10347,a),flip(a)].">
      <j1 rule="hyper" parents="63 10158 10347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10353">
    <literal><![CDATA[
      T(x * y,T(x,y) \ z) = T(x * y,x \ z)
    ]]></literal>
    <justification jstring="[para(3002(a,1),10348(a,1,2))].">
      <j1 rule="para" parents="3002 10348"/>
    </justification>
  </clause>

  <clause id="10354">
    <literal><![CDATA[
      (x * (y * z)) / T(y * x,z) = L(K(x,y) * z,y,x)
    ]]></literal>
    <justification jstring="[para(10348(a,1),4446(a,1,2))].">
      <j1 rule="para" parents="10348 4446"/>
    </justification>
  </clause>

  <clause id="10355">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10346,a(flip),b,10350,a)].">
      <j1 rule="hyper" parents="63 10346 10350"/>
    </justification>
  </clause>

  <clause id="10356">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y) * u) = T(K(y,z) * (x \ 1),u)
    ]]></literal>
    <justification jstring="[para(4158(a,1),10350(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4158 10350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10357">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,10256,a,b,10352,a)].">
      <j1 rule="hyper" parents="40 10256 10352"/>
    </justification>
  </clause>

  <clause id="10359">
    <literal><![CDATA[
      x / T(x,y * K(z,u)) = K(K(z,u) * y,x)
    ]]></literal>
    <justification jstring="[hyper(209,a,10352,a(flip),b,2928,a(flip))].">
      <j1 rule="hyper" parents="209 10352 2928"/>
    </justification>
  </clause>

  <clause id="10361">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) = T(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(3832(a,1),10352(a,2,2))].">
      <j1 rule="para" parents="3832 10352"/>
    </justification>
  </clause>

  <clause id="10362">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10158,a(flip),b,10357,a)].">
      <j1 rule="hyper" parents="63 10158 10357"/>
    </justification>
  </clause>

  <clause id="10363">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4115,a(flip),b,10357,a)].">
      <j1 rule="hyper" parents="63 4115 10357"/>
    </justification>
  </clause>

  <clause id="10365">
    <literal><![CDATA[
      K(K(x,y),K(z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,10357,a(flip),b,4097,a),flip(a)].">
      <j1 rule="hyper" parents="134 10357 4097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10367">
    <literal><![CDATA[
      x * (y * K(x,K(z,u))) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(10357(a,1),2913(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10357 2913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10368">
    <literal><![CDATA[
      T(x,K(K(y,z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(10357(a,1),3961(a,1,1))].">
      <j1 rule="para" parents="10357 3961"/>
    </justification>
  </clause>

  <clause id="10369">
    <literal><![CDATA[
      x \ (K(y,K(z,u)) * w) = (x \ w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(10357(a,1),4162(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10357 4162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10370">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,10365,a)].">
      <j1 rule="hyper" parents="56 10365"/>
    </justification>
  </clause>

  <clause id="10371">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4134,a,10370,a),flip(a)].">
      <j1 rule="hyper" parents="4134 10370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10372">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3626,a,b,10370,a)].">
      <j1 rule="hyper" parents="63 3626 10370"/>
    </justification>
  </clause>

  <clause id="10373">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3633,a(flip),b,10370,a),flip(a)].">
      <j1 rule="hyper" parents="63 3633 10370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10374">
    <literal><![CDATA[
      K(x,y) * K(z,u) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,10370,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="139 10370 22"/>
    </justification>
  </clause>

  <clause id="10376">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4020(a,1),10371(a,1,2))].">
      <j1 rule="para" parents="4020 10371"/>
    </justification>
  </clause>

  <clause id="10378">
    <literal><![CDATA[
      K(x,T(y,z * u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[para(10236(a,1),10371(a,1,2))].">
      <j1 rule="para" parents="10236 10371"/>
    </justification>
  </clause>

  <clause id="10379">
    <literal><![CDATA[
      T(x * K(y,z),K(u,w)) = T(x,K(u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(10371(a,1),10302(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10371 10302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10380">
    <literal><![CDATA[
      K(K(x,y) * (z \ 1),u) = K(z \ K(x,y),u)
    ]]></literal>
    <justification jstring="[para(4158(a,1),10372(a,1,1))].">
      <j1 rule="para" parents="4158 10372"/>
    </justification>
  </clause>

  <clause id="10381">
    <literal><![CDATA[
      T(x,y * T(z,K(u,w))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(3832(a,1),10362(a,1,2))].">
      <j1 rule="para" parents="3832 10362"/>
    </justification>
  </clause>

  <clause id="10383">
    <literal><![CDATA[
      K(x,T(y,z)) * T(z,u) = T(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,10376,a(flip),b,4126,a)].">
      <j1 rule="hyper" parents="138 10376 4126"/>
    </justification>
  </clause>

  <clause id="10384">
    <literal><![CDATA[
      x \ T(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(133,a,10355,a,b,2815,a(flip))].">
      <j1 rule="hyper" parents="133 10355 2815"/>
    </justification>
  </clause>

  <clause id="10385">
    <literal><![CDATA[
      T(x,K(y,z) * (z * u)) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(2800(a,1),10355(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2800 10355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10386">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(3002(a,1),10355(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3002 10355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10387">
    <literal><![CDATA[
      x \ (y * K(z,K(u,w))) = K(z,K(u,w)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(316,a,3781,a,b,10363,a)].">
      <j1 rule="hyper" parents="316 3781 10363"/>
    </justification>
  </clause>

  <clause id="10388">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,6423,a,b,10363,a)].">
      <j1 rule="hyper" parents="35 6423 10363"/>
    </justification>
  </clause>

  <clause id="10391">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = T(x,w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(10388(a,1),10302(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10388 10302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10392">
    <literal><![CDATA[
      (x \ y) \ (K(z,u) * K(x,w)) = (T(x,w) \ y) \ K(z,u)
    ]]></literal>
    <justification jstring="[para(10374(a,1),2906(a,1,2))].">
      <j1 rule="para" parents="10374 2906"/>
    </justification>
  </clause>

  <clause id="10393">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = z * (K(u,w) * K(x,y))
    ]]></literal>
    <justification jstring="[para(10374(a,1),10307(a,2,2))].">
      <j1 rule="para" parents="10374 10307"/>
    </justification>
  </clause>

  <clause id="10394">
    <literal><![CDATA[
      K((x * y) / z,T(u,y * x)) = K(z \ (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,3873,a(flip),b,10378,a),flip(a)].">
      <j1 rule="hyper" parents="316 3873 10378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10395">
    <literal><![CDATA[
      T(x,y * T(z,u * w)) = T(x,y * T(z,w * u))
    ]]></literal>
    <justification jstring="[para(10236(a,1),10381(a,1,2,2))].">
      <j1 rule="para" parents="10236 10381"/>
    </justification>
  </clause>

  <clause id="10396">
    <literal><![CDATA[
      T(x,K(y,z * x) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10346,a(flip),b,10351,a)].">
      <j1 rule="hyper" parents="63 10346 10351"/>
    </justification>
  </clause>

  <clause id="10397">
    <literal><![CDATA[
      T(x * y,(x * y) \ (y * z)) = T(x * y,x \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3693,a,b,10353,a)].">
      <j1 rule="hyper" parents="63 3693 10353"/>
    </justification>
  </clause>

  <clause id="10398">
    <literal><![CDATA[
      (x * y) / T(z * x,z \ y) = (z * x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(10353(a,1),3720(a,1,2))].">
      <j1 rule="para" parents="10353 3720"/>
    </justification>
  </clause>

  <clause id="10399">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10255,a(flip),b,10359,a),flip(a)].">
      <j1 rule="hyper" parents="63 10255 10359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10400">
    <literal><![CDATA[
      K(K(x,y) * (z \ 1),u) = K(z \ K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,3520,a(flip),b,10399,a),flip(a)].">
      <j1 rule="hyper" parents="316 3520 10399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10401">
    <literal><![CDATA[
      T(x,K(y,z) * (u * z)) = T(x,u * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10355,a,b,10361,a)].">
      <j1 rule="hyper" parents="63 10355 10361"/>
    </justification>
  </clause>

  <clause id="10402">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(z,w) = T(z,w) * K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(10328(a,1),10383(a,1,1))].">
      <j1 rule="para" parents="10328 10383"/>
    </justification>
  </clause>

  <clause id="10403">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(2832,a,10384,a)].">
      <j1 rule="hyper" parents="2832 10384"/>
    </justification>
  </clause>

  <clause id="10404">
    <literal><![CDATA[
      K(x,K(y,z) * (T(z,y) \ u)) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(2859(a,1),10403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2859 10403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10405">
    <literal><![CDATA[
      T(x,T(y,z) * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(2728(a,1),10385(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2728 10385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10406">
    <literal><![CDATA[
      T(x,T(y \ z,y) * u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(2774(a,1),10385(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2774 10385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10407">
    <literal><![CDATA[
      K(T(x,y) * y,z) = z / T(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(209,a,10405,a(flip),b,2928,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="209 10405 2928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10408">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2937,a,b,10407,a),flip(a)].">
      <j1 rule="hyper" parents="316 2937 10407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10409">
    <literal><![CDATA[
      (x * T(y,z)) \ ((T(y,z) * z) * x) = L(z * K(z * y,x),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(10408(a,1),3649(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10408 3649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10410">
    <literal><![CDATA[
      T(x,T(y,z) \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3498,a(flip),b,10386,a),flip(a)].">
      <j1 rule="hyper" parents="63 3498 10386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10411">
    <literal><![CDATA[
      T(x,((y * z) / y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(3142(a,2),10386(a,1,2))].">
      <j1 rule="para" parents="3142 10386"/>
    </justification>
  </clause>

  <clause id="10412">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,y \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[para(3124(a,1),10386(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3124 10386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10413">
    <literal><![CDATA[
      T(x,y / (y * z)) = T(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4475,a(flip),b,10410,a),flip(a)].">
      <j1 rule="hyper" parents="63 4475 10410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10414">
    <literal><![CDATA[
      L(x \ 1,x,y) * T(z,y \ (x \ y)) = T(z * ((y * x) \ y),K(x,y))
    ]]></literal>
    <justification jstring="[para(10413(a,1),7448(a,1,2))].">
      <j1 rule="para" parents="10413 7448"/>
    </justification>
  </clause>

  <clause id="10415">
    <literal><![CDATA[
      T(x,K(y,z) * (u * z)) = T(x,u * T(z,y * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,10361,a(flip),b,10396,a),flip(a)].">
      <j1 rule="hyper" parents="63 10361 10396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10416">
    <literal><![CDATA[
      K(x \ K(y,z),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10380,a(flip),b,10400,a)].">
      <j1 rule="hyper" parents="63 10380 10400"/>
    </justification>
  </clause>

  <clause id="10417">
    <literal><![CDATA[
      K(x \ K(y,z),u) * K(w,v5) = K(w,v5) * K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[para(10416(a,1),10374(a,1,1))].">
      <j1 rule="para" parents="10416 10374"/>
    </justification>
  </clause>

  <clause id="10418">
    <literal><![CDATA[
      K(x,T(T(y,z),z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(3042(a,1),10404(a,1,2))].">
      <j1 rule="para" parents="3042 10404"/>
    </justification>
  </clause>

  <clause id="10419">
    <literal><![CDATA[
      K(x,(L(y,z,y) * z) \ u) = K(x,T(z * y,y) \ u)
    ]]></literal>
    <justification jstring="[para(1649(a,1),10418(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1649 10418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10420">
    <literal><![CDATA[
      T(x,(y / z) * (y / z)) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[para(3029(a,1),10406(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3029 10406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10421">
    <literal><![CDATA[
      T(x,y \ (L(z,y,z) \ u)) = T(x,T(y * z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3710,a(flip),b,10411,a)].">
      <j1 rule="hyper" parents="63 3710 10411"/>
    </justification>
  </clause>

  <clause id="10422">
    <literal><![CDATA[
      (x \ y) \ (x \ (x \ y)) = y \ (T(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(316,a,3119,a(flip),b,10237,a),flip(a)].">
      <j1 rule="hyper" parents="316 3119 10237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10423">
    <literal><![CDATA[
      K(x \ y,x \ 1) * (y \ (T(y,x) / x)) = (x \ (x \ y)) / (x \ y)
    ]]></literal>
    <justification jstring="[para(10422(a,1),3016(a,1,2))].">
      <j1 rule="para" parents="10422 3016"/>
    </justification>
  </clause>

  <clause id="10424">
    <literal><![CDATA[
      K(x,y) * ((z / L(y,u,w)) * L(L(y,u,w),v5,v6)) = L(T(y,x),u,w) \ (L(L(y,u,w),v5,v6) * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,4385,a(flip),b,10250,a),flip(a)].">
      <j1 rule="hyper" parents="133 4385 10250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10426">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * (y * u)) / u) = T(y,z) \ (x \ ((x * (y * u)) / u))
    ]]></literal>
    <justification jstring="[hyper(133,a,9349,a(flip),b,10258,a),flip(a)].">
      <j1 rule="hyper" parents="133 9349 10258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10427">
    <literal><![CDATA[
      K(T(x / (y / (y / z)),1 / u) / (y / z),u) = K((x / z) / (z \ y),u)
    ]]></literal>
    <justification jstring="[para(10263(a,1),4905(a,2,1))].">
      <j1 rule="para" parents="10263 4905"/>
    </justification>
  </clause>

  <clause id="10428">
    <literal><![CDATA[
      R(x,y,(z \ (u / w)) * v5) = R(x,y,(z \ (w \ u)) * v5)
    ]]></literal>
    <justification jstring="[para(116(a,1),10267(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="116 10267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10429">
    <literal><![CDATA[
      K(x,K(y,z)) * ((u \ 1) * w) = (u \ K(x,K(y,z))) * w
    ]]></literal>
    <justification jstring="[para(10388(a,1),10297(a,1,1))].">
      <j1 rule="para" parents="10388 10297"/>
    </justification>
  </clause>

  <clause id="10430">
    <literal><![CDATA[
      ((x / T(y,z)) * L(T((x / y) \ z,K(y,z)),u,w)) \ T(z,y) = (x / T(y,z)) \ (L(z / (x / y),u,w) \ T(z,y))
    ]]></literal>
    <justification jstring="[para(10299(a,2),9190(a,1,1,2,1))].">
      <j1 rule="para" parents="10299 9190"/>
    </justification>
  </clause>

  <clause id="10431">
    <literal><![CDATA[
      K((x \ y) \ z,T(u,y)) = K(z / (x \ y),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(35,a,4131,a,b,10316,a)].">
      <j1 rule="hyper" parents="35 4131 10316"/>
    </justification>
  </clause>

  <clause id="10432">
    <literal><![CDATA[
      x * (K(y \ x,z) / y) = T(x * (1 / y),z)
    ]]></literal>
    <justification jstring="[hyper(139,a,10322,a(flip),b,3645,a)].">
      <j1 rule="hyper" parents="139 10322 3645"/>
    </justification>
  </clause>

  <clause id="10433">
    <literal><![CDATA[
      x * (K(y,T(z,y \ x)) / (y \ x)) = T(x * (1 / (y \ x)),z)
    ]]></literal>
    <justification jstring="[para(3871(a,1),10432(a,1,2,1))].">
      <j1 rule="para" parents="3871 10432"/>
    </justification>
  </clause>

  <clause id="10434">
    <literal><![CDATA[
      R(T(x,K(y,z)),u,w) \ (K(y,z) * v5) = K(y,z) * (R(x,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(27(a,2),10332(a,1,1))].">
      <j1 rule="para" parents="27 10332"/>
    </justification>
  </clause>

  <clause id="10435">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * (y * z),K(y,z)) = K(y,z) * (x \ (u * (z * y)))
    ]]></literal>
    <justification jstring="[para(4160(a,2),10332(a,1,2))].">
      <j1 rule="para" parents="4160 10332"/>
    </justification>
  </clause>

  <clause id="10436">
    <literal><![CDATA[
      L((x * y) \ z,y * x,(y * x) \ 1) = (1 / (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,3059,a,b,10333,a)].">
      <j1 rule="hyper" parents="63 3059 10333"/>
    </justification>
  </clause>

  <clause id="10438">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(u,z)) = T(x,K(u,z)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,4231,a,b,10340,a)].">
      <j1 rule="hyper" parents="63 4231 10340"/>
    </justification>
  </clause>

  <clause id="10439">
    <literal><![CDATA[
      K(x,y) * (z * L(K(y,x) * u,w,v5)) = T(z,K(y,x)) * L(u,w,v5)
    ]]></literal>
    <justification jstring="[para(4850(a,2),10340(a,1,2,2))].">
      <j1 rule="para" parents="4850 10340"/>
    </justification>
  </clause>

  <clause id="10441">
    <literal><![CDATA[
      ((x * y) \ z) * K(x,K(u,w)) = (T(x,K(u,w)) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,4100,a(flip),b,10369,a),flip(a)].">
      <j1 rule="hyper" parents="63 4100 10369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10442">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(u,w)) = T(z * K(u,w),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,4095,a,b,10379,a)].">
      <j1 rule="hyper" parents="316 4095 10379"/>
    </justification>
  </clause>

  <clause id="10443">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ K(z,y)) = u \ K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(3982(a,1),10387(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3982 10387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10444">
    <literal><![CDATA[
      K(x,y) * (x * K(z,K(u,w))) = T(x * K(z,K(u,w)),y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2800,a,b,10391,a)].">
      <j1 rule="hyper" parents="316 2800 10391"/>
    </justification>
  </clause>

  <clause id="10445">
    <literal><![CDATA[
      K(x / (y / z),T(u,z * x)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3393,a(flip),b,10394,a)].">
      <j1 rule="hyper" parents="63 3393 10394"/>
    </justification>
  </clause>

  <clause id="10446">
    <literal><![CDATA[
      (x * y) / T(a(z,u,w) * x,y) = (a(z,u,w) * x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(5249(a,1),10398(a,1,2))].">
      <j1 rule="para" parents="5249 10398"/>
    </justification>
  </clause>

  <clause id="10447">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3722,a(flip),b,10412,a),flip(a)].">
      <j1 rule="hyper" parents="63 3722 10412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10448">
    <literal><![CDATA[
      T(x,R(y,z,u) \ (T(w,y) \ v5)) = T(x,w \ (R(y,z,u) \ v5))
    ]]></literal>
    <justification jstring="[para(2837(a,1),10447(a,1,2,2,1))].">
      <j1 rule="para" parents="2837 10447"/>
    </justification>
  </clause>

  <clause id="10449">
    <literal><![CDATA[
      T(x,y * T(z,u * x)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10401,a(flip),b,10415,a),flip(a)].">
      <j1 rule="hyper" parents="63 10401 10415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10450">
    <literal><![CDATA[
      T(x,y * T(z,x * u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10395,a,b,10449,a)].">
      <j1 rule="hyper" parents="63 10395 10449"/>
    </justification>
  </clause>

  <clause id="10451">
    <literal><![CDATA[
      T(x,y * T(z,x * y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(114(a,1),10450(a,2,2))].">
      <j1 rule="para" parents="114 10450"/>
    </justification>
  </clause>

  <clause id="10452">
    <literal><![CDATA[
      (x * T(y,z * x)) \ (y * (z * x)) = R(T(z,y * x),x,T(y,z * x))
    ]]></literal>
    <justification jstring="[para(10451(a,1),812(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10451 812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10453">
    <literal><![CDATA[
      T(x,(y \ z) * (y \ z)) = T(x,z * (y \ (z / y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3523,a(flip),b,10420,a),flip(a)].">
      <j1 rule="hyper" parents="63 3523 10420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10454">
    <literal><![CDATA[
      K(x / (y \ z),T(u,y)) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4268,a(flip),b,10431,a),flip(a)].">
      <j1 rule="hyper" parents="63 4268 10431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10455">
    <literal><![CDATA[
      K((x * y) / z,T(u,x)) = K(y / (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(4155,a,10454,a),flip(a)].">
      <j1 rule="hyper" parents="4155 10454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10456">
    <literal><![CDATA[
      T(x,K(y,z)) * T(u,K(y,z)) = T(x * u,K(y,z))
    ]]></literal>
    <justification jstring="[para(3957(a,1),10438(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3957 10438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10458">
    <literal><![CDATA[
      K((x / y) \ z,T(u,y)) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10329,a(flip),b,10445,a)].">
      <j1 rule="hyper" parents="63 10329 10445"/>
    </justification>
  </clause>

  <clause id="10459">
    <literal><![CDATA[
      K(x \ (y * z),T(u,z)) = K((x / z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(4155,a,10458,a),flip(a)].">
      <j1 rule="hyper" parents="4155 10458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10460">
    <literal><![CDATA[
      K(x / (y \ z),u) = K((z / x) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4270,a(flip),b,10459,a)].">
      <j1 rule="hyper" parents="63 4270 10459"/>
    </justification>
  </clause>

  <clause id="10461">
    <literal><![CDATA[
      K(x / ((y \ z) * u),w) = K((z / (x / u)) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3390,a(flip),b,10460,a)].">
      <j1 rule="hyper" parents="63 3390 10460"/>
    </justification>
  </clause>

  <clause id="10462">
    <literal><![CDATA[
      ((x \ y) * (x \ y)) * T(y \ x,y * (x \ (y / x))) = L(x \ y,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10453(a,1),912(a,1,2))].">
      <j1 rule="para" parents="10453 912"/>
    </justification>
  </clause>

  <clause id="10463">
    <literal><![CDATA[
      x * (T(y,K(z,u)) * K(x,K(z,u))) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10367,a,b,10456,a)].">
      <j1 rule="hyper" parents="63 10367 10456"/>
    </justification>
  </clause>

  <clause id="10464">
    <literal><![CDATA[
      K((x / ((y * z) / u)) \ w,T(v5,y)) = K(z / (y \ ((w \ x) * u)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10455,a(flip),b,10461,a),flip(a)].">
      <j1 rule="hyper" parents="63 10455 10461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10465">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5442,a(flip),b,10419,a),flip(a)].">
      <j1 rule="hyper" parents="63 5442 10419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10467">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),10465(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 10465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10468">
    <literal><![CDATA[
      K(x,T(y,z) \ (z * u)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3714,a(flip),b,10467,a),flip(a)].">
      <j1 rule="hyper" parents="63 3714 10467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10469">
    <literal><![CDATA[
      T(x,T(y * z,z) \ u) = T(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5309,a(flip),b,10421,a),flip(a)].">
      <j1 rule="hyper" parents="63 5309 10421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10471">
    <literal><![CDATA[
      T(x,(y / z) \ (z \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),10469(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 10469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10472">
    <literal><![CDATA[
      T(x,T(y,z) \ (z * u)) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),10471(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 10471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10473">
    <literal><![CDATA[
      L(L(x * K(y,z),u,w) \ L(L(x * K(y,z),u,w),v5,v6),L(x * K(y,z),u,w),v7) \ v7 = L(x,u,w) * (K(y,z) * (L(L(x * K(y,z),u,w),v5,v6) \ v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,9281,a,b,10184,a)].">
      <j1 rule="hyper" parents="63 9281 10184"/>
    </justification>
  </clause>

  <clause id="10474">
    <literal><![CDATA[
      L(R(x * K(y,z),u,w) \ L(R(x * K(y,z),u,w),v5,v6),R(x * K(y,z),u,w),v7) \ v7 = R(x,u,w) * (K(y,z) * (L(R(x * K(y,z),u,w),v5,v6) \ v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,9281,a,b,10185,a)].">
      <j1 rule="hyper" parents="63 9281 10185"/>
    </justification>
  </clause>

  <clause id="10475">
    <literal><![CDATA[
      L(x,y,R(z,u,w) * (K(v5,v6) * v7)) = L(x,y,v7 * R(z * K(v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(10185(a,1),1668(a,1,3))].">
      <j1 rule="para" parents="10185 1668"/>
    </justification>
  </clause>

  <clause id="10476">
    <literal><![CDATA[
      a(R(x,y,z) * (K(y,x) * u),w,v5) = a(((y * z) \ ((y * x) * z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(10185(a,1),3256(a,1,1))].">
      <j1 rule="para" parents="10185 3256"/>
    </justification>
  </clause>

  <clause id="10477">
    <literal><![CDATA[
      a(x,y,((K(z,u) * w) * (v5 * (v6 * z))) * v7) = a(x,y,v7 * ((v5 * (v6 * T(z,u))) * w))
    ]]></literal>
    <justification jstring="[para(10189(a,1),5623(a,2,3,2))].">
      <j1 rule="para" parents="10189 5623"/>
    </justification>
  </clause>

  <clause id="10478">
    <literal><![CDATA[
      a((x * (K(y,z) * u)) * w,v5,v6) = a((x * u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(10190(a,1),4041(a,1,1))].">
      <j1 rule="para" parents="10190 4041"/>
    </justification>
  </clause>

  <clause id="10479">
    <literal><![CDATA[
      a(x,y,((z * (K(u,w) * v5)) * v6) \ v7) = a(x,y,((z * v5) * v6) \ v7)
    ]]></literal>
    <justification jstring="[para(10190(a,1),5687(a,1,3,1))].">
      <j1 rule="para" parents="10190 5687"/>
    </justification>
  </clause>

  <clause id="10480">
    <literal><![CDATA[
      a((x * (y \ K(z,u))) * w,v5,v6) = a((x * (y \ 1)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(10191(a,1),4041(a,1,1))].">
      <j1 rule="para" parents="10191 4041"/>
    </justification>
  </clause>

  <clause id="10481">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * u) * (K(w,v5) * v6) = (u * (a(x,y,z) \ K(w,v5))) * v6
    ]]></literal>
    <justification jstring="[para(5006(a,2),10191(a,1,1))].">
      <j1 rule="para" parents="5006 10191"/>
    </justification>
  </clause>

  <clause id="10482">
    <literal><![CDATA[
      (x * (y \ K(z,u))) * ((w \ K(z,u)) \ v5) = (x * (y \ 1)) * ((w \ 1) \ v5)
    ]]></literal>
    <justification jstring="[para(10218(a,1),10191(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10218 10191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10483">
    <literal><![CDATA[
      (x * (y \ K(z,u))) * ((w \ 1) \ v5) = (x * (y \ 1)) * ((w \ K(u,z)) \ v5)
    ]]></literal>
    <justification jstring="[para(10219(a,1),10191(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10219 10191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10484">
    <literal><![CDATA[
      (x \ (y / z)) * ((y / z) \ u) = (x \ (z \ y)) * ((z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(3143(a,1),10192(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3143 10192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10485">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (w / v5)) * v6)) = a(x,y,z \ ((u \ (v5 \ w)) * v6))
    ]]></literal>
    <justification jstring="[para(10192(a,1),5509(a,1,3,2))].">
      <j1 rule="para" parents="10192 5509"/>
    </justification>
  </clause>

  <clause id="10486">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w / v5)) * v6)) = a(x,y,z * ((u \ (v5 \ w)) * v6))
    ]]></literal>
    <justification jstring="[para(10192(a,1),5593(a,1,3,2))].">
      <j1 rule="para" parents="10192 5593"/>
    </justification>
  </clause>

  <clause id="10487">
    <literal><![CDATA[
      a(x,y,((z \ (u / w)) * v5) * v6) = a(x,y,((z \ (w \ u)) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(10192(a,1),5695(a,1,3,1))].">
      <j1 rule="para" parents="10192 5695"/>
    </justification>
  </clause>

  <clause id="10488">
    <literal><![CDATA[
      L(x,y,(z \ (K(u,w) * v5)) * v6) = L(x,y,v6 * (z \ v5))
    ]]></literal>
    <justification jstring="[para(10194(a,1),1675(a,1,3))].">
      <j1 rule="para" parents="10194 1675"/>
    </justification>
  </clause>

  <clause id="10489">
    <literal><![CDATA[
      (x / (y \ z)) * ((y \ z) * y) = (x / (z / y)) * z
    ]]></literal>
    <justification jstring="[para(2727(a,1),10196(a,1,2))].">
      <j1 rule="para" parents="2727 10196"/>
    </justification>
  </clause>

  <clause id="10490">
    <literal><![CDATA[
      x * L(y,y \ z,(y \ z) \ x) = (x / (z / y)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,1606,a,b,10489,a)].">
      <j1 rule="hyper" parents="63 1606 10489"/>
    </justification>
  </clause>

  <clause id="10491">
    <literal><![CDATA[
      L(x,x \ y,(x \ y) \ 1) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,890,a(flip),b,10489,a)].">
      <j1 rule="hyper" parents="63 890 10489"/>
    </justification>
  </clause>

  <clause id="10492">
    <literal><![CDATA[
      L(x,y,a(z,u,L(y,y \ w,(y \ w) \ 1))) = L(x,a(z,u,(1 / (w / y)) * w),y)
    ]]></literal>
    <justification jstring="[para(10491(a,1),8924(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="10491 8924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10493">
    <literal><![CDATA[
      L(x,x \ 1,(x \ 1) \ y) = y \ (y / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(133,a,8,a(flip),b,10490,a),flip(a)].">
      <j1 rule="hyper" parents="133 8 10490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10494">
    <literal><![CDATA[
      (x / y) * ((z * (x / y)) \ u) = (y \ x) * ((z * (y \ x)) \ u)
    ]]></literal>
    <justification jstring="[para(10214(a,1),3074(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10214 3074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10495">
    <literal><![CDATA[
      (1 / x) * (((1 / x) * y) \ z) = (x \ 1) * (((x \ 1) * y) \ z)
    ]]></literal>
    <justification jstring="[para(2256(a,1),10215(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2256 10215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10496">
    <literal><![CDATA[
      K(x,T(y,z)) * ((x \ z) \ u) = (T(x,y) \ z) \ u
    ]]></literal>
    <justification jstring="[para(2809(a,1),10226(a,1,2,1))].">
      <j1 rule="para" parents="2809 10226"/>
    </justification>
  </clause>

  <clause id="10497">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (K(w,v5) * v6)) \ v7)) = a(x,y,z \ ((u \ v6) \ v7))
    ]]></literal>
    <justification jstring="[para(10226(a,1),5496(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10226 5496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10498">
    <literal><![CDATA[
      K(x,y) * (z * ((x \ z) \ u)) = z * ((T(x,y) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,10496,a(flip),b,10315,a),flip(a)].">
      <j1 rule="hyper" parents="139 10496 10315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10499">
    <literal><![CDATA[
      L(x,y,z \ ((T(u,w) \ v5) \ v6)) = L(x,y,z \ ((u \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(10496(a,1),4036(a,1,3,2))].">
      <j1 rule="para" parents="10496 4036"/>
    </justification>
  </clause>

  <clause id="10500">
    <literal><![CDATA[
      a(x,y,z * ((u * (w \ K(v5,v6))) \ v7)) = a(x,y,z * ((u * (w \ 1)) \ v7))
    ]]></literal>
    <justification jstring="[para(10227(a,1),5500(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10227 5500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10501">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ ((x * y) * z) = K(u,z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(14(a,2),10242(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14 10242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10502">
    <literal><![CDATA[
      L(L(x,y,z) * K(u,w),v5,v6) \ v7 = K(w,u) * (L(L(x,v5,v6),y,z) \ v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,836,a,b,10244,a),flip(a)].">
      <j1 rule="hyper" parents="316 836 10244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10503">
    <literal><![CDATA[
      K(x,y) * (L(z / x,u,w) \ v5) = L(z / T(x,y),u,w) \ v5
    ]]></literal>
    <justification jstring="[para(3259(a,1),10244(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3259 10244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10504">
    <literal><![CDATA[
      K(x,y) * (L(z \ T(x,y),u,w) \ v5) = L(z \ x,u,w) \ v5
    ]]></literal>
    <justification jstring="[para(3849(a,1),10244(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3849 10244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10505">
    <literal><![CDATA[
      K(x,x \ y) * (L(z / (x \ y),u,w) \ v5) = L(z / (y / x),u,w) \ v5
    ]]></literal>
    <justification jstring="[para(3834(a,1),10244(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3834 10244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10506">
    <literal><![CDATA[
      L(R(x * K(y,z),u,w),v5,v6) \ v7 = K(z,y) * (L(R(x,u,w),v5,v6) \ v7)
    ]]></literal>
    <justification jstring="[para(4604(a,2),10244(a,1,1,1))].">
      <j1 rule="para" parents="4604 10244"/>
    </justification>
  </clause>

  <clause id="10507">
    <literal><![CDATA[
      a(((x * T(y,z)) \ u) * w,v5,v6) = a(((x * y) \ u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(10259(a,1),1806(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10259 1806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10509">
    <literal><![CDATA[
      (x / (L(y,z,y) * z)) * L(L(y,z,y) * z,u,w) = (x / (z * y)) * L(T(L(y,z,y) * z,y),u,w)
    ]]></literal>
    <justification jstring="[para(1649(a,1),10270(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1649 10270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10510">
    <literal><![CDATA[
      x * (y * ((x \ K(y * x,z)) * x)) = T(x * (y * K(x \ 1,x)),z)
    ]]></literal>
    <justification jstring="[para(10272(a,1),7864(a,1,2,2))].">
      <j1 rule="para" parents="10272 7864"/>
    </justification>
  </clause>

  <clause id="10511">
    <literal><![CDATA[
      L(T(x,y),T(x,y) \ 1,T(x,y) * T(z,x)) = (T(z * x,K(x,y)) * (x \ 1)) \ ((1 / (1 / T(x,y))) * T(z,x))
    ]]></literal>
    <justification jstring="[para(10278(a,1),9792(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10278 9792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10512">
    <literal><![CDATA[
      T((x / y) \ (z \ u),K(y,u)) = (x / T(y,u)) \ (z \ T(u,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,4242,a(flip),b,10287,a(flip))].">
      <j1 rule="hyper" parents="35 4242 10287"/>
    </justification>
  </clause>

  <clause id="10513">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(z,y) * w) = w \ (((x \ 1) \ u) * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(133,a,10290,a(flip),b,3004,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 10290 3004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10514">
    <literal><![CDATA[
      a(x,y,(((z \ K(u,w)) \ v5) \ v6) * v7) = a(x,y,(((z \ 1) \ v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[para(10291(a,1),5693(a,1,3,1))].">
      <j1 rule="para" parents="10291 5693"/>
    </justification>
  </clause>

  <clause id="10515">
    <literal><![CDATA[
      (x \ K(y,z)) \ (K(z,y) * (((x \ 1) \ L(x \ K(y,z),u,w)) * v5)) = ((x \ K(y,z)) \ v5) * ((x \ K(y,z)) \ L(x \ K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(10292(a,2),5140(a,1,2))].">
      <j1 rule="para" parents="10292 5140"/>
    </justification>
  </clause>

  <clause id="10516">
    <literal><![CDATA[
      a(x * ((T(y,z) * u) \ w),v5,v6) = a(((y * u) \ w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(3021(a,1),10319(a,1,1,2))].">
      <j1 rule="para" parents="3021 10319"/>
    </justification>
  </clause>

  <clause id="10517">
    <literal><![CDATA[
      a(x,y,(z * ((u * (K(w,v5) * v6)) * v7)) * v8) = a(x,y,(z * ((u * v6) * v7)) * v8)
    ]]></literal>
    <justification jstring="[para(10325(a,1),5695(a,1,3,1,2))].">
      <j1 rule="para" parents="10325 5695"/>
    </justification>
  </clause>

  <clause id="10518">
    <literal><![CDATA[
      K(x,(y / z) \ u) * z = z * K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(1946(a,1),10330(a,1,1))].">
      <j1 rule="para" parents="1946 10330"/>
    </justification>
  </clause>

  <clause id="10519">
    <literal><![CDATA[
      K(x,T(y \ (z * u),u)) = K(x,(y / u) \ z)
    ]]></literal>
    <justification jstring="[hyper(35,a,4127,a,b,10518,a)].">
      <j1 rule="hyper" parents="35 4127 10518"/>
    </justification>
  </clause>

  <clause id="10520">
    <literal><![CDATA[
      K(x,y / (z \ u)) = K(x,(u / y) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4454,a(flip),b,10519,a)].">
      <j1 rule="hyper" parents="63 4454 10519"/>
    </justification>
  </clause>

  <clause id="10521">
    <literal><![CDATA[
      K(x,T(y,z) \ (z * u)) = K(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[hyper(316,a,10468,a,b,10520,a)].">
      <j1 rule="hyper" parents="316 10468 10520"/>
    </justification>
  </clause>

  <clause id="10522">
    <literal><![CDATA[
      T(x,T(y,z) \ (z * u)) = x * K(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[hyper(139,a,10521,a(flip),b,2806,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 10521 2806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10523">
    <literal><![CDATA[
      T(x,T(y,z) \ (z * u)) = T(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[hyper(316,a,2815,a,b,10522,a),flip(a)].">
      <j1 rule="hyper" parents="316 2815 10522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10524">
    <literal><![CDATA[
      T(x,y / (z \ u)) = T(x,(u / y) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10472,a(flip),b,10523,a),flip(a)].">
      <j1 rule="hyper" parents="63 10472 10523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10525">
    <literal><![CDATA[
      T(x,y / (z \ u)) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(316,a,3511,a(flip),b,10524,a),flip(a)].">
      <j1 rule="hyper" parents="316 3511 10524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10526">
    <literal><![CDATA[
      T(x,(y / z) \ (y / u)) = T(x,z / u)
    ]]></literal>
    <justification jstring="[para(83(a,1),10524(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 10524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10527">
    <literal><![CDATA[
      T(x,(y * z) * (u \ w)) = T(x,y * (z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3607,a(flip),b,10525,a),flip(a)].">
      <j1 rule="hyper" parents="63 3607 10525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10528">
    <literal><![CDATA[
      T(x,R(y / z,z,y \ u) \ (u / w)) = T(x,(z * (y \ u)) / w)
    ]]></literal>
    <justification jstring="[para(349(a,2),10526(a,1,2,1))].">
      <j1 rule="para" parents="349 10526"/>
    </justification>
  </clause>

  <clause id="10529">
    <literal><![CDATA[
      T(x,y * (z / (u \ w))) = T(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3501,a(flip),b,10527,a),flip(a)].">
      <j1 rule="hyper" parents="63 3501 10527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10530">
    <literal><![CDATA[
      T(x,y * (z * (u \ w))) / x = K(x,y * (z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(136,a,10529,a(flip),b,2794,a(flip))].">
      <j1 rule="hyper" parents="136 10529 2794"/>
    </justification>
  </clause>

  <clause id="10531">
    <literal><![CDATA[
      ((x * (1 / (1 / y))) \ z) \ ((x * y) \ z) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(10339(a,2),2248(a,1,1))].">
      <j1 rule="para" parents="10339 2248"/>
    </justification>
  </clause>

  <clause id="10533">
    <literal><![CDATA[
      ((x \ y) \ K(z,u)) * K(x,w) = (T(x,w) \ y) \ K(z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3781,a(flip),b,10392,a)].">
      <j1 rule="hyper" parents="63 3781 10392"/>
    </justification>
  </clause>

  <clause id="10534">
    <literal><![CDATA[
      K(x * y,z) * (y * K(u,w)) = y * (K(u,w) * K(y * x,z))
    ]]></literal>
    <justification jstring="[para(3866(a,1),10393(a,1,1))].">
      <j1 rule="para" parents="3866 10393"/>
    </justification>
  </clause>

  <clause id="10535">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(z,u) = T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,10302,a(flip),b,10402,a),flip(a)].">
      <j1 rule="hyper" parents="316 10302 10402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10536">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ ((z * z) \ u)) * w) = R(x,y,T(u / z,z \ 1) * w)
    ]]></literal>
    <justification jstring="[para(579(a,1),10428(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="579 10428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10537">
    <literal><![CDATA[
      (x \ K(y,K(z,u))) * (a(w,v5,w) * v6) = K(y,K(z,u)) * ((x \ a(w,v5,w)) * v6)
    ]]></literal>
    <justification jstring="[para(5420(a,1),10429(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5420 10429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10538">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,4090,a,b,10442,a)].">
      <j1 rule="hyper" parents="35 4090 10442"/>
    </justification>
  </clause>

  <clause id="10539">
    <literal><![CDATA[
      K(x,K(y,z * (u * w))) = K(x,K(y,z * (w * u)))
    ]]></literal>
    <justification jstring="[para(3933(a,1),10538(a,1,2,2))].">
      <j1 rule="para" parents="3933 10538"/>
    </justification>
  </clause>

  <clause id="10540">
    <literal><![CDATA[
      K(x,K(y,z * (x * u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,4123,a(flip),b,10539,a),flip(a)].">
      <j1 rule="hyper" parents="316 4123 10539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10541">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(35,a,2794,a(flip),b,10444,a)].">
      <j1 rule="hyper" parents="35 2794 10444"/>
    </justification>
  </clause>

  <clause id="10542">
    <literal><![CDATA[
      K(T(x,K(y,z)) * u,w) = K(x * u,w)
    ]]></literal>
    <justification jstring="[para(3638(a,1),10541(a,1,1))].">
      <j1 rule="para" parents="3638 10541"/>
    </justification>
  </clause>

  <clause id="10543">
    <literal><![CDATA[
      x * K(T(y \ (z \ u),K(w,v5)) * x,(u \ z) * y) = ((u \ (z * y)) \ x) * (u \ (z * y))
    ]]></literal>
    <justification jstring="[para(10542(a,2),8127(a,1,2))].">
      <j1 rule="para" parents="10542 8127"/>
    </justification>
  </clause>

  <clause id="10544">
    <literal><![CDATA[
      x * T(y * K(x,K(z,u)),K(z,u)) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[para(4067(a,2),10463(a,1,2))].">
      <j1 rule="para" parents="4067 10463"/>
    </justification>
  </clause>

  <clause id="10545">
    <literal><![CDATA[
      a((x * (y / z)) * u,w,v5) = a((x * (z \ y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(2721(a,1),10478(a,1,1,1,2))].">
      <j1 rule="para" parents="2721 10478"/>
    </justification>
  </clause>

  <clause id="10546">
    <literal><![CDATA[
      L(x,y,(z \ (u * w)) * v5) = L(x,y,v5 * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[para(2728(a,1),10488(a,1,3,1,2))].">
      <j1 rule="para" parents="2728 10488"/>
    </justification>
  </clause>

  <clause id="10547">
    <literal><![CDATA[
      L(x,y,(z \ R(T(u,w),v5,v6)) * v7) = L(x,y,v7 * (z \ R(u,v5,v6)))
    ]]></literal>
    <justification jstring="[para(2812(a,1),10488(a,1,3,1,2))].">
      <j1 rule="para" parents="2812 10488"/>
    </justification>
  </clause>

  <clause id="10548">
    <literal><![CDATA[
      L(x,y,(z \ L(T(u,w),v5,v6)) * v7) = L(x,y,v7 * (z \ L(u,v5,v6)))
    ]]></literal>
    <justification jstring="[para(2804(a,1),10488(a,1,3,1,2))].">
      <j1 rule="para" parents="2804 10488"/>
    </justification>
  </clause>

  <clause id="10549">
    <literal><![CDATA[
      x * ((T(y,z) \ x) \ K(y \ x,(y \ x) \ 1)) = K(y,z) * (x * (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(1087(a,1),10498(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1087 10498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10550">
    <literal><![CDATA[
      K(x,y * (z / (u \ w))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(2808,a,10530,a),flip(a)].">
      <j1 rule="hyper" parents="2808 10530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10551">
    <literal><![CDATA[
      T((x \ 1) * x,y) = ((z * (1 / (1 / x))) \ u) \ ((z * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,2224,a,b,10531,a)].">
      <j1 rule="hyper" parents="316 2224 10531"/>
    </justification>
  </clause>

  <clause id="10552">
    <literal><![CDATA[
      (T(x,y) \ z) \ K(x \ z,(x \ z) \ 1) = (1 / (x \ z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(1087(a,1),10533(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1087 10533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10553">
    <literal><![CDATA[
      x * T((T(x,K(y,z)) * u) \ w,K(y,z)) = T(x * ((x * u) \ w),K(y,z))
    ]]></literal>
    <justification jstring="[para(10441(a,1),10544(a,1,2,1))].">
      <j1 rule="para" parents="10441 10544"/>
    </justification>
  </clause>

  <clause id="10554">
    <literal><![CDATA[
      a(((x \ 1) * (x \ y)) * z,u,w) = a(z * (y / (x * x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3234,a(flip),b,10545,a),flip(a)].">
      <j1 rule="hyper" parents="63 3234 10545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10555">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ ((v5 * w) * u))) = L(x,y,L(T(v5,w),w,u) * z)
    ]]></literal>
    <justification jstring="[para(247(a,1),10546(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="247 10546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10560">
    <literal><![CDATA[
      L((x * (y / (x * y))) \ z,a(x \ 1,x,y),((y / (x * y)) * x) \ 1) = (1 / (x * (y / (x * y)))) * z
    ]]></literal>
    <justification jstring="[para(8865(a,1),10436(a,1,2))].">
      <j1 rule="para" parents="8865 10436"/>
    </justification>
  </clause>

  <clause id="10561">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * z) * y) = K(z,y) * a(x,z,y)
    ]]></literal>
    <justification jstring="[para(114(a,1),10501(a,1,1,2))].">
      <j1 rule="para" parents="114 10501"/>
    </justification>
  </clause>

  <clause id="10562">
    <literal><![CDATA[
      L(1 / (K(x,y) * a(z,x,y)),(z * (y * x)) \ ((z * x) * y),z * (y * x)) = 1 / (1 / (((z * x) * y) \ (z * (y * x))))
    ]]></literal>
    <justification jstring="[para(10561(a,1),1299(a,1,1,2))].">
      <j1 rule="para" parents="10561 1299"/>
    </justification>
  </clause>

  <clause id="10563">
    <literal><![CDATA[
      ((x * (y * z)) * (1 / (1 / (K(z,y) * a(x,z,y))))) \ (x * (y * z)) = 1 / (1 / (((x * z) * y) \ (x * (y * z))))
    ]]></literal>
    <justification jstring="[para(10561(a,1),2531(a,1,1,2,2,2))].">
      <j1 rule="para" parents="10561 2531"/>
    </justification>
  </clause>

  <clause id="10564">
    <literal><![CDATA[
      (x * (y * (z \ L(z,u,w)))) \ (((z \ L(z,u,w)) * x) * y) = K(z \ L(z,u,w),y) * a(x,z \ L(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(5023(a,2),10561(a,1,2,1))].">
      <j1 rule="para" parents="5023 10561"/>
    </justification>
  </clause>

  <clause id="10565">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) \ (u * (z * w))) = a(x,y,K(w,u) * a(z,w,u))
    ]]></literal>
    <justification jstring="[para(10561(a,1),5490(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10561 5490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10568">
    <literal><![CDATA[
      L(x / y,z,u) * ((x / y) \ w) = L(y \ x,z,u) * ((y \ x) \ w)
    ]]></literal>
    <justification jstring="[para(3143(a,1),10188(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3143 10188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10569">
    <literal><![CDATA[
      (x \ K(y,z)) * (L(u \ K(y,z),w,v5) \ v6) = (x \ 1) * (L(u \ 1,w,v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(139,a,10228,a(flip),b,10211,a),flip(a)].">
      <j1 rule="hyper" parents="139 10228 10211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10570">
    <literal><![CDATA[
      K(x \ 1,x) * a(y,x \ 1,x) = a(y * (1 / x),x,x)
    ]]></literal>
    <justification jstring="[para(2387(a,1),10239(a,1,2))].">
      <j1 rule="para" parents="2387 10239"/>
    </justification>
  </clause>

  <clause id="10571">
    <literal><![CDATA[
      (x \ a(y,x \ 1,x)) * x = a(y * (1 / x),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5300,a(flip),b,10570,a)].">
      <j1 rule="hyper" parents="63 5300 10570"/>
    </justification>
  </clause>

  <clause id="10572">
    <literal><![CDATA[
      (x \ a(y,x \ 1,x)) * x = a(x \ y,x,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,6954,a(flip),b,10571,a),flip(a)].">
      <j1 rule="hyper" parents="316 6954 10571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10573">
    <literal><![CDATA[
      x * (a(x \ y,x,x) / x) = a(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(10572(a,1),79(a,1,2,1))].">
      <j1 rule="para" parents="10572 79"/>
    </justification>
  </clause>

  <clause id="10574">
    <literal><![CDATA[
      (x / y) \ (x * (1 / y)) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8701,a,b,10573,a)].">
      <j1 rule="hyper" parents="63 8701 10573"/>
    </justification>
  </clause>

  <clause id="10575">
    <literal><![CDATA[
      a(x,y,((z \ u) \ (u * (1 / z))) * w) = a(x,y,a(u,z \ 1,z) * w)
    ]]></literal>
    <justification jstring="[para(10574(a,1),5549(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10574 5549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10576">
    <literal><![CDATA[
      (x / y) * (L(x / y,z,u) \ w) = (y \ x) * (L(y \ x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(10245(a,1),3202(a,1,2))].">
      <j1 rule="para" parents="10245 3202"/>
    </justification>
  </clause>

  <clause id="10577">
    <literal><![CDATA[
      a(x \ (y * (L(z / u,w,v5) \ v6)),v7,v8) = a(x \ (y * (L(u \ z,w,v5) \ v6)),v7,v8)
    ]]></literal>
    <justification jstring="[para(10245(a,1),4556(a,1,1,2,2))].">
      <j1 rule="para" parents="10245 4556"/>
    </justification>
  </clause>

  <clause id="10578">
    <literal><![CDATA[
      (x * T(y,z)) * (L(u * T(y,z),w,v5) \ v6) = (x * y) * (L(u * y,w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(10246(a,1),10202(a,1,2))].">
      <j1 rule="para" parents="10246 10202"/>
    </justification>
  </clause>

  <clause id="10579">
    <literal><![CDATA[
      a(x,y,(z * L(u \ K(w,v5),v6,v7)) \ v8) = a(x,y,(L(u \ 1,v6,v7) * z) \ v8)
    ]]></literal>
    <justification jstring="[para(10252(a,1),5945(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10252 5945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10580">
    <literal><![CDATA[
      (x \ 1) / (T(x,x) \ L(x,y,z)) = x / ((x \ L(x,y,z)) * (x * x))
    ]]></literal>
    <justification jstring="[para(10253(a,1),589(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10253 589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10581">
    <literal><![CDATA[
      a(x,y,(1 / (1 / z)) \ L(u,w,v5)) = a(x,y,z \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5477,a(flip),b,10264,a)].">
      <j1 rule="hyper" parents="63 5477 10264"/>
    </justification>
  </clause>

  <clause id="10582">
    <literal><![CDATA[
      a(x,y,((z \ K(u,w)) \ v5) * v6) = a(x,y,(z \ v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,6698,a(flip),b,10293,a),flip(a)].">
      <j1 rule="hyper" parents="316 6698 10293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10583">
    <literal><![CDATA[
      a(x,y,((z * (u \ (z \ u))) \ w) * v5) = a(x,y,(a(u,z,z) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(8181(a,1),10582(a,1,3,1,1))].">
      <j1 rule="para" parents="8181 10582"/>
    </justification>
  </clause>

  <clause id="10585">
    <literal><![CDATA[
      T(T(x,K(y,z)) \ u,K(y,z)) = x \ T(u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(253,a,10331,a(flip),b,4245,a(flip))].">
      <j1 rule="hyper" parents="253 10331 4245"/>
    </justification>
  </clause>

  <clause id="10586">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u,K(y,z)) = T(x \ u,K(y,z))
    ]]></literal>
    <justification jstring="[para(4107(a,1),10585(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4107 10585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10587">
    <literal><![CDATA[
      x * (K(y,z) * K(u \ K(y,z),u)) = x / (u * (K(z,y) / u))
    ]]></literal>
    <justification jstring="[para(10417(a,1),4007(a,1,2))].">
      <j1 rule="para" parents="10417 4007"/>
    </justification>
  </clause>

  <clause id="10588">
    <literal><![CDATA[
      T(x * (1 / (y \ x)),z) = x * (1 / (T(y,z) \ x))
    ]]></literal>
    <justification jstring="[para(10303(a,1),10433(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10303 10433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10589">
    <literal><![CDATA[
      (x * y) / (a(z,u,w) * y) = (a(z,u,w) * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5277,a(flip),b,10446,a)].">
      <j1 rule="hyper" parents="63 5277 10446"/>
    </justification>
  </clause>

  <clause id="10590">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (a(y,z,u) * w) = (x * a(y,z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,2496,a(flip),b,10589,a)].">
      <j1 rule="hyper" parents="138 2496 10589"/>
    </justification>
  </clause>

  <clause id="10591">
    <literal><![CDATA[
      (x * y) / (y * a(z,u,w)) = (a(z,u,w) * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2339,a(flip),b,10589,a)].">
      <j1 rule="hyper" parents="63 2339 10589"/>
    </justification>
  </clause>

  <clause id="10592">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (a(x,y,z) * w)) = R(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2280,a(flip),b,10589,a),flip(a)].">
      <j1 rule="hyper" parents="63 2280 10589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10594">
    <literal><![CDATA[
      (((x * y) / (a(z,u,w) * y)) * (a(z,u,w) * y)) \ (a(z,u,w) * y) = (y * x) \ T(a(z,u,w) * y,(a(z,u,w) * y) \ (y * x))
    ]]></literal>
    <justification jstring="[para(10589(a,2),2876(a,1,1,1))].">
      <j1 rule="para" parents="10589 2876"/>
    </justification>
  </clause>

  <clause id="10595">
    <literal><![CDATA[
      T((x * y) / ((a(z,u,w) * y) \ (y * x)),x * y) = L(a(z,u,w) * y,(a(z,u,w) * y) \ (x * y),a(z,u,w) * y)
    ]]></literal>
    <justification jstring="[para(10589(a,1),3223(a,1,1,2))].">
      <j1 rule="para" parents="10589 3223"/>
    </justification>
  </clause>

  <clause id="10596">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),w) = (u * w) / (w * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,2334,a,b,10591,a)].">
      <j1 rule="hyper" parents="316 2334 10591"/>
    </justification>
  </clause>

  <clause id="10597">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (w * a(y,z,u)) = (x * a(y,z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,2496,a(flip),b,10591,a)].">
      <j1 rule="hyper" parents="138 2496 10591"/>
    </justification>
  </clause>

  <clause id="10598">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) = T(x,z \ (R(y,w,v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3504,a(flip),b,10448,a)].">
      <j1 rule="hyper" parents="63 3504 10448"/>
    </justification>
  </clause>

  <clause id="10600">
    <literal><![CDATA[
      T(x,y \ (R(z,u,w) \ v5)) = T(x,y \ (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,10447,a(flip),b,10598,a),flip(a)].">
      <j1 rule="hyper" parents="63 10447 10598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10601">
    <literal><![CDATA[
      T(x,y \ (z \ ((z * u) * w))) = T(x,y \ (u * w))
    ]]></literal>
    <justification jstring="[para(199(a,1),10600(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="199 10600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10602">
    <literal><![CDATA[
      T(x,(y \ z) \ (u * w)) = T(x,z \ ((y * u) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,3691,a(flip),b,10601,a),flip(a)].">
      <j1 rule="hyper" parents="63 3691 10601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10603">
    <literal><![CDATA[
      T(x,y \ ((z * u) * w)) = T(x,(y \ z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,3684,a(flip),b,10602,a),flip(a)].">
      <j1 rule="hyper" parents="63 3684 10602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10604">
    <literal><![CDATA[
      T(x,(y \ z) * (u * y)) = T(x,T(z * u,y))
    ]]></literal>
    <justification jstring="[para(22(a,2),10603(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22 10603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10605">
    <literal><![CDATA[
      a(x * (y * ((T(z,u) \ 1) * (T(z,u) \ 1))),w,v5) = a(((T(z,u) \ 1) * (z \ 1)) * (y * x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3370,a(flip),b,10480,a)].">
      <j1 rule="hyper" parents="63 3370 10480"/>
    </justification>
  </clause>

  <clause id="10606">
    <literal><![CDATA[
      L(x,x \ y,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(34,a,4383,a(flip),b,10494,a)].">
      <j1 rule="hyper" parents="34 4383 10494"/>
    </justification>
  </clause>

  <clause id="10608">
    <literal><![CDATA[
      L(x,x \ (y \ z),y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(316,a,168,a(flip),b,10606,a),flip(a)].">
      <j1 rule="hyper" parents="316 168 10606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10610">
    <literal><![CDATA[
      L(x,x \ y,z) \ (z * y) = T(z * (y / x),x)
    ]]></literal>
    <justification jstring="[para(10606(a,2),3738(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10606 3738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10612">
    <literal><![CDATA[
      (x * y) \ L(x * y,(x * y) \ y,x) = T(x * (y / (x * y)),x * y) \ 1
    ]]></literal>
    <justification jstring="[para(10610(a,1),5076(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10610 5076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10613">
    <literal><![CDATA[
      ((x \ 1) * ((x \ 1) * (((x \ 1) * y) \ y))) / (x \ 1) = ((y / x) / y) / (1 / x)
    ]]></literal>
    <justification jstring="[para(10495(a,1),8249(a,1,1,2))].">
      <j1 rule="para" parents="10495 8249"/>
    </justification>
  </clause>

  <clause id="10614">
    <literal><![CDATA[
      L(x,y,z \ ((T(u,w) * u) * (T(u,w) \ v5))) = L(x,y,z \ ((u \ 1) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,8267,a,b,10499,a)].">
      <j1 rule="hyper" parents="63 8267 10499"/>
    </justification>
  </clause>

  <clause id="10615">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,z,u) \ T(x,w)) = L(y / T(x,w),z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,7194,a,b,10503,a)].">
      <j1 rule="hyper" parents="63 7194 10503"/>
    </justification>
  </clause>

  <clause id="10616">
    <literal><![CDATA[
      T(x,y) \ (L(z / T(x,y),u,w) \ v5) = x \ (L(z / x,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(133,a,10503,a(flip),b,2799,a)].">
      <j1 rule="hyper" parents="133 10503 2799"/>
    </justification>
  </clause>

  <clause id="10617">
    <literal><![CDATA[
      L(x \ T(y,z),u,w) \ (x \ T(y,z)) = L(x \ y,u,w) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(34,a,6545,a,b,10504,a),flip(a)].">
      <j1 rule="hyper" parents="34 6545 10504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10618">
    <literal><![CDATA[
      x * (K(y,x) * K(x * y,z)) = T(y * x,z) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,2874,a(flip),b,10534,a),flip(a)].">
      <j1 rule="hyper" parents="63 2874 10534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10619">
    <literal><![CDATA[
      x * (K((y \ z) * u,x) * K(x * ((z \ y) \ u),w)) = T(((z \ y) \ u) * x,w) / ((z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4269(a,1),10618(a,1,2,1))].">
      <j1 rule="para" parents="4269 10618"/>
    </justification>
  </clause>

  <clause id="10620">
    <literal><![CDATA[
      L((x * y) \ x,y,y \ 1) = (x * (1 / (1 / y))) \ x
    ]]></literal>
    <justification jstring="[hyper(39,a,7244,a,b,10551,a(flip))].">
      <j1 rule="hyper" parents="39 7244 10551"/>
    </justification>
  </clause>

  <clause id="10621">
    <literal><![CDATA[
      a((x * y) \ x,y,y \ 1) = ((x * (1 / (1 / y))) \ x) \ ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(10620(a,1),9140(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10620 9140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10623">
    <literal><![CDATA[
      a(((x \ 1) * (x \ y)) * z,u,w) = a(z * ((x * x) \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,3150,a(flip),b,10554,a),flip(a)].">
      <j1 rule="hyper" parents="316 3150 10554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10624">
    <literal><![CDATA[
      a(x,y,((1 / z) \ 1) \ L(u,w,v5)) = a(x,y,z \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5546,a(flip),b,10581,a)].">
      <j1 rule="hyper" parents="63 5546 10581"/>
    </justification>
  </clause>

  <clause id="10625">
    <literal><![CDATA[
      x / (y * (K(z,u) / y)) = x * ((y \ K(u,z)) * y)
    ]]></literal>
    <justification jstring="[para(307(a,1),10587(a,1,2)),flip(a)].">
      <j1 rule="para" parents="307 10587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10626">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (a(y,z,u) * w) = (a(y,z,u) * x) * w
    ]]></literal>
    <justification jstring="[hyper(316,a,2292,a,b,10590,a),flip(a)].">
      <j1 rule="hyper" parents="316 2292 10590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10627">
    <literal><![CDATA[
      L(x,a(y,z,u),(x * a(y,z,u)) \ w) \ w = a(y,z,u) * ((x * a(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(133,a,10,a(flip),b,10590,a)].">
      <j1 rule="hyper" parents="133 10 10590"/>
    </justification>
  </clause>

  <clause id="10628">
    <literal><![CDATA[
      R(x,a(y,z,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(35,a,109,a,b,10590,a)].">
      <j1 rule="hyper" parents="35 109 10590"/>
    </justification>
  </clause>

  <clause id="10629">
    <literal><![CDATA[
      L(x,a(y,z,u),w * w) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,32,a(flip),b,10590,a),flip(a)].">
      <j1 rule="hyper" parents="35 32 10590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10630">
    <literal><![CDATA[
      ((x * x) * a(y,z,u)) \ w = a(y,z,u) \ ((x * x) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1677,a(flip),b,10629,a)].">
      <j1 rule="hyper" parents="63 1677 10629"/>
    </justification>
  </clause>

  <clause id="10631">
    <literal><![CDATA[
      R(x,a(y,z,u),y) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,8660,a(flip),b,10628,a),flip(a)].">
      <j1 rule="hyper" parents="316 8660 10628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10632">
    <literal><![CDATA[
      R(x,a(y,z,u),u) = L(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,6997,a(flip),b,10628,a),flip(a)].">
      <j1 rule="hyper" parents="316 6997 10628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10633">
    <literal><![CDATA[
      L(x,a(y,z,u),w \ L(w,v5,v6)) = L(x,a(y,z,u),w * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,9207,a(flip),b,10628,a)].">
      <j1 rule="hyper" parents="63 9207 10628"/>
    </justification>
  </clause>

  <clause id="10634">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) \ 1,a(x,y,a(z,u,w)),y) = y / (a(z,u,w) \ (x \ (a(z,u,w) * (x * y))))
    ]]></literal>
    <justification jstring="[hyper(63,a,8752,a(flip),b,10628,a),flip(a)].">
      <j1 rule="hyper" parents="63 8752 10628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10635">
    <literal><![CDATA[
      L(x,L(y,z,u),a(w,v5,y)) = L(x,a(w,v5,y),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8215,a(flip),b,10628,a)].">
      <j1 rule="hyper" parents="63 8215 10628"/>
    </justification>
  </clause>

  <clause id="10636">
    <literal><![CDATA[
      L(x,a(y,z,u),w \ 1) = R(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1033,a(flip),b,10628,a),flip(a)].">
      <j1 rule="hyper" parents="63 1033 10628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10637">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,u),w),x,a(y,z,u) * w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(10628(a,1),3422(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10628 3422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10638">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,u),w),x,w * a(y,z,u)) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(10628(a,1),3424(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10628 3424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10639">
    <literal><![CDATA[
      L(L(x,a(y,y,x),z),y,y) \ (x * z) = a(y,y,x) * z
    ]]></literal>
    <justification jstring="[para(10628(a,1),4971(a,1,1,1))].">
      <j1 rule="para" parents="10628 4971"/>
    </justification>
  </clause>

  <clause id="10640">
    <literal><![CDATA[
      L(x * a(y,z,x),x,a(y,z,x)) = x * a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10089,a(flip),b,10632,a),flip(a)].">
      <j1 rule="hyper" parents="63 10089 10632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10641">
    <literal><![CDATA[
      L(x,a(y,z,u),w \ 1) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10628,a(flip),b,10636,a),flip(a)].">
      <j1 rule="hyper" parents="316 10628 10636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10642">
    <literal><![CDATA[
      (x \ a(x,y,z)) * R(u,a(x,y,z),x) = (x \ 1) * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(10636(a,1),8434(a,1,2))].">
      <j1 rule="para" parents="10636 8434"/>
    </justification>
  </clause>

  <clause id="10643">
    <literal><![CDATA[
      a(x,y,y) * ((z / y) * L(y,y,x)) = L(z,a(x,y,y),L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9036,a,b,10635,a)].">
      <j1 rule="hyper" parents="63 9036 10635"/>
    </justification>
  </clause>

  <clause id="10644">
    <literal><![CDATA[
      L(x,a(y,z,z) \ z,a(u,w,z)) = L(x,a(u,w,z),L(z,z,y))
    ]]></literal>
    <justification jstring="[para(7297(a,2),10635(a,1,2))].">
      <j1 rule="para" parents="7297 10635"/>
    </justification>
  </clause>

  <clause id="10646">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),x * (z * y)) = (u * (x * (z * y))) / ((x * y) * T(z,y))
    ]]></literal>
    <justification jstring="[para(5524(a,1),10596(a,2,2))].">
      <j1 rule="para" parents="5524 10596"/>
    </justification>
  </clause>

  <clause id="10647">
    <literal><![CDATA[
      a(x * (y * ((z \ 1) * (z \ 1))),u,w) = a((y * x) * ((z * z) \ 1),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3233,a(flip),b,10623,a)].">
      <j1 rule="hyper" parents="63 3233 10623"/>
    </justification>
  </clause>

  <clause id="10648">
    <literal><![CDATA[
      a(x,y,z \ R(u,w,v5)) = a(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(83(a,1),10624(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="83 10624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10650">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u \ R(w,v5,v6)) \ L(w,v5,v6)) = a(x,y,T((R(w,v5,v6) / u) * z,z \ u))
    ]]></literal>
    <justification jstring="[para(3740(a,1),10648(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3740 10648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10651">
    <literal><![CDATA[
      a(x,y,z \ L(u,w,(v5 \ 1) * v6)) = a(x,y,z \ R(u,w,v6 * v5))
    ]]></literal>
    <justification jstring="[para(4707(a,1),10648(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="4707 10648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10652">
    <literal><![CDATA[
      T(x,R(y / z,z,y \ u) \ (u / w)) = T(x,z * ((y \ u) / w))
    ]]></literal>
    <justification jstring="[hyper(316,a,3607,a(flip),b,10528,a),flip(a)].">
      <j1 rule="hyper" parents="316 3607 10528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10653">
    <literal><![CDATA[
      L(x,x,y) * (a(y,x,x) * (x \ z)) = L(z,a(y,x,x),L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6994,a,b,10643,a)].">
      <j1 rule="hyper" parents="63 6994 10643"/>
    </justification>
  </clause>

  <clause id="10654">
    <literal><![CDATA[
      T(x,(y / z) \ (u / w)) = T(x,z * ((y \ u) / w))
    ]]></literal>
    <justification jstring="[hyper(63,a,3504,a(flip),b,10652,a)].">
      <j1 rule="hyper" parents="63 3504 10652"/>
    </justification>
  </clause>

  <clause id="10656">
    <literal><![CDATA[
      T(x,y * ((z \ u) / w)) = T(x,y * (z \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3511,a(flip),b,10654,a),flip(a)].">
      <j1 rule="hyper" parents="63 3511 10654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10657">
    <literal><![CDATA[
      (x * (y / z)) * ((y / z) \ u) = (x * (z \ y)) * ((z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(116(a,1),10279(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="116 10279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10658">
    <literal><![CDATA[
      x * ((y \ L(T(x,z),u,w)) * (T(x,z) \ L(L(x,v5,v6),v5,v6))) = L(L(x,v5,v6),v5,v6) * (y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(10280(a,2),10064(a,1,2))].">
      <j1 rule="para" parents="10280 10064"/>
    </justification>
  </clause>

  <clause id="10659">
    <literal><![CDATA[
      a(((x \ K(y,z)) * u) * (x * x),w,v5) = a(K(y,z) * (u * x),w,v5)
    ]]></literal>
    <justification jstring="[para(406(a,1),10282(a,2,1))].">
      <j1 rule="para" parents="406 10282"/>
    </justification>
  </clause>

  <clause id="10660">
    <literal><![CDATA[
      (x * y) \ T(x * K(z,u),y) = K(z,u) * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[para(10535(a,1),10308(a,1,2))].">
      <j1 rule="para" parents="10535 10308"/>
    </justification>
  </clause>

  <clause id="10661">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (K(y,z) * u) = (K(y,z) * ((x * u) \ u)) * K(z,y)
    ]]></literal>
    <justification jstring="[para(10660(a,1),7632(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10660 7632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10662">
    <literal><![CDATA[
      a(x,y,(z * (u \ (w / v5))) * v6) = a(x,y,(z * (u \ (v5 \ w))) * v6)
    ]]></literal>
    <justification jstring="[para(2721(a,1),10320(a,1,3,1,2,2))].">
      <j1 rule="para" parents="2721 10320"/>
    </justification>
  </clause>

  <clause id="10663">
    <literal><![CDATA[
      x \ T(T(x,y) / y,T(y \ 1,x)) = (y \ (y \ x)) / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6431,a,b,10423,a)].">
      <j1 rule="hyper" parents="63 6431 10423"/>
    </justification>
  </clause>

  <clause id="10665">
    <literal><![CDATA[
      K((x / ((y * z) / u)) \ w,T(v5,y)) = K((((w \ x) * u) / z) \ y,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,10460,a(flip),b,10464,a),flip(a)].">
      <j1 rule="hyper" parents="316 10460 10464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10666">
    <literal><![CDATA[
      a(x,y,((z * (u / w)) * v5) \ v6) = a(x,y,((z * (w \ u)) * v5) \ v6)
    ]]></literal>
    <justification jstring="[para(2721(a,1),10479(a,1,3,1,1,2))].">
      <j1 rule="para" parents="2721 10479"/>
    </justification>
  </clause>

  <clause id="10667">
    <literal><![CDATA[
      a(x,y,((z * (T(u,w) \ v5)) * v6) \ v7) = a(x,y,((z * (u \ v5)) * v6) \ v7)
    ]]></literal>
    <justification jstring="[para(2859(a,1),10479(a,1,3,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2859 10479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10668">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (u \ 1)) * (w * (v5 * v6)))) = a(x,y,z \ (w * (v5 * (v6 * (u \ (1 / u))))))
    ]]></literal>
    <justification jstring="[hyper(63,a,9514,a(flip),b,10485,a),flip(a)].">
      <j1 rule="hyper" parents="63 9514 10485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10669">
    <literal><![CDATA[
      a(x,y,(z \ (1 / u)) * (w * ((u * z) \ K(u,u \ 1)))) = a(x,y,(z * u) * ((z \ (u \ 1)) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9675,a,b,10486,a)].">
      <j1 rule="hyper" parents="63 9675 10486"/>
    </justification>
  </clause>

  <clause id="10670">
    <literal><![CDATA[
      a(x,y,(((z * (u * u)) \ w) * v5) * v6) = a(x,y,((z \ ((u * u) \ w)) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,7560,a,b,10487,a)].">
      <j1 rule="hyper" parents="63 7560 10487"/>
    </justification>
  </clause>

  <clause id="10671">
    <literal><![CDATA[
      a(x,y,(((z * z) \ (u \ w)) * v5) * v6) = a(x,y,((u \ ((z * z) \ w)) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5792,a,b,10487,a)].">
      <j1 rule="hyper" parents="63 5792 10487"/>
    </justification>
  </clause>

  <clause id="10672">
    <literal><![CDATA[
      a(x,y,z \ (((u * w) \ v5) \ v6)) = a(x,y,z \ (((w * u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(2765(a,1),10497(a,1,3,2,1))].">
      <j1 rule="para" parents="2765 10497"/>
    </justification>
  </clause>

  <clause id="10673">
    <literal><![CDATA[
      a(x,y,z \ (((u * K(w,v5)) \ v6) \ v7)) = a(x,y,z \ ((u \ v6) \ v7))
    ]]></literal>
    <justification jstring="[para(4150(a,1),10497(a,1,3,2,1))].">
      <j1 rule="para" parents="4150 10497"/>
    </justification>
  </clause>

  <clause id="10674">
    <literal><![CDATA[
      x * (y * ((x \ K(y * x,z)) * x)) = T((1 / (1 / x)) * y,z)
    ]]></literal>
    <justification jstring="[para(2259(a,1),10510(a,2,1))].">
      <j1 rule="para" parents="2259 10510"/>
    </justification>
  </clause>

  <clause id="10675">
    <literal><![CDATA[
      L(x,y,(z \ L(T(u,w),v5,v6)) * v7) = L(x,y,v7 * (z \ R(u,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9146,a(flip),b,10547,a)].">
      <j1 rule="hyper" parents="63 9146 10547"/>
    </justification>
  </clause>

  <clause id="10676">
    <literal><![CDATA[
      (T(x,y) \ z) \ K(x \ z,(x \ z) \ 1) = 1 / (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,10181,a(flip),b,10552,a),flip(a)].">
      <j1 rule="hyper" parents="316 10181 10552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10677">
    <literal><![CDATA[
      (x / y) * (L(y \ x,z,u) * ((y \ x) \ w)) = L(x / y,z,u) * w
    ]]></literal>
    <justification jstring="[hyper(139,a,10568,a(flip),b,1126,a)].">
      <j1 rule="hyper" parents="139 10568 1126"/>
    </justification>
  </clause>

  <clause id="10679">
    <literal><![CDATA[
      (x \ 1) / (T(x,x) \ L(x,y,z)) = x / (L(x,y,z) * (x \ (x * x)))
    ]]></literal>
    <justification jstring="[para(1136(a,1),10580(a,2,2))].">
      <j1 rule="para" parents="1136 10580"/>
    </justification>
  </clause>

  <clause id="10680">
    <literal><![CDATA[
      (x * a(y,z,u)) \ ((x * (a(y,z,u) * w)) / w) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7123,a(flip),b,10637,a)].">
      <j1 rule="hyper" parents="63 7123 10637"/>
    </justification>
  </clause>

  <clause id="10681">
    <literal><![CDATA[
      (x \ a(x,y,z)) * L(u,x,a(x,y,z)) = (x \ 1) * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(10631(a,1),10642(a,1,2))].">
      <j1 rule="para" parents="10631 10642"/>
    </justification>
  </clause>

  <clause id="10682">
    <literal><![CDATA[
      a(x,y,z \ L(u,w,(v5 \ 1) * v6)) = a(x,y,z \ L(u,w,v6 * v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,10648,a(flip),b,10651,a),flip(a)].">
      <j1 rule="hyper" parents="316 10648 10651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10683">
    <literal><![CDATA[
      a(((x \ K(y,z)) * u) * (x * x),w,v5) = a(u * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,1806,a(flip),b,10659,a),flip(a)].">
      <j1 rule="hyper" parents="316 1806 10659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10686">
    <literal><![CDATA[
      a((x \ K(y,z)) * (u * (x * x)),w,v5) = a(u * x,w,v5)
    ]]></literal>
    <justification jstring="[para(32(a,1),10683(a,1,1))].">
      <j1 rule="para" parents="32 10683"/>
    </justification>
  </clause>

  <clause id="10687">
    <literal><![CDATA[
      a((x \ 1) * (y * (x * x)),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(180(a,1),10686(a,1,1,1,2))].">
      <j1 rule="para" parents="180 10686"/>
    </justification>
  </clause>

  <clause id="10688">
    <literal><![CDATA[
      a((x \ 1) \ y,x \ 1,x \ 1) = a(y * x,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7944,a(flip),b,10687,a)].">
      <j1 rule="hyper" parents="63 7944 10687"/>
    </justification>
  </clause>

  <clause id="10689">
    <literal><![CDATA[
      a((x \ 1) \ y,x \ 1,x) = a(y * x,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2534,a(flip),b,10688,a)].">
      <j1 rule="hyper" parents="63 2534 10688"/>
    </justification>
  </clause>

  <clause id="10690">
    <literal><![CDATA[
      a((x \ y) * x,x \ 1,x) = ((y / x) / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,7240,a(flip),b,10689,a),flip(a)].">
      <j1 rule="hyper" parents="63 7240 10689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10691">
    <literal><![CDATA[
      ((x / y) / (1 / y)) \ x = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2783,a(flip),b,10690,a),flip(a)].">
      <j1 rule="hyper" parents="63 2783 10690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10693">
    <literal><![CDATA[
      a(x,y \ 1,y) \ x = (x / y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,10691,a)].">
      <j1 rule="hyper" parents="39 2301 10691"/>
    </justification>
  </clause>

  <clause id="10694">
    <literal><![CDATA[
      a(x,y,(z * ((u \ 1) \ ((u * u) \ w))) * v5) = a(x,y,(z * T(w / u,u \ 1)) * v5)
    ]]></literal>
    <justification jstring="[para(579(a,1),10662(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="579 10662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10695">
    <literal><![CDATA[
      K(((x * y) / z) * (u \ w),T(v5,x)) = K((((w \ u) * z) / y) \ x,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3556,a(flip),b,10665,a)].">
      <j1 rule="hyper" parents="63 3556 10665"/>
    </justification>
  </clause>

  <clause id="10696">
    <literal><![CDATA[
      a(x,y,(((z * z) \ (u * w)) * v5) \ v6) = a(x,y,((u * ((z * z) \ w)) * v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5935,a,b,10666,a)].">
      <j1 rule="hyper" parents="63 5935 10666"/>
    </justification>
  </clause>

  <clause id="10697">
    <literal><![CDATA[
      a(x,y,((z * (T(u * u,w) \ v5)) * v6) \ (z * (v6 * v5))) = a(x,y,a(v6,v5 / T(u * u,w),z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8227,a(flip),b,10666,a),flip(a)].">
      <j1 rule="hyper" parents="63 8227 10666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10698">
    <literal><![CDATA[
      a(x,y,z \ ((((u \ 1) * w) \ v5) \ v6)) = a(x,y,z \ (((w * u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,7745,a(flip),b,10672,a),flip(a)].">
      <j1 rule="hyper" parents="316 7745 10672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10699">
    <literal><![CDATA[
      a(x,y,z \ ((((u * u) * w) \ v5) \ v6)) = a(x,y,z \ ((w \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,7740,a(flip),b,10672,a),flip(a)].">
      <j1 rule="hyper" parents="316 7740 10672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10700">
    <literal><![CDATA[
      a(x,y,z \ ((((u \ 1) * (w * u)) \ v5) \ v6)) = a(x,y,z \ ((R(w,u,u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(565(a,1),10672(a,1,3,2,1,1)),flip(a)].">
      <j1 rule="para" parents="565 10672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10701">
    <literal><![CDATA[
      a(x,y,z \ ((T(u / (w \ 1),w) \ v5) \ v6)) = a(x,y,z \ ((((w * w) * (w \ u)) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(613(a,2),10672(a,1,3,2,1,1))].">
      <j1 rule="para" parents="613 10672"/>
    </justification>
  </clause>

  <clause id="10702">
    <literal><![CDATA[
      a(x,y,z \ (((R(u \ w,u,u) * u) \ v5) \ v6)) = a(x,y,z \ ((((w * (u \ 1)) * u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(624(a,1),10672(a,1,3,2,1,1)),flip(a)].">
      <j1 rule="para" parents="624 10672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10703">
    <literal><![CDATA[
      a(x,y,z \ ((((u * T(w,w \ u)) * (w \ 1)) \ v5) \ v6)) = a(x,y,z \ (((w * (u * T(w \ 1,w \ u))) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(6207(a,1),10672(a,1,3,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6207 10672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10704">
    <literal><![CDATA[
      a(x,y,z \ (((L(1 / u,w,w) \ 1) \ v5) \ v6)) = a(x,y,z \ (((a(w,w,u) * u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(6584(a,2),10672(a,1,3,2,1,1))].">
      <j1 rule="para" parents="6584 10672"/>
    </justification>
  </clause>

  <clause id="10705">
    <literal><![CDATA[
      a(x,y,z \ ((((u \ 1) * w) \ (u \ w)) \ v5)) = a(x,y,z \ ((u * (w \ (u \ w))) \ v5))
    ]]></literal>
    <justification jstring="[para(7697(a,1),10672(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="7697 10672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10706">
    <literal><![CDATA[
      a(x,y,z \ ((((u \ (u \ w)) * (u * u)) \ v5) \ v6)) = a(x,y,z \ (((L(1 / w,u,u) \ 1) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(8621(a,1),10672(a,1,3,2,1,1)),flip(a)].">
      <j1 rule="para" parents="8621 10672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10707">
    <literal><![CDATA[
      a(x,y,z \ (((u * (w * T(v5,v6))) \ v7) \ v8)) = a(x,y,z \ (((u * (w * v5)) \ v7) \ v8))
    ]]></literal>
    <justification jstring="[para(3942(a,1),10673(a,1,3,2,1,1))].">
      <j1 rule="para" parents="3942 10673"/>
    </justification>
  </clause>

  <clause id="10708">
    <literal><![CDATA[
      L(x,y,z * (u \ R(w,v5,v6))) = L(x,y,z * (u \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10548,a(flip),b,10675,a),flip(a)].">
      <j1 rule="hyper" parents="63 10548 10675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10709">
    <literal><![CDATA[
      (x / y) * ((z / (y \ x)) * L(y \ x,u,w)) = L(x / y,u,w) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,4326,a(flip),b,10677,a)].">
      <j1 rule="hyper" parents="63 4326 10677"/>
    </justification>
  </clause>

  <clause id="10710">
    <literal><![CDATA[
      L(x / y,z,u) * (u * z) = (x / y) * ((u * (z * (y \ x))) / (y \ x))
    ]]></literal>
    <justification jstring="[para(4378(a,1),10677(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4378 10677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10712">
    <literal><![CDATA[
      (x \ 1) / (T(x,x) \ L(x,y,z)) = x / (x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(4329(a,1),10679(a,2,2))].">
      <j1 rule="para" parents="4329 10679"/>
    </justification>
  </clause>

  <clause id="10713">
    <literal><![CDATA[
      (x \ 1) / (x \ L(x,y,z)) = x / (x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(113(a,1),10712(a,1,2,1))].">
      <j1 rule="para" parents="113 10712"/>
    </justification>
  </clause>

  <clause id="10714">
    <literal><![CDATA[
      x / (x * L(x,y,z)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,2094,a(flip),b,10713,a),flip(a)].">
      <j1 rule="hyper" parents="63 2094 10713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10715">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ x = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(204,a,10714,a)].">
      <j1 rule="hyper" parents="204 10714"/>
    </justification>
  </clause>

  <clause id="10716">
    <literal><![CDATA[
      ((x * L(x,y,z)) * a(u,w,v5)) * ((x * L(x,y,z)) \ x) = (L(x,y,z) \ 1) * ((x * L(x,y,z)) * a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(10714(a,1),5353(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10714 5353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10717">
    <literal><![CDATA[
      (x \ (y \ z)) * L(x \ (y \ z),x,y) = (((y * x) \ z) \ 1) \ (x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(298(a,1),10715(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="298 10715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10718">
    <literal><![CDATA[
      L(a(x,y,z),u * L(u,w,v5),L(u,w,v5) \ 1) * u = (L(u,w,v5) \ 1) * (((L(u,w,v5) \ 1) \ u) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(10715(a,1),2308(a,1,1,2))].">
      <j1 rule="para" parents="10715 2308"/>
    </justification>
  </clause>

  <clause id="10719">
    <literal><![CDATA[
      a(x,y,z * (u \ (L(w,v5,v6) \ w))) = a(x,y,z * (u \ (w * L(w,v5,v6))))
    ]]></literal>
    <justification jstring="[para(10715(a,1),7780(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="10715 7780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10720">
    <literal><![CDATA[
      (x * a(y,z,u)) \ ((x * (a(y,z,u) * w)) / w) = a(w \ 1,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(964(a,1),10680(a,1,2))].">
      <j1 rule="para" parents="964 10680"/>
    </justification>
  </clause>

  <clause id="10721">
    <literal><![CDATA[
      a(x * (y * y),a(z,u,w),v5) = (v5 * a(z,u,w)) \ ((v5 * (a(z,u,w) * x)) / x)
    ]]></literal>
    <justification jstring="[para(1056(a,1),10680(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1056 10680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10722">
    <literal><![CDATA[
      (x * a(y,z,u)) \ ((x * (a(y,z,u) * (w * v5))) / (w * v5)) = a(w * (v5 \ 1),a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(8910(a,1),10680(a,1,2))].">
      <j1 rule="para" parents="8910 10680"/>
    </justification>
  </clause>

  <clause id="10723">
    <literal><![CDATA[
      K((x * y) * (z \ (u \ w)),T(v5,x)) = K((((w \ u) * z) / y) \ x,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3564,a(flip),b,10695,a)].">
      <j1 rule="hyper" parents="63 3564 10695"/>
    </justification>
  </clause>

  <clause id="10724">
    <literal><![CDATA[
      (x / (y / z)) * L(y / z,u,w) = (x / (z \ y)) * L(z \ y,u,w)
    ]]></literal>
    <justification jstring="[hyper(34,a,4385,a,b,10709,a)].">
      <j1 rule="hyper" parents="34 4385 10709"/>
    </justification>
  </clause>

  <clause id="10725">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((u / (x \ L(x,y,z))) * L(x \ L(x,y,z),w,v5)) = L(L(x,y,z) / x,w,v5) * u
    ]]></literal>
    <justification jstring="[para(1272(a,1),10709(a,1,1))].">
      <j1 rule="para" parents="1272 10709"/>
    </justification>
  </clause>

  <clause id="10727">
    <literal><![CDATA[
      K(x * (y * (z \ (u \ w))),T(v5,x)) = K((((w \ u) * z) / y) \ x,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3552,a(flip),b,10723,a)].">
      <j1 rule="hyper" parents="63 3552 10723"/>
    </justification>
  </clause>

  <clause id="10728">
    <literal><![CDATA[
      K((((x \ y) * z) / u) \ w,v5) = K((u * (z \ (y \ x))) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3866,a(flip),b,10727,a),flip(a)].">
      <j1 rule="hyper" parents="63 3866 10727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10729">
    <literal><![CDATA[
      K((((x \ y) * z) / u) \ w,v5) = K(u * ((z \ (y \ x)) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,3552,a(flip),b,10728,a),flip(a)].">
      <j1 rule="hyper" parents="316 3552 10728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10730">
    <literal><![CDATA[
      K(x * (((y \ z) * u) \ w),v5) = K(x * ((u \ (z \ y)) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3556,a(flip),b,10729,a)].">
      <j1 rule="hyper" parents="63 3556 10729"/>
    </justification>
  </clause>

  <clause id="10731">
    <literal><![CDATA[
      K(x * (y \ ((z \ u) \ w)),v5) = K(x * ((y \ (u \ z)) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,6536,a(flip),b,10730,a)].">
      <j1 rule="hyper" parents="63 6536 10730"/>
    </justification>
  </clause>

  <clause id="10732">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(10165(a,1),10234(a,1,2))].">
      <j1 rule="para" parents="10165 10234"/>
    </justification>
  </clause>

  <clause id="10733">
    <literal><![CDATA[
      R(x,y * K(z,u),w) = R(x,y,K(z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10231,a(flip),b,10334,a)].">
      <j1 rule="hyper" parents="63 10231 10334"/>
    </justification>
  </clause>

  <clause id="10734">
    <literal><![CDATA[
      R(x,y * K(z,u),w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,4685,a(flip),b,10733,a),flip(a)].">
      <j1 rule="hyper" parents="316 4685 10733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10737">
    <literal><![CDATA[
      R(x,y * z,u) = R(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(94(a,1),10734(a,1,2))].">
      <j1 rule="para" parents="94 10734"/>
    </justification>
  </clause>

  <clause id="10738">
    <literal><![CDATA[
      R(x,T(y,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(2733(a,1),10734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2733 10734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10739">
    <literal><![CDATA[
      R(x,y / z,u) = R(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(2732(a,1),10734(a,1,2))].">
      <j1 rule="para" parents="2732 10734"/>
    </justification>
  </clause>

  <clause id="10740">
    <literal><![CDATA[
      R(x,K(y,z) * u,w) = R(x,u,w)
    ]]></literal>
    <justification jstring="[para(3631(a,1),10734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3631 10734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10741">
    <literal><![CDATA[
      R(x,y \ K(z,u),w) = R(x,y \ 1,w)
    ]]></literal>
    <justification jstring="[para(3780(a,1),10734(a,1,2))].">
      <j1 rule="para" parents="3780 10734"/>
    </justification>
  </clause>

  <clause id="10742">
    <literal><![CDATA[
      R(x,y * (K(z,u) * w),v5) = R(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(3941(a,1),10734(a,1,2))].">
      <j1 rule="para" parents="3941 10734"/>
    </justification>
  </clause>

  <clause id="10743">
    <literal><![CDATA[
      R(x,(y * z) \ ((z * u) * y),w) = R(x,L(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(3953(a,1),10734(a,1,2))].">
      <j1 rule="para" parents="3953 10734"/>
    </justification>
  </clause>

  <clause id="10744">
    <literal><![CDATA[
      R(x,R(y * K(z,u),w,v5),v6) = R(x,R(y,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(4604(a,2),10734(a,1,2))].">
      <j1 rule="para" parents="4604 10734"/>
    </justification>
  </clause>

  <clause id="10745">
    <literal><![CDATA[
      R(x,R(y / z,u,w),v5) = R(x,R(z \ y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(262(a,1),10738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="262 10738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10746">
    <literal><![CDATA[
      T(x,y) * R(L(L(y,z,u),w,v5),x,L(L(y,z,u),w,v5)) = T(x * L(L(y,w,v5),z,u),L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(10738(a,1),4609(a,1,2))].">
      <j1 rule="para" parents="10738 4609"/>
    </justification>
  </clause>

  <clause id="10748">
    <literal><![CDATA[
      T((x * y) * ((x / (y \ 1)) \ 1),x * y) = R(a(x,y,y),(y \ 1) \ x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8295,a,b,10739,a)].">
      <j1 rule="hyper" parents="63 8295 10739"/>
    </justification>
  </clause>

  <clause id="10749">
    <literal><![CDATA[
      R(x,R(y * K(z,y),z,u),w) = R(x,(z * u) \ ((z * y) * u),w)
    ]]></literal>
    <justification jstring="[para(2746(a,2),10739(a,1,2))].">
      <j1 rule="para" parents="2746 10739"/>
    </justification>
  </clause>

  <clause id="10751">
    <literal><![CDATA[
      R(x,(y / z) \ u,w) = R(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(3143(a,1),10740(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3143 10740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10752">
    <literal><![CDATA[
      R(x,(y * z) \ u,w) = R(x,(z * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(6234(a,1),10740(a,1,2))].">
      <j1 rule="para" parents="6234 10740"/>
    </justification>
  </clause>

  <clause id="10754">
    <literal><![CDATA[
      R(x,y \ 1,y) * K(z,u) = (x * (K(z,u) / y)) * y
    ]]></literal>
    <justification jstring="[hyper(138,a,10741,a(flip),b,4480,a)].">
      <j1 rule="hyper" parents="138 10741 4480"/>
    </justification>
  </clause>

  <clause id="10755">
    <literal><![CDATA[
      R(x,y \ 1,y \ z) * z = (x * (y \ K(u,w))) * ((y \ K(u,w)) \ z)
    ]]></literal>
    <justification jstring="[para(10741(a,1),4797(a,1,1))].">
      <j1 rule="para" parents="10741 4797"/>
    </justification>
  </clause>

  <clause id="10756">
    <literal><![CDATA[
      (x * ((y / z) \ 1)) * T(y / z,y \ z) = R(x,(z \ y) \ 1,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4716,a,b,10751,a)].">
      <j1 rule="hyper" parents="63 4716 10751"/>
    </justification>
  </clause>

  <clause id="10757">
    <literal><![CDATA[
      T(((1 / (x / y)) * z) * (x / y),y / x) = R(z,(y \ x) \ 1,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4715,a,b,10751,a)].">
      <j1 rule="hyper" parents="63 4715 10751"/>
    </justification>
  </clause>

  <clause id="10758">
    <literal><![CDATA[
      a(x,y,z \ (((u * (1 / (w / v5))) * (v5 \ w)) * v6)) = a(x,y,z \ (R(u,(v5 \ w) \ 1,v5 \ w) * v6))
    ]]></literal>
    <justification jstring="[para(10751(a,1),9321(a,2,3,2,1))].">
      <j1 rule="para" parents="10751 9321"/>
    </justification>
  </clause>

  <clause id="10759">
    <literal><![CDATA[
      (x * R(y / z,z,y)) * (z * (y \ 1)) = R(x,R(z \ y,z,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1874,a,b,10745,a)].">
      <j1 rule="hyper" parents="63 1874 10745"/>
    </justification>
  </clause>

  <clause id="10760">
    <literal><![CDATA[
      R(x,(y * z) \ ((y * u) * z),w) = R(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10752,a,b,10743,a)].">
      <j1 rule="hyper" parents="63 10752 10743"/>
    </justification>
  </clause>

  <clause id="10761">
    <literal><![CDATA[
      R(x * K(y,z),u \ 1,u) = (x * (K(y,z) / u)) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,4604,a,b,10754,a)].">
      <j1 rule="hyper" parents="63 4604 10754"/>
    </justification>
  </clause>

  <clause id="10762">
    <literal><![CDATA[
      (x * (K(y,z) / z)) * T(z,y) = R(x,z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,3268,a,b,10754,a)].">
      <j1 rule="hyper" parents="35 3268 10754"/>
    </justification>
  </clause>

  <clause id="10763">
    <literal><![CDATA[
      (T(x,y) \ R(z,u \ 1,u)) * T(x,y) = (z * (K(x \ z,T(x,y)) / u)) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,4407,a(flip),b,10761,a)].">
      <j1 rule="hyper" parents="63 4407 10761"/>
    </justification>
  </clause>

  <clause id="10765">
    <literal><![CDATA[
      R(x,(y * z) \ ((y * u) * z),w) = R(x,R(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10744,a(flip),b,10749,a),flip(a)].">
      <j1 rule="hyper" parents="63 10744 10749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10767">
    <literal><![CDATA[
      R(x,R(y,z,u),w) = R(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10760,a(flip),b,10765,a),flip(a)].">
      <j1 rule="hyper" parents="63 10760 10765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10768">
    <literal><![CDATA[
      R(x,R(y,z,u),w * v5) = R(x,L(y,z,u),v5 * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,4676,a,b,10767,a),flip(a)].">
      <j1 rule="hyper" parents="316 4676 10767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10771">
    <literal><![CDATA[
      L((x * (((y \ 1) * (y * x)) \ 1)) \ 1,x * (((y \ 1) * (y * x)) \ 1),x \ 1) * T(z,(x \ 1) \ ((x * (((y \ 1) * (y * x)) \ 1)) \ (x \ 1))) = T(z * ((((y \ 1) * (y * x)) \ 1) \ (x \ 1)),K(x * (((y \ 1) * (y * x)) \ 1),x \ 1))
    ]]></literal>
    <justification jstring="[para(8314(a,1),10414(a,2,1,2,1))].">
      <j1 rule="para" parents="8314 10414"/>
    </justification>
  </clause>

  <clause id="10772">
    <literal><![CDATA[
      (x * T(y,z * x)) \ (y * (z * x)) = R(T(z,y * x),x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,4679,a(flip),b,10452,a),flip(a)].">
      <j1 rule="hyper" parents="316 4679 10452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10774">
    <literal><![CDATA[
      L(x,y,((z * u) \ (u * (w * z))) \ v5) = L(x,y,R(T(w,u * z),z,u) \ v5)
    ]]></literal>
    <justification jstring="[para(10772(a,1),10288(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10772 10288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10775">
    <literal><![CDATA[
      L(x,y,z * R(u * K(w,v5),w,v5)) = L(x,y,L(T(u,w),w,v5) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4489,a(flip),b,10555,a)].">
      <j1 rule="hyper" parents="63 4489 10555"/>
    </justification>
  </clause>

  <clause id="10776">
    <literal><![CDATA[
      L(x,y,z * R(u * K(w,v5),w,v5)) = L(x,y,L(u,w,v5) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1663,a(flip),b,10775,a),flip(a)].">
      <j1 rule="hyper" parents="316 1663 10775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10778">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) \ (u * (z * w))) = a(x,y,a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5484,a(flip),b,10565,a),flip(a)].">
      <j1 rule="hyper" parents="316 5484 10565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10780">
    <literal><![CDATA[
      a((x * y) \ x,y,y \ 1) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,10531,a(flip),b,10621,a),flip(a)].">
      <j1 rule="hyper" parents="316 10531 10621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10782">
    <literal><![CDATA[
      a((x * y) \ x,y,y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2534,a(flip),b,10780,a)].">
      <j1 rule="hyper" parents="63 2534 10780"/>
    </justification>
  </clause>

  <clause id="10783">
    <literal><![CDATA[
      a((x * y) \ y,x,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4176,a,b,10782,a)].">
      <j1 rule="hyper" parents="63 4176 10782"/>
    </justification>
  </clause>

  <clause id="10784">
    <literal><![CDATA[
      ((x / (y \ 1)) / x) * K(y \ 1,y) = (((y * x) \ x) * y) * y
    ]]></literal>
    <justification jstring="[para(10783(a,1),3303(a,1,2))].">
      <j1 rule="para" parents="10783 3303"/>
    </justification>
  </clause>

  <clause id="10785">
    <literal><![CDATA[
      (((x * y) \ y) * x) * T(x,x \ 1) = (y / (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(35,a,3268,a,b,10784,a)].">
      <j1 rule="hyper" parents="35 3268 10784"/>
    </justification>
  </clause>

  <clause id="10787">
    <literal><![CDATA[
      ((x / (y \ 1)) / x) / y = y * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[hyper(136,a,10785,a(flip),b,3676,a(flip))].">
      <j1 rule="hyper" parents="136 10785 3676"/>
    </justification>
  </clause>

  <clause id="10788">
    <literal><![CDATA[
      (x * (y * (z / u))) / (z / u) = (x * (y * (u \ z))) / (u \ z)
    ]]></literal>
    <justification jstring="[hyper(34,a,4415,a(flip),b,10710,a(flip))].">
      <j1 rule="hyper" parents="34 4415 10710"/>
    </justification>
  </clause>

  <clause id="10789">
    <literal><![CDATA[
      (a(x,x \ y,z / u) * ((x \ y) * (u \ z))) / (u \ z) = (x \ (y * (z / u))) / (z / u)
    ]]></literal>
    <justification jstring="[para(8458(a,1),10788(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8458 10788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10790">
    <literal><![CDATA[
      L(x,K(y,z) * u,w) = L(x,u,w * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,652,a(flip),b,10732,a)].">
      <j1 rule="hyper" parents="63 652 10732"/>
    </justification>
  </clause>

  <clause id="10791">
    <literal><![CDATA[
      L(x,K(y,z) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,1676,a(flip),b,10790,a),flip(a)].">
      <j1 rule="hyper" parents="316 1676 10790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10795">
    <literal><![CDATA[
      L(x,(y \ 1) * (y * z),u) = L(x,L(z,y,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(464(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="464 10791"/>
    </justification>
  </clause>

  <clause id="10796">
    <literal><![CDATA[
      L(x,T(y,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(1325(a,2),10791(a,1,2))].">
      <j1 rule="para" parents="1325 10791"/>
    </justification>
  </clause>

  <clause id="10797">
    <literal><![CDATA[
      L(x,y * z,u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(2728(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="2728 10791"/>
    </justification>
  </clause>

  <clause id="10798">
    <literal><![CDATA[
      L(x,y / z,u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(2721(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="2721 10791"/>
    </justification>
  </clause>

  <clause id="10799">
    <literal><![CDATA[
      L(x,(y \ z) * y,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(2727(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="2727 10791"/>
    </justification>
  </clause>

  <clause id="10800">
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(2797(a,2),10791(a,1,2))].">
      <j1 rule="para" parents="2797 10791"/>
    </justification>
  </clause>

  <clause id="10801">
    <literal><![CDATA[
      L(x,T(y,z) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(2859(a,1),10791(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2859 10791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10802">
    <literal><![CDATA[
      L(x,(y * z) * u,w) = L(x,(z * y) * u,w)
    ]]></literal>
    <justification jstring="[para(2759(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="2759 10791"/>
    </justification>
  </clause>

  <clause id="10803">
    <literal><![CDATA[
      L(x,(y * z) / u,w) = L(x,(z * y) / u,w)
    ]]></literal>
    <justification jstring="[para(2766(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="2766 10791"/>
    </justification>
  </clause>

  <clause id="10804">
    <literal><![CDATA[
      L(x,y / (y / z),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(3095(a,2),10791(a,1,2))].">
      <j1 rule="para" parents="3095 10791"/>
    </justification>
  </clause>

  <clause id="10805">
    <literal><![CDATA[
      L(x,(y / z) * u,w) = L(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(2774(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="2774 10791"/>
    </justification>
  </clause>

  <clause id="10807">
    <literal><![CDATA[
      L(x,((y \ z) \ z) * u,w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(2853(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="2853 10791"/>
    </justification>
  </clause>

  <clause id="10808">
    <literal><![CDATA[
      L(x,y * T(z,u),w) = L(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(3128(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="3128 10791"/>
    </justification>
  </clause>

  <clause id="10809">
    <literal><![CDATA[
      L(x,(y / z) \ u,w) = L(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(3143(a,1),10791(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3143 10791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10810">
    <literal><![CDATA[
      L(x,L(T(y,z),u,w),v5) = L(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(2804(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="2804 10791"/>
    </justification>
  </clause>

  <clause id="10811">
    <literal><![CDATA[
      L(x,y \ T(z,u),w) = L(x,y \ z,w)
    ]]></literal>
    <justification jstring="[para(3137(a,1),10791(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3137 10791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10812">
    <literal><![CDATA[
      L(x,((y / z) * u) * w,v5) = L(x,((z \ y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(2777(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="2777 10791"/>
    </justification>
  </clause>

  <clause id="10813">
    <literal><![CDATA[
      L(x,L(T(y,z),u,w) \ v5,v6) = L(x,L(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(2903(a,1),10791(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2903 10791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10814">
    <literal><![CDATA[
      L(x,L(y,z,u) * (u * z),w) = L(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[para(2764(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="2764 10791"/>
    </justification>
  </clause>

  <clause id="10815">
    <literal><![CDATA[
      L(x,y * K(z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(3622(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="3622 10791"/>
    </justification>
  </clause>

  <clause id="10816">
    <literal><![CDATA[
      L(x,y * (z * ((u \ 1) \ 1)),w) = L(x,y * (z * u),w)
    ]]></literal>
    <justification jstring="[para(4218(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="4218 10791"/>
    </justification>
  </clause>

  <clause id="10817">
    <literal><![CDATA[
      L(x,(y * z) \ u,w) = L(x,(z * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(6234(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="6234 10791"/>
    </justification>
  </clause>

  <clause id="10818">
    <literal><![CDATA[
      L(x,((y \ z) * y) \ u,w) = L(x,z \ u,w)
    ]]></literal>
    <justification jstring="[para(6248(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="6248 10791"/>
    </justification>
  </clause>

  <clause id="10820">
    <literal><![CDATA[
      L(x,y \ K(z,u),w) = L(x,y \ 1,w)
    ]]></literal>
    <justification jstring="[para(10296(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="10296 10791"/>
    </justification>
  </clause>

  <clause id="10821">
    <literal><![CDATA[
      L(x,(y \ T(z,u)) \ w,v5) = L(x,(y \ z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(10223(a,1),10791(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10223 10791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10822">
    <literal><![CDATA[
      L(x,y \ (y / z),u) = L(x,y \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(10283(a,1),10791(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10283 10791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10823">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),v5) = L(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(10295(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="10295 10791"/>
    </justification>
  </clause>

  <clause id="10824">
    <literal><![CDATA[
      L(x,y * (K(z,u) * w),v5) = L(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(10307(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="10307 10791"/>
    </justification>
  </clause>

  <clause id="10825">
    <literal><![CDATA[
      L(x,(y \ (K(z,u) * w)) \ v5,v6) = L(x,(y \ w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(10226(a,1),10791(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10226 10791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10826">
    <literal><![CDATA[
      L(x,(y * (K(z,u) * w)) * v5,v6) = L(x,(y * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(10325(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="10325 10791"/>
    </justification>
  </clause>

  <clause id="10827">
    <literal><![CDATA[
      L(x,L(y / z,u,w) \ v5,v6) = L(x,L(z \ y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(10245(a,1),10791(a,1,2))].">
      <j1 rule="para" parents="10245 10791"/>
    </justification>
  </clause>

  <clause id="10828">
    <literal><![CDATA[
      L(x,T(y,z),u) = L(x,y,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(1652,a,10796,a)].">
      <j1 rule="hyper" parents="1652 10796"/>
    </justification>
  </clause>

  <clause id="10832">
    <literal><![CDATA[
      (x * T(y,z)) \ ((T(y,z) * z) * x) = L(z * K(z * y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10409,a,b,10796,a)].">
      <j1 rule="hyper" parents="63 10409 10796"/>
    </justification>
  </clause>

  <clause id="10833">
    <literal><![CDATA[
      L(T(x,y) \ (z \ u),x,z) = (z * T(x,y)) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,298,a(flip),b,10796,a),flip(a)].">
      <j1 rule="hyper" parents="63 298 10796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10834">
    <literal><![CDATA[
      L(x,y \ (z * y),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(22(a,1),10796(a,1,2))].">
      <j1 rule="para" parents="22 10796"/>
    </justification>
  </clause>

  <clause id="10835">
    <literal><![CDATA[
      L(x,L(y / z,u,w),v5) = L(x,L(z \ y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(261(a,1),10796(a,1,2)),flip(a)].">
      <j1 rule="para" parents="261 10796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10837">
    <literal><![CDATA[
      L(x,L((y \ z) \ z,u,w),v5) = L(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(315(a,1),10796(a,1,2))].">
      <j1 rule="para" parents="315 10796"/>
    </justification>
  </clause>

  <clause id="10842">
    <literal><![CDATA[
      L(x,K(y,z) * (u * w),v5) = L(x,w * u,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,10791,a,b,10797,a)].">
      <j1 rule="hyper" parents="316 10791 10797"/>
    </justification>
  </clause>

  <clause id="10843">
    <literal><![CDATA[
      L(L(x * y,z,u) \ (x * y),y * x,z) = a(u,z,x * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,9998,a,b,10797,a),flip(a)].">
      <j1 rule="hyper" parents="316 9998 10797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10844">
    <literal><![CDATA[
      L(x,y * z,u * w) = L(x,z * y,w * u)
    ]]></literal>
    <justification jstring="[hyper(316,a,1668,a,b,10797,a)].">
      <j1 rule="hyper" parents="316 1668 10797"/>
    </justification>
  </clause>

  <clause id="10847">
    <literal><![CDATA[
      a(x,y,L(z,u * w,v5 * v6)) = a(x,y,L(z,w * u,v6 * v5))
    ]]></literal>
    <justification jstring="[para(10797(a,1),5557(a,1,3))].">
      <j1 rule="para" parents="10797 5557"/>
    </justification>
  </clause>

  <clause id="10848">
    <literal><![CDATA[
      a(x,y,L(z,u * w,v5) * (v5 * (w * u))) = a(x,y,v5 * ((w * u) * z))
    ]]></literal>
    <justification jstring="[para(10797(a,1),5472(a,1,3,1))].">
      <j1 rule="para" parents="10797 5472"/>
    </justification>
  </clause>

  <clause id="10849">
    <literal><![CDATA[
      L(x,((y * z) \ y) * z,u) = L(x,a(y,z,z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(7348(a,1),10797(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7348 10797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10850">
    <literal><![CDATA[
      L(x,(y * (z * u)) * (K(w,v5) * v6),v7) = L(x,v6 * (y * (z * (u * K(w,v5)))),v7)
    ]]></literal>
    <justification jstring="[para(10337(a,1),10797(a,1,2))].">
      <j1 rule="para" parents="10337 10797"/>
    </justification>
  </clause>

  <clause id="10851">
    <literal><![CDATA[
      L(x,y / z,u / w) = L(x,z \ y,w \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,1586,a(flip),b,10798,a),flip(a)].">
      <j1 rule="hyper" parents="316 1586 10798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10853">
    <literal><![CDATA[
      L(x,y / (z / (u * u)),w) = L(x,z \ (y * (u * u)),w)
    ]]></literal>
    <justification jstring="[para(676(a,1),10798(a,1,2))].">
      <j1 rule="para" parents="676 10798"/>
    </justification>
  </clause>

  <clause id="10854">
    <literal><![CDATA[
      L(x,(y * y) \ (z * u),w) = L(x,z * (u / (y * y)),w)
    ]]></literal>
    <justification jstring="[para(683(a,1),10798(a,1,2)),flip(a)].">
      <j1 rule="para" parents="683 10798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10856">
    <literal><![CDATA[
      a(x,y,z \ (L(u,(u * w) \ w,v5) * (v5 * (w / (u * w))))) = a(x,y,z \ (v5 * a(u \ 1,u,w)))
    ]]></literal>
    <justification jstring="[para(10798(a,1),8868(a,1,3,2,1))].">
      <j1 rule="para" parents="10798 8868"/>
    </justification>
  </clause>

  <clause id="10857">
    <literal><![CDATA[
      L(x,L(y * z,u,w),v5) = L(x,L(z * y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(1360(a,1),10799(a,1,2))].">
      <j1 rule="para" parents="1360 10799"/>
    </justification>
  </clause>

  <clause id="10858">
    <literal><![CDATA[
      a(x,y,L(z,(u * u) \ w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(10799(a,1),7517(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10799 7517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10859">
    <literal><![CDATA[
      L(x,y * (z / u),w) = L(x,y * (u \ z),w)
    ]]></literal>
    <justification jstring="[para(3151(a,1),10815(a,1,2))].">
      <j1 rule="para" parents="3151 10815"/>
    </justification>
  </clause>

  <clause id="10860">
    <literal><![CDATA[
      L(x,y * (z * K(u,w)),v5) = L(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(3763(a,1),10815(a,1,2))].">
      <j1 rule="para" parents="3763 10815"/>
    </justification>
  </clause>

  <clause id="10861">
    <literal><![CDATA[
      L(x,y \ (z * K(u,w)),v5) = L(x,y \ z,v5)
    ]]></literal>
    <justification jstring="[para(3781(a,2),10815(a,1,2))].">
      <j1 rule="para" parents="3781 10815"/>
    </justification>
  </clause>

  <clause id="10862">
    <literal><![CDATA[
      L(x,y \ (z * u),w) = L(x,y \ (u * z),w)
    ]]></literal>
    <justification jstring="[para(3922(a,1),10815(a,1,2))].">
      <j1 rule="para" parents="3922 10815"/>
    </justification>
  </clause>

  <clause id="10863">
    <literal><![CDATA[
      L(x,y * (z * u),w) = L(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[para(3933(a,1),10815(a,1,2))].">
      <j1 rule="para" parents="3933 10815"/>
    </justification>
  </clause>

  <clause id="10864">
    <literal><![CDATA[
      L(x,y \ (z * T(u,w)),v5) = L(x,y \ (z * u),v5)
    ]]></literal>
    <justification jstring="[para(3913(a,1),10815(a,1,2))].">
      <j1 rule="para" parents="3913 10815"/>
    </justification>
  </clause>

  <clause id="10865">
    <literal><![CDATA[
      L(x,y \ (z / u),w) = L(x,y \ (u \ z),w)
    ]]></literal>
    <justification jstring="[para(3917(a,1),10815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3917 10815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10866">
    <literal><![CDATA[
      L(x,(y * z) \ ((z * u) * y),w) = L(x,L(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(3953(a,1),10815(a,1,2))].">
      <j1 rule="para" parents="3953 10815"/>
    </justification>
  </clause>

  <clause id="10867">
    <literal><![CDATA[
      L(x,y * (z * (u / w)),v5) = L(x,y * (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(4028(a,1),10815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4028 10815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10868">
    <literal><![CDATA[
      L(x,y \ (z \ (u * T(w,v5))),v6) = L(x,y \ (z \ (u * w)),v6)
    ]]></literal>
    <justification jstring="[para(4033(a,1),10815(a,1,2))].">
      <j1 rule="para" parents="4033 10815"/>
    </justification>
  </clause>

  <clause id="10869">
    <literal><![CDATA[
      L(x,y \ (z * (u * T(w,v5))),v6) = L(x,y \ (z * (u * w)),v6)
    ]]></literal>
    <justification jstring="[para(4049(a,1),10815(a,1,2))].">
      <j1 rule="para" parents="4049 10815"/>
    </justification>
  </clause>

  <clause id="10871">
    <literal><![CDATA[
      L(x,y * L(T(z,u),w,v5),v6) = L(x,y * L(z,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(4453(a,1),10815(a,1,2))].">
      <j1 rule="para" parents="4453 10815"/>
    </justification>
  </clause>

  <clause id="10872">
    <literal><![CDATA[
      L(x,L(y * K(z,u),w,v5),v6) = L(x,L(y,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(4837(a,2),10815(a,1,2))].">
      <j1 rule="para" parents="4837 10815"/>
    </justification>
  </clause>

  <clause id="10873">
    <literal><![CDATA[
      L(x,L(y \ K(z,u),w,v5),v6) = L(x,L(y \ 1,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(4846(a,1),10815(a,1,2))].">
      <j1 rule="para" parents="4846 10815"/>
    </justification>
  </clause>

  <clause id="10874">
    <literal><![CDATA[
      L(x,T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(10828(a,2),1652(a,1))].">
      <j1 rule="para" parents="10828 1652"/>
    </justification>
  </clause>

  <clause id="10875">
    <literal><![CDATA[
      L(x,y / T(z,u),w) = L(x,z \ y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10798,a,b,10801,a)].">
      <j1 rule="hyper" parents="63 10798 10801"/>
    </justification>
  </clause>

  <clause id="10876">
    <literal><![CDATA[
      L(x,y * ((z * z) \ z),u) = L(x,y * (z \ 1),u)
    ]]></literal>
    <justification jstring="[para(283(a,1),10808(a,1,2,2))].">
      <j1 rule="para" parents="283 10808"/>
    </justification>
  </clause>

  <clause id="10877">
    <literal><![CDATA[
      L(x,y \ R(z / u,w,v5),v6) = L(x,y \ R(u \ z,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(262(a,1),10811(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="262 10811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10878">
    <literal><![CDATA[
      L(x,y \ ((z * u) * (z \ 1)),w) = L(x,y \ R(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(625(a,1),10811(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="625 10811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10879">
    <literal><![CDATA[
      L(x,y \ R(z / u,u,w),v5) = L(x,y \ ((u * w) \ (z * w)),v5)
    ]]></literal>
    <justification jstring="[para(512(a,1),10811(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="512 10811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10880">
    <literal><![CDATA[
      L(x,y \ (R(z,u,w) \ (v5 * z)),v6) = L(x,y \ (z * (R(z,u,w) \ v5)),v6)
    ]]></literal>
    <justification jstring="[para(3237(a,1),10811(a,1,2,2))].">
      <j1 rule="para" parents="3237 10811"/>
    </justification>
  </clause>

  <clause id="10881">
    <literal><![CDATA[
      L(x,y \ (L(z,u,w) \ (v5 * z)),v6) = L(x,y \ (z * (L(z,u,w) \ v5)),v6)
    ]]></literal>
    <justification jstring="[para(4434(a,1),10811(a,1,2,2))].">
      <j1 rule="para" parents="4434 10811"/>
    </justification>
  </clause>

  <clause id="10883">
    <literal><![CDATA[
      L(x,(y * z) * u,w) = L(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10797,a,b,10802,a),flip(a)].">
      <j1 rule="hyper" parents="316 10797 10802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10884">
    <literal><![CDATA[
      L(((x * y) * z) \ L((x * y) * z,u,a(w,v5,v6)),(y * x) * z,u * a(w,v5,v6)) = a((x * y) * z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,5385,a(flip),b,10802,a),flip(a)].">
      <j1 rule="hyper" parents="316 5385 10802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10885">
    <literal><![CDATA[
      L(x,(y * z) * a(u,w,z),v5) = L(x,z * (y * a(u,w,z)),v5)
    ]]></literal>
    <justification jstring="[para(6858(a,1),10802(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6858 10802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10886">
    <literal><![CDATA[
      L(x,(y * z) / u,w) = L(x,u \ (z * y),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10798,a(flip),b,10803,a),flip(a)].">
      <j1 rule="hyper" parents="316 10798 10803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10887">
    <literal><![CDATA[
      L(x,(y \ z) * u,w) = L(x,u * (z / y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10797,a,b,10805,a),flip(a)].">
      <j1 rule="hyper" parents="63 10797 10805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10889">
    <literal><![CDATA[
      L(x,((y \ 1) \ z) * y,u) = L(x,z * (y * y),u)
    ]]></literal>
    <justification jstring="[para(576(a,1),10805(a,1,2)),flip(a)].">
      <j1 rule="para" parents="576 10805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10890">
    <literal><![CDATA[
      L(x,((y * z) \ ((u * z) * y)) \ w,v5) = L(x,R(u * K(z,y),z,y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(4488(a,1),10809(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4488 10809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10891">
    <literal><![CDATA[
      L(x,(y * z) \ (z * (u * y)),w) = L(x,L(T(u,y),y,z),w)
    ]]></literal>
    <justification jstring="[para(247(a,1),10817(a,1,2)),flip(a)].">
      <j1 rule="para" parents="247 10817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10892">
    <literal><![CDATA[
      L(x,y \ (y / z),(u \ (w / v5)) \ v6) = L(x,y \ (z \ y),(u \ (v5 \ w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,4198,a(flip),b,10822,a),flip(a)].">
      <j1 rule="hyper" parents="316 4198 10822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10893">
    <literal><![CDATA[
      L(L(x \ 1,x,x \ y) \ z,y \ (x \ y),y) = (y / x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1643,a(flip),b,10822,a),flip(a)].">
      <j1 rule="hyper" parents="63 1643 10822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10894">
    <literal><![CDATA[
      L(x,L(y,y,z),u) = L(x,z \ ((y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[para(1447(a,2),10822(a,1,2))].">
      <j1 rule="para" parents="1447 10822"/>
    </justification>
  </clause>

  <clause id="10895">
    <literal><![CDATA[
      L(L(x,y \ (z \ y),z),z * (y \ (y / z)),z) = z * (z * (L(z,z,z \ y) \ ((y \ (y / z)) * x)))
    ]]></literal>
    <justification jstring="[para(10822(a,1),2028(a,1,1))].">
      <j1 rule="para" parents="10822 2028"/>
    </justification>
  </clause>

  <clause id="10896">
    <literal><![CDATA[
      L(x,y \ (T(z,u) * w),v5) = L(x,y \ (z * w),v5)
    ]]></literal>
    <justification jstring="[para(2800(a,1),10823(a,1,2,2))].">
      <j1 rule="para" parents="2800 10823"/>
    </justification>
  </clause>

  <clause id="10897">
    <literal><![CDATA[
      L(x,y \ ((z * u) * w),v5) = L(x,y \ ((u * z) * w),v5)
    ]]></literal>
    <justification jstring="[para(2759(a,1),10823(a,1,2,2))].">
      <j1 rule="para" parents="2759 10823"/>
    </justification>
  </clause>

  <clause id="10898">
    <literal><![CDATA[
      L(x,y \ ((z / u) * w),v5) = L(x,y \ ((u \ z) * w),v5)
    ]]></literal>
    <justification jstring="[para(2774(a,1),10823(a,1,2,2))].">
      <j1 rule="para" parents="2774 10823"/>
    </justification>
  </clause>

  <clause id="10899">
    <literal><![CDATA[
      L(x,y \ ((T(z,u) * w) * v5),v6) = L(x,y \ ((z * w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(2811(a,1),10823(a,1,2,2))].">
      <j1 rule="para" parents="2811 10823"/>
    </justification>
  </clause>

  <clause id="10900">
    <literal><![CDATA[
      L(x,y * (((z \ u) * z) * w),v5) = L(x,y * (u * w),v5)
    ]]></literal>
    <justification jstring="[para(2779(a,1),10824(a,1,2,2))].">
      <j1 rule="para" parents="2779 10824"/>
    </justification>
  </clause>

  <clause id="10901">
    <literal><![CDATA[
      L(x,(y \ T(z,u)) * w,v5) = L(x,(y \ z) * w,v5)
    ]]></literal>
    <justification jstring="[para(10195(a,1),10824(a,1,2))].">
      <j1 rule="para" parents="10195 10824"/>
    </justification>
  </clause>

  <clause id="10902">
    <literal><![CDATA[
      L(x,y * (z * (K(u,w) * v5)),v6) = L(x,y * (z * v5),v6)
    ]]></literal>
    <justification jstring="[para(10307(a,1),10824(a,1,2,2))].">
      <j1 rule="para" parents="10307 10824"/>
    </justification>
  </clause>

  <clause id="10903">
    <literal><![CDATA[
      L(x,y * ((z \ K(u,w)) * v5),v6) = L(x,y * ((z \ 1) * v5),v6)
    ]]></literal>
    <justification jstring="[para(10297(a,1),10824(a,1,2,2))].">
      <j1 rule="para" parents="10297 10824"/>
    </justification>
  </clause>

  <clause id="10904">
    <literal><![CDATA[
      L(x,(y \ (z / u)) * w,v5) = L(x,(y \ (u \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(10192(a,1),10824(a,1,2))].">
      <j1 rule="para" parents="10192 10824"/>
    </justification>
  </clause>

  <clause id="10905">
    <literal><![CDATA[
      L(x,y * ((z * (K(u,w) * v5)) * v6),v7) = L(x,y * ((z * v5) * v6),v7)
    ]]></literal>
    <justification jstring="[para(10325(a,1),10824(a,1,2,2))].">
      <j1 rule="para" parents="10325 10824"/>
    </justification>
  </clause>

  <clause id="10906">
    <literal><![CDATA[
      L(x,((y \ z) * y) * u,w) = L(x,u * z,w)
    ]]></literal>
    <justification jstring="[para(2779(a,1),10842(a,1,2))].">
      <j1 rule="para" parents="2779 10842"/>
    </justification>
  </clause>

  <clause id="10907">
    <literal><![CDATA[
      L(x,(y * T(z,u)) * w,v5) = L(x,w * (y * z),v5)
    ]]></literal>
    <justification jstring="[para(4166(a,1),10842(a,1,2))].">
      <j1 rule="para" parents="4166 10842"/>
    </justification>
  </clause>

  <clause id="10908">
    <literal><![CDATA[
      L(x,y * (T(z,u) * w),v5) = L(x,(z * w) * y,v5)
    ]]></literal>
    <justification jstring="[para(7825(a,1),10842(a,1,2))].">
      <j1 rule="para" parents="7825 10842"/>
    </justification>
  </clause>

  <clause id="10909">
    <literal><![CDATA[
      L(x,(y * (K(z,u) * w)) * v5,v6) = L(x,v5 * (y * w),v6)
    ]]></literal>
    <justification jstring="[para(10325(a,1),10842(a,1,2))].">
      <j1 rule="para" parents="10325 10842"/>
    </justification>
  </clause>

  <clause id="10910">
    <literal><![CDATA[
      a(x,y,L(L(z,u * w,v5 * v6),v7,v8)) = a(x,y,L(L(z,v7,v8),w * u,v6 * v5))
    ]]></literal>
    <justification jstring="[para(10844(a,1),5952(a,1,3,1))].">
      <j1 rule="para" parents="10844 5952"/>
    </justification>
  </clause>

  <clause id="10911">
    <literal><![CDATA[
      L(x,y * ((z * z) \ (u * w)),v5) = L(x,y * (u * (w / (z * z))),v5)
    ]]></literal>
    <justification jstring="[para(683(a,1),10859(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="683 10859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10913">
    <literal><![CDATA[
      L(x,y * (z \ (u / w)),v5) = L(x,y * (z \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(3917(a,1),10860(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3917 10860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10914">
    <literal><![CDATA[
      L(x,y * (z * (u * T(w,v5))),v6) = L(x,y * (z * (u * w)),v6)
    ]]></literal>
    <justification jstring="[para(3942(a,1),10860(a,1,2,2))].">
      <j1 rule="para" parents="3942 10860"/>
    </justification>
  </clause>

  <clause id="10915">
    <literal><![CDATA[
      L(x,y \ (z \ (u / w)),v5) = L(x,y \ (z \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(3917(a,1),10861(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3917 10861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10916">
    <literal><![CDATA[
      L(x,y \ (z \ ((u \ w) * u)),v5) = L(x,y \ (z \ w),v5)
    ]]></literal>
    <justification jstring="[para(3921(a,1),10861(a,1,2,2))].">
      <j1 rule="para" parents="3921 10861"/>
    </justification>
  </clause>

  <clause id="10917">
    <literal><![CDATA[
      L(x,y \ ((z * u) \ ((u * w) * z)),v5) = L(x,y \ L(w,u,z),v5)
    ]]></literal>
    <justification jstring="[para(3953(a,1),10861(a,1,2,2))].">
      <j1 rule="para" parents="3953 10861"/>
    </justification>
  </clause>

  <clause id="10919">
    <literal><![CDATA[
      L(x,y \ (z / a(L(u,z,w),z,w)),v5) = L(x,y \ (u * (R(u,z,w) \ z)),v5)
    ]]></literal>
    <justification jstring="[para(8650(a,1),10865(a,2,2,2))].">
      <j1 rule="para" parents="8650 10865"/>
    </justification>
  </clause>

  <clause id="10920">
    <literal><![CDATA[
      L(x,L(y,z,u) * (z * u),w) = L(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[para(100(a,1),10883(a,1,2)),flip(a)].">
      <j1 rule="para" parents="100 10883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10921">
    <literal><![CDATA[
      L(x,y * ((z \ 1) * (u * z)),w) = L(x,R(u,z,z) * y,w)
    ]]></literal>
    <justification jstring="[para(565(a,1),10883(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="565 10883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10922">
    <literal><![CDATA[
      L(x,(y \ 1) * (y * z),u) = L(x,R(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(565(a,1),10883(a,1,2)),flip(a)].">
      <j1 rule="para" parents="565 10883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10923">
    <literal><![CDATA[
      L(x,((y \ 1) * (z * y)) * u,w) = L(x,u * R(z,y,y),w)
    ]]></literal>
    <justification jstring="[para(565(a,1),10883(a,2,2,2))].">
      <j1 rule="para" parents="565 10883"/>
    </justification>
  </clause>

  <clause id="10924">
    <literal><![CDATA[
      L(x,y * ((R(z,z,u) \ u) * z),w) = L(x,L(u,z,z) * y,w)
    ]]></literal>
    <justification jstring="[para(4658(a,1),10883(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4658 10883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10925">
    <literal><![CDATA[
      L(x,y * ((K(z \ u,z) * w) * u),v5) = L(x,(((z \ u) * z) * w) * y,v5)
    ]]></literal>
    <justification jstring="[para(6261(a,1),10883(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6261 10883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10926">
    <literal><![CDATA[
      L(x,y * ((L(z,z,u) \ u) * z),w) = L(x,R(u,z,z) * y,w)
    ]]></literal>
    <justification jstring="[para(7158(a,1),10883(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7158 10883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10927">
    <literal><![CDATA[
      L(x,(y * z) \ (z * (u * y)),w) = L(x,R(u,y,z),w)
    ]]></literal>
    <justification jstring="[para(20(a,2),10886(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 10886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10928">
    <literal><![CDATA[
      L(x,(y * y) \ (z * u),w) = L(x,u * (z / (y * y)),w)
    ]]></literal>
    <justification jstring="[para(683(a,1),10886(a,1,2)),flip(a)].">
      <j1 rule="para" parents="683 10886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10929">
    <literal><![CDATA[
      a(x,y,L(z,u * w,u \ w) * ((w * u) * (u \ w))) = a(x,y,(w / u) * ((((u \ w) * u) * u) * z))
    ]]></literal>
    <justification jstring="[para(10906(a,1),9676(a,1,3,1))].">
      <j1 rule="para" parents="10906 9676"/>
    </justification>
  </clause>

  <clause id="10930">
    <literal><![CDATA[
      L((T(x,y) \ (a(z,u,w) \ v5)) \ ((a(z,u,w) * T(x,y)) \ v5),T(x,y) \ (a(z,u,w) \ v5),x * a(z,u,w)) = a(T(x,y) \ (a(z,u,w) \ v5),x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(10833(a,1),5385(a,1,1,2))].">
      <j1 rule="para" parents="10833 5385"/>
    </justification>
  </clause>

  <clause id="10931">
    <literal><![CDATA[
      a(x,y,L(L(T(z \ 1,u) \ (w \ v5),v6,v7),z,w)) = a(x,y,L((w * T(z \ 1,u)) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(10833(a,1),7521(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10833 7521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10932">
    <literal><![CDATA[
      (T(x,y) \ (z \ u)) \ ((z * T(x,y)) \ u) = (((z * x) \ u) \ (x \ (z \ u))) \ 1
    ]]></literal>
    <justification jstring="[para(10833(a,1),7449(a,1,2))].">
      <j1 rule="para" parents="10833 7449"/>
    </justification>
  </clause>

  <clause id="10933">
    <literal><![CDATA[
      L(x,L((y * y) \ (z * u),w,v5),v6) = L(x,L(z * (u / (y * y)),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(683(a,1),10835(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="683 10835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10934">
    <literal><![CDATA[
      L(x,L(y * a(z,y,u),u,z),w) = L(x,(z * u) \ ((z * y) * u),w)
    ]]></literal>
    <justification jstring="[para(8578(a,1),10864(a,1,2))].">
      <j1 rule="para" parents="8578 10864"/>
    </justification>
  </clause>

  <clause id="10935">
    <literal><![CDATA[
      L(x,(y * (a(y,z,(u * u) \ u) \ z)) * (u \ 1),w) = L(x,y * (z * ((u * u) \ u)),w)
    ]]></literal>
    <justification jstring="[para(8531(a,1),10876(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8531 10876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10937">
    <literal><![CDATA[
      L(x,((y \ 1) * z) * (y * y),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),10889(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 10889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10938">
    <literal><![CDATA[
      L(x,y \ ((z * T(u,w)) * L(v5,z,T(u,w))),v6) = L(x,y \ (u * (T(z,T(u,w)) * v5)),v6)
    ]]></literal>
    <justification jstring="[para(3285(a,2),10896(a,1,2,2))].">
      <j1 rule="para" parents="3285 10896"/>
    </justification>
  </clause>

  <clause id="10940">
    <literal><![CDATA[
      L(x,L(y,z,z \ 1),u) = L(x,R(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10922,a(flip),b,10795,a),flip(a)].">
      <j1 rule="hyper" parents="63 10922 10795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10941">
    <literal><![CDATA[
      T(a(x \ 1,x,y) * (z * L(y,x,x \ 1)),K(z,y)) = L(z,R(y,x,x),a(x \ 1,x,y)) * y
    ]]></literal>
    <justification jstring="[para(10940(a,1),9536(a,2,1))].">
      <j1 rule="para" parents="10940 9536"/>
    </justification>
  </clause>

  <clause id="10942">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * u) * z),w) = L(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10817,a,b,10866,a)].">
      <j1 rule="hyper" parents="63 10817 10866"/>
    </justification>
  </clause>

  <clause id="10943">
    <literal><![CDATA[
      L(x,L((y * y) \ (z * y),u,w),v5) = L(x,L(L(y \ z,u,w),y,y),v5)
    ]]></literal>
    <justification jstring="[para(1539(a,1),10866(a,1,2))].">
      <j1 rule="para" parents="1539 10866"/>
    </justification>
  </clause>

  <clause id="10945">
    <literal><![CDATA[
      L(x,(y \ (z * z)) \ (((y \ 1) * u) * (z * z)),w) = L(x,L(u,y \ 1,z * z),w)
    ]]></literal>
    <justification jstring="[para(389(a,1),10942(a,1,2,1))].">
      <j1 rule="para" parents="389 10942"/>
    </justification>
  </clause>

  <clause id="10947">
    <literal><![CDATA[
      L(x,L(a(y,z,u) \ z,y,u),w) = L(x,(y * u) \ (y * (z * u)),w)
    ]]></literal>
    <justification jstring="[para(8531(a,1),10942(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8531 10942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10949">
    <literal><![CDATA[
      L(x,y * R(z * u,u \ 1,u),w) = L(x,y * (R(z,u,u) * u),w)
    ]]></literal>
    <justification jstring="[para(1042(a,1),10816(a,1,2,2))].">
      <j1 rule="para" parents="1042 10816"/>
    </justification>
  </clause>

  <clause id="10950">
    <literal><![CDATA[
      L(x,((T(y,z) * u) \ w) \ v5,v6) = L(x,((y * u) \ w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(2870(a,1),10825(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2870 10825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10951">
    <literal><![CDATA[
      L(x,(y / (z * z)) \ u,w) = L(x,y \ (u * (z * z)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10798,a(flip),b,10853,a)].">
      <j1 rule="hyper" parents="63 10798 10853"/>
    </justification>
  </clause>

  <clause id="10952">
    <literal><![CDATA[
      L(x,(y * y) \ (z * u),w) = L(x,z * ((y * y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10859,a(flip),b,10854,a),flip(a)].">
      <j1 rule="hyper" parents="316 10859 10854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10953">
    <literal><![CDATA[
      L(x,L(y \ 1,y,z),u) = L(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[para(8186(a,1),10873(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8186 10873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10955">
    <literal><![CDATA[
      L(x,(y * z) \ y,u) = L(x,y \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(232(a,1),10953(a,1,2))].">
      <j1 rule="para" parents="232 10953"/>
    </justification>
  </clause>

  <clause id="10956">
    <literal><![CDATA[
      (x * ((x \ y) / y)) \ y = L(y,(y * x) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,10608,a(flip),b,10955,a)].">
      <j1 rule="hyper" parents="316 10608 10955"/>
    </justification>
  </clause>

  <clause id="10957">
    <literal><![CDATA[
      L(x,(y * z) \ z,u) = L(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10817,a,b,10955,a)].">
      <j1 rule="hyper" parents="63 10817 10955"/>
    </justification>
  </clause>

  <clause id="10958">
    <literal><![CDATA[
      L(x,L(y * (z * z),u,w) \ (z * z),v5) = L(x,(z * z) \ (L(y,u,w) \ (z * z)),v5)
    ]]></literal>
    <justification jstring="[para(1058(a,2),10957(a,1,2,1))].">
      <j1 rule="para" parents="1058 10957"/>
    </justification>
  </clause>

  <clause id="10960">
    <literal><![CDATA[
      (x * ((x \ (x \ y)) / (x \ y))) \ (x \ y) = L(x \ y,y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,10818,a(flip),b,10956,a),flip(a)].">
      <j1 rule="hyper" parents="316 10818 10956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10961">
    <literal><![CDATA[
      L(x,(y * (z * u)) \ ((z * y) * u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(14(a,2),10897(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14 10897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10962">
    <literal><![CDATA[
      L(x,(y \ ((z \ u) * z)) / w,v5) = L(x,w \ (y \ u),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10798,a,b,10916,a)].">
      <j1 rule="hyper" parents="63 10798 10916"/>
    </justification>
  </clause>

  <clause id="10964">
    <literal><![CDATA[
      L(x,y \ (z * (y * y)),u) = L(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(281(a,1),10951(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="281 10951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10965">
    <literal><![CDATA[
      L(x,(y \ z) * (y * y),u) = L(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(388(a,1),10964(a,1,2))].">
      <j1 rule="para" parents="388 10964"/>
    </justification>
  </clause>

  <clause id="10966">
    <literal><![CDATA[
      a(x,y,L(z,(u \ 1) \ w,v5)) = a(x,y,L(z,u \ w,v5))
    ]]></literal>
    <justification jstring="[para(10965(a,1),7517(a,1,3))].">
      <j1 rule="para" parents="10965 7517"/>
    </justification>
  </clause>

  <clause id="10967">
    <literal><![CDATA[
      a(x,y,z * (((u \ w) * (u * u)) * L(v5,(u \ 1) \ w,(u \ 1) \ w))) = a(x,y,(((u \ w) * (u * u)) \ v5) * z)
    ]]></literal>
    <justification jstring="[para(10965(a,1),8687(a,1,3,2,2))].">
      <j1 rule="para" parents="10965 8687"/>
    </justification>
  </clause>

  <clause id="10968">
    <literal><![CDATA[
      L(x,y * ((z * z) \ u),w) = L(x,u * (y / (z * z)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10928,a(flip),b,10952,a),flip(a)].">
      <j1 rule="hyper" parents="63 10928 10952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10969">
    <literal><![CDATA[
      a(x,y,L(z,u \ L(u,w,v5),v6)) = a(x,y,L(z,u * L(u,w,v5),v6))
    ]]></literal>
    <justification jstring="[para(4590(a,1),10966(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="4590 10966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10970">
    <literal><![CDATA[
      L(x,((y * y) \ z) * u,w) = L(x,z * ((y * y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10887,a,b,10968,a)].">
      <j1 rule="hyper" parents="316 10887 10968"/>
    </justification>
  </clause>

  <clause id="10972">
    <literal><![CDATA[
      L(x,y * ((z * z) \ (T(u,w) * v5)),v6) = L(x,(u * v5) * ((z * z) \ y),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,10908,a(flip),b,10970,a),flip(a)].">
      <j1 rule="hyper" parents="63 10908 10970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10973">
    <literal><![CDATA[
      L(x,y \ ((z \ 1) * (z * u)),w) = L(x,y \ R(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10862,a,b,10878,a)].">
      <j1 rule="hyper" parents="63 10862 10878"/>
    </justification>
  </clause>

  <clause id="10974">
    <literal><![CDATA[
      L(x,(y * z) \ (z * (u * y)),w) = L(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10810,a(flip),b,10891,a),flip(a)].">
      <j1 rule="hyper" parents="316 10810 10891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10976">
    <literal><![CDATA[
      L(x,(y * (z * u)) / T(u * y,w),v5) = L(x,L(z,u,y),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10875,a,b,10974,a)].">
      <j1 rule="hyper" parents="63 10875 10974"/>
    </justification>
  </clause>

  <clause id="10977">
    <literal><![CDATA[
      L(x,R(y,z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10927,a(flip),b,10974,a)].">
      <j1 rule="hyper" parents="63 10927 10974"/>
    </justification>
  </clause>

  <clause id="10978">
    <literal><![CDATA[
      L(x,((y \ z) * y) \ (z / ((z \ y) \ 1)),u) = L(x,L(z \ y,y \ z,y),u)
    ]]></literal>
    <justification jstring="[para(9335(a,1),10974(a,1,2,2))].">
      <j1 rule="para" parents="9335 10974"/>
    </justification>
  </clause>

  <clause id="10979">
    <literal><![CDATA[
      a(x,y,L(z,u * (w * u),v5)) = a(x,y,L(z,L(w,u,u),v5))
    ]]></literal>
    <justification jstring="[para(10974(a,1),10858(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10974 10858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10981">
    <literal><![CDATA[
      L(x,(y \ 1) * (y * z),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10922,a,b,10977,a)].">
      <j1 rule="hyper" parents="63 10922 10977"/>
    </justification>
  </clause>

  <clause id="10984">
    <literal><![CDATA[
      L(x,R(L(y,z,u),w,v5),v6) = L(x,L(L(y,w,v5),z,u),v6)
    ]]></literal>
    <justification jstring="[para(30(a,1),10977(a,2,2))].">
      <j1 rule="para" parents="30 10977"/>
    </justification>
  </clause>

  <clause id="10985">
    <literal><![CDATA[
      L(x,L(y,z,u * u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(497(a,1),10977(a,1,2)),flip(a)].">
      <j1 rule="para" parents="497 10977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10987">
    <literal><![CDATA[
      L(x,L(y,z,(u * u) \ w),v5) = L(x,R(y,z,w),v5)
    ]]></literal>
    <justification jstring="[para(4712(a,1),10977(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4712 10977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10989">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) * v5) * L(v6,L(z,u,w),v5 \ 1)) = a(x,y,v5 * (R(z,u,w) * v6))
    ]]></literal>
    <justification jstring="[para(10977(a,1),6136(a,1,3,2))].">
      <j1 rule="para" parents="10977 6136"/>
    </justification>
  </clause>

  <clause id="10990">
    <literal><![CDATA[
      x * L(y,L(x,x,z),z \ L(z,x,x)) = (x / R(x,x,z)) * (R(x,x,z) * y)
    ]]></literal>
    <justification jstring="[para(10977(a,1),7673(a,1,2))].">
      <j1 rule="para" parents="10977 7673"/>
    </justification>
  </clause>

  <clause id="10991">
    <literal><![CDATA[
      a(x,y,L(R(z,u,(z * u) \ w),L(z,u,(z * u) \ w),w)) = a(x,y,w \ (u * ((z * u) \ w)))
    ]]></literal>
    <justification jstring="[para(10977(a,1),6746(a,1,3))].">
      <j1 rule="para" parents="10977 6746"/>
    </justification>
  </clause>

  <clause id="10992">
    <literal><![CDATA[
      a(x,y,z * (R(u,w,v5) * L(v6,L(u,w,v5),L(u,w,v5)))) = a(x,y,T(v6 / R(u,w,v5),u) * z)
    ]]></literal>
    <justification jstring="[para(10977(a,1),9016(a,1,3,2,2))].">
      <j1 rule="para" parents="10977 9016"/>
    </justification>
  </clause>

  <clause id="10993">
    <literal><![CDATA[
      L(x,L(y \ z,y,y),u) = L(x,(y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),10981(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 10981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10994">
    <literal><![CDATA[
      L(x,L(y,z,(u * u) \ w),v5) = L(x,L(y,z,w),v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,10977,a(flip),b,10987,a),flip(a)].">
      <j1 rule="hyper" parents="316 10977 10987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10995">
    <literal><![CDATA[
      L(x,L(y,z,u \ 1),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(1590(a,1),10994(a,1,2))].">
      <j1 rule="para" parents="1590 10994"/>
    </justification>
  </clause>

  <clause id="10997">
    <literal><![CDATA[
      L(x,L(R(y,z,u),w,v5),v6) = L(x,L(L(y,z,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(29(a,1),10984(a,1,2))].">
      <j1 rule="para" parents="29 10984"/>
    </justification>
  </clause>

  <clause id="10999">
    <literal><![CDATA[
      L(x,y * ((z * y) / T(y * y,u)),w) = L(x,L(z,y,y),w)
    ]]></literal>
    <justification jstring="[para(696(a,1),10976(a,1,2))].">
      <j1 rule="para" parents="696 10976"/>
    </justification>
  </clause>

  <clause id="11000">
    <literal><![CDATA[
      a(x,y,L(z,L(R(u,u,w),(u * u) \ w,(u * u) \ w),v5)) = a(x,y,L(z,((u * u) \ w) * (u \ w),v5))
    ]]></literal>
    <justification jstring="[para(4731(a,1),10979(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="4731 10979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11001">
    <literal><![CDATA[
      a(x,y,L(z,L(L(u,u,w),R(w,u,u),R(w,u,u)),v5)) = a(x,y,L(z,R(w,u,u) * (u * w),v5))
    ]]></literal>
    <justification jstring="[para(7167(a,1),10979(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="7167 10979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11002">
    <literal><![CDATA[
      a(x,y,L(z,(u \ w) * (v5 * (u \ w)),v6)) = a(x,y,L(z,L(v5,w / u,w / u),v6))
    ]]></literal>
    <justification jstring="[para(10851(a,2),10979(a,2,3,2))].">
      <j1 rule="para" parents="10851 10979"/>
    </justification>
  </clause>

  <clause id="11003">
    <literal><![CDATA[
      a(x,y,L(z,u * ((w \ v5) * u),v6)) = a(x,y,L(z,L(v5 / w,u,u),v6))
    ]]></literal>
    <justification jstring="[para(10835(a,2),10979(a,2,3))].">
      <j1 rule="para" parents="10835 10979"/>
    </justification>
  </clause>

  <clause id="11004">
    <literal><![CDATA[
      L(x,y * (z * (y / T(y * y,u))),w) = L(x,L(z,y,y),w)
    ]]></literal>
    <justification jstring="[para(696(a,1),10999(a,1,2,2))].">
      <j1 rule="para" parents="696 10999"/>
    </justification>
  </clause>

  <clause id="11005">
    <literal><![CDATA[
      L(x,y * (z * (y \ K(u,y * y))),w) = L(x,L(z,y,y),w)
    ]]></literal>
    <justification jstring="[para(2951(a,1),11004(a,1,2,2,2))].">
      <j1 rule="para" parents="2951 11004"/>
    </justification>
  </clause>

  <clause id="11006">
    <literal><![CDATA[
      L(x,y * (z * (y \ 1)),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(180(a,1),11005(a,1,2,2,2,2))].">
      <j1 rule="para" parents="180 11005"/>
    </justification>
  </clause>

  <clause id="11007">
    <literal><![CDATA[
      L(x,y \ (z \ (u * (w / v5))),v6) = L(x,y \ (z \ (u * (v5 \ w))),v6)
    ]]></literal>
    <justification jstring="[para(116(a,1),10868(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="116 10868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11008">
    <literal><![CDATA[
      L(x,y \ ((z * T(u,w)) * v5),v6) = L(x,y \ (v5 * (z * u)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,10862,a,b,10869,a)].">
      <j1 rule="hyper" parents="63 10862 10869"/>
    </justification>
  </clause>

  <clause id="11009">
    <literal><![CDATA[
      (x * ((y * z) * a(u,y,z))) \ (x * ((u * y) * z)) = L(T(u,y * z),z * (y * a(u,y,z)),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9622,a,b,10885,a)].">
      <j1 rule="hyper" parents="63 9622 10885"/>
    </justification>
  </clause>

  <clause id="11010">
    <literal><![CDATA[
      L(x,y \ (z * (T(u,w) * v5)),v6) = L(x,y \ ((u * v5) * z),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,10862,a,b,10899,a)].">
      <j1 rule="hyper" parents="63 10862 10899"/>
    </justification>
  </clause>

  <clause id="11011">
    <literal><![CDATA[
      L(x,y * (((z \ K(u,w)) \ 1) * (v5 * T(z \ K(u,w),(z \ K(u,w)) \ v5))),v6) = L(x,y * ((z \ 1) * (v5 * T((z \ K(u,w)) \ 1,(z \ K(u,w)) \ v5))),v6)
    ]]></literal>
    <justification jstring="[para(6207(a,2),10903(a,1,2,2))].">
      <j1 rule="para" parents="6207 10903"/>
    </justification>
  </clause>

  <clause id="11013">
    <literal><![CDATA[
      R(x,y,((T(z,u) * w) \ ((T(z,u) * u) * w)) * v5) = R(x,y,L(u * K(u * z,w),z,w) * v5)
    ]]></literal>
    <justification jstring="[para(10832(a,1),6274(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10832 6274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11014">
    <literal><![CDATA[
      L(x,y \ R(z \ u,z,w),v5) = L(x,y \ ((z * w) \ (u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10877,a(flip),b,10879,a)].">
      <j1 rule="hyper" parents="63 10877 10879"/>
    </justification>
  </clause>

  <clause id="11018">
    <literal><![CDATA[
      L(x,y \ R(z \ (z * u),z,z),w) = L(x,y \ L(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10917,a(flip),b,11014,a),flip(a)].">
      <j1 rule="hyper" parents="316 10917 11014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11019">
    <literal><![CDATA[
      L(x,y \ R(z,u,u),w) = L(x,y \ L(z,u,u),w)
    ]]></literal>
    <justification jstring="[para(9(a,1),11018(a,1,2,2,1))].">
      <j1 rule="para" parents="9 11018"/>
    </justification>
  </clause>

  <clause id="11020">
    <literal><![CDATA[
      L(x,y \ ((z \ 1) * (z * u)),w) = L(x,y \ L(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10973,a,b,11019,a)].">
      <j1 rule="hyper" parents="63 10973 11019"/>
    </justification>
  </clause>

  <clause id="11023">
    <literal><![CDATA[
      L(x,y * (z * (u * (K(w,v5) * v6))),v7) = L(x,y * ((u * v6) * z),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,10863,a,b,10905,a)].">
      <j1 rule="hyper" parents="63 10863 10905"/>
    </justification>
  </clause>

  <clause id="11024">
    <literal><![CDATA[
      L(x,y * ((z * z) \ (u * w)),v5) = L(x,y * (u * ((z * z) \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,10867,a(flip),b,10911,a),flip(a)].">
      <j1 rule="hyper" parents="316 10867 10911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11025">
    <literal><![CDATA[
      L(x,L(y * a(z,y,u),u,z),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10942,a(flip),b,10934,a),flip(a)].">
      <j1 rule="hyper" parents="316 10942 10934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11026">
    <literal><![CDATA[
      L(x,L(a(y,z,u) \ z,y,u),w) = L(x,L(T(z,u),u,y),w)
    ]]></literal>
    <justification jstring="[para(247(a,1),10947(a,2,2))].">
      <j1 rule="para" parents="247 10947"/>
    </justification>
  </clause>

  <clause id="11027">
    <literal><![CDATA[
      L(x,L(a(y,z,u) \ z,y,u),w) = L(x,L(z,u,y),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10810,a(flip),b,11026,a),flip(a)].">
      <j1 rule="hyper" parents="316 10810 11026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11030">
    <literal><![CDATA[
      L(x,L(a(y,z,u) \ z,y,u \ 1),w) = L(x,L(z,u \ 1,y),w)
    ]]></literal>
    <justification jstring="[para(2534(a,1),11027(a,1,2,1,1))].">
      <j1 rule="para" parents="2534 11027"/>
    </justification>
  </clause>

  <clause id="11032">
    <literal><![CDATA[
      L(x,L(a(y,z,u) \ z,y,u),w) = L(x,L(z,u \ 1,y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10995,a(flip),b,11030,a)].">
      <j1 rule="hyper" parents="63 10995 11030"/>
    </justification>
  </clause>

  <clause id="11033">
    <literal><![CDATA[
      L(x,L(y,z \ 1,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11027,a(flip),b,11032,a),flip(a)].">
      <j1 rule="hyper" parents="63 11027 11032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11041">
    <literal><![CDATA[
      L(x,a(y,z,u) \ 1,a(y,z,u) \ w) * w = (x * (a(y,z,u) \ K(v5,v6))) * ((a(y,z,u) \ K(v5,v6)) \ w)
    ]]></literal>
    <justification jstring="[para(8256(a,1),10755(a,1,1))].">
      <j1 rule="para" parents="8256 10755"/>
    </justification>
  </clause>

  <clause id="11043">
    <literal><![CDATA[
      (x * R(y / z,z,y)) * (z * (y \ 1)) = R(x,L(z \ y,z,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,10768,a(flip),b,10759,a),flip(a)].">
      <j1 rule="hyper" parents="316 10768 10759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11044">
    <literal><![CDATA[
      L(x \ y,y \ (x \ y),x) = L(x \ y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8494,a(flip),b,10960,a),flip(a)].">
      <j1 rule="hyper" parents="63 8494 10960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11045">
    <literal><![CDATA[
      R(x,L(y \ z,y,z),z * y) = R(x,(y * (z \ 1)) \ 1,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7868,a(flip),b,11043,a),flip(a)].">
      <j1 rule="hyper" parents="63 7868 11043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11046">
    <literal><![CDATA[
      (x \ T(y,z)) * L(T(u,K(y,z)),w,v5) = (x \ y) * L(u * K(y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,4839,a,b,10265,a),flip(a)].">
      <j1 rule="hyper" parents="316 4839 10265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11047">
    <literal><![CDATA[
      (x / T(y,z)) * L(T(u,K(z,y)),w,v5) = (x / y) * L(u * K(z,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,4839,a,b,10276,a),flip(a)].">
      <j1 rule="hyper" parents="316 4839 10276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11048">
    <literal><![CDATA[
      ((x * y) * z) \ (z * (x * y)) = K(K(x,y) * z,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3183,a(flip),b,10277,a)].">
      <j1 rule="hyper" parents="63 3183 10277"/>
    </justification>
  </clause>

  <clause id="11049">
    <literal><![CDATA[
      K(K(x,y) * z,x * y) = K(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(329,a,11048,a),flip(a)].">
      <j1 rule="hyper" parents="329 11048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11051">
    <literal><![CDATA[
      K(x * K(y,z),y * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10373,a(flip),b,11049,a)].">
      <j1 rule="hyper" parents="63 10373 11049"/>
    </justification>
  </clause>

  <clause id="11052">
    <literal><![CDATA[
      x * K(((y * z) \ x) * K(y,z),y * z) = ((y * z) \ x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,11051,a,b,95,a)].">
      <j1 rule="hyper" parents="139 11051 95"/>
    </justification>
  </clause>

  <clause id="11053">
    <literal><![CDATA[
      x * K(T((y * z) \ x,K(z,y)),z * y) = ((z * y) \ x) * (z * y)
    ]]></literal>
    <justification jstring="[para(6250(a,2),11052(a,1,2,1))].">
      <j1 rule="para" parents="6250 11052"/>
    </justification>
  </clause>

  <clause id="11054">
    <literal><![CDATA[
      x * K((y * z) \ x,z * y) = ((z * y) \ x) * (z * y)
    ]]></literal>
    <justification jstring="[para(10372(a,1),11053(a,1,2))].">
      <j1 rule="para" parents="10372 11053"/>
    </justification>
  </clause>

  <clause id="11055">
    <literal><![CDATA[
      x * K(y \ (z \ x),y * z) = ((y * z) \ x) * (y * z)
    ]]></literal>
    <justification jstring="[para(4285(a,1),11054(a,1,2))].">
      <j1 rule="para" parents="4285 11054"/>
    </justification>
  </clause>

  <clause id="11057">
    <literal><![CDATA[
      ((K(x,y) * ((T(x,y) \ z) * u)) \ w) * (K(x,y) * ((T(x,y) \ z) * u)) = w * K(K(x,y) \ (((T(x,y) \ z) * u) \ w),(x \ z) * u)
    ]]></literal>
    <justification jstring="[para(2902(a,1),11055(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2902 11055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11058">
    <literal><![CDATA[
      x \ (K(y,z) * L(x * u,w,v5)) = x * (K(y,z) * L(x \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,10307,a(flip),b,10318,a),flip(a)].">
      <j1 rule="hyper" parents="63 10307 10318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11059">
    <literal><![CDATA[
      x \ (K(y,z) * L(x * u,w,v5)) = x * L(K(y,z) * (x \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(4850(a,2),11058(a,2,2))].">
      <j1 rule="para" parents="4850 11058"/>
    </justification>
  </clause>

  <clause id="11060">
    <literal><![CDATA[
      x \ L(K(y,z) * (x * u),w,v5) = x * L(K(y,z) * (x \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(4850(a,2),11059(a,1,2))].">
      <j1 rule="para" parents="4850 11059"/>
    </justification>
  </clause>

  <clause id="11061">
    <literal><![CDATA[
      ((x * y) \ K(x,x \ 1)) * (x * y) = x * (K(y \ (x \ 1),y * x) / x)
    ]]></literal>
    <justification jstring="[para(3590(a,1),10321(a,2,2,1))].">
      <j1 rule="para" parents="3590 10321"/>
    </justification>
  </clause>

  <clause id="11062">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (y \ 1),1 / y)
    ]]></literal>
    <justification jstring="[para(3331(a,1),10427(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3331 10427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11063">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(316,a,3560,a,b,11062,a),flip(a)].">
      <j1 rule="hyper" parents="316 3560 11062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11064">
    <literal><![CDATA[
      K((x / y) / (1 / y),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3560,a,b,11063,a)].">
      <j1 rule="hyper" parents="63 3560 11063"/>
    </justification>
  </clause>

  <clause id="11065">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,11064,a(flip),b,2742,a),flip(a)].">
      <j1 rule="hyper" parents="139 11064 2742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11066">
    <literal><![CDATA[
      T(x \ (y * (z * u)),K(z,u)) = K(z,u) * (x \ (y * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10586,a(flip),b,10435,a)].">
      <j1 rule="hyper" parents="63 10586 10435"/>
    </justification>
  </clause>

  <clause id="11067">
    <literal><![CDATA[
      L(x,y,z * R(u * K(w,v5),v6,v7)) = L(x,y,R(u,v6,v7) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1684,a(flip),b,10475,a),flip(a)].">
      <j1 rule="hyper" parents="63 1684 10475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11069">
    <literal><![CDATA[
      L(x,y,R(z,u,w) * v5) = L(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10776,a(flip),b,11067,a),flip(a)].">
      <j1 rule="hyper" parents="63 10776 11067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11071">
    <literal><![CDATA[
      L(x,y,L(L(z,z,u) \ u,z,z)) = L(x,y,L(u,z,z) * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,7170,a,b,11069,a)].">
      <j1 rule="hyper" parents="63 7170 11069"/>
    </justification>
  </clause>

  <clause id="11072">
    <literal><![CDATA[
      L(x,y,R(L(z,u,w),v5,v6) * v7) = L(x,y,L(L(z,v5,v6),u,w) * v7)
    ]]></literal>
    <justification jstring="[para(30(a,1),11069(a,2,3,1))].">
      <j1 rule="para" parents="30 11069"/>
    </justification>
  </clause>

  <clause id="11073">
    <literal><![CDATA[
      L(x,y,L(z * (u \ 1),u,u)) = L(x,y,L(z,u,u) * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,7171,a(flip),b,11071,a)].">
      <j1 rule="hyper" parents="63 7171 11071"/>
    </justification>
  </clause>

  <clause id="11074">
    <literal><![CDATA[
      L(x,y,L(R(z,u,w),v5,v6) * v7) = L(x,y,L(L(z,u,w),v5,v6) * v7)
    ]]></literal>
    <justification jstring="[para(29(a,1),11072(a,1,3,1))].">
      <j1 rule="para" parents="29 11072"/>
    </justification>
  </clause>

  <clause id="11075">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w),v5,v6) * (v6 * v5)) = L(x,y,v6 * (v5 * R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,1669,a(flip),b,11074,a),flip(a)].">
      <j1 rule="hyper" parents="63 1669 11074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11076">
    <literal><![CDATA[
      L(x,y,z * (u * R(w,v5,v6))) = L(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,1669,a(flip),b,11075,a),flip(a)].">
      <j1 rule="hyper" parents="63 1669 11075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11077">
    <literal><![CDATA[
      L(x,y,a(z,z \ u,R(w,v5,v6)) * ((z \ u) * L(w,v5,v6))) = L(x,y,z \ (u * R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(8458(a,1),11076(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8458 11076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11078">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * ((u * K(w,v5)) * (v6 * v6)) = (u * (a(x,y,z) \ K(w,v5))) * (v6 * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,4906,a(flip),b,10481,a)].">
      <j1 rule="hyper" parents="63 4906 10481"/>
    </justification>
  </clause>

  <clause id="11079">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u * K(w,v5)) = u * (a(x,y,z) \ K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(35,a,10201,a,b,10481,a(flip))].">
      <j1 rule="hyper" parents="35 10201 10481"/>
    </justification>
  </clause>

  <clause id="11080">
    <literal><![CDATA[
      R(T(a(x,y,z) \ 1,u),w * K(v5,v6),(w * K(v5,v6)) \ u) = u \ ((w * (a(x,y,z) \ K(v5,v6))) * ((w * K(v5,v6)) \ u))
    ]]></literal>
    <justification jstring="[para(11079(a,1),724(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11079 724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11081">
    <literal><![CDATA[
      (x * K(y,z)) * ((a(u,w,v5) \ 1) * L((a(u,w,v5) \ 1) \ ((x * K(y,z)) \ v6),x * K(y,z),a(u,w,v5) \ 1)) = (a(u,w,v5) \ 1) * ((x * K(y,z)) * ((x * (a(u,w,v5) \ K(y,z))) \ v6))
    ]]></literal>
    <justification jstring="[para(11079(a,1),6232(a,2,2,2,1))].">
      <j1 rule="para" parents="11079 6232"/>
    </justification>
  </clause>

  <clause id="11082">
    <literal><![CDATA[
      ((1 / x) * (T(y,x \ 1) * K(z,u))) * x = (y * (x \ 1)) * ((x \ K(u,z)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,7866,a,b,10483,a)].">
      <j1 rule="hyper" parents="63 7866 10483"/>
    </justification>
  </clause>

  <clause id="11083">
    <literal><![CDATA[
      L(L(x * K(y,z),u,w),v5,v6) \ v7 = K(z,y) * (L(L(x,v5,v6),u,w) \ v7)
    ]]></literal>
    <justification jstring="[para(4837(a,2),10502(a,1,1,1))].">
      <j1 rule="para" parents="4837 10502"/>
    </justification>
  </clause>

  <clause id="11084">
    <literal><![CDATA[
      (x / y) \ (L(z / (x / y),u,w) \ v5) = (y \ x) \ (L(z / (y \ x),u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(133,a,10505,a(flip),b,2773,a)].">
      <j1 rule="hyper" parents="133 10505 2773"/>
    </justification>
  </clause>

  <clause id="11085">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(z,y) * w) = T(((x \ 1) \ u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10169,a(flip),b,10513,a),flip(a)].">
      <j1 rule="hyper" parents="316 10169 10513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11086">
    <literal><![CDATA[
      a(x,y,(((z \ 1) \ (u \ K(w,v5))) \ v6) * v7) = a(x,y,(((z \ 1) \ u) \ v6) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,8336,a,b,10514,a)].">
      <j1 rule="hyper" parents="63 8336 10514"/>
    </justification>
  </clause>

  <clause id="11087">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ ((z * z) \ u)) * w) = R(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,4762,a(flip),b,10536,a),flip(a)].">
      <j1 rule="hyper" parents="316 4762 10536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11089">
    <literal><![CDATA[
      R(x,y,z * ((u \ 1) \ w)) = R(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6439,a(flip),b,11087,a)].">
      <j1 rule="hyper" parents="63 6439 11087"/>
    </justification>
  </clause>

  <clause id="11090">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ u) \ (z * u)) = R(x,y,(z \ u) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8218,a,b,11089,a)].">
      <j1 rule="hyper" parents="63 8218 11089"/>
    </justification>
  </clause>

  <clause id="11092">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ u) * w) = R(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,4676,a,b,11089,a)].">
      <j1 rule="hyper" parents="63 4676 11089"/>
    </justification>
  </clause>

  <clause id="11093">
    <literal><![CDATA[
      R(x,y,(z \ L(z,u,w)) * v5) = R(x,y,(z * L(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(4590(a,1),11092(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4590 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11094">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ u) \ (z * u)) = L(x,y,a(z \ u,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5374,a(flip),b,11090,a),flip(a)].">
      <j1 rule="hyper" parents="316 5374 11090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11095">
    <literal><![CDATA[
      L(x,y,a(z \ u,z,u)) = L(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7851,a(flip),b,11094,a),flip(a)].">
      <j1 rule="hyper" parents="63 7851 11094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11096">
    <literal><![CDATA[
      R(x \ L(x,y,z),u,(w * L(w,v5,v6)) * v7) = L(x \ L(x,y,z),u,(w \ L(w,v5,v6)) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,8380,a(flip),b,11093,a),flip(a)].">
      <j1 rule="hyper" parents="63 8380 11093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11098">
    <literal><![CDATA[
      L(x,y,z \ ((u * T(u,w)) * (T(u,w) \ v5))) = L(x,y,z \ ((u \ 1) \ v5))
    ]]></literal>
    <justification jstring="[para(256(a,1),10614(a,1,3,2,1))].">
      <j1 rule="para" parents="256 10614"/>
    </justification>
  </clause>

  <clause id="11099">
    <literal><![CDATA[
      a(x * (y * ((z \ 1) * (z \ 1))),u,w) = a((y * x) / (z * z),u,w)
    ]]></literal>
    <justification jstring="[para(432(a,1),10647(a,2,1))].">
      <j1 rule="para" parents="432 10647"/>
    </justification>
  </clause>

  <clause id="11100">
    <literal><![CDATA[
      a(x * (y * ((z \ 1) * (z \ 1))),u,w) = a(y * (x / (z * z)),u,w)
    ]]></literal>
    <justification jstring="[para(683(a,1),11099(a,2,1))].">
      <j1 rule="para" parents="683 11099"/>
    </justification>
  </clause>

  <clause id="11101">
    <literal><![CDATA[
      a(x * (y * ((z \ 1) * (z \ 1))),u,w) = a(y * ((z * z) \ x),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,3150,a(flip),b,11100,a),flip(a)].">
      <j1 rule="hyper" parents="316 3150 11100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11102">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (K(y,z) * u) = T((x * u) \ u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,4110,a(flip),b,10661,a),flip(a)].">
      <j1 rule="hyper" parents="316 4110 10661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11103">
    <literal><![CDATA[
      T((x * y) \ y,K(z,u)) = (T(x,K(z,u)) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,10343,a(flip),b,11102,a),flip(a)].">
      <j1 rule="hyper" parents="63 10343 11102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11104">
    <literal><![CDATA[
      x * T(T((x * y) \ y,K(z,u)),K(z,u)) = T(x * ((x * y) \ y),K(z,u))
    ]]></literal>
    <justification jstring="[para(11103(a,2),10553(a,1,2,1))].">
      <j1 rule="para" parents="11103 10553"/>
    </justification>
  </clause>

  <clause id="11105">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * L(w,v5,v5)))) = a(x,y,z * (u \ a(v5,v5,w)))
    ]]></literal>
    <justification jstring="[para(4952(a,1),10719(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="4952 10719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11106">
    <literal><![CDATA[
      a(x \ 1,a(y,z,u),w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10680,a(flip),b,10720,a),flip(a)].">
      <j1 rule="hyper" parents="63 10680 10720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11107">
    <literal><![CDATA[
      a(L(x * y,y,x),a(z,u,w),v5) = a(y \ (x \ 1),a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,9896,a,b,11106,a)].">
      <j1 rule="hyper" parents="63 9896 11106"/>
    </justification>
  </clause>

  <clause id="11108">
    <literal><![CDATA[
      ((1 / x) * a(x,a(y,z,x),u)) \ 1 = (L(x,a(y,z,1 / x),u) \ x) * x
    ]]></literal>
    <justification jstring="[para(11106(a,1),9478(a,1,1,2))].">
      <j1 rule="para" parents="11106 9478"/>
    </justification>
  </clause>

  <clause id="11109">
    <literal><![CDATA[
      L(x,y * (K(z \ u,z) * (w * u)),v5) = L(x,(((z \ u) * z) * w) * y,v5)
    ]]></literal>
    <justification jstring="[para(406(a,1),10925(a,1,2,2))].">
      <j1 rule="para" parents="406 10925"/>
    </justification>
  </clause>

  <clause id="11110">
    <literal><![CDATA[
      L(x,L(y * (z / (z * z)),u,w),v5) = L(x,L(L(z \ y,u,w),z,z),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10943,a(flip),b,10933,a),flip(a)].">
      <j1 rule="hyper" parents="63 10943 10933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11111">
    <literal><![CDATA[
      L(x,L(L(y \ z,u,w),y,y),v5) = L(x,L(z * (y \ 1),u,w),v5)
    ]]></literal>
    <justification jstring="[para(281(a,1),11110(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="281 11110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11112">
    <literal><![CDATA[
      L(x,y * (T(z,u) * ((w * w) \ v5)),v6) = L(x,(z * v5) * ((w * w) \ y),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,11024,a(flip),b,10972,a)].">
      <j1 rule="hyper" parents="63 11024 10972"/>
    </justification>
  </clause>

  <clause id="11113">
    <literal><![CDATA[
      (x / T(y,z)) * L(T(u,K(y,z)),w,v5) = (x / y) * L(u * K(z,y),w,v5)
    ]]></literal>
    <justification jstring="[para(4106(a,1),11047(a,1,2,1))].">
      <j1 rule="para" parents="4106 11047"/>
    </justification>
  </clause>

  <clause id="11114">
    <literal><![CDATA[
      ((x \ (1 / y)) * (y * x)) / (y * (K(x \ (y \ 1),x * y) / y)) = a(y,x,x \ (1 / y))
    ]]></literal>
    <justification jstring="[para(11061(a,1),4969(a,1,2))].">
      <j1 rule="para" parents="11061 4969"/>
    </justification>
  </clause>

  <clause id="11115">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) * y,1 / y)
    ]]></literal>
    <justification jstring="[para(3391(a,1),11065(a,2,2))].">
      <j1 rule="para" parents="3391 11065"/>
    </justification>
  </clause>

  <clause id="11116">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(4612(a,1),11115(a,2,2))].">
      <j1 rule="para" parents="4612 11115"/>
    </justification>
  </clause>

  <clause id="11117">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = K(x,y \ 1) / y
    ]]></literal>
    <justification jstring="[hyper(316,a,10304,a(flip),b,11116,a),flip(a)].">
      <j1 rule="hyper" parents="316 10304 11116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11118">
    <literal><![CDATA[
      x / ((y / (x \ y)) / (1 / (x \ y))) = K(y,(x \ y) \ 1) / (x \ y)
    ]]></literal>
    <justification jstring="[para(80(a,1),11117(a,1,1))].">
      <j1 rule="para" parents="80 11117"/>
    </justification>
  </clause>

  <clause id="11119">
    <literal><![CDATA[
      K(x,(y \ x) \ 1) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(80(a,1),11118(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="80 11118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11121">
    <literal><![CDATA[
      K(x,x \ y) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(3541(a,1),11119(a,1,1))].">
      <j1 rule="para" parents="3541 11119"/>
    </justification>
  </clause>

  <clause id="11122">
    <literal><![CDATA[
      K((x * y) * z,((x * y) * z) \ (x * (z * y))) / (K(y,z) * a(x,y,z)) = (x * (z * y)) / ((x * (z * y)) / (1 / ((x * (z * y)) \ ((x * y) * z))))
    ]]></literal>
    <justification jstring="[para(10561(a,1),11121(a,1,2))].">
      <j1 rule="para" parents="10561 11121"/>
    </justification>
  </clause>

  <clause id="11123">
    <literal><![CDATA[
      L(x,y,z \ ((u * u) * (u \ w))) = L(x,y,z \ ((u \ 1) \ w))
    ]]></literal>
    <justification jstring="[para(10271(a,1),11098(a,1,3,2))].">
      <j1 rule="para" parents="10271 11098"/>
    </justification>
  </clause>

  <clause id="11124">
    <literal><![CDATA[
      L(x,y,(z * z) * (u \ (z \ w))) = L(x,y,u \ ((z \ 1) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,1680,a(flip),b,11123,a)].">
      <j1 rule="hyper" parents="63 1680 11123"/>
    </justification>
  </clause>

  <clause id="11125">
    <literal><![CDATA[
      T(x * ((x * y) \ y),K(z,u)) = x * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(4107(a,1),11104(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4107 11104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11126">
    <literal><![CDATA[
      ((x * ((x * y) \ y)) \ x) \ T(x,x * ((x * y) \ y)) = x * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9571,a,b,11125,a)].">
      <j1 rule="hyper" parents="63 9571 11125"/>
    </justification>
  </clause>

  <clause id="11128">
    <literal><![CDATA[
      (L(x,a(y,z,1 / x),u) \ x) * x = (a(x,a(y,z,x),u) / x) \ 1
    ]]></literal>
    <justification jstring="[para(8428(a,1),11108(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8428 11108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11129">
    <literal><![CDATA[
      (a(x,a(y,z,x),u) / x) \ 1 = (L(x,a(y,z,x),u) \ x) * x
    ]]></literal>
    <justification jstring="[para(2535(a,1),11128(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2535 11128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11130">
    <literal><![CDATA[
      (a(x,a(y,z,x),u) / x) \ 1 = a(u,x,a(y,z,x)) * x
    ]]></literal>
    <justification jstring="[para(9472(a,1),11129(a,2,1))].">
      <j1 rule="para" parents="9472 11129"/>
    </justification>
  </clause>

  <clause id="11131">
    <literal><![CDATA[
      L(x,(((y \ z) * y) * u) * w,v5) = L(x,w * (u * z),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10824,a(flip),b,11109,a),flip(a)].">
      <j1 rule="hyper" parents="63 10824 11109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11133">
    <literal><![CDATA[
      L(x,(((y \ z) * y) * (K(u,w) * v5)) * v6,v7) = L(x,v6 * (v5 * z),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,10826,a,b,11131,a)].">
      <j1 rule="hyper" parents="63 10826 11131"/>
    </justification>
  </clause>

  <clause id="11135">
    <literal><![CDATA[
      L(x,(((y \ z) * y) * (K(u,w) * v5)) * ((v6 * v6) \ v7),v8) = L(x,v7 * ((v6 * v6) \ (v5 * z)),v8)
    ]]></literal>
    <justification jstring="[hyper(316,a,10970,a(flip),b,11133,a),flip(a)].">
      <j1 rule="hyper" parents="316 10970 11133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11136">
    <literal><![CDATA[
      L(x,(y * ((z * z) \ u)) * w,v5) = L(x,(y * u) * ((z * z) \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10908,a(flip),b,11112,a)].">
      <j1 rule="hyper" parents="63 10908 11112"/>
    </justification>
  </clause>

  <clause id="11138">
    <literal><![CDATA[
      (1 / ((x * y) \ y)) \ T(x,x * ((x * y) \ y)) = x * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(6277(a,1),11126(a,1,1))].">
      <j1 rule="para" parents="6277 11126"/>
    </justification>
  </clause>

  <clause id="11139">
    <literal><![CDATA[
      (1 / ((x * y) \ y)) \ T(x,R(y,x,x) \ y) = x * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(6273(a,1),11138(a,1,2))].">
      <j1 rule="para" parents="6273 11138"/>
    </justification>
  </clause>

  <clause id="11140">
    <literal><![CDATA[
      (1 / ((x * y) \ y)) \ x = x * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(3509(a,1),11139(a,1,2))].">
      <j1 rule="para" parents="3509 11139"/>
    </justification>
  </clause>

  <clause id="11141">
    <literal><![CDATA[
      x / (x * ((x * y) \ y)) = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(210,a,11140,a)].">
      <j1 rule="hyper" parents="210 11140"/>
    </justification>
  </clause>

  <clause id="11143">
    <literal><![CDATA[
      L(K(x \ y,x \ 1) / x,x \ 1,y) = (y / (x * x)) / (y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(434(a,1),10324(a,2,1))].">
      <j1 rule="para" parents="434 10324"/>
    </justification>
  </clause>

  <clause id="11144">
    <literal><![CDATA[
      L(K(x \ y,x \ 1) / x,x \ 1,y) = y / ((y * (x \ 1)) * (x * x))
    ]]></literal>
    <justification jstring="[hyper(316,a,393,a(flip),b,11143,a),flip(a)].">
      <j1 rule="hyper" parents="316 393 11143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11145">
    <literal><![CDATA[
      L(K(x \ y,x \ 1) / x,x \ 1,y) = y / (y * ((x \ 1) * (x * x)))
    ]]></literal>
    <justification jstring="[para(32(a,1),11144(a,2,2))].">
      <j1 rule="para" parents="32 11144"/>
    </justification>
  </clause>

  <clause id="11146">
    <literal><![CDATA[
      L(K(x \ y,x \ 1) / x,x \ 1,y) = y / (y * x)
    ]]></literal>
    <justification jstring="[para(229(a,1),11145(a,2,2,2))].">
      <j1 rule="para" parents="229 11145"/>
    </justification>
  </clause>

  <clause id="11147">
    <literal><![CDATA[
      x \ T(x / y,y \ 1) = x / (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10323,a(flip),b,11146,a)].">
      <j1 rule="hyper" parents="63 10323 11146"/>
    </justification>
  </clause>

  <clause id="11148">
    <literal><![CDATA[
      x \ T(T(x,y) / y,T(y,x) \ 1) = x / (x * T(y,x))
    ]]></literal>
    <justification jstring="[para(2933(a,2),11147(a,1,2,1))].">
      <j1 rule="para" parents="2933 11147"/>
    </justification>
  </clause>

  <clause id="11149">
    <literal><![CDATA[
      a((x / (x * y)) \ z,u,w) = a((x \ (x / y)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(11147(a,1),4199(a,1,1,1))].">
      <j1 rule="para" parents="11147 4199"/>
    </justification>
  </clause>

  <clause id="11150">
    <literal><![CDATA[
      a(x,y,z \ (u / (u * w))) = a(x,y,z \ (u \ (u / w)))
    ]]></literal>
    <justification jstring="[para(11147(a,1),5494(a,1,3,2))].">
      <j1 rule="para" parents="11147 5494"/>
    </justification>
  </clause>

  <clause id="11151">
    <literal><![CDATA[
      L(x,(y / (y * z)) * u,w) = L(x,(y \ (y / z)) * u,w)
    ]]></literal>
    <justification jstring="[para(11147(a,1),10901(a,1,2,1))].">
      <j1 rule="para" parents="11147 10901"/>
    </justification>
  </clause>

  <clause id="11152">
    <literal><![CDATA[
      x \ T(T(x,y) / y,T(y \ 1,x)) = x / (x * T(y,x))
    ]]></literal>
    <justification jstring="[para(3711(a,2),11148(a,1,2))].">
      <j1 rule="para" parents="3711 11148"/>
    </justification>
  </clause>

  <clause id="11153">
    <literal><![CDATA[
      a(((x * y) \ x) \ z,u,w) = a((x \ (x / y)) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3121,a(flip),b,11149,a)].">
      <j1 rule="hyper" parents="63 3121 11149"/>
    </justification>
  </clause>

  <clause id="11154">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) \ u)) = a(x,y,z \ (u \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5497,a(flip),b,11150,a)].">
      <j1 rule="hyper" parents="63 5497 11150"/>
    </justification>
  </clause>

  <clause id="11155">
    <literal><![CDATA[
      L(x,((y * z) \ y) * u,w) = L(x,(y \ (y / z)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10805,a(flip),b,11151,a)].">
      <j1 rule="hyper" parents="63 10805 11151"/>
    </justification>
  </clause>

  <clause id="11156">
    <literal><![CDATA[
      x \ T(T(x,y) / y,T(y \ 1,x)) = x / (y * x)
    ]]></literal>
    <justification jstring="[para(114(a,1),11152(a,2,2))].">
      <j1 rule="para" parents="114 11152"/>
    </justification>
  </clause>

  <clause id="11157">
    <literal><![CDATA[
      (x \ (x \ y)) / (x \ y) = y / (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10663,a(flip),b,11156,a)].">
      <j1 rule="hyper" parents="63 10663 11156"/>
    </justification>
  </clause>

  <clause id="11158">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ (T(w,v5) / v5)))) = a(x,y,z \ (u * (w / (v5 * w))))
    ]]></literal>
    <justification jstring="[para(11156(a,1),5774(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="11156 5774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11159">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 \ (T(v5,v6) / v6))))) = a(x,y,z \ (u * (w * (v5 / (v6 * v5)))))
    ]]></literal>
    <justification jstring="[para(11156(a,1),6327(a,1,3,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11156 6327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11160">
    <literal><![CDATA[
      (x \ (x \ y)) / (x \ y) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,234,a,b,11157,a),flip(a)].">
      <j1 rule="hyper" parents="316 234 11157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11161">
    <literal><![CDATA[
      a(x,x \ 1,x \ y) = x * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(11160(a,1),8492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11160 8492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11162">
    <literal><![CDATA[
      a(x,x \ 1,x \ y) = a(x,x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(316,a,8495,a,b,11161,a),flip(a)].">
      <j1 rule="hyper" parents="316 8495 11161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11163">
    <literal><![CDATA[
      (x * R(1 / x,x,y)) \ y = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(11161(a,1),8627(a,1,1))].">
      <j1 rule="para" parents="11161 8627"/>
    </justification>
  </clause>

  <clause id="11164">
    <literal><![CDATA[
      a(x,x \ 1,(x \ 1) \ y) = a(x,x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5814,a,b,11162,a)].">
      <j1 rule="hyper" parents="63 5814 11162"/>
    </justification>
  </clause>

  <clause id="11165">
    <literal><![CDATA[
      (x * (y / (x * y))) \ y = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(234(a,1),11163(a,1,1,2))].">
      <j1 rule="para" parents="234 11163"/>
    </justification>
  </clause>

  <clause id="11166">
    <literal><![CDATA[
      x / ((y \ 1) * (y * x)) = y * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(210,a,11165,a)].">
      <j1 rule="hyper" parents="210 11165"/>
    </justification>
  </clause>

  <clause id="11167">
    <literal><![CDATA[
      a(x,x \ 1,y * x) * y = x \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(11164(a,1),8457(a,1,1))].">
      <j1 rule="para" parents="11164 8457"/>
    </justification>
  </clause>

  <clause id="11168">
    <literal><![CDATA[
      (x * (y / (x * y))) * y = x \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(8500(a,1),11167(a,1,1))].">
      <j1 rule="para" parents="8500 11167"/>
    </justification>
  </clause>

  <clause id="11169">
    <literal><![CDATA[
      x * (y * (x / (y * x))) = y \ ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2219,a(flip),b,11168,a)].">
      <j1 rule="hyper" parents="63 2219 11168"/>
    </justification>
  </clause>

  <clause id="11170">
    <literal><![CDATA[
      (x \ 1) * (y * (x / (y * x))) = y \ ((y \ 1) \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(744(a,1),11169(a,1,2,2))].">
      <j1 rule="para" parents="744 11169"/>
    </justification>
  </clause>

  <clause id="11171">
    <literal><![CDATA[
      a(((x * y) \ x) \ z,u,w) = a((x \ (y \ x)) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,4202,a(flip),b,11153,a),flip(a)].">
      <j1 rule="hyper" parents="316 4202 11153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11172">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) \ u)) = a(x,y,z \ (u \ (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5606,a(flip),b,11154,a),flip(a)].">
      <j1 rule="hyper" parents="316 5606 11154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11173">
    <literal><![CDATA[
      L(x,((y * z) \ y) * u,w) = L(x,(y \ (z \ y)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10904,a(flip),b,11155,a),flip(a)].">
      <j1 rule="hyper" parents="316 10904 11155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11174">
    <literal><![CDATA[
      a(x,y,L(z * u,z * u,L(u,u,z))) = a(x,y,z \ (z \ (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7239,a,b,11172,a)].">
      <j1 rule="hyper" parents="63 7239 11172"/>
    </justification>
  </clause>

  <clause id="11175">
    <literal><![CDATA[
      a(x,y,L(z * u,z * u,z)) = a(x,y,z \ (z \ (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6745,a,b,11172,a)].">
      <j1 rule="hyper" parents="63 6745 11172"/>
    </justification>
  </clause>

  <clause id="11176">
    <literal><![CDATA[
      L(x,(y \ (z \ y)) * z,u) = L(x,a(y,z,z) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10849,a(flip),b,11173,a),flip(a)].">
      <j1 rule="hyper" parents="63 10849 11173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11177">
    <literal><![CDATA[
      a(x,y,L(z * u,u * z,u)) = a(x,y,u \ (u \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5535,a,b,11175,a)].">
      <j1 rule="hyper" parents="63 5535 11175"/>
    </justification>
  </clause>

  <clause id="11178">
    <literal><![CDATA[
      a(x,y,L(z * u,u * z,u)) = a(x,y,L(z \ u,u,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,8608,a(flip),b,11177,a),flip(a)].">
      <j1 rule="hyper" parents="316 8608 11177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11179">
    <literal><![CDATA[
      a(x,y,L(z * u,z * u,L(u,u,z))) = a(x,y,L(u \ z,z,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,8608,a(flip),b,11174,a),flip(a)].">
      <j1 rule="hyper" parents="316 8608 11174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11180">
    <literal><![CDATA[
      a(x,y,L(z * u,u * z,L(u,u,z))) = a(x,y,L(u \ z,z,z))
    ]]></literal>
    <justification jstring="[para(10797(a,1),11179(a,1,3))].">
      <j1 rule="para" parents="10797 11179"/>
    </justification>
  </clause>

  <clause id="11181">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ (T(w,v5) / v5)))) = a(x,y,z \ (u * ((v5 * w) \ w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5599,a(flip),b,11158,a),flip(a)].">
      <j1 rule="hyper" parents="316 5599 11158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11182">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ (v5 \ T(w,v5))))) = a(x,y,z \ (u * ((v5 * w) \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5776,a(flip),b,11181,a)].">
      <j1 rule="hyper" parents="63 5776 11181"/>
    </justification>
  </clause>

  <clause id="11183">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * v5) \ v5))) = a(x,y,z \ (u * (v5 \ (w \ v5))))
    ]]></literal>
    <justification jstring="[hyper(63,a,5775,a(flip),b,11182,a),flip(a)].">
      <j1 rule="hyper" parents="63 5775 11182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11185">
    <literal><![CDATA[
      a(x,y,z \ (u * (R(w,v5,v5) \ (v5 \ 1)))) = a(x,y,z \ (u * (v5 \ ((w * v5) \ v5))))
    ]]></literal>
    <justification jstring="[hyper(63,a,7808,a,b,11183,a)].">
      <j1 rule="hyper" parents="63 7808 11183"/>
    </justification>
  </clause>

  <clause id="11186">
    <literal><![CDATA[
      a(x,y * K(z,u),w) = a(x,y,K(z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10232,a(flip),b,10335,a)].">
      <j1 rule="hyper" parents="63 10232 10335"/>
    </justification>
  </clause>

  <clause id="11187">
    <literal><![CDATA[
      a(x,y * K(z,u),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,5484,a(flip),b,11186,a),flip(a)].">
      <j1 rule="hyper" parents="316 5484 11186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11190">
    <literal><![CDATA[
      a(x,y * z,u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(94(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="94 11187"/>
    </justification>
  </clause>

  <clause id="11191">
    <literal><![CDATA[
      a(x,(y \ z) * y,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(306(a,1),11187(a,1,2)),flip(a)].">
      <j1 rule="para" parents="306 11187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11192">
    <literal><![CDATA[
      a(x,L(y,y,z) * z,u) = a(x,z / (y \ 1),u)
    ]]></literal>
    <justification jstring="[para(1454(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="1454 11187"/>
    </justification>
  </clause>

  <clause id="11193">
    <literal><![CDATA[
      a(x,(y * z) / y,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(2722(a,2),11187(a,1,2))].">
      <j1 rule="para" parents="2722 11187"/>
    </justification>
  </clause>

  <clause id="11194">
    <literal><![CDATA[
      a(x,T(y,z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(2733(a,1),11187(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2733 11187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11195">
    <literal><![CDATA[
      a(x,y / z,u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(2732(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="2732 11187"/>
    </justification>
  </clause>

  <clause id="11197">
    <literal><![CDATA[
      a(x,y / (y / z),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(3090(a,2),11187(a,1,2))].">
      <j1 rule="para" parents="3090 11187"/>
    </justification>
  </clause>

  <clause id="11198">
    <literal><![CDATA[
      a(x,y * (z / u),w) = a(x,y * (u \ z),w)
    ]]></literal>
    <justification jstring="[para(3151(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="3151 11187"/>
    </justification>
  </clause>

  <clause id="11199">
    <literal><![CDATA[
      a(x,y * T(z,u),w) = a(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(3268(a,1),11187(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3268 11187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11200">
    <literal><![CDATA[
      a(x,K(y,z) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(3631(a,1),11187(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3631 11187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11202">
    <literal><![CDATA[
      a(x,y \ K(z,u),w) = a(x,y \ 1,w)
    ]]></literal>
    <justification jstring="[para(3780(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="3780 11187"/>
    </justification>
  </clause>

  <clause id="11203">
    <literal><![CDATA[
      a(x,y \ T(z,u),w) = a(x,y \ z,w)
    ]]></literal>
    <justification jstring="[para(3846(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="3846 11187"/>
    </justification>
  </clause>

  <clause id="11204">
    <literal><![CDATA[
      a(x,y * (z * K(u,w)),v5) = a(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(3763(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="3763 11187"/>
    </justification>
  </clause>

  <clause id="11205">
    <literal><![CDATA[
      a(x,y \ (z * u),w) = a(x,y \ (u * z),w)
    ]]></literal>
    <justification jstring="[para(3922(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="3922 11187"/>
    </justification>
  </clause>

  <clause id="11206">
    <literal><![CDATA[
      a(x,y * (z * u),w) = a(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[para(3933(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="3933 11187"/>
    </justification>
  </clause>

  <clause id="11208">
    <literal><![CDATA[
      a(x,y \ (K(z,u) * w),v5) = a(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(3914(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="3914 11187"/>
    </justification>
  </clause>

  <clause id="11209">
    <literal><![CDATA[
      a(x,y \ (z / u),w) = a(x,y \ (u \ z),w)
    ]]></literal>
    <justification jstring="[para(3917(a,1),11187(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3917 11187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11210">
    <literal><![CDATA[
      a(x,y \ ((z \ u) * z),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(3921(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="3921 11187"/>
    </justification>
  </clause>

  <clause id="11211">
    <literal><![CDATA[
      a(x,y * ((z \ u) * z),w) = a(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(3934(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="3934 11187"/>
    </justification>
  </clause>

  <clause id="11212">
    <literal><![CDATA[
      a(x,y * (K(z,u) * w),v5) = a(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(3941(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="3941 11187"/>
    </justification>
  </clause>

  <clause id="11213">
    <literal><![CDATA[
      a(x,L(T(y,z),u,w),v5) = a(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(4449(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="4449 11187"/>
    </justification>
  </clause>

  <clause id="11214">
    <literal><![CDATA[
      a(x,(y * z) \ ((z * u) * y),w) = a(x,L(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(3953(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="3953 11187"/>
    </justification>
  </clause>

  <clause id="11215">
    <literal><![CDATA[
      a(x,y * (z * (u / w)),v5) = a(x,y * (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(4028(a,1),11187(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4028 11187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11217">
    <literal><![CDATA[
      a(x,L(y / z,u,w),v5) = a(x,L(z \ y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(4844(a,1),11187(a,1,2))].">
      <j1 rule="para" parents="4844 11187"/>
    </justification>
  </clause>

  <clause id="11221">
    <literal><![CDATA[
      a(x,T(y,z),T(u,w)) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,5476,a(flip),b,11194,a),flip(a)].">
      <j1 rule="hyper" parents="316 5476 11194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11225">
    <literal><![CDATA[
      a(x * y,z * u,w) = a(y * x,u * z,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,2771,a,b,11190,a)].">
      <j1 rule="hyper" parents="316 2771 11190"/>
    </justification>
  </clause>

  <clause id="11226">
    <literal><![CDATA[
      a(x,(y \ (y \ z)) * (y * y),u) = a(x,z * a(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(8620(a,1),11190(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8620 11190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11227">
    <literal><![CDATA[
      a(x,y,(z * u) \ (w \ (z * (u * w)))) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(11193(a,1),8303(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11193 8303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11230">
    <literal><![CDATA[
      a(x,T(y / z,u),w) = a(x,z \ y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11194,a,b,11195,a)].">
      <j1 rule="hyper" parents="63 11194 11195"/>
    </justification>
  </clause>

  <clause id="11231">
    <literal><![CDATA[
      a(x,y / (z * (u * u)),w) = a(x,z \ (y / (u * u)),w)
    ]]></literal>
    <justification jstring="[para(393(a,1),11195(a,1,2))].">
      <j1 rule="para" parents="393 11195"/>
    </justification>
  </clause>

  <clause id="11232">
    <literal><![CDATA[
      a(x,y / (z / (u * u)),w) = a(x,z \ (y * (u * u)),w)
    ]]></literal>
    <justification jstring="[para(676(a,1),11195(a,1,2))].">
      <j1 rule="para" parents="676 11195"/>
    </justification>
  </clause>

  <clause id="11233">
    <literal><![CDATA[
      a(x,(y * y) \ (z * u),w) = a(x,z * (u / (y * y)),w)
    ]]></literal>
    <justification jstring="[para(683(a,1),11195(a,1,2)),flip(a)].">
      <j1 rule="para" parents="683 11195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11234">
    <literal><![CDATA[
      L((1 / x) * y,z,a(a(u,w,u) / x,x \ a(u,w,u),y)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(11195(a,1),9679(a,1,3))].">
      <j1 rule="para" parents="11195 9679"/>
    </justification>
  </clause>

  <clause id="11235">
    <literal><![CDATA[
      a(x,K(y,z) * (u * w),v5) = a(x,w * u,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,11190,a,b,11200,a),flip(a)].">
      <j1 rule="hyper" parents="316 11190 11200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11241">
    <literal><![CDATA[
      a(x,(y / z) \ u,w) = a(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(3143(a,1),11200(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3143 11200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11243">
    <literal><![CDATA[
      a(x,((y / z) * u) * w,v5) = a(x,((z \ y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(2777(a,1),11200(a,1,2))].">
      <j1 rule="para" parents="2777 11200"/>
    </justification>
  </clause>

  <clause id="11244">
    <literal><![CDATA[
      a(x,(y * z) \ u,w) = a(x,(z * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(6234(a,1),11200(a,1,2))].">
      <j1 rule="para" parents="6234 11200"/>
    </justification>
  </clause>

  <clause id="11245">
    <literal><![CDATA[
      a(x,(y * K(z,u)) \ w,v5) = a(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(10163(a,1),11200(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10163 11200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11246">
    <literal><![CDATA[
      a(x,(y * (z / u)) \ w,v5) = a(x,(y * (u \ z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(10214(a,1),11200(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10214 11200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11247">
    <literal><![CDATA[
      a(x,(T(y,z) \ u) \ w,v5) = a(x,(y \ u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(10496(a,1),11200(a,1,2))].">
      <j1 rule="para" parents="10496 11200"/>
    </justification>
  </clause>

  <clause id="11248">
    <literal><![CDATA[
      a(x,L(y / z,u,w) \ v5,v6) = a(x,L(z \ y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(10245(a,1),11200(a,1,2))].">
      <j1 rule="para" parents="10245 11200"/>
    </justification>
  </clause>

  <clause id="11250">
    <literal><![CDATA[
      a(x,y * ((z * z) \ z),u) = a(x,y * (z \ 1),u)
    ]]></literal>
    <justification jstring="[para(283(a,1),11199(a,1,2,2))].">
      <j1 rule="para" parents="283 11199"/>
    </justification>
  </clause>

  <clause id="11252">
    <literal><![CDATA[
      ((x * ((x \ K(y,z)) * a(u,w,v5))) \ a(u,w,v5)) * K(y,z) = a(x,x \ 1,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,4522,a,b,11202,a)].">
      <j1 rule="hyper" parents="63 4522 11202"/>
    </justification>
  </clause>

  <clause id="11253">
    <literal><![CDATA[
      a(x,y * ((y * z) \ z),u) = a(x,a(z,y,y) \ 1,u)
    ]]></literal>
    <justification jstring="[para(7398(a,1),11202(a,1,2))].">
      <j1 rule="para" parents="7398 11202"/>
    </justification>
  </clause>

  <clause id="11255">
    <literal><![CDATA[
      a(x,(y \ z) * (y * y),u) = a(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(613(a,1),11230(a,1,2))].">
      <j1 rule="para" parents="613 11230"/>
    </justification>
  </clause>

  <clause id="11256">
    <literal><![CDATA[
      a(x,R(y \ z,y,u),w) = a(x,(y * u) \ (z * u),w)
    ]]></literal>
    <justification jstring="[para(621(a,1),11230(a,1,2))].">
      <j1 rule="para" parents="621 11230"/>
    </justification>
  </clause>

  <clause id="11257">
    <literal><![CDATA[
      a(x,y * R(z * K(u,z),u,w),v5) = a(x,y * ((u * w) \ ((u * z) * w)),v5)
    ]]></literal>
    <justification jstring="[para(2746(a,2),11198(a,1,2,2))].">
      <j1 rule="para" parents="2746 11198"/>
    </justification>
  </clause>

  <clause id="11259">
    <literal><![CDATA[
      a(x,y * (z * (u \ K(w,v5))),v6) = a(x,y * (z * (u \ 1)),v6)
    ]]></literal>
    <justification jstring="[para(3940(a,1),11204(a,1,2,2))].">
      <j1 rule="para" parents="3940 11204"/>
    </justification>
  </clause>

  <clause id="11260">
    <literal><![CDATA[
      a(x,y * R(z * K(u,w),v5,v6),v7) = a(x,y * R(z,v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(4604(a,2),11204(a,1,2,2))].">
      <j1 rule="para" parents="4604 11204"/>
    </justification>
  </clause>

  <clause id="11261">
    <literal><![CDATA[
      a(x,(y * z) / u,w) = a(x,u \ (z * y),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,11195,a,b,11205,a)].">
      <j1 rule="hyper" parents="316 11195 11205"/>
    </justification>
  </clause>

  <clause id="11262">
    <literal><![CDATA[
      a(x,y \ (((z * z) \ 1) * u),w) = a(x,y \ (u / (z * z)),w)
    ]]></literal>
    <justification jstring="[para(432(a,1),11205(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="432 11205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11263">
    <literal><![CDATA[
      a(x,L(y \ z,y,u),w) = a(x,(u * y) \ (z * u),w)
    ]]></literal>
    <justification jstring="[para(102(a,2),11205(a,1,2))].">
      <j1 rule="para" parents="102 11205"/>
    </justification>
  </clause>

  <clause id="11264">
    <literal><![CDATA[
      a(x,(y * z) * u,w) = a(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,11190,a,b,11206,a)].">
      <j1 rule="hyper" parents="316 11190 11206"/>
    </justification>
  </clause>

  <clause id="11265">
    <literal><![CDATA[
      a(x,y \ ((T(z,u) * w) / v5),v6) = a(x,y \ ((z * w) / v5),v6)
    ]]></literal>
    <justification jstring="[para(2871(a,1),11208(a,1,2,2))].">
      <j1 rule="para" parents="2871 11208"/>
    </justification>
  </clause>

  <clause id="11266">
    <literal><![CDATA[
      a(x,y \ ((T(z,u) \ w) * v5),v6) = a(x,y \ ((z \ w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(2902(a,1),11208(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2902 11208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11267">
    <literal><![CDATA[
      a(x,y \ ((z / u) \ w),v5) = a(x,y \ ((u \ z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(3143(a,1),11208(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3143 11208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11268">
    <literal><![CDATA[
      a(x,y \ (L(z / u,w,v5) \ v6),v7) = a(x,y \ (L(u \ z,w,v5) \ v6),v7)
    ]]></literal>
    <justification jstring="[para(10245(a,1),11208(a,1,2,2))].">
      <j1 rule="para" parents="10245 11208"/>
    </justification>
  </clause>

  <clause id="11269">
    <literal><![CDATA[
      x / (y * ((y \ (x / z)) * z)) = a(y,y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2398,a,b,11209,a)].">
      <j1 rule="hyper" parents="63 2398 11209"/>
    </justification>
  </clause>

  <clause id="11270">
    <literal><![CDATA[
      a(x,((y \ z) * y) * u,w) = a(x,u * z,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11190,a,b,11211,a)].">
      <j1 rule="hyper" parents="63 11190 11211"/>
    </justification>
  </clause>

  <clause id="11271">
    <literal><![CDATA[
      a(x,y * (K(z,u) * w),v5) = a(x,w * y,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,11190,a,b,11212,a),flip(a)].">
      <j1 rule="hyper" parents="316 11190 11212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11273">
    <literal><![CDATA[
      a(x,y * ((z * u) \ w),v5) = a(x,y * ((u * z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(6234(a,1),11212(a,1,2,2))].">
      <j1 rule="para" parents="6234 11212"/>
    </justification>
  </clause>

  <clause id="11274">
    <literal><![CDATA[
      a(x,y,a(z * u,z * u,w)) = a(x,y,a(w,u * z,u * z))
    ]]></literal>
    <justification jstring="[para(11225(a,1),7280(a,2,3)),flip(a)].">
      <j1 rule="para" parents="11225 7280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11275">
    <literal><![CDATA[
      a(x,(R(T(y,z),u,w) \ v5) * v6,v7) = a(x,v6 * (R(y,u,w) \ v5),v7)
    ]]></literal>
    <justification jstring="[para(3413(a,1),11235(a,1,2))].">
      <j1 rule="para" parents="3413 11235"/>
    </justification>
  </clause>

  <clause id="11276">
    <literal><![CDATA[
      a(x,(L(T(y,z),u,w) \ v5) * v6,v7) = a(x,v6 * (L(y,u,w) \ v5),v7)
    ]]></literal>
    <justification jstring="[para(4450(a,1),11235(a,1,2))].">
      <j1 rule="para" parents="4450 11235"/>
    </justification>
  </clause>

  <clause id="11280">
    <literal><![CDATA[
      a(x,(y * z) \ (z * (u * y)),w) = a(x,L(T(u,y),y,z),w)
    ]]></literal>
    <justification jstring="[para(247(a,1),11244(a,1,2)),flip(a)].">
      <j1 rule="para" parents="247 11244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11281">
    <literal><![CDATA[
      a(x,(y * (z * u)) \ w,v5) = a(x,(y * (u * z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(3933(a,1),11245(a,1,2,1))].">
      <j1 rule="para" parents="3933 11245"/>
    </justification>
  </clause>

  <clause id="11282">
    <literal><![CDATA[
      a(x,(y * (K(z,u) * w)) \ v5,v6) = a(x,(y * w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(3941(a,1),11245(a,1,2,1))].">
      <j1 rule="para" parents="3941 11245"/>
    </justification>
  </clause>

  <clause id="11283">
    <literal><![CDATA[
      a(x,(y * z) \ (z * (u * y)),w) = a(x,R(u,y,z),w)
    ]]></literal>
    <justification jstring="[para(20(a,2),11261(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 11261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11284">
    <literal><![CDATA[
      a(x,L(y,z,u) * (z * u),w) = a(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[para(100(a,1),11264(a,1,2)),flip(a)].">
      <j1 rule="para" parents="100 11264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11285">
    <literal><![CDATA[
      a(x,y * R(T(z,u),w,v5),v6) = a(x,R(z,w,v5) * y,v6)
    ]]></literal>
    <justification jstring="[para(2812(a,1),11271(a,1,2,2))].">
      <j1 rule="para" parents="2812 11271"/>
    </justification>
  </clause>

  <clause id="11286">
    <literal><![CDATA[
      a(x,y * L(z * K(u,w),v5,v6),v7) = a(x,L(z,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[para(10251(a,1),11271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10251 11271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11287">
    <literal><![CDATA[
      a(x,L(y,y,z) * z,u) = a(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,11195,a(flip),b,11192,a),flip(a)].">
      <j1 rule="hyper" parents="316 11195 11192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11290">
    <literal><![CDATA[
      a(x,(y * (z \ 1)) \ (((z \ 1) * (1 / z)) * y),u) = a(x,y \ (y / z),u)
    ]]></literal>
    <justification jstring="[para(7645(a,1),11214(a,2,2))].">
      <j1 rule="para" parents="7645 11214"/>
    </justification>
  </clause>

  <clause id="11291">
    <literal><![CDATA[
      a(x,L(a(y,z,u) \ z,y,u),w) = a(x,(u * y) \ (y * (z * u)),w)
    ]]></literal>
    <justification jstring="[para(8531(a,1),11214(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8531 11214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11292">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = (w / x) \ (a(x,R(y \ u,y,z),x) \ w)
    ]]></literal>
    <justification jstring="[para(11256(a,2),4943(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11256 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11295">
    <literal><![CDATA[
      a(x,(y * (z * z)) \ u,w) = a(x,y \ (u / (z * z)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11195,a(flip),b,11231,a)].">
      <j1 rule="hyper" parents="63 11195 11231"/>
    </justification>
  </clause>

  <clause id="11296">
    <literal><![CDATA[
      a(x,(y / (z * z)) \ u,w) = a(x,y \ (u * (z * z)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11195,a(flip),b,11232,a)].">
      <j1 rule="hyper" parents="63 11195 11232"/>
    </justification>
  </clause>

  <clause id="11297">
    <literal><![CDATA[
      a(x,(y * y) \ (z * u),w) = a(x,z * ((y * y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,11198,a(flip),b,11233,a),flip(a)].">
      <j1 rule="hyper" parents="316 11198 11233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11299">
    <literal><![CDATA[
      a(x,y * ((T(z,u) * w) \ ((T(z,u) * u) * w)),v5) = a(x,y * L(u * K(u * z,w),z,w),v5)
    ]]></literal>
    <justification jstring="[para(10832(a,1),11273(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10832 11273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11300">
    <literal><![CDATA[
      a(x,(y * (T(z,y * u) * u)) \ w,v5) = a(x,(L(z,u,y) * (y * u)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(598(a,1),11281(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="598 11281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11301">
    <literal><![CDATA[
      a(x,(L(y,z,u) * (u * z)) \ (y * (z * u)),w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(5784(a,2),11281(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5784 11281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11302">
    <literal><![CDATA[
      a(x,(y * ((K(z,u) * w) * (v5 \ z))) \ v6,v7) = a(x,(y * ((v5 \ T(z,u)) * w)) \ v6,v7)
    ]]></literal>
    <justification jstring="[para(10195(a,1),11281(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10195 11281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11303">
    <literal><![CDATA[
      a(x,(y * (T(z,u) * w)) \ v5,v6) = a(x,(y * (z * w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(2800(a,1),11282(a,1,2,1,2))].">
      <j1 rule="para" parents="2800 11282"/>
    </justification>
  </clause>

  <clause id="11304">
    <literal><![CDATA[
      a(x,(y * (z * z)) \ u,w) = a(x,y \ ((z * z) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,11209,a(flip),b,11295,a),flip(a)].">
      <j1 rule="hyper" parents="316 11209 11295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11305">
    <literal><![CDATA[
      a(x,(y * z) \ (u * (z * z)),w) = a(x,(y * (z \ 1)) \ u,w)
    ]]></literal>
    <justification jstring="[para(562(a,1),11296(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="562 11296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11306">
    <literal><![CDATA[
      a(x,y * ((z * z) \ z),u) = a(x,L(z \ y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11263,a,b,11297,a),flip(a)].">
      <j1 rule="hyper" parents="63 11263 11297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11308">
    <literal><![CDATA[
      a(x,L(y \ z,y,y),u) = a(x,z * (y \ 1),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11250,a(flip),b,11306,a),flip(a)].">
      <j1 rule="hyper" parents="63 11250 11306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11309">
    <literal><![CDATA[
      a(x,(y * z) * (y \ 1),u) = a(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),11308(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 11308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11310">
    <literal><![CDATA[
      a(x,(y \ 1) * (z * y),u) = a(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11264,a(flip),b,11309,a)].">
      <j1 rule="hyper" parents="63 11264 11309"/>
    </justification>
  </clause>

  <clause id="11311">
    <literal><![CDATA[
      a(x,(y * (z * (u * u))) \ w,v5) = a(x,(y * z) \ ((u * u) \ w),v5)
    ]]></literal>
    <justification jstring="[para(32(a,1),11304(a,1,2,1))].">
      <j1 rule="para" parents="32 11304"/>
    </justification>
  </clause>

  <clause id="11312">
    <literal><![CDATA[
      a(x,(y \ 1) \ (y \ z),u) = a(x,z * a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11255,a(flip),b,11226,a)].">
      <j1 rule="hyper" parents="63 11255 11226"/>
    </justification>
  </clause>

  <clause id="11313">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,w),z,w * u)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7132,a,b,11227,a)].">
      <j1 rule="hyper" parents="63 7132 11227"/>
    </justification>
  </clause>

  <clause id="11314">
    <literal><![CDATA[
      a(x,y,a(z \ K(u,z \ 1),u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9313,a(flip),b,11227,a)].">
      <j1 rule="hyper" parents="63 9313 11227"/>
    </justification>
  </clause>

  <clause id="11316">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((R(u,w,w) \ w) \ (z * L(w,w,u)))) = a(x,y,a(R(u,w,w) \ w,u,z))
    ]]></literal>
    <justification jstring="[para(7166(a,1),11227(a,1,3,2,2,2))].">
      <j1 rule="para" parents="7166 11227"/>
    </justification>
  </clause>

  <clause id="11318">
    <literal><![CDATA[
      a(x,y,a(z \ 1,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(3806(a,1),11314(a,1,3))].">
      <j1 rule="para" parents="3806 11314"/>
    </justification>
  </clause>

  <clause id="11319">
    <literal><![CDATA[
      a(x,y,(z \ (u \ w)) * ((u * z) \ w)) = a(x,y,a(w \ (u * z),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9370,a,b,11318,a)].">
      <j1 rule="hyper" parents="63 9370 11318"/>
    </justification>
  </clause>

  <clause id="11320">
    <literal><![CDATA[
      a(x,y,a(R(z,u,u),z * u,z * u)) = a(x,y,a(u,z * u,L(z,u,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8226,a,b,11318,a)].">
      <j1 rule="hyper" parents="63 8226 11318"/>
    </justification>
  </clause>

  <clause id="11322">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) \ y,x,a(z \ 1,u,w)) = L(y,a(z \ 1,u,w),x)
    ]]></literal>
    <justification jstring="[para(11318(a,1),8902(a,1,1,1))].">
      <j1 rule="para" parents="11318 8902"/>
    </justification>
  </clause>

  <clause id="11323">
    <literal><![CDATA[
      a(x,(y * z) \ (z * (u * y)),w) = a(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,11213,a(flip),b,11280,a),flip(a)].">
      <j1 rule="hyper" parents="316 11213 11280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11325">
    <literal><![CDATA[
      a(x,R(y,z,u),w) = a(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11283,a(flip),b,11323,a)].">
      <j1 rule="hyper" parents="63 11283 11323"/>
    </justification>
  </clause>

  <clause id="11326">
    <literal><![CDATA[
      ((x * (y * z)) / L(z,z,y)) \ (x * R(y,z,z)) = a(x,L(y,z,z),L(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7162,a,b,11325,a)].">
      <j1 rule="hyper" parents="63 7162 11325"/>
    </justification>
  </clause>

  <clause id="11327">
    <literal><![CDATA[
      a(x,R(L(y,z,u),w,v5),v6) = a(x,L(L(y,w,v5),z,u),v6)
    ]]></literal>
    <justification jstring="[para(30(a,1),11325(a,2,2))].">
      <j1 rule="para" parents="30 11325"/>
    </justification>
  </clause>

  <clause id="11328">
    <literal><![CDATA[
      a(x,L(y,z,u * u),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(497(a,1),11325(a,1,2)),flip(a)].">
      <j1 rule="para" parents="497 11325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11329">
    <literal><![CDATA[
      a(x,L(y,z,(u \ 1) \ w),v5) = a(x,R(y,z,u \ w),v5)
    ]]></literal>
    <justification jstring="[para(4789(a,1),11325(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4789 11325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11330">
    <literal><![CDATA[
      a(L(x,y,z),u,w) * a(u * w,L(x,y,z),a(L(x,y,z),u,w)) = R(x,y,z) \ R(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(11325(a,1),9380(a,1,2))].">
      <j1 rule="para" parents="11325 9380"/>
    </justification>
  </clause>

  <clause id="11331">
    <literal><![CDATA[
      (x * (a(L(y,z,u),w,v5) * a(v5 * w,L(y,z,u),a(L(y,z,u),w,v5)))) / x = R(y,z,u) \ R(R(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(11325(a,1),9698(a,1,1,2,2))].">
      <j1 rule="para" parents="11325 9698"/>
    </justification>
  </clause>

  <clause id="11332">
    <literal><![CDATA[
      a(x,L(R(y,z,u),w,v5),v6) = a(x,L(L(y,z,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(29(a,1),11327(a,1,2))].">
      <j1 rule="para" parents="29 11327"/>
    </justification>
  </clause>

  <clause id="11333">
    <literal><![CDATA[
      a(x,L(y,z,(u \ 1) \ w),v5) = a(x,L(y,z,u \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,11325,a(flip),b,11329,a),flip(a)].">
      <j1 rule="hyper" parents="316 11325 11329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11334">
    <literal><![CDATA[
      L(R(x,y,z),R(x,y,z) * L(x \ L(x,u,w),y,z),v5) \ R(x,y,z) = a(v5,L(L(x,y,z),u,w),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10123,a,b,11332,a)].">
      <j1 rule="hyper" parents="63 10123 11332"/>
    </justification>
  </clause>

  <clause id="11335">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ (u * (z * w))))) = a(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9374,a(flip),b,11313,a)].">
      <j1 rule="hyper" parents="63 9374 11313"/>
    </justification>
  </clause>

  <clause id="11336">
    <literal><![CDATA[
      (x * L(x \ L(x,y,z),x,z * y)) \ (x * (x \ L(x,y,z))) = a(z * y,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8454,a(flip),b,11313,a)].">
      <j1 rule="hyper" parents="63 8454 11313"/>
    </justification>
  </clause>

  <clause id="11337">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),a(z,u,w),u)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8839,a,b,11335,a)].">
      <j1 rule="hyper" parents="63 8839 11335"/>
    </justification>
  </clause>

  <clause id="11339">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w \ (v5 * v6)),a(z,u,w \ ((v5 \ 1) * v6)),u)) = a(x,y,a(w \ ((v5 \ 1) * v6),u,z))
    ]]></literal>
    <justification jstring="[para(6682(a,1),11337(a,1,3,1))].">
      <j1 rule="para" parents="6682 11337"/>
    </justification>
  </clause>

  <clause id="11341">
    <literal><![CDATA[
      a(x,y,L(a(z,u,L(w \ v5,v5,v5)),a(z,u,L(w,v5,v5) \ v5),u)) = a(x,y,a(L(w,v5,v5) \ v5,u,z))
    ]]></literal>
    <justification jstring="[para(8612(a,2),11337(a,1,3,1))].">
      <j1 rule="para" parents="8612 11337"/>
    </justification>
  </clause>

  <clause id="11343">
    <literal><![CDATA[
      x \ R(x,y * (L(y,z,u) \ y),L(y,z,u)) = a(x,L(y \ 1,z,u) \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9524,a,b,11248,a)].">
      <j1 rule="hyper" parents="63 9524 11248"/>
    </justification>
  </clause>

  <clause id="11345">
    <literal><![CDATA[
      a(x,y * R(z * K(u,w),v5,v6),v7) = a(x,R(z,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,11190,a,b,11260,a),flip(a)].">
      <j1 rule="hyper" parents="316 11190 11260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11346">
    <literal><![CDATA[
      a(x,y \ (((z * z) \ 1) * u),w) = a(x,y \ ((z * z) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,11209,a(flip),b,11262,a),flip(a)].">
      <j1 rule="hyper" parents="316 11209 11262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11347">
    <literal><![CDATA[
      a(x,y \ ((T(z,u) * w) / v5),v6) = a(x,y \ (v5 \ (z * w)),v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,11209,a(flip),b,11265,a),flip(a)].">
      <j1 rule="hyper" parents="316 11209 11265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11349">
    <literal><![CDATA[
      a(x,(y * (z \ 1)) \ ((z * z) \ u),w) = a(x,(y * z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11210,a(flip),b,11305,a),flip(a)].">
      <j1 rule="hyper" parents="63 11210 11305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11351">
    <literal><![CDATA[
      a(x,y \ ((z \ (z \ 1)) * u),w) = a(x,y \ ((z * z) \ u),w)
    ]]></literal>
    <justification jstring="[para(433(a,1),11346(a,1,2,2,1))].">
      <j1 rule="para" parents="433 11346"/>
    </justification>
  </clause>

  <clause id="11352">
    <literal><![CDATA[
      a(x,y \ (z \ (T(u,w) * v5)),v6) = a(x,y \ (z \ (u * v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,11209,a(flip),b,11347,a)].">
      <j1 rule="hyper" parents="63 11209 11347"/>
    </justification>
  </clause>

  <clause id="11353">
    <literal><![CDATA[
      a(x,y \ (((z \ 1) \ T(z,z \ 1)) * u),w) = a(x,y \ (((z \ 1) * (z \ 1)) \ u),w)
    ]]></literal>
    <justification jstring="[para(115(a,2),11351(a,1,2,2,1,2))].">
      <j1 rule="para" parents="115 11351"/>
    </justification>
  </clause>

  <clause id="11354">
    <literal><![CDATA[
      a(x,y \ (z \ ((u / w) * v5)),v6) = a(x,y \ (z \ ((w \ u) * v5)),v6)
    ]]></literal>
    <justification jstring="[para(116(a,1),11352(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="116 11352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11355">
    <literal><![CDATA[
      a(x,L(a(y,z,u) \ z,y,u),w) = a(x,L(z,u,y),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,11323,a(flip),b,11291,a),flip(a)].">
      <j1 rule="hyper" parents="316 11323 11291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11356">
    <literal><![CDATA[
      a(x,(y * (z * (u \ L(u \ 1,u \ 1,u)))) \ w,v5) = a(x,(y * z) \ (((u \ 1) * (u \ 1)) \ w),v5)
    ]]></literal>
    <justification jstring="[para(387(a,2),11311(a,1,2,1,2,2))].">
      <j1 rule="para" parents="387 11311"/>
    </justification>
  </clause>

  <clause id="11357">
    <literal><![CDATA[
      a(x,(y * z) \ ((u * u) \ (y * (w * (z * (u * u))))),v5) = a(x,L(T(w,z * (u * u)),z * (u * u),y),v5)
    ]]></literal>
    <justification jstring="[para(247(a,1),11311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="247 11311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11358">
    <literal><![CDATA[
      a(x,y \ (z \ ((u \ w) * u)),v5) = a(x,y \ (z \ w),v5)
    ]]></literal>
    <justification jstring="[para(12(a,1),11354(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12 11354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11359">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = (w / x) \ (a(x,y \ u,x) \ w)
    ]]></literal>
    <justification jstring="[para(6117(a,1),11292(a,2,2,1))].">
      <j1 rule="para" parents="6117 11292"/>
    </justification>
  </clause>

  <clause id="11360">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = L(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,4943,a(flip),b,11359,a),flip(a)].">
      <j1 rule="hyper" parents="316 4943 11359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11362">
    <literal><![CDATA[
      L((1 / x) * y,z,a(a(u,w,u) / x,x \ 1,y)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(8045(a,1),11234(a,1,3))].">
      <j1 rule="para" parents="8045 11234"/>
    </justification>
  </clause>

  <clause id="11364">
    <literal><![CDATA[
      L((1 / x) * y,z,a(x \ 1,x \ 1,y)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(8058(a,1),11362(a,1,3))].">
      <j1 rule="para" parents="8058 11362"/>
    </justification>
  </clause>

  <clause id="11365">
    <literal><![CDATA[
      L((1 / x) * y,z,a(x,x \ 1,y)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,7848,a(flip),b,11364,a)].">
      <j1 rule="hyper" parents="63 7848 11364"/>
    </justification>
  </clause>

  <clause id="11366">
    <literal><![CDATA[
      K(x,x \ 1) * (y / ((1 / x) * y)) = a(x,x \ 1,y) * x
    ]]></literal>
    <justification jstring="[para(11365(a,1),7841(a,1,2,2))].">
      <j1 rule="para" parents="11365 7841"/>
    </justification>
  </clause>

  <clause id="11367">
    <literal><![CDATA[
      a(x,x \ 1,y) * x = R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3386,a(flip),b,11366,a),flip(a)].">
      <j1 rule="hyper" parents="63 3386 11366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11369">
    <literal><![CDATA[
      a(x,y,(z \ (a(z,z \ 1,u) \ z)) * w) = a(x,y,(R(z,z \ 1,u) \ z) * w)
    ]]></literal>
    <justification jstring="[para(11367(a,1),7778(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="11367 7778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11370">
    <literal><![CDATA[
      a(x,L(y,z,u) \ (L(y \ 1,w,v5) \ 1),v6) = a(x,y * (L(y,z,u) \ (L(y,w,v5) \ y)),v6)
    ]]></literal>
    <justification jstring="[para(6598(a,1),11268(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6598 11268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11371">
    <literal><![CDATA[
      a(x,(y * (z \ 1)) \ ((z \ (z \ 1)) * y),u) = a(x,y \ (y / z),u)
    ]]></literal>
    <justification jstring="[para(633(a,1),11290(a,1,2,2,1))].">
      <j1 rule="para" parents="633 11290"/>
    </justification>
  </clause>

  <clause id="11372">
    <literal><![CDATA[
      a(x,(y * (z \ 1)) \ ((z * z) \ y),u) = a(x,y \ (y / z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11351,a(flip),b,11371,a)].">
      <j1 rule="hyper" parents="63 11351 11371"/>
    </justification>
  </clause>

  <clause id="11373">
    <literal><![CDATA[
      a(x,(y * z) \ y,u) = a(x,y \ (y / z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11349,a(flip),b,11372,a)].">
      <j1 rule="hyper" parents="63 11349 11372"/>
    </justification>
  </clause>

  <clause id="11374">
    <literal><![CDATA[
      a(x,(y * z) \ y,u) = a(x,y \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,11209,a(flip),b,11373,a),flip(a)].">
      <j1 rule="hyper" parents="316 11209 11373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11375">
    <literal><![CDATA[
      a(x,(y * z) \ z,u) = a(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11244,a,b,11374,a)].">
      <j1 rule="hyper" parents="63 11244 11374"/>
    </justification>
  </clause>

  <clause id="11376">
    <literal><![CDATA[
      a(x,L(y \ 1,y,z),u) = a(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8050,a,b,11374,a)].">
      <j1 rule="hyper" parents="63 8050 11374"/>
    </justification>
  </clause>

  <clause id="11377">
    <literal><![CDATA[
      L(x,y \ (z \ y),y \ (z \ y)) = a(y \ (z \ y),L(z \ 1,z,y),x) \ x
    ]]></literal>
    <justification jstring="[para(11376(a,2),4950(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11376 4950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11378">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,w),w,a(y \ 1,z,u)) = L(x,a(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(9445(a,1),11322(a,1,1))].">
      <j1 rule="para" parents="9445 11322"/>
    </justification>
  </clause>

  <clause id="11379">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,w),w,a(y,z,u)) = L(x,a(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,7848,a(flip),b,11378,a)].">
      <j1 rule="hyper" parents="63 7848 11378"/>
    </justification>
  </clause>

  <clause id="11380">
    <literal><![CDATA[
      L(x,a(y \ 1,z,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9456,a(flip),b,11379,a),flip(a)].">
      <j1 rule="hyper" parents="63 9456 11379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11381">
    <literal><![CDATA[
      a(x,y,L(L(z,u,u \ 1),a(u,u,z),w) \ (z * w)) = a(x,y,w * a(u \ 1,u,z))
    ]]></literal>
    <justification jstring="[para(11380(a,1),5741(a,1,3,1))].">
      <j1 rule="para" parents="11380 5741"/>
    </justification>
  </clause>

  <clause id="11382">
    <literal><![CDATA[
      a(x,y,z * L(a(u \ 1,w,v5) \ 1,a(u,w,v5),w)) = a(x,y,z * (w \ (u \ (((u \ 1) * (w * v5)) / v5))))
    ]]></literal>
    <justification jstring="[para(11380(a,1),8699(a,1,3,2))].">
      <j1 rule="para" parents="11380 8699"/>
    </justification>
  </clause>

  <clause id="11383">
    <literal><![CDATA[
      T(x \ y,x * (y \ (x / y))) = L(x \ y,y \ x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(34,a,1260,a,b,10462,a),flip(a)].">
      <j1 rule="hyper" parents="34 1260 10462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11384">
    <literal><![CDATA[
      L(x \ y,y \ x,(x \ y) \ 1) = T(x \ y,x * (y \ (x / y)))
    ]]></literal>
    <justification jstring="[hyper(316,a,8024,a,b,11383,a)].">
      <j1 rule="hyper" parents="316 8024 11383"/>
    </justification>
  </clause>

  <clause id="11385">
    <literal><![CDATA[
      L(x \ y,y \ x,(x \ y) \ 1) = T(x \ y,(y \ x) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(316,a,10453,a,b,11384,a),flip(a)].">
      <j1 rule="hyper" parents="316 10453 11384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11386">
    <literal><![CDATA[
      L(x \ y,y \ x,(x \ y) \ 1) = T(x \ y,((y \ x) / y) * x)
    ]]></literal>
    <justification jstring="[hyper(316,a,3523,a,b,11385,a),flip(a)].">
      <j1 rule="hyper" parents="316 3523 11385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11387">
    <literal><![CDATA[
      (x \ y) / T(y \ x,((x \ y) / x) * y) = (1 / (y \ x)) * (x \ y)
    ]]></literal>
    <justification jstring="[para(11386(a,1),1595(a,1,2))].">
      <j1 rule="para" parents="11386 1595"/>
    </justification>
  </clause>

  <clause id="11388">
    <literal><![CDATA[
      (1 / (x \ y)) * (y \ x) = (x \ y) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6650,a(flip),b,11387,a),flip(a)].">
      <j1 rule="hyper" parents="63 6650 11387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11389">
    <literal><![CDATA[
      (x \ y) \ (y \ x) = y \ (x * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,8568,a(flip),b,11388,a),flip(a)].">
      <j1 rule="hyper" parents="63 8568 11388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11390">
    <literal><![CDATA[
      (((x \ y) * x) \ (x \ y)) \ ((x \ y) \ ((x \ y) * x)) = (y / x) \ (y * ((x \ y) \ ((x \ y) * x)))
    ]]></literal>
    <justification jstring="[hyper(316,a,3200,a(flip),b,11389,a),flip(a)].">
      <j1 rule="hyper" parents="316 3200 11389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11391">
    <literal><![CDATA[
      a(((x * y) \ ((x * z) * y)) * u,w,v5) = a(R(z,x,y) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,4041,a(flip),b,10476,a),flip(a)].">
      <j1 rule="hyper" parents="63 4041 10476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11393">
    <literal><![CDATA[
      (x * y) \ L(x * y,(x * y) \ y,x) = (x * (y / (x * y))) \ 1
    ]]></literal>
    <justification jstring="[para(2218(a,1),10612(a,2,1))].">
      <j1 rule="para" parents="2218 10612"/>
    </justification>
  </clause>

  <clause id="11395">
    <literal><![CDATA[
      (x * y) \ L(x * y,y \ (x \ y),x) = (x * (y / (x * y))) \ 1
    ]]></literal>
    <justification jstring="[para(10957(a,1),11393(a,1,2))].">
      <j1 rule="para" parents="10957 11393"/>
    </justification>
  </clause>

  <clause id="11396">
    <literal><![CDATA[
      x \ (y * L(y \ x,x \ (y \ x),y)) = (y * (x / (y * x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,9937,a(flip),b,11395,a)].">
      <j1 rule="hyper" parents="63 9937 11395"/>
    </justification>
  </clause>

  <clause id="11397">
    <literal><![CDATA[
      x \ (y * L(y \ x,y \ 1,y)) = (y * (x / (y * x))) \ 1
    ]]></literal>
    <justification jstring="[para(11044(a,1),11396(a,1,2,2))].">
      <j1 rule="para" parents="11044 11396"/>
    </justification>
  </clause>

  <clause id="11398">
    <literal><![CDATA[
      (x * (y / (x * y))) \ 1 = y \ ((x \ 1) * (x * y))
    ]]></literal>
    <justification jstring="[para(1357(a,1),11397(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1357 11397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11399">
    <literal><![CDATA[
      ((x * (y / (x * y))) \ 1) * z = (y \ ((x \ 1) * (x * y))) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,11398,a,b,11,a)].">
      <j1 rule="hyper" parents="138 11398 11"/>
    </justification>
  </clause>

  <clause id="11402">
    <literal><![CDATA[
      (((x * y) \ z) \ 1) \ (y \ (x \ z)) = (y \ (x \ z)) * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(298(a,1),10717(a,1,2)),flip(a)].">
      <j1 rule="para" parents="298 10717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11403">
    <literal><![CDATA[
      a(x,y,(((z * (u \ 1)) \ w) \ 1) \ (u \ (z \ w))) = a(x,y,((u \ 1) \ (z \ w)) * ((z * (u \ 1)) \ w))
    ]]></literal>
    <justification jstring="[para(11402(a,1),6743(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11402 6743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11404">
    <literal><![CDATA[
      (T(x,y) \ R(z,x \ 1,x)) * T(x,y) = T(z * (1 / x),T(x,y)) * x
    ]]></literal>
    <justification jstring="[para(10432(a,1),10763(a,2,1))].">
      <j1 rule="para" parents="10432 10763"/>
    </justification>
  </clause>

  <clause id="11405">
    <literal><![CDATA[
      R((T(x,y) \ z) * T(x,y),x \ 1,x) = T(z * (1 / x),T(x,y)) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,1768,a,b,11404,a)].">
      <j1 rule="hyper" parents="63 1768 11404"/>
    </justification>
  </clause>

  <clause id="11406">
    <literal><![CDATA[
      L(x,y,R(T(z,u * w),w,u) \ v5) = L(x,y,L(z,w,u) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,6788,a(flip),b,10774,a),flip(a)].">
      <j1 rule="hyper" parents="63 6788 10774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11407">
    <literal><![CDATA[
      L(x,y,R(z,u,w) \ v5) = L(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3409,a(flip),b,11406,a)].">
      <j1 rule="hyper" parents="63 3409 11406"/>
    </justification>
  </clause>

  <clause id="11409">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ (L(v5,R(z,u,w) \ v6,R(z,u,w)) * v6)) = L(x,y,(R(z,u,w) \ v6) * T(v5,v6))
    ]]></literal>
    <justification jstring="[para(714(a,1),11407(a,1,3)),flip(a)].">
      <j1 rule="para" parents="714 11407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11410">
    <literal><![CDATA[
      L(x,((y * z) \ ((u * z) * y)) \ w,v5) = L(x,K(y,z) * (R(u,z,y) \ w),v5)
    ]]></literal>
    <justification jstring="[para(10243(a,1),10890(a,2,2))].">
      <j1 rule="para" parents="10243 10890"/>
    </justification>
  </clause>

  <clause id="11411">
    <literal><![CDATA[
      L(x,y \ (a(L(z,u,w),u,w) \ u),v5) = L(x,y \ (z * (R(z,u,w) \ u)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10865,a(flip),b,10919,a)].">
      <j1 rule="hyper" parents="63 10865 10919"/>
    </justification>
  </clause>

  <clause id="11412">
    <literal><![CDATA[
      L(x,y \ ((z * (y / z)) / ((y \ z) \ 1)),u) = L(x,L(y \ z,z \ y,z),u)
    ]]></literal>
    <justification jstring="[para(3204(a,1),10978(a,1,2))].">
      <j1 rule="para" parents="3204 10978"/>
    </justification>
  </clause>

  <clause id="11413">
    <literal><![CDATA[
      x * L(y,L(x,x,z),z \ L(z,x,x)) = (R(x,x,z) \ x) * (R(x,x,z) * y)
    ]]></literal>
    <justification jstring="[para(1772(a,1),10990(a,2,1))].">
      <j1 rule="para" parents="1772 10990"/>
    </justification>
  </clause>

  <clause id="11415">
    <literal><![CDATA[
      a(x,y * ((z * u) \ ((z * w) * u)),v5) = a(x,R(w,z,u) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11345,a(flip),b,11257,a),flip(a)].">
      <j1 rule="hyper" parents="63 11345 11257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11416">
    <literal><![CDATA[
      a(x,y * ((z * u) \ ((z * w) * u)),v5) = a(x,y * R(w,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11260,a(flip),b,11257,a),flip(a)].">
      <j1 rule="hyper" parents="63 11260 11257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11418">
    <literal><![CDATA[
      a(x,(L(y,z,u) * (u * z)) \ w,v5) = a(x,(u * (y * z)) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11303,a(flip),b,11300,a),flip(a)].">
      <j1 rule="hyper" parents="63 11303 11300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11420">
    <literal><![CDATA[
      a(x,(y * (z * u)) \ (z * (u * y)),w) = a(x,a(y,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11301,a(flip),b,11418,a),flip(a)].">
      <j1 rule="hyper" parents="63 11301 11418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11421">
    <literal><![CDATA[
      a(x,((y * z) * u) \ (y * (z * u)),w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11244,a,b,11420,a)].">
      <j1 rule="hyper" parents="63 11244 11420"/>
    </justification>
  </clause>

  <clause id="11422">
    <literal><![CDATA[
      a(x,(y * z) \ (u \ (y * (z * u))),w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(7150(a,1),11420(a,1,2))].">
      <j1 rule="para" parents="7150 11420"/>
    </justification>
  </clause>

  <clause id="11423">
    <literal><![CDATA[
      a(x,L(y \ L(y,z,u),y,u * z),w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(489(a,2),11421(a,1,2))].">
      <j1 rule="para" parents="489 11421"/>
    </justification>
  </clause>

  <clause id="11424">
    <literal><![CDATA[
      a(x,R(y,z,z) \ y,u) = a(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(8111(a,1),11421(a,1,2))].">
      <j1 rule="para" parents="8111 11421"/>
    </justification>
  </clause>

  <clause id="11425">
    <literal><![CDATA[
      a(x,a(y,z,z) \ 1,u) = a(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(7657(a,1),11424(a,1,2))].">
      <j1 rule="para" parents="7657 11424"/>
    </justification>
  </clause>

  <clause id="11426">
    <literal><![CDATA[
      a(x,y * ((y * z) \ z),u) = a(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11253,a,b,11425,a)].">
      <j1 rule="hyper" parents="63 11253 11425"/>
    </justification>
  </clause>

  <clause id="11427">
    <literal><![CDATA[
      a(x,(((y * z) \ u) * y) \ (z \ u),w) = a(x,a(z,y,(y * z) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11358,a(flip),b,11422,a)].">
      <j1 rule="hyper" parents="63 11358 11422"/>
    </justification>
  </clause>

  <clause id="11428">
    <literal><![CDATA[
      a(x,y \ L(y,z,z),u) = a(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11328,a(flip),b,11423,a)].">
      <j1 rule="hyper" parents="63 11328 11423"/>
    </justification>
  </clause>

  <clause id="11429">
    <literal><![CDATA[
      a(x,L(y \ L(y,z,u),y,z * u),w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(1668(a,1),11423(a,1,2))].">
      <j1 rule="para" parents="1668 11423"/>
    </justification>
  </clause>

  <clause id="11430">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) \ (z / y)) * L(y,x,x) = z * a(y,a(y,x,x),z)
    ]]></literal>
    <justification jstring="[para(11428(a,1),8820(a,2,2))].">
      <j1 rule="para" parents="11428 8820"/>
    </justification>
  </clause>

  <clause id="11431">
    <literal><![CDATA[
      a(x,a(x,y,y),z) * z = ((a(y,y,x) \ 1) \ (z / x)) * L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2290,a,b,11430,a)].">
      <j1 rule="hyper" parents="316 2290 11430"/>
    </justification>
  </clause>

  <clause id="11432">
    <literal><![CDATA[
      a(x,(y * ((y * z) \ u)) \ (z \ u),w) = a(x,a(z,y,(y * z) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11244,a,b,11427,a)].">
      <j1 rule="hyper" parents="63 11244 11427"/>
    </justification>
  </clause>

  <clause id="11433">
    <literal><![CDATA[
      L(x,((y * z) \ ((u * z) * y)) \ w,v5) = L(x,R(u,z,y) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,10791,a(flip),b,11410,a),flip(a)].">
      <j1 rule="hyper" parents="316 10791 11410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11435">
    <literal><![CDATA[
      L(x,((T(y,T(z * u,w)) * u) \ T(y * (z * u),K(z * u,w))) \ v5,v6) = L(x,R(z,u,T(y,T(z * u,w))) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(4018(a,2),11433(a,1,2,1,2))].">
      <j1 rule="para" parents="4018 11433"/>
    </justification>
  </clause>

  <clause id="11436">
    <literal><![CDATA[
      L(x,y \ (((y \ z) \ 1) \ (z * (y / z))),u) = L(x,L(y \ z,z \ y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10865,a(flip),b,11412,a)].">
      <j1 rule="hyper" parents="63 10865 11412"/>
    </justification>
  </clause>

  <clause id="11437">
    <literal><![CDATA[
      (R(x,x,y) \ x) * (R(x,x,y) * z) = x * L(z,L(x,x,y),a(y,x,x))
    ]]></literal>
    <justification jstring="[para(7484(a,1),11413(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7484 11413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11438">
    <literal><![CDATA[
      (R(x,x,y) \ x) * (R(x,x,y) * z) = x * L(z,a(y,x,x),L(x,x,y))
    ]]></literal>
    <justification jstring="[para(10635(a,1),11437(a,2,2))].">
      <j1 rule="para" parents="10635 11437"/>
    </justification>
  </clause>

  <clause id="11439">
    <literal><![CDATA[
      (R(x,x,y) \ x) * (R(x,x,y) * z) = L(x,x,y) * (a(y,x,x) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,7311,a(flip),b,11438,a),flip(a)].">
      <j1 rule="hyper" parents="316 7311 11438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11440">
    <literal><![CDATA[
      (x \ L(x,y,y)) * (R(y,y,x) * z) = L(y,y,x) * (a(x,y,y) * z)
    ]]></literal>
    <justification jstring="[para(7666(a,1),11439(a,1,1))].">
      <j1 rule="para" parents="7666 11439"/>
    </justification>
  </clause>

  <clause id="11441">
    <literal><![CDATA[
      L(x,y \ (((y \ z) \ 1) \ (z * (z \ y))),u) = L(x,L(y \ z,z \ y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11007,a(flip),b,11436,a)].">
      <j1 rule="hyper" parents="63 11007 11436"/>
    </justification>
  </clause>

  <clause id="11442">
    <literal><![CDATA[
      L(x,L(y \ z,z \ y,z),u) = L(x,y \ (((y \ z) \ 1) \ y),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11441(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 11441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11444">
    <literal><![CDATA[
      a(x,y,(z * ((u * (w \ K(v5,v6))) * v7)) * v8) = a(x,y,(z * ((u * (w \ 1)) * v7)) * v8)
    ]]></literal>
    <justification jstring="[para(10296(a,1),10517(a,1,3,1,2,1,2))].">
      <j1 rule="para" parents="10296 10517"/>
    </justification>
  </clause>

  <clause id="11445">
    <literal><![CDATA[
      a(x,y,z * (((K(u,K(w,v5)) * ((v6 \ a(v7,v8,v7)) * v9)) * v10) * v11)) = a(x,y,z * (v11 * (((a(v7,v8,v7) * v9) * (v6 \ K(u,K(w,v5)))) * v10)))
    ]]></literal>
    <justification jstring="[para(10537(a,1),6002(a,1,3,2,1,1))].">
      <j1 rule="para" parents="10537 6002"/>
    </justification>
  </clause>

  <clause id="11446">
    <literal><![CDATA[
      K(x,y) * (z * (1 / (x \ z))) = z * (1 / (T(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(10676(a,1),10549(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10676 10549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11447">
    <literal><![CDATA[
      K(x,y) * (z * (1 / (x \ z))) = T(z * (1 / (x \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(316,a,10588,a,b,11446,a),flip(a)].">
      <j1 rule="hyper" parents="316 10588 11446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11448">
    <literal><![CDATA[
      K(x,y) * ((z * (1 / (x \ z))) * L((z * (1 / (x \ z))) \ (K(x,y) \ 1),u,w)) = T(z * (1 / (x \ z)),y) \ L(K(x,y) * (z * (1 / (x \ z))),u,w)
    ]]></literal>
    <justification jstring="[para(11447(a,1),1494(a,2,1))].">
      <j1 rule="para" parents="11447 1494"/>
    </justification>
  </clause>

  <clause id="11449">
    <literal><![CDATA[
      (x \ K(y,z)) * (L(x \ K(y,z),u,w) \ v5) = x * (L(x,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,7154,a(flip),b,10569,a),flip(a)].">
      <j1 rule="hyper" parents="316 7154 10569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11450">
    <literal><![CDATA[
      (x * (L(x,y,z) \ (x * u))) * L(x \ K(u,x),y,z) = R(u,x,x)
    ]]></literal>
    <justification jstring="[para(11449(a,1),6272(a,1,1))].">
      <j1 rule="para" parents="11449 6272"/>
    </justification>
  </clause>

  <clause id="11451">
    <literal><![CDATA[
      (x * (x * (L(x,y,z) \ u))) * L(x \ K(u,x),y,z) = R(u,x,x)
    ]]></literal>
    <justification jstring="[para(1129(a,1),11450(a,1,1,2))].">
      <j1 rule="para" parents="1129 11450"/>
    </justification>
  </clause>

  <clause id="11453">
    <literal><![CDATA[
      a(x,y,(z * L(u \ K(w,v5),v6,v7)) \ v8) = a(x,y,(z * L(u,v6,v7)) \ v8)
    ]]></literal>
    <justification jstring="[hyper(316,a,6398,a(flip),b,10579,a),flip(a)].">
      <j1 rule="hyper" parents="316 6398 10579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11454">
    <literal><![CDATA[
      a(x,y,(z * ((u * (L(u,w,v5) \ u)) * K(v6,v7))) \ v8) = a(x,y,(z * L(u,w,v5)) \ v8)
    ]]></literal>
    <justification jstring="[hyper(63,a,9486,a,b,11453,a)].">
      <j1 rule="hyper" parents="63 9486 11453"/>
    </justification>
  </clause>

  <clause id="11455">
    <literal><![CDATA[
      ((x / ((y \ 1) \ 1)) / x) / (y \ 1) = ((x / y) / x) / (1 / y)
    ]]></literal>
    <justification jstring="[para(3340(a,1),10613(a,1,1))].">
      <j1 rule="para" parents="3340 10613"/>
    </justification>
  </clause>

  <clause id="11456">
    <literal><![CDATA[
      (x \ 1) * (((x \ 1) * y) \ y) = ((y / x) / y) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10787,a(flip),b,11455,a)].">
      <j1 rule="hyper" parents="63 10787 11455"/>
    </justification>
  </clause>

  <clause id="11457">
    <literal><![CDATA[
      (x \ 1) * (((x \ 1) * y) \ y) = ((y / x) / y) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,3364,a(flip),b,11456,a),flip(a)].">
      <j1 rule="hyper" parents="316 3364 11456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11458">
    <literal><![CDATA[
      a(x,y,((z \ ((u * u) \ w)) * v5) * v6) = a(x,y,v6 * (v5 * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6035,a(flip),b,10671,a),flip(a)].">
      <j1 rule="hyper" parents="63 6035 10671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11460">
    <literal><![CDATA[
      a(x,y,(((z * (u * u)) \ w) * v5) * v6) = a(x,y,v6 * (v5 * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10670,a,b,11458,a)].">
      <j1 rule="hyper" parents="63 10670 11458"/>
    </justification>
  </clause>

  <clause id="11461">
    <literal><![CDATA[
      a(x,y,(z * (u \ ((w * w) \ v5))) * v6) = a(x,y,v6 * (z * (u \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5542,a,b,11458,a)].">
      <j1 rule="hyper" parents="63 5542 11458"/>
    </justification>
  </clause>

  <clause id="11463">
    <literal><![CDATA[
      a(x,y,((z * ((u * u) \ w)) * v5) \ v6) = a(x,y,(v5 * (z * w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,6014,a(flip),b,10696,a),flip(a)].">
      <j1 rule="hyper" parents="63 6014 10696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11465">
    <literal><![CDATA[
      a(x * (y * y),a(z,u,w),v5) = a(x,a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,10680,a(flip),b,10721,a),flip(a)].">
      <j1 rule="hyper" parents="316 10680 10721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11466">
    <literal><![CDATA[
      a(x \ (y \ 1),a(z,u,w),v5) = a(x \ y,a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(584(a,1),11465(a,1,1)),flip(a)].">
      <j1 rule="para" parents="584 11465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11467">
    <literal><![CDATA[
      a(L(x * y,y,x),a(z,u,w),v5) = a(y \ x,a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11107,a,b,11466,a)].">
      <j1 rule="hyper" parents="63 11107 11466"/>
    </justification>
  </clause>

  <clause id="11468">
    <literal><![CDATA[
      a(L(x * y,x,y),a(z,u,w),v5) = a(x \ y,a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,2791,a,b,11467,a)].">
      <j1 rule="hyper" parents="63 2791 11467"/>
    </justification>
  </clause>

  <clause id="11469">
    <literal><![CDATA[
      a(x \ a(y,z,x),a(u,w,v5),v6) = a(x * a(y,z,x),a(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(10640(a,1),11468(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10640 11468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11470">
    <literal><![CDATA[
      L(x,y * (z * (u * (w * K(v5,v6)))),v7) = L(x,(z * (u * w)) * y,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,10824,a(flip),b,10850,a),flip(a)].">
      <j1 rule="hyper" parents="63 10824 10850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11472">
    <literal><![CDATA[
      L(x,y \ (z \ y),(y \ (z \ y)) \ 1) * 1 = x * (((z * a(z \ y,z,z)) * ((y \ (y / z)) * x)) / x)
    ]]></literal>
    <justification jstring="[para(10892(a,1),7356(a,1,1))].">
      <j1 rule="para" parents="10892 7356"/>
    </justification>
  </clause>

  <clause id="11473">
    <literal><![CDATA[
      (((x * y) \ z) \ (y \ (x \ z))) \ 1 = (y \ (x \ z)) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10298,a(flip),b,10932,a),flip(a)].">
      <j1 rule="hyper" parents="63 10298 10932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11474">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ K(z,u)) \ 1) = (x * ((1 / y) * K(u,z))) * y
    ]]></literal>
    <justification jstring="[para(4070(a,1),11082(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4070 11082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11475">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ K(z,u)) \ 1) = (x * (1 / y)) * (K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,10201,a(flip),b,11474,a),flip(a)].">
      <j1 rule="hyper" parents="316 10201 11474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11477">
    <literal><![CDATA[
      L(x,y,a(z,u,L(y,y \ w,(y \ w) \ 1))) = L(x,a(z,u,(w / y) * w),y)
    ]]></literal>
    <justification jstring="[para(5572(a,1),10492(a,2,2))].">
      <j1 rule="para" parents="5572 10492"/>
    </justification>
  </clause>

  <clause id="11478">
    <literal><![CDATA[
      L(x,y,a(z,u,L(y,y \ w,(y \ w) \ 1))) = L(x,a(z,u,(y \ w) * w),y)
    ]]></literal>
    <justification jstring="[para(5543(a,1),11477(a,2,2))].">
      <j1 rule="para" parents="5543 11477"/>
    </justification>
  </clause>

  <clause id="11479">
    <literal><![CDATA[
      L(x,y,a(z,u,(1 / (w / y)) * w)) = L(x,a(z,u,(y \ w) * w),y)
    ]]></literal>
    <justification jstring="[para(10491(a,1),11478(a,1,3,3))].">
      <j1 rule="para" parents="10491 11478"/>
    </justification>
  </clause>

  <clause id="11480">
    <literal><![CDATA[
      L(x,a(y,z,(u \ w) * w),u) = L(x,u,a(y,z,(w / u) * w))
    ]]></literal>
    <justification jstring="[para(5572(a,1),11479(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5572 11479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11481">
    <literal><![CDATA[
      L(x,a(y,z,(u \ w) * w),u) = L(x,u,a(y,z,(u \ w) * w))
    ]]></literal>
    <justification jstring="[para(5543(a,1),11480(a,2,3))].">
      <j1 rule="para" parents="5543 11480"/>
    </justification>
  </clause>

  <clause id="11482">
    <literal><![CDATA[
      L(x,(y \ (z * z)) \ ((y \ 1) * (u * (z * z))),w) = L(x,L(u,y \ 1,z * z),w)
    ]]></literal>
    <justification jstring="[para(32(a,1),10945(a,1,2,2))].">
      <j1 rule="para" parents="32 10945"/>
    </justification>
  </clause>

  <clause id="11483">
    <literal><![CDATA[
      a(x,y,L(z,u * ((w * w) \ (v5 * ((w * w) \ u))),v6)) = a(x,y,L(z,L(v5,u / (w * w),u / (w * w)),v6))
    ]]></literal>
    <justification jstring="[para(10970(a,1),11002(a,1,3))].">
      <j1 rule="para" parents="10970 11002"/>
    </justification>
  </clause>

  <clause id="11484">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ ((v5 * w) \ w)))) = a(x,y,z \ (u * (R(v5,w,w) \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6343,a(flip),b,11185,a),flip(a)].">
      <j1 rule="hyper" parents="63 6343 11185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11485">
    <literal><![CDATA[
      L(x,L(T(y,z * z),z * z,u \ 1),w) = L(x,L(y,u \ 1,z * z),w)
    ]]></literal>
    <justification jstring="[para(709(a,1),11482(a,1,2))].">
      <j1 rule="para" parents="709 11482"/>
    </justification>
  </clause>

  <clause id="11486">
    <literal><![CDATA[
      L(x,L(y,z \ 1,u * u),w) = L(x,L(y,u * u,z \ 1),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10810,a(flip),b,11485,a),flip(a)].">
      <j1 rule="hyper" parents="63 10810 11485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11488">
    <literal><![CDATA[
      L(x,L(y,z \ 1,u * u),w) = L(x,L(y,u * u,z),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10995,a(flip),b,11486,a),flip(a)].">
      <j1 rule="hyper" parents="316 10995 11486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11490">
    <literal><![CDATA[
      L(x,L(y,z * z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10985,a(flip),b,11488,a),flip(a)].">
      <j1 rule="hyper" parents="63 10985 11488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11492">
    <literal><![CDATA[
      L(x,y \ ((y \ 1) * z),u) = L(x,(y * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(486(a,1),11490(a,1,2))].">
      <j1 rule="para" parents="486 11490"/>
    </justification>
  </clause>

  <clause id="11493">
    <literal><![CDATA[
      L(x,(y * y) \ L((y \ 1) \ z,u,w),v5) = L(x,y \ (y * L(y \ z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(1350(a,1),11492(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1350 11492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11494">
    <literal><![CDATA[
      L(x,(y * y) \ L((y \ 1) \ z,u,w),v5) = L(x,L(y \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,7644,a(flip),b,11493,a),flip(a)].">
      <j1 rule="hyper" parents="316 7644 11493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11496">
    <literal><![CDATA[
      a(x,y,(z \ (K(u,w) * (v5 * (v6 \ u)))) * v7) = a(x,y,v7 * (z \ ((v6 \ T(u,w)) * v5)))
    ]]></literal>
    <justification jstring="[para(406(a,1),10268(a,1,3,1,2))].">
      <j1 rule="para" parents="406 10268"/>
    </justification>
  </clause>

  <clause id="11497">
    <literal><![CDATA[
      (x / T(y,z)) * L(K(y,z) * ((x / y) \ u),w,v5) = L(u / (x / y),w,v5) * (x / y)
    ]]></literal>
    <justification jstring="[para(4850(a,2),10269(a,1,2))].">
      <j1 rule="para" parents="4850 10269"/>
    </justification>
  </clause>

  <clause id="11498">
    <literal><![CDATA[
      (((x \ K(y,z)) * u) / (x \ 1)) * L(x \ 1,w,v5) = L(x \ K(y,z),w,v5) * u
    ]]></literal>
    <justification jstring="[hyper(316,a,10187,a(flip),b,10273,a),flip(a)].">
      <j1 rule="hyper" parents="316 10187 10273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11499">
    <literal><![CDATA[
      L(x \ K(y,z),u,w) * ((x \ K(y,z)) \ v5) = (v5 / (x \ 1)) * L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),11498(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11500">
    <literal><![CDATA[
      (x / (y \ K(z,u))) * L(y \ K(z,u),w,v5) = (x / (y \ 1)) * L(y \ 1,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,4325,a(flip),b,11499,a)].">
      <j1 rule="hyper" parents="63 4325 11499"/>
    </justification>
  </clause>

  <clause id="11501">
    <literal><![CDATA[
      K(x,y) * ((z / T(y,x)) \ (a(z / y,u,w) \ v5)) = a(y \ z,u,w) \ ((z / y) \ v5)
    ]]></literal>
    <justification jstring="[para(1813(a,1),10285(a,2,1))].">
      <j1 rule="para" parents="1813 10285"/>
    </justification>
  </clause>

  <clause id="11502">
    <literal><![CDATA[
      (x \ T(y,z)) * L(T((x \ y) \ y,K(y,z)),u,w) = L(x,u,w) * (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(3897(a,1),10300(a,1,2,1))].">
      <j1 rule="para" parents="3897 10300"/>
    </justification>
  </clause>

  <clause id="11503">
    <literal><![CDATA[
      (x \ y) * L(((x \ y) \ y) * K(y,z),u,w) = L(x,u,w) * (x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11046,a(flip),b,11502,a)].">
      <j1 rule="hyper" parents="63 11046 11502"/>
    </justification>
  </clause>

  <clause id="11504">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ T(y,z),u,w) = L(x,u,w) * (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(3846(a,1),11503(a,1,2,1))].">
      <j1 rule="para" parents="3846 11503"/>
    </justification>
  </clause>

  <clause id="11505">
    <literal><![CDATA[
      T((x \ y) * L((x \ y) \ y,z,u),w) = L(x,z,u) * (x \ T(y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,4881,a,b,11504,a)].">
      <j1 rule="hyper" parents="63 4881 11504"/>
    </justification>
  </clause>

  <clause id="11506">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ u),w) = L(x,y,z) * (x \ T(u,w))
    ]]></literal>
    <justification jstring="[para(604(a,1),11505(a,1,1))].">
      <j1 rule="para" parents="604 11505"/>
    </justification>
  </clause>

  <clause id="11507">
    <literal><![CDATA[
      x * (L(x,y,z) \ T(L(x,y,z) * (x \ u),w)) = T(u,w)
    ]]></literal>
    <justification jstring="[para(11506(a,2),75(a,1,2,2))].">
      <j1 rule="para" parents="11506 75"/>
    </justification>
  </clause>

  <clause id="11508">
    <literal><![CDATA[
      L(x,y,z) * (x \ T(x * (L(x,y,z) \ u),w)) = T(u,w)
    ]]></literal>
    <justification jstring="[para(75(a,1),11506(a,1,1)),flip(a)].">
      <j1 rule="para" parents="75 11506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11509">
    <literal><![CDATA[
      x * K(x,y) = z * (L(z,u,w) \ T(L(z,u,w) * (z \ x),y))
    ]]></literal>
    <justification jstring="[hyper(316,a,2815,a(flip),b,11507,a)].">
      <j1 rule="hyper" parents="316 2815 11507"/>
    </justification>
  </clause>

  <clause id="11510">
    <literal><![CDATA[
      T((x \ L(x,y,z)) * u,w) = (x \ L(x,y,z)) * T(u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,11507,a(flip),b,9557,a),flip(a)].">
      <j1 rule="hyper" parents="139 11507 9557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11511">
    <literal><![CDATA[
      T((L(x,y,z) \ x) \ u,w) = (L(x,y,z) \ x) \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,11507,a(flip),b,2113,a),flip(a)].">
      <j1 rule="hyper" parents="133 11507 2113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11512">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ u),w) = x * (L(x,y,z) \ T(u,w))
    ]]></literal>
    <justification jstring="[para(75(a,1),11507(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="75 11507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11513">
    <literal><![CDATA[
      T((x \ L(x,y,z)) * u,w) = T(u,w) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(11507(a,1),9556(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11507 9556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11514">
    <literal><![CDATA[
      x * K(y * (L(y,z,u) \ x),w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3926,a,b,11508,a)].">
      <j1 rule="hyper" parents="63 3926 11508"/>
    </justification>
  </clause>

  <clause id="11515">
    <literal><![CDATA[
      T((x \ L(x,y,z)) \ u,w) = (x \ L(x,y,z)) \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,11508,a(flip),b,2111,a),flip(a)].">
      <j1 rule="hyper" parents="133 11508 2111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11516">
    <literal><![CDATA[
      T(x * (L(y,z,u) \ y),w) = (L(y,z,u) \ y) * T(x,w)
    ]]></literal>
    <justification jstring="[para(11508(a,1),7845(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11508 7845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11517">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ (((L(x,y,z) \ x) * u) * w) = w * T(u,w)
    ]]></literal>
    <justification jstring="[para(11514(a,1),9078(a,2,2))].">
      <j1 rule="para" parents="11514 9078"/>
    </justification>
  </clause>

  <clause id="11518">
    <literal><![CDATA[
      T(x * (y \ L(y,z,u)),w) = (y \ L(y,z,u)) * T(x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5062,a(flip),b,11510,a)].">
      <j1 rule="hyper" parents="63 5062 11510"/>
    </justification>
  </clause>

  <clause id="11519">
    <literal><![CDATA[
      T(x \ (L(y,z,u) \ y),x) = ((x \ 1) \ 1) \ (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(38,a,1159,a(flip),b,11511,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 1159 11511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11520">
    <literal><![CDATA[
      T((L(x,y,z) \ x) \ (u / w),w) = (L(x,y,z) \ x) \ (w \ u)
    ]]></literal>
    <justification jstring="[para(116(a,1),11511(a,2,2))].">
      <j1 rule="para" parents="116 11511"/>
    </justification>
  </clause>

  <clause id="11521">
    <literal><![CDATA[
      T((x \ y) * (L(x \ y,z,u) \ x),w) = L(y / T(x,w),z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(316,a,10615,a(flip),b,11512,a),flip(a)].">
      <j1 rule="hyper" parents="316 10615 11512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11525">
    <literal><![CDATA[
      T(x * (y \ L(y,z,u)),w) = T(x,w) * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5062,a(flip),b,11513,a)].">
      <j1 rule="hyper" parents="63 5062 11513"/>
    </justification>
  </clause>

  <clause id="11526">
    <literal><![CDATA[
      (x \ 1) * T((x \ L(x,y,z)) * u,x \ 1) = (x \ L(x,y,z)) * (u * (x \ 1))
    ]]></literal>
    <justification jstring="[para(11513(a,2),6308(a,1,2))].">
      <j1 rule="para" parents="11513 6308"/>
    </justification>
  </clause>

  <clause id="11528">
    <literal><![CDATA[
      T((x \ L(x,y,z)) \ (u / w),w) = (x \ L(x,y,z)) \ (w \ u)
    ]]></literal>
    <justification jstring="[para(116(a,1),11515(a,2,2))].">
      <j1 rule="para" parents="116 11515"/>
    </justification>
  </clause>

  <clause id="11530">
    <literal><![CDATA[
      T((L(x,y,z) \ x) * u,w) = (L(x,y,z) \ x) * T(u,w)
    ]]></literal>
    <justification jstring="[para(6496(a,2),11516(a,1,1))].">
      <j1 rule="para" parents="6496 11516"/>
    </justification>
  </clause>

  <clause id="11534">
    <literal><![CDATA[
      L(x,y,z) * T(u * (x \ L(x,w,v5)),x) = (x \ L(x,w,v5)) * (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(11525(a,2),9325(a,1,2))].">
      <j1 rule="para" parents="11525 9325"/>
    </justification>
  </clause>

  <clause id="11535">
    <literal><![CDATA[
      (x * ((L(y,z,u) \ y) * w)) / T((L(y,z,u) \ y) * x,w) = R(w,L(y,z,u) \ y,T(x,w))
    ]]></literal>
    <justification jstring="[para(11530(a,2),8361(a,1,2))].">
      <j1 rule="para" parents="11530 8361"/>
    </justification>
  </clause>

  <clause id="11537">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(34,a,9558,a,b,11509,a)].">
      <j1 rule="hyper" parents="34 9558 11509"/>
    </justification>
  </clause>

  <clause id="11538">
    <literal><![CDATA[
      K(L(x,y,z) * (x \ u),w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(34,a,3926,a,b,11509,a)].">
      <j1 rule="hyper" parents="34 3926 11509"/>
    </justification>
  </clause>

  <clause id="11539">
    <literal><![CDATA[
      K(x \ (y \ L(y,z,u)),w) = K(x \ 1,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3520,a(flip),b,11537,a)].">
      <j1 rule="hyper" parents="63 3520 11537"/>
    </justification>
  </clause>

  <clause id="11540">
    <literal><![CDATA[
      (K(x,y) * x) * (L(z,u,w) * L(z \ 1,v5,v6)) = T(x * (L(z,u,w) * L(z \ 1,v5,v6)),y)
    ]]></literal>
    <justification jstring="[para(11537(a,1),7067(a,1,1,1))].">
      <j1 rule="para" parents="11537 7067"/>
    </justification>
  </clause>

  <clause id="11542">
    <literal><![CDATA[
      K(L(x,y,z) * u,w) = K(x * u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),11538(a,1,1,2))].">
      <j1 rule="para" parents="9 11538"/>
    </justification>
  </clause>

  <clause id="11544">
    <literal><![CDATA[
      (x \ K(x * y,x \ 1)) \ (y * (x \ L(x,z,u))) = (y * (x \ L(x,z,u))) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(11542(a,1),5141(a,1,1,2))].">
      <j1 rule="para" parents="11542 5141"/>
    </justification>
  </clause>

  <clause id="11545">
    <literal><![CDATA[
      ((x \ (y \ L(y,z,u))) * x) * y = L(y * K(x \ 1,x),z,u)
    ]]></literal>
    <justification jstring="[para(11539(a,1),7267(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11539 7267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11547">
    <literal><![CDATA[
      (((L(x,y,z) \ x) / u) \ 1) \ 1 = u \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(39,a,3171,a(flip),b,11519,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 3171 11519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11548">
    <literal><![CDATA[
      (L(x,y,z) \ x) / (u \ 1) = (1 / u) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(38,a,2525,a(flip),b,11520,a(flip))].">
      <j1 rule="hyper" parents="38 2525 11520"/>
    </justification>
  </clause>

  <clause id="11549">
    <literal><![CDATA[
      1 / ((L(x,y,z) \ x) \ (u \ 1)) = ((L(x,y,z) \ x) \ (1 / u)) \ 1
    ]]></literal>
    <justification jstring="[para(11520(a,1),8365(a,1,2))].">
      <j1 rule="para" parents="11520 8365"/>
    </justification>
  </clause>

  <clause id="11550">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * ((1 / u) \ 1)) * ((1 / u) * ((L(x,y,z) \ x) \ ((1 / u) \ (L(x,y,z) \ x)))) = (L(x,y,z) \ x) / (u \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,7696,a,b,11548,a)].">
      <j1 rule="hyper" parents="316 7696 11548"/>
    </justification>
  </clause>

  <clause id="11551">
    <literal><![CDATA[
      (L(x,y,z) \ u) * a(x,x \ L(x,y,z),u) = (x \ L(x,y,z)) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8912,a,b,11528,a)].">
      <j1 rule="hyper" parents="63 8912 11528"/>
    </justification>
  </clause>

  <clause id="11552">
    <literal><![CDATA[
      x \ (((x \ (y \ L(y,z,u))) \ L(y * K(x \ 1,x),z,u)) / y) = a(x \ (y \ L(y,z,u)),x,y)
    ]]></literal>
    <justification jstring="[para(11545(a,1),8476(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11545 8476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11554">
    <literal><![CDATA[
      T(L(x / y,z,u) \ x,w) = L(x / T(y,w),z,u) \ x
    ]]></literal>
    <justification jstring="[para(6574(a,1),11521(a,1,1))].">
      <j1 rule="para" parents="6574 11521"/>
    </justification>
  </clause>

  <clause id="11555">
    <literal><![CDATA[
      T(x * y,z) \ T(L(T(u,w) / (x * y),v5,v6) \ T(u,w),z) = T(x * (y * L(y \ (x \ u),v5,v6)),w) \ T(u,w)
    ]]></literal>
    <justification jstring="[para(11554(a,2),9204(a,1,2))].">
      <j1 rule="para" parents="11554 9204"/>
    </justification>
  </clause>

  <clause id="11556">
    <literal><![CDATA[
      T(x,y) \ T(L(z / x,u,w) \ z,y) = x \ (L(z / x,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(11554(a,2),10616(a,1,2))].">
      <j1 rule="para" parents="11554 10616"/>
    </justification>
  </clause>

  <clause id="11557">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ (((L(x,y,z) \ x) * u) * w) = u * w
    ]]></literal>
    <justification jstring="[hyper(316,a,114,a(flip),b,11517,a),flip(a)].">
      <j1 rule="hyper" parents="316 114 11517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11558">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * (u * w) = ((L(x,y,z) \ x) * u) * w
    ]]></literal>
    <justification jstring="[hyper(139,a,114,a(flip),b,11517,a)].">
      <j1 rule="hyper" parents="139 114 11517"/>
    </justification>
  </clause>

  <clause id="11560">
    <literal><![CDATA[
      R(L(x,y,z) \ x,u,w) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(39,a,199,a,b,11557,a)].">
      <j1 rule="hyper" parents="39 199 11557"/>
    </justification>
  </clause>

  <clause id="11563">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,(w \ 1) \ v5) = R(L(x,y,z) \ x,u,w \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,4789,a(flip),b,11560,a),flip(a)].">
      <j1 rule="hyper" parents="63 4789 11560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11564">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),L(x,y,z),z * y) = R(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(11560(a,1),1563(a,1,1))].">
      <j1 rule="para" parents="11560 1563"/>
    </justification>
  </clause>

  <clause id="11565">
    <literal><![CDATA[
      L(L(x \ (y \ x),z,u) \ (x \ (y \ x)),w,v5) = R((x \ (L(y,z,u) * (y \ x))) \ 1,w,v5)
    ]]></literal>
    <justification jstring="[para(1907(a,1),11560(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1907 11560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11566">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ L(L(x,y,z) \ x,u,w),L(x,y,z) \ x,u * w) = a(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(11560(a,1),3422(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11560 3422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11567">
    <literal><![CDATA[
      (x * y) * L(L(z,u,w) \ z,y,x) = ((L(z,u,w) \ z) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(11560(a,1),6643(a,1,2))].">
      <j1 rule="para" parents="11560 6643"/>
    </justification>
  </clause>

  <clause id="11570">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x \ 1,x \ u) * u = (L(x,y,z) \ 1) * ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(11560(a,1),7818(a,1,1))].">
      <j1 rule="para" parents="11560 7818"/>
    </justification>
  </clause>

  <clause id="11571">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(x,y,z) \ u) \ u = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(11560(a,1),8279(a,1,1))].">
      <j1 rule="para" parents="11560 8279"/>
    </justification>
  </clause>

  <clause id="11572">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x \ 1,L(x,y,z) \ u) \ u = (x \ 1) * ((L(x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(11560(a,1),8280(a,1,1))].">
      <j1 rule="para" parents="11560 8280"/>
    </justification>
  </clause>

  <clause id="11573">
    <literal><![CDATA[
      x * (y * L(L(x,z,u) \ x,x,y)) = (x * (L(x,z,u) \ x)) * y
    ]]></literal>
    <justification jstring="[para(11560(a,1),9027(a,1,2,2))].">
      <j1 rule="para" parents="11560 9027"/>
    </justification>
  </clause>

  <clause id="11574">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * x = (L(x,y,z) \ x) * (u * x)
    ]]></literal>
    <justification jstring="[para(5160(a,1),11558(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5160 11558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11582">
    <literal><![CDATA[
      x * (L(L(x,y,z) \ x,x,u) * u) = (x * (L(x,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,6529,a,b,11573,a)].">
      <j1 rule="hyper" parents="63 6529 11573"/>
    </justification>
  </clause>

  <clause id="11583">
    <literal><![CDATA[
      (x \ 1) * (L(L(x,y,z) \ x,x \ 1,u) * u) = ((x \ 1) * (L(x \ 1,y,z) \ (x \ 1))) * u
    ]]></literal>
    <justification jstring="[para(7090(a,1),11582(a,1,2,1,1))].">
      <j1 rule="para" parents="7090 11582"/>
    </justification>
  </clause>

  <clause id="11584">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,(w \ 1) \ v5) = L(L(x,y,z) \ x,u,w \ v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,11560,a(flip),b,11563,a),flip(a)].">
      <j1 rule="hyper" parents="316 11560 11563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11585">
    <literal><![CDATA[
      L((x * (y * z)) \ ((x * y) * z),u,w) = R(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,897,a(flip),b,11564,a)].">
      <j1 rule="hyper" parents="63 897 11564"/>
    </justification>
  </clause>

  <clause id="11586">
    <literal><![CDATA[
      R(a(x,y,z),u,w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14(a,2),11585(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14 11585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11587">
    <literal><![CDATA[
      x \ R(a(y,z,u),x,x) = a(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,11586,a,b,2459,a)].">
      <j1 rule="hyper" parents="133 11586 2459"/>
    </justification>
  </clause>

  <clause id="11588">
    <literal><![CDATA[
      T((x * y) * ((x / (y \ 1)) \ 1),x * y) = L(a(x,y,y),(y \ 1) \ x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10748,a,b,11586,a)].">
      <j1 rule="hyper" parents="63 10748 11586"/>
    </justification>
  </clause>

  <clause id="11589">
    <literal><![CDATA[
      (L(x,y,y) * (a(y,y,x) \ z)) \ (x * (a(y,y,x) \ z)) = L(a(y,y,x),L(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8066,a,b,11586,a)].">
      <j1 rule="hyper" parents="63 8066 11586"/>
    </justification>
  </clause>

  <clause id="11590">
    <literal><![CDATA[
      (1 / x) * (a(y,z,u) * x) = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5366,a,b,11586,a)].">
      <j1 rule="hyper" parents="63 5366 11586"/>
    </justification>
  </clause>

  <clause id="11591">
    <literal><![CDATA[
      L(a(x,y,z),u,w \ ((v5 \ 1) \ v6)) = R(a(x,y,z),u,w \ (v5 \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,6716,a(flip),b,11586,a),flip(a)].">
      <j1 rule="hyper" parents="63 6716 11586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11592">
    <literal><![CDATA[
      L(a(x,y,z),u,(w \ 1) * v5) = R(a(x,y,z),u,v5 * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,4707,a(flip),b,11586,a),flip(a)].">
      <j1 rule="hyper" parents="63 4707 11586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11593">
    <literal><![CDATA[
      L(a(x,y,z),u,L(w \ 1,v5,v6)) = R(a(x,y,z),u,L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,1713,a(flip),b,11586,a),flip(a)].">
      <j1 rule="hyper" parents="63 1713 11586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11594">
    <literal><![CDATA[
      L(a(x,y,z),u,w * (v5 \ 1)) = R(a(x,y,z),u,w * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,1711,a(flip),b,11586,a),flip(a)].">
      <j1 rule="hyper" parents="63 1711 11586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11595">
    <literal><![CDATA[
      L(a(x,y,z),u,w * (v5 * v5)) = R(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1701,a(flip),b,11586,a),flip(a)].">
      <j1 rule="hyper" parents="63 1701 11586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11596">
    <literal><![CDATA[
      L(a(x,y,z),u,w \ 1) = R(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1033,a(flip),b,11586,a),flip(a)].">
      <j1 rule="hyper" parents="63 1033 11586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11597">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (u * w) = (u * a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(138,a,11586,a(flip),b,2335,a)].">
      <j1 rule="hyper" parents="138 11586 2335"/>
    </justification>
  </clause>

  <clause id="11599">
    <literal><![CDATA[
      L(a(x,y,z),u,(a(x,y,z) * u) \ w) \ w = u * ((a(x,y,z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(11586(a,1),348(a,1,1))].">
      <j1 rule="para" parents="11586 348"/>
    </justification>
  </clause>

  <clause id="11600">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ L(L(a(x,y,z),v5,v5),u,w) = a(L(a(x,y,z),u,w),v5,v5)
    ]]></literal>
    <justification jstring="[para(11586(a,1),2384(a,1,2,1))].">
      <j1 rule="para" parents="11586 2384"/>
    </justification>
  </clause>

  <clause id="11601">
    <literal><![CDATA[
      L(a(x,y,z) \ L(a(x,y,z),u,w),a(x,y,z),w * u) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(11586(a,1),3424(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11586 3424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11602">
    <literal><![CDATA[
      L(a(x,y,z),u \ 1,(a(x,y,z) * u) \ w) \ w = (u \ 1) * ((a(x,y,z) * (u \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(11586(a,1),4833(a,1,1))].">
      <j1 rule="para" parents="11586 4833"/>
    </justification>
  </clause>

  <clause id="11603">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(a(u,w,v5),x,L(x,y,z)) = (a(u,w,v5) * L(x,y,z)) * T(1 / x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(11586(a,1),9498(a,1,2))].">
      <j1 rule="para" parents="11586 9498"/>
    </justification>
  </clause>

  <clause id="11604">
    <literal><![CDATA[
      L(a(x,y,z),u,w \ 1) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,11586,a(flip),b,11596,a),flip(a)].">
      <j1 rule="hyper" parents="316 11586 11596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11606">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ a(y,z,u) = a(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,7169,a,b,11587,a)].">
      <j1 rule="hyper" parents="63 7169 11587"/>
    </justification>
  </clause>

  <clause id="11607">
    <literal><![CDATA[
      L(a(x,y,z),u,w * (v5 * v5)) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,11586,a(flip),b,11595,a),flip(a)].">
      <j1 rule="hyper" parents="316 11586 11595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11608">
    <literal><![CDATA[
      L(a(x,y,z),u,w * a(v5,v5,w)) = L(a(x,y,z),u,v5 \ (v5 \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8623,a(flip),b,11607,a)].">
      <j1 rule="hyper" parents="63 8623 11607"/>
    </justification>
  </clause>

  <clause id="11609">
    <literal><![CDATA[
      x * (y * L(a(z,u,x),x,y)) = (x * a(z,u,x)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,6947,a(flip),b,11597,a)].">
      <j1 rule="hyper" parents="63 6947 11597"/>
    </justification>
  </clause>

  <clause id="11610">
    <literal><![CDATA[
      x \ (y \ ((y * a(z,u,y)) * x)) = L(a(z,u,y),y,x)
    ]]></literal>
    <justification jstring="[para(11609(a,1),69(a,1,2,2))].">
      <j1 rule="para" parents="11609 69"/>
    </justification>
  </clause>

  <clause id="11611">
    <literal><![CDATA[
      a(x,y,z) * a(z,a(x,y,z),u) = L(a(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8450,a(flip),b,11610,a)].">
      <j1 rule="hyper" parents="63 8450 11610"/>
    </justification>
  </clause>

  <clause id="11612">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),z,u) = a(z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(133,a,11610,a(flip),b,8450,a(flip))].">
      <j1 rule="hyper" parents="133 11610 8450"/>
    </justification>
  </clause>

  <clause id="11613">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),z,u) = a(z,a(x,y,z),z \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,9118,a(flip),b,11611,a)].">
      <j1 rule="hyper" parents="133 9118 11611"/>
    </justification>
  </clause>

  <clause id="11614">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ 1,z,u) = a(z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1064,a,b,11612,a)].">
      <j1 rule="hyper" parents="63 1064 11612"/>
    </justification>
  </clause>

  <clause id="11615">
    <literal><![CDATA[
      a(x,y,z) \ a(z,a(x,y,z),u) = L(a(x,y,z) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,11612,a(flip),b,1064,a)].">
      <j1 rule="hyper" parents="133 11612 1064"/>
    </justification>
  </clause>

  <clause id="11617">
    <literal><![CDATA[
      L(a(x,y,z),u,(w \ 1) * v5) = L(a(x,y,z),u,v5 * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,11586,a(flip),b,11592,a),flip(a)].">
      <j1 rule="hyper" parents="316 11586 11592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11618">
    <literal><![CDATA[
      L(a(x,y,z),u,w * (v5 \ 1)) = L(a(x,y,z),u,w * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,11586,a(flip),b,11594,a),flip(a)].">
      <j1 rule="hyper" parents="316 11586 11594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11619">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) \ a(z,y,y) = a(z,y,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(7768(a,1),11606(a,1,1))].">
      <j1 rule="para" parents="7768 11606"/>
    </justification>
  </clause>

  <clause id="11620">
    <literal><![CDATA[
      L(x,x,a(y,z,z)) \ a(z,z,y) = a(z,z,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(7768(a,2),11606(a,1,1))].">
      <j1 rule="para" parents="7768 11606"/>
    </justification>
  </clause>

  <clause id="11621">
    <literal><![CDATA[
      L(a(x,y,z),u,w * a(v5,v5,w)) = L(a(x,y,z),u,L(w,v5,v5))
    ]]></literal>
    <justification jstring="[para(5093(a,1),11618(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5093 11618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11622">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) \ a(z,y,y) = (x \ 1) * a(z,y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2290,a(flip),b,11619,a),flip(a)].">
      <j1 rule="hyper" parents="316 2290 11619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11623">
    <literal><![CDATA[
      a(x,a(y,z,x),x \ u) = a(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11612,a(flip),b,11613,a),flip(a)].">
      <j1 rule="hyper" parents="63 11612 11613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11624">
    <literal><![CDATA[
      a(a(x,y,z),z,z \ u) = a(z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,7009,a,b,11623,a)].">
      <j1 rule="hyper" parents="63 7009 11623"/>
    </justification>
  </clause>

  <clause id="11625">
    <literal><![CDATA[
      a(x,y,z) * (z \ L(z,y,x)) = a(z,a(x,y,z),y)
    ]]></literal>
    <justification jstring="[para(9997(a,1),11614(a,1,2))].">
      <j1 rule="para" parents="9997 11614"/>
    </justification>
  </clause>

  <clause id="11626">
    <literal><![CDATA[
      L(x,y,z) * (x \ a(z,y,x)) = a(x,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6999,a,b,11625,a)].">
      <j1 rule="hyper" parents="63 6999 11625"/>
    </justification>
  </clause>

  <clause id="11627">
    <literal><![CDATA[
      x * (L(x,y,z) \ a(x,a(z,y,x),y)) = a(z,y,x)
    ]]></literal>
    <justification jstring="[para(11626(a,1),75(a,1,2,2))].">
      <j1 rule="para" parents="11626 75"/>
    </justification>
  </clause>

  <clause id="11628">
    <literal><![CDATA[
      L(x,y,z) \ L(x,a(z,y,x),y) = a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9470,a(flip),b,11627,a)].">
      <j1 rule="hyper" parents="63 9470 11627"/>
    </justification>
  </clause>

  <clause id="11629">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,x) = L(x,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(139,a,11627,a(flip),b,9470,a(flip))].">
      <j1 rule="hyper" parents="139 11627 9470"/>
    </justification>
  </clause>

  <clause id="11630">
    <literal><![CDATA[
      a(x,y,z) * L(z,y,x) = L(z,a(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,11628,a)].">
      <j1 rule="hyper" parents="38 2295 11628"/>
    </justification>
  </clause>

  <clause id="11631">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,a(z,y,L(x,y,z) \ 1),y) = (x \ 1) * a(z,y,L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(9873(a,1),11629(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9873 11629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11632">
    <literal><![CDATA[
      L(x,a(y,z,x),z) \ L(x,z,y) = a(y,z,x) \ 1
    ]]></literal>
    <justification jstring="[para(11630(a,1),6983(a,1,1))].">
      <j1 rule="para" parents="11630 6983"/>
    </justification>
  </clause>

  <clause id="11633">
    <literal><![CDATA[
      L(x,a(y,a(z,u,y),x),a(z,u,y)) \ L(x,a(z,u,y),y) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,9447,a(flip),b,11632,a),flip(a)].">
      <j1 rule="hyper" parents="316 9447 11632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11634">
    <literal><![CDATA[
      L(x,a(y,a(y,z,u),x),a(y,z,u)) \ L(x,y,a(y,z,u)) = a(y,a(y,z,u),x) \ 1
    ]]></literal>
    <justification jstring="[para(8660(a,1),11632(a,1,2))].">
      <j1 rule="para" parents="8660 11632"/>
    </justification>
  </clause>

  <clause id="11635">
    <literal><![CDATA[
      L(a(x,y,z),u,L(w \ 1,v5,v6)) = L(a(x,y,z),u,L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,11586,a(flip),b,11593,a),flip(a)].">
      <j1 rule="hyper" parents="316 11586 11593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11636">
    <literal><![CDATA[
      L(a(x,y,z),z,L(u,u,z)) = L(a(x,y,z),z,z / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9127,a(flip),b,11635,a),flip(a)].">
      <j1 rule="hyper" parents="63 9127 11635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11637">
    <literal><![CDATA[
      L(a(x,y,z),z,L(u,u,z)) = L(a(x,y,z),z,u \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1586,a(flip),b,11636,a),flip(a)].">
      <j1 rule="hyper" parents="316 1586 11636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11638">
    <literal><![CDATA[
      L(a(x,y,z),u,w \ (w \ v5)) = L(a(x,y,z),u,L(v5,w,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,11621,a(flip),b,11608,a),flip(a)].">
      <j1 rule="hyper" parents="63 11621 11608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11639">
    <literal><![CDATA[
      L(a(x,y,z \ u),z \ u,L(u,z,z)) = L(a(x,y,z \ u),z \ u,u \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9119,a,b,11638,a),flip(a)].">
      <j1 rule="hyper" parents="63 9119 11638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11640">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(u,u,x)) = L(L(x,y,z) \ x,x,u \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9095,a,b,11584,a)].">
      <j1 rule="hyper" parents="63 9095 11584"/>
    </justification>
  </clause>

  <clause id="11641">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u \ x) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10073,a(flip),b,11640,a),flip(a)].">
      <j1 rule="hyper" parents="63 10073 11640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11643">
    <literal><![CDATA[
      L(a(x,y,z),u,w \ ((v5 \ 1) \ v6)) = L(a(x,y,z),u,w \ (v5 \ v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,11586,a(flip),b,11591,a),flip(a)].">
      <j1 rule="hyper" parents="316 11586 11591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11644">
    <literal><![CDATA[
      L(a(x,y,z),u,R(w,w,(v5 \ 1) \ v6) \ (v5 \ v6)) = L(a(x,y,z),u,((v5 \ 1) \ v6) * (w \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,4659,a(flip),b,11643,a),flip(a)].">
      <j1 rule="hyper" parents="63 4659 11643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11645">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * T(w,u) = w * (u * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,100,a(flip),b,11567,a),flip(a)].">
      <j1 rule="hyper" parents="63 100 11567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11646">
    <literal><![CDATA[
      L(x * a(L(y,z,u) \ y,x,w),w,L(y,z,u) \ y) = ((L(y,z,u) \ y) * w) \ (w * (x * (L(y,z,u) \ y)))
    ]]></literal>
    <justification jstring="[para(11645(a,1),8578(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11645 8578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11649">
    <literal><![CDATA[
      (L(x,y,z) \ u) * a(x,x \ L(x,y,z),u) = x \ ((x \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,1501,a(flip),b,11551,a),flip(a)].">
      <j1 rule="hyper" parents="316 1501 11551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11650">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((u * x) * (x \ 1)) = R(u * (x \ L(x,y,z)),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6155,a(flip),b,11526,a),flip(a)].">
      <j1 rule="hyper" parents="63 6155 11526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11651">
    <literal><![CDATA[
      R(x * (y \ L(y,z,u)),y,y) = (y \ L(y,z,u)) * R(x,y,y)
    ]]></literal>
    <justification jstring="[para(565(a,1),11650(a,1,2)),flip(a)].">
      <j1 rule="para" parents="565 11650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11652">
    <literal><![CDATA[
      R(x * (y \ L(y,z,u)),y,y) = R(x,y,y) * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5027,a,b,11651,a),flip(a)].">
      <j1 rule="hyper" parents="316 5027 11651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11653">
    <literal><![CDATA[
      R(x * (y \ L(y,y,x)),y,y) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,7661,a(flip),b,11652,a),flip(a)].">
      <j1 rule="hyper" parents="316 7661 11652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11654">
    <literal><![CDATA[
      R(a(x,y,y) \ x,y,y) = x
    ]]></literal>
    <justification jstring="[para(8430(a,1),11653(a,1,1))].">
      <j1 rule="para" parents="8430 11653"/>
    </justification>
  </clause>

  <clause id="11655">
    <literal><![CDATA[
      a(T(x,y),y,y) \ T(x,y) = y \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(42,a,626,a(flip),b,11654,a),flip(a)].">
      <j1 rule="hyper" parents="42 626 11654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11656">
    <literal><![CDATA[
      a(x,y,y) \ T(x,y) = y \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(1810(a,1),11655(a,1,1))].">
      <j1 rule="para" parents="1810 11655"/>
    </justification>
  </clause>

  <clause id="11657">
    <literal><![CDATA[
      T(a(x,y,y) \ x,y) = y \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,5316,a,b,11656,a)].">
      <j1 rule="hyper" parents="63 5316 11656"/>
    </justification>
  </clause>

  <clause id="11659">
    <literal><![CDATA[
      a(x,y,z \ (u \ (a(w,v5,v5) \ w))) = a(x,y,z \ (u \ (v5 \ (w / (v5 \ 1)))))
    ]]></literal>
    <justification jstring="[para(11656(a,1),5604(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="11656 5604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11660">
    <literal><![CDATA[
      T(a(x,L(y,z,u),L(y,z,u)) \ x,y) = L(y,z,u) \ (x / (L(y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(4305,a,11657,a)].">
      <j1 rule="hyper" parents="4305 11657"/>
    </justification>
  </clause>

  <clause id="11661">
    <literal><![CDATA[
      T(a(x,R(y,z,u),R(y,z,u)) \ x,R(y,z,u)) = K(y,w) * (R(T(y,w),z,u) \ (x / (R(y,z,u) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(316,a,3410,a,b,11657,a),flip(a)].">
      <j1 rule="hyper" parents="316 3410 11657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11662">
    <literal><![CDATA[
      a(x,y,z \ (u \ (a(w,v5,v5) \ w))) = a(x,y,z \ (u \ (v5 \ ((v5 \ 1) \ w))))
    ]]></literal>
    <justification jstring="[hyper(316,a,5920,a(flip),b,11659,a),flip(a)].">
      <j1 rule="hyper" parents="316 5920 11659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11663">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ a(w,v5,v5)))) = a(x,y,z \ (u \ (v5 \ ((v5 \ 1) \ w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,8854,a(flip),b,11662,a)].">
      <j1 rule="hyper" parents="63 8854 11662"/>
    </justification>
  </clause>

  <clause id="11664">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ ((w \ 1) \ v5)))) = a(x,y,z \ (u \ (v5 * a(v5,w,w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,7204,a(flip),b,11663,a),flip(a)].">
      <j1 rule="hyper" parents="63 7204 11663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11665">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ ((w \ 1) \ v5)))) = a(x,y,z \ (u \ R(v5,w,w)))
    ]]></literal>
    <justification jstring="[para(2381(a,1),11664(a,2,3,2,2))].">
      <j1 rule="para" parents="2381 11664"/>
    </justification>
  </clause>

  <clause id="11666">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * L(y,w,v5) = (y \ L(y,z,u)) * (x * L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,4313,a(flip),b,11534,a)].">
      <j1 rule="hyper" parents="63 4313 11534"/>
    </justification>
  </clause>

  <clause id="11667">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * L(x,w,v5))) / (L(x,w,v5) * (x \ L(x,y,z))) = R(u * K(x \ L(x,y,z),L(x,w,v5)),x \ L(x,y,z),L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(11666(a,1),4488(a,1,1))].">
      <j1 rule="para" parents="11666 4488"/>
    </justification>
  </clause>

  <clause id="11668">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) \ u = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(10094(a,1),11571(a,1,1))].">
      <j1 rule="para" parents="10094 11571"/>
    </justification>
  </clause>

  <clause id="11669">
    <literal><![CDATA[
      T((x * y) * ((x / (y \ 1)) \ 1),x * y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,8224,a(flip),b,11588,a),flip(a)].">
      <j1 rule="hyper" parents="316 8224 11588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11671">
    <literal><![CDATA[
      (x * y) \ a(x,y,y) = (x / (y \ 1)) \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,11669,a(flip),b,7544,a(flip))].">
      <j1 rule="hyper" parents="133 11669 7544"/>
    </justification>
  </clause>

  <clause id="11672">
    <literal><![CDATA[
      R(x,y,(z * u) \ a(z,u,u)) = R(x,y,z / (u \ 1))
    ]]></literal>
    <justification jstring="[para(11671(a,2),1033(a,1,3))].">
      <j1 rule="para" parents="11671 1033"/>
    </justification>
  </clause>

  <clause id="11673">
    <literal><![CDATA[
      R(x,y,(z * u) \ a(z,u,u)) = R(x,y,(u \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,4680,a(flip),b,11672,a),flip(a)].">
      <j1 rule="hyper" parents="316 4680 11672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11674">
    <literal><![CDATA[
      R(x,y,(z * u) \ a(z,u,u)) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,4789,a(flip),b,11673,a),flip(a)].">
      <j1 rule="hyper" parents="316 4789 11673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11675">
    <literal><![CDATA[
      R(x,y,R(z,u,u) * u) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7411,a(flip),b,11674,a)].">
      <j1 rule="hyper" parents="63 7411 11674"/>
    </justification>
  </clause>

  <clause id="11676">
    <literal><![CDATA[
      R(x,y,L(z * u,u,u)) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4805,a,b,11675,a)].">
      <j1 rule="hyper" parents="63 4805 11675"/>
    </justification>
  </clause>

  <clause id="11677">
    <literal><![CDATA[
      R(x,y,z \ (z \ u)) = R(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4806,a(flip),b,11675,a),flip(a)].">
      <j1 rule="hyper" parents="63 4806 11675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11678">
    <literal><![CDATA[
      R(x,y,L(z * u,z,z)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),11677(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 11677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11679">
    <literal><![CDATA[
      a(x,y,z \ (R(u,u,L(w,v5,v5)) \ (v5 \ (v5 \ w)))) = a(x,y,z \ (u * (v5 \ (v5 \ w))))
    ]]></literal>
    <justification jstring="[para(11677(a,1),6349(a,1,3,2,1))].">
      <j1 rule="para" parents="11677 6349"/>
    </justification>
  </clause>

  <clause id="11680">
    <literal><![CDATA[
      a(x,L(y * z,y,y),y \ z) * x = R(x,L(y * z,y,y),y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8607,a(flip),b,11678,a)].">
      <j1 rule="hyper" parents="63 8607 11678"/>
    </justification>
  </clause>

  <clause id="11681">
    <literal><![CDATA[
      R(x * K(y * z,x),L(y * z,y,y),y \ z) = (L(y * z,y,y) * x) * (L(y * z,y,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,4288,a(flip),b,11678,a),flip(a)].">
      <j1 rule="hyper" parents="63 4288 11678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11682">
    <literal><![CDATA[
      a(x,x,L(a(y,z,u),w,v5)) \ 1 = a(L(a(y,z,u),w,v5),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5090,a(flip),b,11600,a)].">
      <j1 rule="hyper" parents="63 5090 11600"/>
    </justification>
  </clause>

  <clause id="11683">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v5) \ 1 = a(v5,v5,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,11682,a)].">
      <j1 rule="hyper" parents="39 2301 11682"/>
    </justification>
  </clause>

  <clause id="11684">
    <literal><![CDATA[
      x \ L(x,x,L(a(y,z,u),w,v5)) = a(x,x,L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,7304,a(flip),b,11683,a)].">
      <j1 rule="hyper" parents="63 7304 11683"/>
    </justification>
  </clause>

  <clause id="11685">
    <literal><![CDATA[
      x * a(x,x,L(a(y,z,u),w,v5)) = L(x,x,L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(139,a,11683,a(flip),b,7304,a(flip))].">
      <j1 rule="hyper" parents="139 11683 7304"/>
    </justification>
  </clause>

  <clause id="11686">
    <literal><![CDATA[
      L(x,a(y,z,u),a(u,a(y,z,u),x)) \ L(x,a(y,z,u),u) = a(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(8810(a,1),11633(a,1,1))].">
      <j1 rule="para" parents="8810 11633"/>
    </justification>
  </clause>

  <clause id="11688">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),u) = a(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(6853(a,1),11686(a,1,1))].">
      <j1 rule="para" parents="6853 11686"/>
    </justification>
  </clause>

  <clause id="11689">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,y)) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(6997(a,1),11688(a,1,2))].">
      <j1 rule="para" parents="6997 11688"/>
    </justification>
  </clause>

  <clause id="11690">
    <literal><![CDATA[
      x * a(x,y,a(z,u,y)) = L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(152,a,11689,a)].">
      <j1 rule="hyper" parents="152 11689"/>
    </justification>
  </clause>

  <clause id="11691">
    <literal><![CDATA[
      x \ (L(x,y,a(z,u,y)) * L(L(x,y,a(z,u,y)) \ x,w,v5)) = a(x,y,a(z,u,y)) \ L(x \ L(x,y,a(z,u,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(11689(a,1),1252(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11689 1252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11693">
    <literal><![CDATA[
      x \ (y * a(x \ y,x,a(z,u,x))) = L(x \ y,x,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,7018,a,b,11690,a)].">
      <j1 rule="hyper" parents="63 7018 11690"/>
    </justification>
  </clause>

  <clause id="11694">
    <literal><![CDATA[
      L(x,y,a(y,z,a(u,w,z))) * L(y,z,a(u,w,z)) = a(y,z,a(u,w,z)) * (x * y)
    ]]></literal>
    <justification jstring="[para(11690(a,1),5382(a,1,2))].">
      <j1 rule="para" parents="11690 5382"/>
    </justification>
  </clause>

  <clause id="11695">
    <literal><![CDATA[
      (x * (a(x,y,a(z,u,y)) \ L(a(x,y,a(z,u,y)),w,v5))) * a(x,y,a(z,u,y)) = (a(x,y,a(z,u,y)) \ L(a(x,y,a(z,u,y)),w,v5)) * L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(11690(a,1),6152(a,2,2))].">
      <j1 rule="para" parents="11690 6152"/>
    </justification>
  </clause>

  <clause id="11696">
    <literal><![CDATA[
      x \ (y * a(y,x,a(z,u,x))) = L(x \ y,x,a(z,u,x))
    ]]></literal>
    <justification jstring="[para(9988(a,1),11693(a,1,2,2))].">
      <j1 rule="para" parents="9988 11693"/>
    </justification>
  </clause>

  <clause id="11697">
    <literal><![CDATA[
      L(x \ y,x,a(z,u,x)) = x \ L(y,x,a(z,u,x))
    ]]></literal>
    <justification jstring="[para(11690(a,1),11696(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11690 11696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11698">
    <literal><![CDATA[
      L(a(x,y,z) \ u,z,a(x,y,z)) = z * ((a(x,y,z) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,298,a(flip),b,11697,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 298 11697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11699">
    <literal><![CDATA[
      L(x \ a(y,z,x),x,a(y,z,x)) = x \ a(y,z,x)
    ]]></literal>
    <justification jstring="[para(2363(a,1),11697(a,2,2))].">
      <j1 rule="para" parents="2363 11697"/>
    </justification>
  </clause>

  <clause id="11700">
    <literal><![CDATA[
      (x * a(y,z,x)) \ (x * u) = x * ((a(y,z,x) * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6998,a(flip),b,11698,a)].">
      <j1 rule="hyper" parents="63 6998 11698"/>
    </justification>
  </clause>

  <clause id="11702">
    <literal><![CDATA[
      (x * (y * (z * (K(u,w) * (v5 * v5))))) / v6 = (x * (y * (z * K(u,w)))) / (v6 / (v5 * v5))
    ]]></literal>
    <justification jstring="[para(3943(a,1),10336(a,1,1,2))].">
      <j1 rule="para" parents="3943 10336"/>
    </justification>
  </clause>

  <clause id="11703">
    <literal><![CDATA[
      a(x,y,(K(z,u) * (w * (v5 * (v6 * z)))) * v7) = a(x,y,v7 * ((v5 * (v6 * T(z,u))) * w))
    ]]></literal>
    <justification jstring="[para(406(a,1),10477(a,1,3,1))].">
      <j1 rule="para" parents="406 10477"/>
    </justification>
  </clause>

  <clause id="11704">
    <literal><![CDATA[
      a(x \ (L(L(y,z,u) \ y,y,w) * w),v5,v6) = a(x \ ((y \ w) * (L(y \ 1,z,u) \ 1)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,9109,a,b,10577,a)].">
      <j1 rule="hyper" parents="63 9109 10577"/>
    </justification>
  </clause>

  <clause id="11705">
    <literal><![CDATA[
      a(x,y,(z * ((u \ 1) \ ((u * u) \ w))) * v5) = a(x,y,(z * (w / u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,5553,a(flip),b,10694,a),flip(a)].">
      <j1 rule="hyper" parents="316 5553 10694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11707">
    <literal><![CDATA[
      a(x,y,(z * ((u \ 1) \ ((u * u) \ w))) * v5) = a(x,y,(z * (u \ w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,5689,a(flip),b,11705,a),flip(a)].">
      <j1 rule="hyper" parents="316 5689 11705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11708">
    <literal><![CDATA[
      a(x,y,z * (u * ((w \ 1) \ v5))) = a(x,y,(u * (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11461,a(flip),b,11707,a)].">
      <j1 rule="hyper" parents="63 11461 11707"/>
    </justification>
  </clause>

  <clause id="11711">
    <literal><![CDATA[
      a(x,y,(L(z,(u \ 1) \ w,(u \ 1) \ w) * (u \ w)) * v5) = a(x,y,(((u \ 1) \ w) \ z) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,8686,a(flip),b,11708,a),flip(a)].">
      <j1 rule="hyper" parents="63 8686 11708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11712">
    <literal><![CDATA[
      a(x,y,z \ ((u * (w \ (u \ w))) \ v5)) = a(x,y,z \ (a(u,u \ 1,w) \ v5))
    ]]></literal>
    <justification jstring="[para(8456(a,1),10705(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="8456 10705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11713">
    <literal><![CDATA[
      a(x,y,z \ ((((u * T(w,v5)) * v6) \ v7) \ v8)) = a(x,y,z \ (((v6 * (u * w)) \ v7) \ v8))
    ]]></literal>
    <justification jstring="[hyper(63,a,10672,a,b,10707,a)].">
      <j1 rule="hyper" parents="63 10672 10707"/>
    </justification>
  </clause>

  <clause id="11714">
    <literal><![CDATA[
      L(x,L(y * (z * z),u,w) \ (z * z),v5) = L(x,T(L(y,u,w) \ 1,z * z),v5)
    ]]></literal>
    <justification jstring="[para(427(a,1),10958(a,2,2))].">
      <j1 rule="para" parents="427 10958"/>
    </justification>
  </clause>

  <clause id="11715">
    <literal><![CDATA[
      L(x,L(y * (z * z),u,w) \ (z * z),v5) = L(x,L(y,u,w) \ 1,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,10796,a(flip),b,11714,a),flip(a)].">
      <j1 rule="hyper" parents="316 10796 11714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11717">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * v5) * L(v6,L(z,u,w),v5 \ 1)) = a(x,y,v5 * (R(z,u,w) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,7425,a(flip),b,10989,a)].">
      <j1 rule="hyper" parents="63 7425 10989"/>
    </justification>
  </clause>

  <clause id="11718">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * ((u * K(w,v5)) * (v6 * v6)) = u * ((a(x,y,z) \ K(w,v5)) * (v6 * v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,32,a(flip),b,11078,a),flip(a)].">
      <j1 rule="hyper" parents="316 32 11078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11719">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 \ (T(v5,v6) / v6))))) = a(x,y,z \ (u * (w * ((v6 * v5) \ v5))))
    ]]></literal>
    <justification jstring="[hyper(316,a,5609,a(flip),b,11159,a),flip(a)].">
      <j1 rule="hyper" parents="316 5609 11159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11721">
    <literal><![CDATA[
      a(x,(y * (K(z,u) * (w * (v5 \ z)))) \ v6,v7) = a(x,(y * ((v5 \ T(z,u)) * w)) \ v6,v7)
    ]]></literal>
    <justification jstring="[para(406(a,1),11302(a,1,2,1,2))].">
      <j1 rule="para" parents="406 11302"/>
    </justification>
  </clause>

  <clause id="11722">
    <literal><![CDATA[
      a(x,y \ (((z \ 1) * (z \ 1)) \ u),w) = a(x,y \ ((T(z \ 1,z) \ z) * u),w)
    ]]></literal>
    <justification jstring="[para(2934(a,2),11353(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2934 11353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11723">
    <literal><![CDATA[
      a(x,y \ (((z \ 1) * (z \ 1)) \ u),w) = a(x,y \ (((z \ 1) \ z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,11266,a(flip),b,11722,a),flip(a)].">
      <j1 rule="hyper" parents="316 11266 11722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11725">
    <literal><![CDATA[
      a(x,y \ (((z \ 1) * (z \ 1)) \ u),w) = a(x,y \ ((z * z) * u),w)
    ]]></literal>
    <justification jstring="[para(282(a,1),11723(a,2,2,2,1))].">
      <j1 rule="para" parents="282 11723"/>
    </justification>
  </clause>

  <clause id="11726">
    <literal><![CDATA[
      a(x,y,L(L(z,a(u,u,z),w),u,u) \ (z * w)) = a(x,y,w * a(u \ 1,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9545,a(flip),b,11381,a)].">
      <j1 rule="hyper" parents="63 9545 11381"/>
    </justification>
  </clause>

  <clause id="11727">
    <literal><![CDATA[
      a(x,y,z * a(u \ 1,u,w)) = a(x,y,a(u,u,w) * z)
    ]]></literal>
    <justification jstring="[para(10639(a,1),11726(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10639 11726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11728">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ (u \ w))) = a(x,y,a(u,u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8835,a,b,11727,a)].">
      <j1 rule="hyper" parents="63 8835 11727"/>
    </justification>
  </clause>

  <clause id="11729">
    <literal><![CDATA[
      a(x,y,a(z,z,z * u) * w) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8894,a,b,11728,a)].">
      <j1 rule="hyper" parents="63 8894 11728"/>
    </justification>
  </clause>

  <clause id="11730">
    <literal><![CDATA[
      a(x,y,z * a(u,u,u * w)) = a(x,y,a(u,u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,11729,a)].">
      <j1 rule="hyper" parents="63 5469 11729"/>
    </justification>
  </clause>

  <clause id="11731">
    <literal><![CDATA[
      a(x,y,(z * ((u * (w \ K(v5,v6))) * v7)) * v8) = a(x,y,(z * ((u * w) * v7)) * v8)
    ]]></literal>
    <justification jstring="[hyper(316,a,7571,a(flip),b,11444,a),flip(a)].">
      <j1 rule="hyper" parents="316 7571 11444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11733">
    <literal><![CDATA[
      a(x,y,((z * (L(z,u,w) \ z)) * v5) \ v6) = a(x,y,(v5 * L(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[para(2822(a,1),11454(a,1,3,1))].">
      <j1 rule="para" parents="2822 11454"/>
    </justification>
  </clause>

  <clause id="11734">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ T(v5,v6)) * v7))) = a(x,y,(u \ (v7 * (w \ v5))) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5693,a(flip),b,11496,a),flip(a)].">
      <j1 rule="hyper" parents="63 5693 11496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11736">
    <literal><![CDATA[
      a(x,y,(z \ (u * (w \ T(v5,v6)))) * v7) = a(x,y,(z \ (u * (w \ v5))) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,5665,a,b,11734,a)].">
      <j1 rule="hyper" parents="63 5665 11734"/>
    </justification>
  </clause>

  <clause id="11737">
    <literal><![CDATA[
      a(x,y,(z \ (u * (w \ (v5 / v6)))) * v7) = a(x,y,(z \ (u * (w \ (v6 \ v5)))) * v7)
    ]]></literal>
    <justification jstring="[para(116(a,1),11736(a,1,3,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="116 11736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11738">
    <literal><![CDATA[
      a(x,y,(z \ (u * ((w * v5) \ v5))) * v6) = a(x,y,(z \ (u * ((v5 * w) \ v5))) * v6)
    ]]></literal>
    <justification jstring="[para(2875(a,1),11736(a,1,3,1,2,2))].">
      <j1 rule="para" parents="2875 11736"/>
    </justification>
  </clause>

  <clause id="11739">
    <literal><![CDATA[
      a(x,y,(z \ (u * (w / (w * v5)))) * v6) = a(x,y,(z \ (u * (w \ (w / v5)))) * v6)
    ]]></literal>
    <justification jstring="[para(11147(a,1),11736(a,1,3,1,2,2))].">
      <j1 rule="para" parents="11147 11736"/>
    </justification>
  </clause>

  <clause id="11740">
    <literal><![CDATA[
      a(x,y,(z \ (u * ((w * v5) \ w))) * v6) = a(x,y,(z \ (u * (w \ (w / v5)))) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,6069,a(flip),b,11739,a)].">
      <j1 rule="hyper" parents="63 6069 11739"/>
    </justification>
  </clause>

  <clause id="11741">
    <literal><![CDATA[
      a(x,y,(z \ (u * ((w * v5) \ w))) * v6) = a(x,y,(z \ (u * (w \ (v5 \ w)))) * v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,11737,a(flip),b,11740,a),flip(a)].">
      <j1 rule="hyper" parents="316 11737 11740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11742">
    <literal><![CDATA[
      a(x,y,(z \ (u * ((w * v5) \ v5))) * v6) = a(x,y,(z \ (u * (v5 \ (w \ v5)))) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,11738,a,b,11741,a)].">
      <j1 rule="hyper" parents="63 11738 11741"/>
    </justification>
  </clause>

  <clause id="11743">
    <literal><![CDATA[
      (x / T(y,z)) * L((x / T(y,z)) \ u,w,v5) = L(u / (x / y),w,v5) * (x / y)
    ]]></literal>
    <justification jstring="[para(10222(a,1),11497(a,1,2,1))].">
      <j1 rule="para" parents="10222 11497"/>
    </justification>
  </clause>

  <clause id="11744">
    <literal><![CDATA[
      (x / T(y,z)) * L((x / T(y,z)) \ u,w,v5) = (y \ x) * L((y \ x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,6293,a(flip),b,11743,a),flip(a)].">
      <j1 rule="hyper" parents="316 6293 11743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11745">
    <literal><![CDATA[
      K(x,y) * ((z / T(y,x)) \ (a(y \ z,u,w) \ v5)) = a(y \ z,u,w) \ ((z / y) \ v5)
    ]]></literal>
    <justification jstring="[para(1813(a,1),11501(a,1,2,2,1))].">
      <j1 rule="para" parents="1813 11501"/>
    </justification>
  </clause>

  <clause id="11747">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x \ 1,L(x,y,z) \ u) \ u = (u / (L(x,y,z) \ 1)) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,6620,a,b,11572,a),flip(a)].">
      <j1 rule="hyper" parents="316 6620 11572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11748">
    <literal><![CDATA[
      (a(x,x,y) \ z) \ (y * (L(y,x,x) \ (a(x,x,y) \ z))) = L(a(x,x,y),L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9161,a(flip),b,11589,a)].">
      <j1 rule="hyper" parents="63 9161 11589"/>
    </justification>
  </clause>

  <clause id="11749">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,a(z,y,L(x,y,z) \ 1),y) = (x \ 1) * a(z,y,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2534(a,1),11631(a,2,2))].">
      <j1 rule="para" parents="2534 11631"/>
    </justification>
  </clause>

  <clause id="11750">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,a(y,z,u),x)) \ L(x,y,a(y,z,u)) = a(y,a(y,z,u),x) \ 1
    ]]></literal>
    <justification jstring="[para(8813(a,1),11634(a,1,1))].">
      <j1 rule="para" parents="8813 11634"/>
    </justification>
  </clause>

  <clause id="11751">
    <literal><![CDATA[
      a(x,y,z \ (R(u,u,L(w,v5,v5)) \ L(w,v5,v5))) = a(x,y,z \ (u * (v5 \ (v5 \ w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,8885,a(flip),b,11679,a)].">
      <j1 rule="hyper" parents="63 8885 11679"/>
    </justification>
  </clause>

  <clause id="11752">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ (w \ v5)))) = a(x,y,z \ (u * L(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6349,a(flip),b,11751,a),flip(a)].">
      <j1 rule="hyper" parents="63 6349 11751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11753">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w \ 1,w) * v5)) = a(x,y,z \ (v5 * L(u,w,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10051,a,b,11752,a)].">
      <j1 rule="hyper" parents="63 10051 11752"/>
    </justification>
  </clause>

  <clause id="11754">
    <literal><![CDATA[
      a(x,y,z \ (u * L(w * v5,w,w))) = a(x,y,z \ (u * (w \ v5)))
    ]]></literal>
    <justification jstring="[para(9(a,1),11752(a,1,3,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 11752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11755">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * K(v5 \ 1,w * v5)) * v5))) = a(x,y,z \ (u * L(w / (v5 \ 1),v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6030,a,b,11753,a)].">
      <j1 rule="hyper" parents="63 6030 11753"/>
    </justification>
  </clause>

  <clause id="11756">
    <literal><![CDATA[
      (x * (y * (z * (K(u,w) * (v5 * v5))))) / v6 = (x * (y * z)) / ((v6 / (v5 * v5)) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,4224,a(flip),b,11702,a),flip(a)].">
      <j1 rule="hyper" parents="316 4224 11702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11757">
    <literal><![CDATA[
      a(x,y,z * ((u * (w * T(v5,v6))) * v7)) = a(x,y,(v7 * (u * (w * v5))) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5541,a(flip),b,11703,a),flip(a)].">
      <j1 rule="hyper" parents="63 5541 11703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11760">
    <literal><![CDATA[
      a(x,y,z * (R(u,w,v5) * v6)) = a(x,y,z * (L(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,6136,a(flip),b,11717,a),flip(a)].">
      <j1 rule="hyper" parents="63 6136 11717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11761">
    <literal><![CDATA[
      a(x,y,z * (((u * (w \ v5)) * a(u * (v5 / w),v6,v6)) * v7)) = a(x,y,z * (L(u * (v5 / w),v6,v6) * v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,9552,a,b,11760,a)].">
      <j1 rule="hyper" parents="63 9552 11760"/>
    </justification>
  </clause>

  <clause id="11762">
    <literal><![CDATA[
      a(x,y,z * (u * ((w \ 1) * R(v5,w \ 1,w)))) = a(x,y,z * (L(v5 * (1 / w),w,w) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5981,a,b,11760,a)].">
      <j1 rule="hyper" parents="63 5981 11760"/>
    </justification>
  </clause>

  <clause id="11763">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u * (K(w,v5) * (v6 * v6))) = u * ((a(x,y,z) \ K(w,v5)) * (v6 * v6))
    ]]></literal>
    <justification jstring="[para(32(a,1),11718(a,1,2))].">
      <j1 rule="para" parents="32 11718"/>
    </justification>
  </clause>

  <clause id="11764">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 \ (v6 \ T(v5,v6)))))) = a(x,y,z \ (u * (w * ((v6 * v5) \ v5))))
    ]]></literal>
    <justification jstring="[hyper(63,a,6329,a(flip),b,11719,a)].">
      <j1 rule="hyper" parents="63 6329 11719"/>
    </justification>
  </clause>

  <clause id="11765">
    <literal><![CDATA[
      a(x,(y * ((z \ T(u,w)) * v5)) \ v6,v7) = a(x,(y * (v5 * (z \ u))) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,11282,a(flip),b,11721,a),flip(a)].">
      <j1 rule="hyper" parents="63 11282 11721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11767">
    <literal><![CDATA[
      a(x,(y * (z * (u \ T(w,v5)))) \ v6,v7) = a(x,(y * (z * (u \ w))) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,11281,a,b,11765,a)].">
      <j1 rule="hyper" parents="63 11281 11765"/>
    </justification>
  </clause>

  <clause id="11768">
    <literal><![CDATA[
      a(x \ y,z,u) \ ((y / x) \ w) = (y / x) \ (a(x \ y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10216,a(flip),b,11745,a),flip(a)].">
      <j1 rule="hyper" parents="63 10216 11745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11769">
    <literal><![CDATA[
      a(x,a(x,y,z),u) \ 1 = u \ L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(6853(a,1),11750(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6853 11750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11770">
    <literal><![CDATA[
      x \ L(x,y,a(y,z,u)) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9455,a(flip),b,11769,a),flip(a)].">
      <j1 rule="hyper" parents="63 9455 11769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11771">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) \ x = a(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(39,a,5076,a,b,11769,a)].">
      <j1 rule="hyper" parents="39 5076 11769"/>
    </justification>
  </clause>

  <clause id="11772">
    <literal><![CDATA[
      L(a(a(x * y,z,u),x * y,y) \ 1,y,x) = a(y,x * y,a(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10011,a,b,11770,a)].">
      <j1 rule="hyper" parents="63 10011 11770"/>
    </justification>
  </clause>

  <clause id="11774">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * x = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,11770,a)].">
      <j1 rule="hyper" parents="38 2295 11770"/>
    </justification>
  </clause>

  <clause id="11775">
    <literal><![CDATA[
      a(x,y,z * L(z,u,a(u,w,v5))) = a(x,y,a(z,u,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(11770(a,1),5566(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11770 5566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11778">
    <literal><![CDATA[
      (x * (y * (z * (K(u,w) * (v5 * v5))))) / v6 = (x * (y * z)) / (v6 * ((v5 * v5) \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(4045(a,1),11756(a,2,2))].">
      <j1 rule="para" parents="4045 11756"/>
    </justification>
  </clause>

  <clause id="11779">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u * (K(w,v5) * (v6 * v6))) = u * (K(w,v5) * (a(x,y,z) \ (v6 * v6)))
    ]]></literal>
    <justification jstring="[para(2467(a,1),11763(a,2,2))].">
      <j1 rule="para" parents="2467 11763"/>
    </justification>
  </clause>

  <clause id="11780">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * ((v5 * v6) \ v6)))) = a(x,y,z \ (u * (w * (v6 \ (v5 \ v6)))))
    ]]></literal>
    <justification jstring="[hyper(63,a,6328,a(flip),b,11764,a),flip(a)].">
      <j1 rule="hyper" parents="63 6328 11764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11782">
    <literal><![CDATA[
      (x * (y * (z * (K(u,w) * (v5 * v5))))) / v6 = (x * (y * z)) / (v6 * (v5 \ (v5 \ K(w,u))))
    ]]></literal>
    <justification jstring="[para(4208(a,1),11778(a,2,2,2))].">
      <j1 rule="para" parents="4208 11778"/>
    </justification>
  </clause>

  <clause id="11783">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * (u * (w * (K(v5,v6) * (v7 * v7))))) / (w * (K(v5,v6) * (a(x,y,z) \ (v7 * v7)))) = R(u,w * (K(v5,v6) * (v7 * v7)),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(11779(a,1),7550(a,1,2))].">
      <j1 rule="para" parents="11779 7550"/>
    </justification>
  </clause>

  <clause id="11784">
    <literal><![CDATA[
      (x * ((L(y,z,u) \ y) * w)) / ((x * (w * (K(v5,v6) * (v7 * v7)))) * (v7 \ (v7 \ K(v6,v5)))) = L(L(y,z,u) \ y,w * (K(v5,v6) * (v7 * v7)),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6657,a(flip),b,11782,a),flip(a)].">
      <j1 rule="hyper" parents="63 6657 11782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11785">
    <literal><![CDATA[
      K(x,y) * (L(a(z,u,w),v5 \ 1,v5) \ v6) = (v5 * ((v5 \ K(y,x)) * a(z,u,w))) \ v6
    ]]></literal>
    <justification jstring="[para(10820(a,1),10240(a,1,2,1))].">
      <j1 rule="para" parents="10820 10240"/>
    </justification>
  </clause>

  <clause id="11786">
    <literal><![CDATA[
      (x * ((x \ K(y,z)) * a(u,w,v5))) \ v6 = K(z,y) * (L(a(u,w,v5),x,x) \ v6)
    ]]></literal>
    <justification jstring="[para(2461(a,1),11785(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2461 11785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11788">
    <literal><![CDATA[
      (K(x,y) * (L(a(z,u,w),v5,v5) \ a(z,u,w))) * K(y,x) = a(v5,v5 \ 1,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(11786(a,1),11252(a,1,1))].">
      <j1 rule="para" parents="11786 11252"/>
    </justification>
  </clause>

  <clause id="11789">
    <literal><![CDATA[
      (K(x,y) * a(z,z,a(u,w,v5))) * K(y,x) = a(z,z \ 1,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(4952(a,1),11788(a,1,1,2))].">
      <j1 rule="para" parents="4952 11788"/>
    </justification>
  </clause>

  <clause id="11790">
    <literal><![CDATA[
      a(x,x \ 1,a(y,z,u)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2254,a(flip),b,11789,a),flip(a)].">
      <j1 rule="hyper" parents="63 2254 11789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11791">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * ((x \ 1) * a(y,z,u)) = x \ (1 * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(11790(a,1),8458(a,1,1))].">
      <j1 rule="para" parents="11790 8458"/>
    </justification>
  </clause>

  <clause id="11792">
    <literal><![CDATA[
      (x \ 1) * (a(x,x,a(y,z,u)) * a(y,z,u)) = x \ (1 * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8425,a(flip),b,11791,a)].">
      <j1 rule="hyper" parents="63 8425 11791"/>
    </justification>
  </clause>

  <clause id="11793">
    <literal><![CDATA[
      (x \ 1) * (x \ ((1 / x) \ a(y,z,u))) = x \ (1 * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(8791(a,1),11792(a,1,2))].">
      <j1 rule="para" parents="8791 11792"/>
    </justification>
  </clause>

  <clause id="11794">
    <literal><![CDATA[
      (x \ 1) * (x \ ((1 / x) \ a(y,z,u))) = x \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(328,a,11793,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="328 11793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11796">
    <literal><![CDATA[
      (x \ a(y,z,u)) / (x \ 1) = x \ ((1 / x) \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(136,a,11794,a(flip),b,6828,a)].">
      <j1 rule="hyper" parents="136 11794 6828"/>
    </justification>
  </clause>

  <clause id="11797">
    <literal><![CDATA[
      (x \ ((1 / x) \ a(y,z,u))) \ ((x \ a(y,z,u)) * x) = a(x \ a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(11796(a,1),6928(a,1,1))].">
      <j1 rule="para" parents="11796 6928"/>
    </justification>
  </clause>

  <clause id="11798">
    <literal><![CDATA[
      a(x,y,L(z * ((u * w) * (1 / w)),v5,v6)) = a(x,y,L(z * L(u,w,w \ 1),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,7045,a(flip),b,10312,a)].">
      <j1 rule="hyper" parents="63 7045 10312"/>
    </justification>
  </clause>

  <clause id="11800">
    <literal><![CDATA[
      a(x,y,L(z * ((u * w) * (w \ 1)),v5,v6)) = a(x,y,L(z * L(u,w,w \ 1),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5712,a(flip),b,11798,a)].">
      <j1 rule="hyper" parents="63 5712 11798"/>
    </justification>
  </clause>

  <clause id="11801">
    <literal><![CDATA[
      a(x,y,L(z * L(u,w,w \ 1),v5,v6)) = a(x,y,L(z * R(u,w,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(565(a,1),11800(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="565 11800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11802">
    <literal><![CDATA[
      a(x,y,L(a(z \ 1,z,u),w,v5)) = a(x,y,L(u * R(u,z,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,6396,a(flip),b,11801,a)].">
      <j1 rule="hyper" parents="63 6396 11801"/>
    </justification>
  </clause>

  <clause id="11803">
    <literal><![CDATA[
      a(x,y,L(a(z \ 1,z,u),w,v5)) = a(x,y,L(a(u,z,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,6380,a(flip),b,11802,a),flip(a)].">
      <j1 rule="hyper" parents="316 6380 11802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11804">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ L(L(z \ 1,u,w),v5,v5 \ 1)) = a(x,y,L(a(z,v5,v5),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9309,a,b,11803,a)].">
      <j1 rule="hyper" parents="63 9309 11803"/>
    </justification>
  </clause>

  <clause id="11805">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ L(L(z \ 1,u,w),v5,v5)) = a(x,y,L(a(z,v5,v5),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6687,a(flip),b,11804,a)].">
      <j1 rule="hyper" parents="63 6687 11804"/>
    </justification>
  </clause>

  <clause id="11806">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,u),w,v5)) = a(x,y,L(a(z,u,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,9412,a(flip),b,11805,a)].">
      <j1 rule="hyper" parents="63 9412 11805"/>
    </justification>
  </clause>

  <clause id="11807">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,w,v5))) = a(x,y,L(a(u,z,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,6381,a(flip),b,11806,a)].">
      <j1 rule="hyper" parents="63 6381 11806"/>
    </justification>
  </clause>

  <clause id="11809">
    <literal><![CDATA[
      (a(x,x \ y,z \ u) * ((x \ y) * (z \ u))) / (z \ u) = (x \ (y * (u / z))) / (u / z)
    ]]></literal>
    <justification jstring="[para(5477(a,1),10789(a,1,1,1))].">
      <j1 rule="para" parents="5477 10789"/>
    </justification>
  </clause>

  <clause id="11810">
    <literal><![CDATA[
      L(x,y \ ((z * T(u,w)) * L(v5,z,u)),v6) = L(x,y \ (u * (T(z,T(u,w)) * v5)),v6)
    ]]></literal>
    <justification jstring="[para(1581(a,1),10938(a,1,2,2,2))].">
      <j1 rule="para" parents="1581 10938"/>
    </justification>
  </clause>

  <clause id="11811">
    <literal><![CDATA[
      L(x,y \ (L(z,u,w) * (u * w)),v5) = L(x,y \ (w * (T(u,T(w,v6)) * z)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11008,a(flip),b,11810,a)].">
      <j1 rule="hyper" parents="63 11008 11810"/>
    </justification>
  </clause>

  <clause id="11813">
    <literal><![CDATA[
      L(x,y \ (L(z,u,w) * (u * w)),v5) = L(x,y \ ((u * z) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,11010,a(flip),b,11811,a),flip(a)].">
      <j1 rule="hyper" parents="316 11010 11811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11816">
    <literal><![CDATA[
      L(x,(y * (z * u)) \ (L(y,z,u) * (z * u)),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10961,a(flip),b,11813,a),flip(a)].">
      <j1 rule="hyper" parents="316 10961 11813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11817">
    <literal><![CDATA[
      L(x,(y * z) \ (((y * z) / u) * L(u,y,z)),w) = L(x,a(u,y,z),w)
    ]]></literal>
    <justification jstring="[para(7107(a,1),11816(a,1,2))].">
      <j1 rule="para" parents="7107 11816"/>
    </justification>
  </clause>

  <clause id="11818">
    <literal><![CDATA[
      L(x,(y * z) \ ((z * (T(y,z) * u)) / u),w) = L(x,a(u,y,z),w)
    ]]></literal>
    <justification jstring="[para(3294(a,1),11817(a,1,2,2))].">
      <j1 rule="para" parents="3294 11817"/>
    </justification>
  </clause>

  <clause id="11819">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * (z * u)) / u),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(3365(a,1),11818(a,1,2))].">
      <j1 rule="para" parents="3365 11818"/>
    </justification>
  </clause>

  <clause id="11820">
    <literal><![CDATA[
      L(x,L(y \ L(y,z,u),y,u * z),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(7099(a,2),11819(a,1,2))].">
      <j1 rule="para" parents="7099 11819"/>
    </justification>
  </clause>

  <clause id="11822">
    <literal><![CDATA[
      ((x \ (1 / y)) * (y * x)) * ((y \ K(x * y,x \ (y \ 1))) * y) = a(y,x,x \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10625,a(flip),b,11114,a)].">
      <j1 rule="hyper" parents="63 10625 11114"/>
    </justification>
  </clause>

  <clause id="11823">
    <literal><![CDATA[
      (x * L(x \ L(x,y,z),x,z * y)) \ L(x,y,z) = a(z * y,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,168,a(flip),b,11336,a)].">
      <j1 rule="hyper" parents="63 168 11336"/>
    </justification>
  </clause>

  <clause id="11825">
    <literal><![CDATA[
      L(x * L(x,y,z),x,z * y) \ (x * L(x,y,z)) = a(z * y,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9653,a(flip),b,11823,a)].">
      <j1 rule="hyper" parents="63 9653 11823"/>
    </justification>
  </clause>

  <clause id="11826">
    <literal><![CDATA[
      a(x * y,z,z * L(z,y,x)) = a(x * y,z,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,10003,a(flip),b,11825,a)].">
      <j1 rule="hyper" parents="63 10003 11825"/>
    </justification>
  </clause>

  <clause id="11830">
    <literal><![CDATA[
      (x \ (y * (z / u))) / (z / u) = (x \ (y * (u \ z))) / (u \ z)
    ]]></literal>
    <justification jstring="[para(8458(a,1),11809(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8458 11809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11833">
    <literal><![CDATA[
      (x \ (1 / y)) * ((y * x) * ((y \ K(x * y,x \ (y \ 1))) * y)) = a(y,x,x \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6840,a(flip),b,11822,a)].">
      <j1 rule="hyper" parents="63 6840 11822"/>
    </justification>
  </clause>

  <clause id="11834">
    <literal><![CDATA[
      (x \ (1 / y)) * (y * (x * ((y \ K(x * y,x \ (y \ 1))) * y))) = a(y,x,x \ (1 / y))
    ]]></literal>
    <justification jstring="[para(6840(a,1),11833(a,1,2))].">
      <j1 rule="para" parents="6840 11833"/>
    </justification>
  </clause>

  <clause id="11835">
    <literal><![CDATA[
      (x \ (1 / y)) * (y * (x * ((y \ K(x * y,x \ (y \ 1))) * y))) = a(y,x,x \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(316,a,5497,a(flip),b,11834,a),flip(a)].">
      <j1 rule="hyper" parents="316 5497 11834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11836">
    <literal><![CDATA[
      (x \ (1 / y)) * T((1 / (1 / y)) * x,x \ (y \ 1)) = a(y,x,x \ (y \ 1))
    ]]></literal>
    <justification jstring="[para(10674(a,1),11835(a,1,2))].">
      <j1 rule="para" parents="10674 11835"/>
    </justification>
  </clause>

  <clause id="11837">
    <literal><![CDATA[
      (x \ (1 / y)) * (L(x \ (1 / y),x,y) \ 1) = a(y,x,x \ (y \ 1))
    ]]></literal>
    <justification jstring="[para(5210(a,1),11836(a,1,2))].">
      <j1 rule="para" parents="5210 11836"/>
    </justification>
  </clause>

  <clause id="11838">
    <literal><![CDATA[
      L(x \ (1 / y),x,y) \ (x \ (1 / y)) = a(y,x,x \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,1002,a(flip),b,11837,a)].">
      <j1 rule="hyper" parents="63 1002 11837"/>
    </justification>
  </clause>

  <clause id="11839">
    <literal><![CDATA[
      L(x \ (1 / y),x,y) \ (x \ (1 / y)) = a(y,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(316,a,5805,a(flip),b,11838,a),flip(a)].">
      <j1 rule="hyper" parents="316 5805 11838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11840">
    <literal><![CDATA[
      (x \ (1 / y)) \ L(x \ (1 / y),x,y) = a(y,x,x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(11839(a,1),5076(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11839 5076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11841">
    <literal><![CDATA[
      (x \ (1 / y)) \ ((y * x) \ K(y,y \ 1)) = a(y,x,x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(11839(a,1),5085(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11839 5085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11842">
    <literal><![CDATA[
      (x \ (1 / y)) \ ((y * x) \ K(y,y \ 1)) = a(y,x,y * x) \ 1
    ]]></literal>
    <justification jstring="[para(9946(a,1),11841(a,2,1))].">
      <j1 rule="para" parents="9946 11841"/>
    </justification>
  </clause>

  <clause id="11843">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ L(z * u,w,v5)) = (z \ 1) * (K(x,y) * L((z \ 1) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(6419(a,1),10326(a,1,1))].">
      <j1 rule="para" parents="6419 10326"/>
    </justification>
  </clause>

  <clause id="11844">
    <literal><![CDATA[
      (x \ 1) * (K(y,z) * L((x \ 1) \ u,w,v5)) = x \ (K(y,z) * L(x * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,10295,a(flip),b,11843,a),flip(a)].">
      <j1 rule="hyper" parents="63 10295 11843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11845">
    <literal><![CDATA[
      (x \ 1) * (K(y,z) * L((x \ 1) \ u,w,v5)) = x \ L(K(y,z) * (x * u),w,v5)
    ]]></literal>
    <justification jstring="[para(4850(a,2),11844(a,2,2))].">
      <j1 rule="para" parents="4850 11844"/>
    </justification>
  </clause>

  <clause id="11846">
    <literal><![CDATA[
      (x \ 1) * L(K(y,z) * ((x \ 1) \ u),w,v5) = x \ L(K(y,z) * (x * u),w,v5)
    ]]></literal>
    <justification jstring="[para(4850(a,2),11845(a,1,2))].">
      <j1 rule="para" parents="4850 11845"/>
    </justification>
  </clause>

  <clause id="11847">
    <literal><![CDATA[
      (x \ 1) * L((x \ K(y,z)) \ u,w,v5) = x \ L(K(z,y) * (x * u),w,v5)
    ]]></literal>
    <justification jstring="[para(10219(a,1),11846(a,1,2,1))].">
      <j1 rule="para" parents="10219 11846"/>
    </justification>
  </clause>

  <clause id="11848">
    <literal><![CDATA[
      (x \ 1) * L((x \ K(y,z)) \ u,w,v5) = x * L(K(z,y) * (x \ u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,11060,a(flip),b,11847,a),flip(a)].">
      <j1 rule="hyper" parents="316 11060 11847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11849">
    <literal><![CDATA[
      x * K(K(y,z) * ((u \ (w \ T(z,y))) * x),(z \ w) * u) = ((z \ (w * u)) \ x) * (z \ (w * u))
    ]]></literal>
    <justification jstring="[para(4242(a,2),10543(a,1,2,1))].">
      <j1 rule="para" parents="4242 10543"/>
    </justification>
  </clause>

  <clause id="11850">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 * (v6 \ (1 / v6)))))) = a(x,y,z \ ((u * (w * v5)) * (v6 \ v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6355,a(flip),b,10668,a),flip(a)].">
      <j1 rule="hyper" parents="63 6355 10668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11851">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 * (v6 \ (1 / v6)))))) = a(x,y,z \ (u * (w * v5)))
    ]]></literal>
    <justification jstring="[para(183(a,1),11850(a,2,3,2))].">
      <j1 rule="para" parents="183 11850"/>
    </justification>
  </clause>

  <clause id="11853">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 * (1 / v6))))) = a(x,y,z \ (u * (w * (v5 * v6))))
    ]]></literal>
    <justification jstring="[para(699(a,1),11851(a,1,3,2,2,2))].">
      <j1 rule="para" parents="699 11851"/>
    </justification>
  </clause>

  <clause id="11854">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * L(1 / v5,v6,v7)))) = a(x,y,z \ (u * (w * L(v5,v6,v7))))
    ]]></literal>
    <justification jstring="[para(1228(a,1),11851(a,1,3,2,2,2))].">
      <j1 rule="para" parents="1228 11851"/>
    </justification>
  </clause>

  <clause id="11855">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 * (v6 \ 1))))) = a(x,y,z \ (u * (w * (v5 * v6))))
    ]]></literal>
    <justification jstring="[hyper(63,a,5777,a(flip),b,11853,a)].">
      <j1 rule="hyper" parents="63 5777 11853"/>
    </justification>
  </clause>

  <clause id="11856">
    <literal><![CDATA[
      a(x,y,z \ (((u * (w \ 1)) * v5) * v6)) = a(x,y,z \ (v6 * (v5 * (u * w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,6003,a,b,11855,a)].">
      <j1 rule="hyper" parents="63 6003 11855"/>
    </justification>
  </clause>

  <clause id="11857">
    <literal><![CDATA[
      a(x,y,z \ (u * R((T(w * (v5 \ 1),v6) \ v7) * T(w * (v5 \ 1),v6),(w * (v5 \ 1)) \ 1,w * (v5 \ 1)))) = a(x,y,z \ (u * (T(v7 * (1 / (w * (v5 \ 1))),T(w * (v5 \ 1),v6)) * (w * v5))))
    ]]></literal>
    <justification jstring="[para(11405(a,2),11855(a,1,3,2,2))].">
      <j1 rule="para" parents="11405 11855"/>
    </justification>
  </clause>

  <clause id="11858">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * (v5 \ 1)) * v6))) = a(x,y,z \ (u * (v6 * (w * v5))))
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,11856,a)].">
      <j1 rule="hyper" parents="63 5490 11856"/>
    </justification>
  </clause>

  <clause id="11859">
    <literal><![CDATA[
      a(x,y,z \ ((u * (w * (L(w,v5,v6) \ w))) * v7)) = a(x,y,z \ (v7 * (u * L(w,v5,v6))))
    ]]></literal>
    <justification jstring="[hyper(63,a,6606,a,b,11854,a)].">
      <j1 rule="hyper" parents="63 6606 11854"/>
    </justification>
  </clause>

  <clause id="11860">
    <literal><![CDATA[
      a(x,y,(z * u) \ (u * (z * L(w,z,u)))) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9870,a(flip),b,11859,a),flip(a)].">
      <j1 rule="hyper" parents="63 9870 11859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11861">
    <literal><![CDATA[
      a(x,y,L(K(z,u) * L(w,u,z),u,z)) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(3299(a,1),11860(a,1,3))].">
      <j1 rule="para" parents="3299 11860"/>
    </justification>
  </clause>

  <clause id="11862">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5716,a(flip),b,11861,a)].">
      <j1 rule="hyper" parents="63 5716 11861"/>
    </justification>
  </clause>

  <clause id="11863">
    <literal><![CDATA[
      a(x,L(y,z,u),L(L(y,w,v5),w,v5)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,2548,a(flip),b,11862,a),flip(a)].">
      <j1 rule="hyper" parents="316 2548 11862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11865">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,u,z)) = a(x,y,u \ (z \ w))
    ]]></literal>
    <justification jstring="[para(298(a,1),11862(a,1,3,1))].">
      <j1 rule="para" parents="298 11862"/>
    </justification>
  </clause>

  <clause id="11866">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * z) * w))) = a(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[para(454(a,1),11862(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="454 11862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11868">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) = L(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(11862(a,1),9943(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11862 9943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11869">
    <literal><![CDATA[
      (a(x,x,y) \ z) \ (y * (L(y,x,x) \ (a(x,x,y) \ z))) = a(x,x,L(y,L(y,x,x),z))
    ]]></literal>
    <justification jstring="[hyper(316,a,11748,a,b,11868,a)].">
      <j1 rule="hyper" parents="316 11748 11868"/>
    </justification>
  </clause>

  <clause id="11870">
    <literal><![CDATA[
      x \ (y * L(y \ x,x * y,a(z,u,w))) = a(x * y,x * y,L(a(z,u,w),x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,10116,a,b,11868,a)].">
      <j1 rule="hyper" parents="316 10116 11868"/>
    </justification>
  </clause>

  <clause id="11872">
    <literal><![CDATA[
      x \ a(y,y,L(z,x,x)) = a(y,y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,11868,a,b,2459,a)].">
      <j1 rule="hyper" parents="133 11868 2459"/>
    </justification>
  </clause>

  <clause id="11873">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ w = L(a(x,x,y),z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(61,a,11868,a)].">
      <j1 rule="hyper" parents="61 11868"/>
    </justification>
  </clause>

  <clause id="11874">
    <literal><![CDATA[
      L(L(x,y,y) \ x,z,u) = a(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(4952(a,2),11868(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4952 11868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11875">
    <literal><![CDATA[
      L(a(x,x,L(y,z,u)),w,x * y) = L(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(11868(a,2),7331(a,1,1))].">
      <j1 rule="para" parents="11868 7331"/>
    </justification>
  </clause>

  <clause id="11877">
    <literal><![CDATA[
      (a(x,x,y) \ 1) \ ((z / y) * L(y,x,x)) = a(x,x,L(y,y,z)) * (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(11868(a,2),9304(a,2,1))].">
      <j1 rule="para" parents="11868 9304"/>
    </justification>
  </clause>

  <clause id="11878">
    <literal><![CDATA[
      L(a(x,x,L(a(y,z,u),w,v5)),L(x,w,v5),x * a(y,z,u)) = a(x,L(x,w,v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(11868(a,2),9414(a,1,1))].">
      <j1 rule="para" parents="11868 9414"/>
    </justification>
  </clause>

  <clause id="11879">
    <literal><![CDATA[
      L(a(x,x,y) \ a(x,x,L(y,z,u)),a(x,x,y),u * z) = a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(11868(a,2),11601(a,1,1,2))].">
      <j1 rule="para" parents="11868 11601"/>
    </justification>
  </clause>

  <clause id="11880">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,u,z)) = a(x,y,T(u,v5) \ (z \ w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5492,a,b,11865,a),flip(a)].">
      <j1 rule="hyper" parents="316 5492 11865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11881">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,z,u)) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6255,a,b,11865,a)].">
      <j1 rule="hyper" parents="63 6255 11865"/>
    </justification>
  </clause>

  <clause id="11883">
    <literal><![CDATA[
      a(x,y,L(((z * (u \ (z \ u))) * w) \ v5,w,a(z,z,u))) = a(x,y,w \ ((z * (u \ (z \ u))) \ v5))
    ]]></literal>
    <justification jstring="[para(8199(a,1),11865(a,1,3))].">
      <j1 rule="para" parents="8199 11865"/>
    </justification>
  </clause>

  <clause id="11884">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,y * z) = a(z,y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9994,a,b,11866,a)].">
      <j1 rule="hyper" parents="63 9994 11866"/>
    </justification>
  </clause>

  <clause id="11885">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,z * y) = a(z,y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9930,a,b,11866,a)].">
      <j1 rule="hyper" parents="63 9930 11866"/>
    </justification>
  </clause>

  <clause id="11886">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,x,z * y),u,a(L(x,y,z) \ x,w,v5)) = a(z,y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8408,a,b,11885,a)].">
      <j1 rule="hyper" parents="63 8408 11885"/>
    </justification>
  </clause>

  <clause id="11887">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ L(L(x,y,z) \ x,x,z * y),u,w) = L(L(x,y,z) \ x,u,w) \ L(a(z,y,L(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(11885(a,1),2138(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11885 2138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11888">
    <literal><![CDATA[
      L(L(x,y,z \ L(u,w,v5)) \ x,x,(z \ R(u,w,v5)) * y) = a(z \ R(u,w,v5),y,L(x,y,z \ R(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(7482(a,1),11885(a,1,1,1))].">
      <j1 rule="para" parents="7482 11885"/>
    </justification>
  </clause>

  <clause id="11889">
    <literal><![CDATA[
      L(a(x,x,y) \ a(x,x,L(y,z,u)),a(x,x,y),u * z) = a(u,z,L(a(x,x,y),z,u))
    ]]></literal>
    <justification jstring="[para(7553(a,1),11885(a,1,1))].">
      <j1 rule="para" parents="7553 11885"/>
    </justification>
  </clause>

  <clause id="11890">
    <literal><![CDATA[
      L(a(x,y,L(z,y,x)) \ (L(z,y,x) \ z),L(z,y,x) \ z,u) * u = (u / (L(z,y,x) \ z)) * (L(1 / (L(z,y,x) \ z),z,x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(11885(a,1),9107(a,1,1,1,1))].">
      <j1 rule="para" parents="11885 9107"/>
    </justification>
  </clause>

  <clause id="11891">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u),w,x * y)) = L(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11868,a,b,11875,a)].">
      <j1 rule="hyper" parents="63 11868 11875"/>
    </justification>
  </clause>

  <clause id="11892">
    <literal><![CDATA[
      a(x,y,z \ (u \ (z * (u * w)))) = a(x,y,L(L(w,u,z),z,u))
    ]]></literal>
    <justification jstring="[para(18(a,2),11881(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="18 11881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11894">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u),w,x * y)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,11868,a,b,11891,a),flip(a)].">
      <j1 rule="hyper" parents="316 11868 11891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11899">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),w,u)) = a(x,y,z * a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8637,a(flip),b,11892,a),flip(a)].">
      <j1 rule="hyper" parents="63 8637 11892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11900">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),w,u)) = a(x,y,z * a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5952,a,b,11899,a)].">
      <j1 rule="hyper" parents="63 5952 11899"/>
    </justification>
  </clause>

  <clause id="11901">
    <literal><![CDATA[
      a(x,y,x * a(z,x,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10108,a(flip),b,11899,a),flip(a)].">
      <j1 rule="hyper" parents="63 10108 11899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11902">
    <literal><![CDATA[
      a(x,y,a(z,x,u) * x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,11901,a)].">
      <j1 rule="hyper" parents="63 5469 11901"/>
    </justification>
  </clause>

  <clause id="11903">
    <literal><![CDATA[
      a(x,x \ 1,a(y,x,z) * x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,1296,a(flip),b,11902,a),flip(a)].">
      <j1 rule="hyper" parents="316 1296 11902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11904">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * w) * z))) = a(x,y,L(L(w,z,u),u,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,8487,a,b,11900,a)].">
      <j1 rule="hyper" parents="316 8487 11900"/>
    </justification>
  </clause>

  <clause id="11905">
    <literal><![CDATA[
      R(x,y * a(z,y,u),y * a(z,y,u)) = x * a(x,y * a(z,y,u),L(L(y,u,z),z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,11900,a,b,2380,a),flip(a)].">
      <j1 rule="hyper" parents="139 11900 2380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11907">
    <literal><![CDATA[
      a(x,y,L(L(z * a(u,w,u),v5,1 / v6),1 / v6,v5)) = a(x,y,v5 \ ((1 / v6) \ (((a(u,w,u) / v6) * z) * v5)))
    ]]></literal>
    <justification jstring="[para(5426(a,1),11904(a,1,3,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5426 11904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11910">
    <literal><![CDATA[
      L(a(x,y,L(z,y,x)),u,a(L(z,y,x) \ z,w,v5)) = a(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(11885(a,1),11886(a,1,1))].">
      <j1 rule="para" parents="11885 11886"/>
    </justification>
  </clause>

  <clause id="11911">
    <literal><![CDATA[
      a(x,y,L(a(z,z,u),y,x)) = a(a(z,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11879,a(flip),b,11889,a),flip(a)].">
      <j1 rule="hyper" parents="63 11879 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11912">
    <literal><![CDATA[
      T(a(a(x,x,y),L(y,x,x),z) * L(y,x,x),a(x,x,y)) = L(a(x,x,y),L(y,x,x),z) \ y
    ]]></literal>
    <justification jstring="[para(11911(a,1),9177(a,1,1,1))].">
      <j1 rule="para" parents="11911 9177"/>
    </justification>
  </clause>

  <clause id="11913">
    <literal><![CDATA[
      a(x,x,L(L(a(y,z,u),w,v5),L(x,w,v5),x * a(y,z,u))) = a(x,L(x,w,v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11868,a,b,11878,a)].">
      <j1 rule="hyper" parents="63 11868 11878"/>
    </justification>
  </clause>

  <clause id="11914">
    <literal><![CDATA[
      a(x,L(x,y,z),a(u,w,v5)) = a(x,x,L(a(u,w,v5),y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11894,a(flip),b,11913,a),flip(a)].">
      <j1 rule="hyper" parents="63 11894 11913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11916">
    <literal><![CDATA[
      L(x * a(x,x,L(a(y,z,u),w,v5)),a(y,z,u),L(x,w,v5)) = L(x,L(x,w,v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(11914(a,1),8921(a,1,1,2))].">
      <j1 rule="para" parents="11914 8921"/>
    </justification>
  </clause>

  <clause id="11917">
    <literal><![CDATA[
      L(L(x,x,L(a(y,z,u),w,v5)),a(y,z,u),L(x,w,v5)) = L(x,L(x,w,v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(11685(a,1),11916(a,1,1))].">
      <j1 rule="para" parents="11685 11916"/>
    </justification>
  </clause>

  <clause id="11918">
    <literal><![CDATA[
      L(L(x,a(y,z,u),x),x,L(a(y,z,u),w,v5)) = L(x,L(x,w,v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7997,a(flip),b,11917,a)].">
      <j1 rule="hyper" parents="63 7997 11917"/>
    </justification>
  </clause>

  <clause id="11920">
    <literal><![CDATA[
      L(x,L(x,y,z),a(u,w,v5)) = L(x,x,L(a(u,w,v5),y,z))
    ]]></literal>
    <justification jstring="[para(5321(a,1),11918(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5321 11918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11921">
    <literal><![CDATA[
      L(x \ L(x,x,L(a(y,z,u),w,v5)),w,v5) = a(L(x,w,v5),L(x,w,v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(11920(a,1),7361(a,1,1,2))].">
      <j1 rule="para" parents="11920 7361"/>
    </justification>
  </clause>

  <clause id="11922">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),a(u,w,v5)) = L(a(x,x,L(a(u,w,v5),y,z)),y,z)
    ]]></literal>
    <justification jstring="[para(11684(a,1),11921(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11684 11921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11923">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),a(u,w,v5)) = a(x,x,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,9943,a(flip),b,11922,a),flip(a)].">
      <j1 rule="hyper" parents="316 9943 11922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11925">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),L(x,y,z),a(u,w,v5)) = a(x,x,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,7328,a,b,11923,a)].">
      <j1 rule="hyper" parents="63 7328 11923"/>
    </justification>
  </clause>

  <clause id="11926">
    <literal><![CDATA[
      a(x,y,z \ ((((u * u) * (u \ w)) \ v5) \ v6)) = a(x,y,z \ (((w / (u \ 1)) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5925,a(flip),b,10701,a),flip(a)].">
      <j1 rule="hyper" parents="63 5925 10701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11928">
    <literal><![CDATA[
      a(x,y,z \ ((((u * u) * (u \ w)) \ v5) \ v6)) = a(x,y,z \ ((((u \ 1) \ w) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,5926,a(flip),b,11926,a),flip(a)].">
      <j1 rule="hyper" parents="316 5926 11926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11929">
    <literal><![CDATA[
      a(x,y,z \ ((((u \ 1) \ w) \ v5) \ v6)) = a(x,y,z \ (((u \ w) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,10699,a(flip),b,11928,a),flip(a)].">
      <j1 rule="hyper" parents="63 10699 11928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11931">
    <literal><![CDATA[
      a(x,y,z \ ((L(1 / u,w,w) \ v5) \ v6)) = a(x,y,z \ (((a(w,w,u) * u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,7743,a(flip),b,10704,a)].">
      <j1 rule="hyper" parents="63 7743 10704"/>
    </justification>
  </clause>

  <clause id="11932">
    <literal><![CDATA[
      a(x * (y \ 1),a(z,u,w),v5) = a(x * y,a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10680,a(flip),b,10722,a),flip(a)].">
      <j1 rule="hyper" parents="63 10680 10722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11933">
    <literal><![CDATA[
      L(x,y,a(z,z \ u,L(w,v5,v6)) * ((z \ u) * L(w,v5,v6))) = L(x,y,z \ (u * R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(5746(a,1),11077(a,1,3,1))].">
      <j1 rule="para" parents="5746 11077"/>
    </justification>
  </clause>

  <clause id="11934">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,(w \ L(w,v5,v6)) * v7) = L(x \ L(x,y,z),u,(w * L(w,v5,v6)) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,8380,a(flip),b,11096,a),flip(a)].">
      <j1 rule="hyper" parents="63 8380 11096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11935">
    <literal><![CDATA[
      L(x,(((y \ z) * y) * (K(u,w) * v5)) * ((v6 * v6) \ v7),v8) = L(x,v7 * (v5 * ((v6 * v6) \ z)),v8)
    ]]></literal>
    <justification jstring="[hyper(316,a,11024,a(flip),b,11135,a),flip(a)].">
      <j1 rule="hyper" parents="316 11024 11135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11936">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((R(u,w,w) \ w) \ (z * L(w,w,u)))) = a(x,y,a(L(u,w,w) \ w,u,z))
    ]]></literal>
    <justification jstring="[para(6771(a,1),11316(a,2,3))].">
      <j1 rule="para" parents="6771 11316"/>
    </justification>
  </clause>

  <clause id="11937">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,T(w,x)) = L(K(w,L(y,z,u) \ y) * x,L(y,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10354,a(flip),b,11535,a),flip(a)].">
      <j1 rule="hyper" parents="63 10354 11535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11938">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,T(w,x)) = L(1 * x,L(y,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[para(6491(a,1),11937(a,2,1,1))].">
      <j1 rule="para" parents="6491 11937"/>
    </justification>
  </clause>

  <clause id="11939">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,T(w,x)) = L(x,L(y,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[para(7(a,1),11938(a,2,1))].">
      <j1 rule="para" parents="7 11938"/>
    </justification>
  </clause>

  <clause id="11941">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,w) = L(x,L(y,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(4739,a,11939,a)].">
      <j1 rule="hyper" parents="4739 11939"/>
    </justification>
  </clause>

  <clause id="11943">
    <literal><![CDATA[
      x * a(x,L(y,z,u) \ y,L(y,z,u) \ y) = L(x,L(y,z,u) \ y,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2381,a,b,11941,a)].">
      <j1 rule="hyper" parents="63 2381 11941"/>
    </justification>
  </clause>

  <clause id="11944">
    <literal><![CDATA[
      L(x \ L(x,L(y,z,u) \ y,w),x,w * (L(y,z,u) \ y)) = a(x,L(y,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[para(11941(a,1),3424(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11941 3424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11945">
    <literal><![CDATA[
      x * a(x,L(y,z,u) \ y,y * L(y,z,u)) = L(x,L(y,z,u) \ y,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(2652(a,1),11943(a,1,2))].">
      <j1 rule="para" parents="2652 11943"/>
    </justification>
  </clause>

  <clause id="11946">
    <literal><![CDATA[
      L(x \ L(x,L(y,z,u) \ y,w),x,w * (y * L(y,z,u))) = a(x,L(y,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8814,a(flip),b,11944,a)].">
      <j1 rule="hyper" parents="63 8814 11944"/>
    </justification>
  </clause>

  <clause id="11947">
    <literal><![CDATA[
      L(x \ L(x,L(y,z,u) \ y,w),x,(y * L(y,z,u)) * w) = a(x,L(y,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1668,a,b,11946,a)].">
      <j1 rule="hyper" parents="63 1668 11946"/>
    </justification>
  </clause>

  <clause id="11948">
    <literal><![CDATA[
      T(x * (L(y,z,u) * L(y \ 1,w,v5)),v6) = T(x,v6) * (L(y,z,u) * L(y \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(2794(a,2),11540(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2794 11540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11950">
    <literal><![CDATA[
      (((x * y) / x) * x) * (L(z,u,w) * L(z \ 1,u,w)) = y * T(x * (L(z,u,w) * L(z \ 1,u,w)),y)
    ]]></literal>
    <justification jstring="[para(11948(a,2),7914(a,2,2))].">
      <j1 rule="para" parents="11948 7914"/>
    </justification>
  </clause>

  <clause id="11951">
    <literal><![CDATA[
      R((x \ (L(y,z,u) * (y \ x))) \ 1,w,v5) = L((x \ (L(y,z,u) * (y \ x))) \ 1,w,v5)
    ]]></literal>
    <justification jstring="[para(1907(a,1),11565(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1907 11565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11952">
    <literal><![CDATA[
      R((x \ ((x / y) * L(y,z,u))) \ 1,w,v5) = L((x \ (L(y,z,u) * (y \ x))) \ 1,w,v5)
    ]]></literal>
    <justification jstring="[para(4325(a,1),11951(a,1,1,1,2))].">
      <j1 rule="para" parents="4325 11951"/>
    </justification>
  </clause>

  <clause id="11953">
    <literal><![CDATA[
      R((x \ ((x / y) * L(y,z,u))) \ 1,w,v5) = L((x \ ((x / y) * L(y,z,u))) \ 1,w,v5)
    ]]></literal>
    <justification jstring="[para(4325(a,1),11952(a,2,1,1,2))].">
      <j1 rule="para" parents="4325 11952"/>
    </justification>
  </clause>

  <clause id="11954">
    <literal><![CDATA[
      L(a(x,y,z),u,(a(x,y,z) * u) \ w) \ w = (u \ 1) * ((a(x,y,z) * (u \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(8806(a,1),11602(a,1,1))].">
      <j1 rule="para" parents="8806 11602"/>
    </justification>
  </clause>

  <clause id="11955">
    <literal><![CDATA[
      (x \ 1) * ((a(y,z,u) * (x \ 1)) \ w) = x * ((a(y,z,u) * x) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11599,a(flip),b,11954,a),flip(a)].">
      <j1 rule="hyper" parents="63 11599 11954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11956">
    <literal><![CDATA[
      (x / (y \ L(a(z,u,w),y,y))) * (y \ 1) = y * ((a(z,u,w) * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5360,a,b,11955,a)].">
      <j1 rule="hyper" parents="63 5360 11955"/>
    </justification>
  </clause>

  <clause id="11957">
    <literal><![CDATA[
      (x / ((y \ 1) * a(z,u,w))) * (y \ 1) = y * ((a(z,u,w) * y) \ x)
    ]]></literal>
    <justification jstring="[para(2462(a,1),11956(a,1,1,2))].">
      <j1 rule="para" parents="2462 11956"/>
    </justification>
  </clause>

  <clause id="11958">
    <literal><![CDATA[
      a(x,y,z * (L(u * (1 / w),w,w) * v5)) = a(x,y,z * (v5 * R((1 / w) * u,w,w)))
    ]]></literal>
    <justification jstring="[para(2605(a,1),11762(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="2605 11762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11959">
    <literal><![CDATA[
      a(x,y,z * (L(u * (1 / w),w,w) * v5)) = a(x,y,z * (v5 * L((1 / w) * u,w,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,7433,a(flip),b,11958,a),flip(a)].">
      <j1 rule="hyper" parents="316 7433 11958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11960">
    <literal><![CDATA[
      T(L(L(x,y,y),a(y,y,x),z),a(y,y,x)) = L(a(y,y,x),L(x,y,y),z) \ x
    ]]></literal>
    <justification jstring="[para(9464(a,1),11912(a,1,1))].">
      <j1 rule="para" parents="9464 11912"/>
    </justification>
  </clause>

  <clause id="11961">
    <literal><![CDATA[
      L(a(x,x,y),L(y,x,x),z) \ y = L(L(y,x,x),a(x,x,y),z)
    ]]></literal>
    <justification jstring="[hyper(2294,a,11960,a),flip(a)].">
      <j1 rule="hyper" parents="2294 11960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11963">
    <literal><![CDATA[
      a(x,x,L(y,L(y,x,x),z)) \ y = L(L(y,x,x),a(x,x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11873,a,b,11961,a)].">
      <j1 rule="hyper" parents="63 11873 11961"/>
    </justification>
  </clause>

  <clause id="11964">
    <literal><![CDATA[
      L(x,y,z \ (u * R(w,v5,v6))) = L(x,y,z \ (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(8458(a,1),11933(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8458 11933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11965">
    <literal><![CDATA[
      L(x,((y * y) \ z) * (((u \ w) * u) * v5),v6) = L(x,z * (v5 * ((y * y) \ w)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,10909,a(flip),b,11935,a)].">
      <j1 rule="hyper" parents="63 10909 11935"/>
    </justification>
  </clause>

  <clause id="11966">
    <literal><![CDATA[
      L(x,((y * y) \ z) * (u * w),v5) = L(x,z * (w * ((y * y) \ u)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10900,a(flip),b,11965,a)].">
      <j1 rule="hyper" parents="63 10900 11965"/>
    </justification>
  </clause>

  <clause id="11967">
    <literal><![CDATA[
      L(x,y * ((z * z) \ (u * w)),v5) = L(x,y * (w * ((z * z) \ u)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10970,a(flip),b,11966,a)].">
      <j1 rule="hyper" parents="63 10970 11966"/>
    </justification>
  </clause>

  <clause id="11968">
    <literal><![CDATA[
      L(x,y * (z * ((u * u) \ u)),w) = L(x,y * L(u \ z,u,u),w)
    ]]></literal>
    <justification jstring="[para(102(a,2),11967(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="102 11967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11969">
    <literal><![CDATA[
      L(x,(y * (a(y,z,(u * u) \ u) \ z)) * (u \ 1),w) = L(x,y * L(u \ z,u,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10935,a,b,11968,a)].">
      <j1 rule="hyper" parents="63 10935 11968"/>
    </justification>
  </clause>

  <clause id="11970">
    <literal><![CDATA[
      L(x,(y * (a(y,z,u) \ z)) * (u \ 1),w) = L(x,y * L(u \ z,u,u),w)
    ]]></literal>
    <justification jstring="[para(5802(a,1),11969(a,1,2,1,2,1))].">
      <j1 rule="para" parents="5802 11969"/>
    </justification>
  </clause>

  <clause id="11972">
    <literal><![CDATA[
      L(x,y * L(z \ u,z,z),w) = L(x,y * (u * (z \ 1)),w)
    ]]></literal>
    <justification jstring="[para(8535(a,1),11970(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8535 11970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11973">
    <literal><![CDATA[
      L(x,y * L(T(z,u),u,u),w) = L(x,y * ((z * u) * (u \ 1)),w)
    ]]></literal>
    <justification jstring="[para(22(a,2),11972(a,1,2,2,1))].">
      <j1 rule="para" parents="22 11972"/>
    </justification>
  </clause>

  <clause id="11974">
    <literal><![CDATA[
      L(x,y * ((z * u) * (u \ 1)),w) = L(x,y * L(z,u,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10871,a(flip),b,11973,a),flip(a)].">
      <j1 rule="hyper" parents="63 10871 11973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11976">
    <literal><![CDATA[
      L(x,y * R(z,u,u),w) = L(x,y * L(z,u,u),w)
    ]]></literal>
    <justification jstring="[para(565(a,1),11974(a,1,2,2))].">
      <j1 rule="para" parents="565 11974"/>
    </justification>
  </clause>

  <clause id="11977">
    <literal><![CDATA[
      R(x \ L(x,y,z),K(u \ x,u),w) = ((u * (x / u)) \ L(x,y,z)) * K(u,u \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10206,a(flip),b,10284,a),flip(a)].">
      <j1 rule="hyper" parents="63 10206 10284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11979">
    <literal><![CDATA[
      R(x \ L(x,y,z),K(u \ x,u),w) = (u * (x / u)) \ L(u * (x / u),y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,4874,a(flip),b,11977,a),flip(a)].">
      <j1 rule="hyper" parents="316 4874 11977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11980">
    <literal><![CDATA[
      (x * (y / x)) \ L(x * (y / x),z,u) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(10170,a,11979,a),flip(a)].">
      <j1 rule="hyper" parents="10170 11979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11982">
    <literal><![CDATA[
      ((x * x) * y) \ L((x * x) * y,z,u) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9575,a(flip),b,11980,a)].">
      <j1 rule="hyper" parents="63 9575 11980"/>
    </justification>
  </clause>

  <clause id="11983">
    <literal><![CDATA[
      (x * (x * y)) \ L(x * (x * y),z,u) = L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(11982(a,1),2151(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11982 2151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11984">
    <literal><![CDATA[
      a(x,(y * y) * z,((y * y) * z) * L((y * y) * z,u,w)) = a(x,z \ L(z,u,w),z)
    ]]></literal>
    <justification jstring="[para(11982(a,1),8238(a,2,2))].">
      <j1 rule="para" parents="11982 8238"/>
    </justification>
  </clause>

  <clause id="11985">
    <literal><![CDATA[
      ((x * y) * x) \ L((x * y) * x,z,u) = L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4877,a,b,11983,a)].">
      <j1 rule="hyper" parents="63 4877 11983"/>
    </justification>
  </clause>

  <clause id="11986">
    <literal><![CDATA[
      (1 / (x * y)) * (x * L(y,z,u)) = L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9592,a(flip),b,11983,a)].">
      <j1 rule="hyper" parents="63 9592 11983"/>
    </justification>
  </clause>

  <clause id="11988">
    <literal><![CDATA[
      a(x,y,(z * u) * (z * L(u,w,v5))) = a(x,y,L(u \ L(u,w,v5),z,z))
    ]]></literal>
    <justification jstring="[para(11986(a,1),5572(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11986 5572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11989">
    <literal><![CDATA[
      (R(x,y,y) * a(x,y,y)) \ L((a(x,y,y) * x) * a(x,y,y),z,u) = L(x \ L(x,z,u),a(x,y,y),a(x,y,y))
    ]]></literal>
    <justification jstring="[para(2377(a,1),11985(a,1,1,1))].">
      <j1 rule="para" parents="2377 11985"/>
    </justification>
  </clause>

  <clause id="11990">
    <literal><![CDATA[
      a(x,y,(z * u) * (z * L(u,w,v5))) = a(x,y,L(u * L(u,w,v5),z,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5893,a(flip),b,11988,a),flip(a)].">
      <j1 rule="hyper" parents="316 5893 11988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11991">
    <literal><![CDATA[
      a(x,y,(z * u) * (L(u,w,v5) * z)) = a(x,y,L(u * L(u,w,v5),z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5491,a,b,11990,a)].">
      <j1 rule="hyper" parents="63 5491 11990"/>
    </justification>
  </clause>

  <clause id="11992">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),z \ v5,z \ v5)) = a(x,y,v5 * ((z \ v5) * L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5511,a(flip),b,11990,a),flip(a)].">
      <j1 rule="hyper" parents="63 5511 11990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11993">
    <literal><![CDATA[
      a(x,(y * y) * z,((y * y) * z) * L((y * y) * z,u,w)) = a(x,z,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,8234,a(flip),b,11984,a),flip(a)].">
      <j1 rule="hyper" parents="316 8234 11984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11995">
    <literal><![CDATA[
      L(((x * x) * y) \ L((x * x) * y,z,u),(x * x) * y,w) = a(w,y,y * L(y,z,u)) \ (((x * x) * y) \ L((x * x) * y,z,u))
    ]]></literal>
    <justification jstring="[para(11993(a,1),10038(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11993 10038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11996">
    <literal><![CDATA[
      a(x,y,a(z,u / T(w * w,v5),v6)) = a(x,y,((v6 * ((w * w) \ u)) * z) \ (v6 * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10667,a(flip),b,10697,a),flip(a)].">
      <j1 rule="hyper" parents="63 10667 10697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11998">
    <literal><![CDATA[
      a(x,y,((z * ((u * u) \ w)) * v5) \ (z * (v5 * w))) = a(x,y,a(v5,(u * u) \ w,z))
    ]]></literal>
    <justification jstring="[para(279(a,1),11996(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="279 11996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11999">
    <literal><![CDATA[
      a(x,y,a(z,(u * u) \ w,v5)) = a(x,y,(z * (v5 * w)) \ (v5 * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11463,a(flip),b,11998,a),flip(a)].">
      <j1 rule="hyper" parents="63 11463 11998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12001">
    <literal><![CDATA[
      a(x,y,a(z,(u * u) \ w,v5)) = a(x,y,a(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,10778,a(flip),b,11999,a),flip(a)].">
      <j1 rule="hyper" parents="316 10778 11999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12002">
    <literal><![CDATA[
      a(x,y,a((z * z) \ u,u,w)) = a(x,y,a(w,(z * z) \ u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7282,a(flip),b,12001,a),flip(a)].">
      <j1 rule="hyper" parents="63 7282 12001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12003">
    <literal><![CDATA[
      a(x,y,a(z,T(u,w * w),v5)) = a(x,y,a(z,u * (w * w),v5))
    ]]></literal>
    <justification jstring="[para(22(a,2),12001(a,1,3,2))].">
      <j1 rule="para" parents="22 12001"/>
    </justification>
  </clause>

  <clause id="12004">
    <literal><![CDATA[
      a(x,y,a(z,L(u \ w,u,u),v5)) = a(x,y,a(z,u * w,v5))
    ]]></literal>
    <justification jstring="[para(102(a,2),12001(a,1,3,2))].">
      <j1 rule="para" parents="102 12001"/>
    </justification>
  </clause>

  <clause id="12005">
    <literal><![CDATA[
      a(x,y,a(z,T(u * (w * (v5 \ 1)),v5 * v5),v6)) = a(x,y,a(z,u * (w * v5),v6))
    ]]></literal>
    <justification jstring="[para(1055(a,2),12001(a,1,3,2))].">
      <j1 rule="para" parents="1055 12001"/>
    </justification>
  </clause>

  <clause id="12006">
    <literal><![CDATA[
      a(x,y,a((z * z) \ u,u,L(w,v5,(z * z) \ u))) = a(x,y,a((z * z) \ u,(z * z) \ u,w))
    ]]></literal>
    <justification jstring="[para(8592(a,1),12001(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8592 12001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12007">
    <literal><![CDATA[
      a(x,y,a(z,u * (w * u),v5)) = a(x,y,a(z,L(w,u,u),v5))
    ]]></literal>
    <justification jstring="[para(11323(a,1),12001(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11323 12001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12008">
    <literal><![CDATA[
      a(x,y,a(z,u * (w \ 1),v5)) = a(x,y,a(z,w * u,v5))
    ]]></literal>
    <justification jstring="[para(11308(a,1),12004(a,1,3))].">
      <j1 rule="para" parents="11308 12004"/>
    </justification>
  </clause>

  <clause id="12009">
    <literal><![CDATA[
      a(x,y,a(z,u * (u \ L(u,w,v5)),v6)) = a(x,y,a(z,L(u \ 1,w,v5),v6))
    ]]></literal>
    <justification jstring="[para(1070(a,1),12008(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="1070 12008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12010">
    <literal><![CDATA[
      a(x,y,a((z * z) \ u,u,w)) = a(x,y,a(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,12001,a(flip),b,12002,a),flip(a)].">
      <j1 rule="hyper" parents="316 12001 12002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12013">
    <literal><![CDATA[
      a(x,y,a(z,u * (w * w),v5)) = a(x,y,a(z,u,v5))
    ]]></literal>
    <justification jstring="[para(11194(a,1),12003(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11194 12003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12014">
    <literal><![CDATA[
      a(x,y,a(z,u \ 1,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(229(a,1),12013(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="229 12013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12016">
    <literal><![CDATA[
      a(x,y,a(z,(u \ 1) \ w,v5)) = a(x,y,a(z,u \ w,v5))
    ]]></literal>
    <justification jstring="[para(11255(a,1),12013(a,1,3))].">
      <j1 rule="para" parents="11255 12013"/>
    </justification>
  </clause>

  <clause id="12017">
    <literal><![CDATA[
      a(x,y,a(z \ 1,u \ 1,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,11318,a(flip),b,12014,a),flip(a)].">
      <j1 rule="hyper" parents="316 11318 12014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12019">
    <literal><![CDATA[
      a(x,y,a(z,L(u \ 1,w,v5),v6)) = a(x,y,a(z,L(u,w,v5),v6))
    ]]></literal>
    <justification jstring="[para(10(a,1),12009(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 12009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12021">
    <literal><![CDATA[
      a(x,y,a(z,u * (w * (v5 \ 1)),v6)) = a(x,y,a(z,u * (w * v5),v6))
    ]]></literal>
    <justification jstring="[para(11194(a,1),12005(a,1,3))].">
      <j1 rule="para" parents="11194 12005"/>
    </justification>
  </clause>

  <clause id="12023">
    <literal><![CDATA[
      a(x,y,L(L((z \ 1) \ (u \ w),z,u),v5,v6)) = a(x,y,L((u * T(z \ 1,v7)) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,6368,a(flip),b,10931,a)].">
      <j1 rule="hyper" parents="63 6368 10931"/>
    </justification>
  </clause>

  <clause id="12024">
    <literal><![CDATA[
      a(x,y,L(L((z \ 1) \ (u \ w),z,u),v5,v6)) = a(x,y,L((u * (z \ 1)) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,10289,a(flip),b,12023,a),flip(a)].">
      <j1 rule="hyper" parents="316 10289 12023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12026">
    <literal><![CDATA[
      T(a(x \ 1,x,y) * (z * L(y,x,x \ 1)),K(y,z)) = L(z,R(y,x,x),a(x \ 1,x,y)) * y
    ]]></literal>
    <justification jstring="[hyper(4120,a,10941,a)].">
      <j1 rule="hyper" parents="4120 10941"/>
    </justification>
  </clause>

  <clause id="12027">
    <literal><![CDATA[
      a(x,y,L(L(z,u,(z * u) \ w),L(z,u,(z * u) \ w),w)) = a(x,y,w \ (u * ((z * u) \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5953,a(flip),b,10991,a)].">
      <j1 rule="hyper" parents="63 5953 10991"/>
    </justification>
  </clause>

  <clause id="12028">
    <literal><![CDATA[
      a(x,y,z * (L(u,w,v5) * L(v6,L(u,w,v5),L(u,w,v5)))) = a(x,y,T(v6 / R(u,w,v5),u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11760,a(flip),b,10992,a)].">
      <j1 rule="hyper" parents="63 11760 10992"/>
    </justification>
  </clause>

  <clause id="12029">
    <literal><![CDATA[
      a(x,y,L(z,L(L(u,u,w),R(w,u,u),R(w,u,u)),v5)) = a(x,y,L(z,w * (u * R(w,u,u)),v5))
    ]]></literal>
    <justification jstring="[para(3112(a,1),11001(a,2,3,2))].">
      <j1 rule="para" parents="3112 11001"/>
    </justification>
  </clause>

  <clause id="12030">
    <literal><![CDATA[
      R(x,y,((T(z,u) * w) \ ((T(z,u) * u) * w)) * v5) = R(x,y,L(u,z,w) * (K(u * z,w) * v5))
    ]]></literal>
    <justification jstring="[para(10184(a,1),11013(a,2,3))].">
      <j1 rule="para" parents="10184 11013"/>
    </justification>
  </clause>

  <clause id="12031">
    <literal><![CDATA[
      a(x,y * ((T(z,u) * w) \ ((T(z,u) * u) * w)),v5) = a(x,L(u,z,w) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,11286,a(flip),b,11299,a),flip(a)].">
      <j1 rule="hyper" parents="316 11286 11299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12033">
    <literal><![CDATA[
      a(x,y * ((z * u) \ ((z * w) * u)),v5) = a(x,L(w,z,u) * y,v5)
    ]]></literal>
    <justification jstring="[para(3187(a,1),12031(a,1,2,2))].">
      <j1 rule="para" parents="3187 12031"/>
    </justification>
  </clause>

  <clause id="12034">
    <literal><![CDATA[
      a(x,L(y,z,u) * w,v5) = a(x,w * R(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11416,a(flip),b,12033,a),flip(a)].">
      <j1 rule="hyper" parents="63 11416 12033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12035">
    <literal><![CDATA[
      a(x,R(y,z,u) * w,v5) = a(x,L(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11415,a(flip),b,12033,a)].">
      <j1 rule="hyper" parents="63 11415 12033"/>
    </justification>
  </clause>

  <clause id="12037">
    <literal><![CDATA[
      a(x,y * R(z,u,w),v5) = a(x,y * L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11190,a,b,12034,a),flip(a)].">
      <j1 rule="hyper" parents="63 11190 12034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12038">
    <literal><![CDATA[
      a(x,y * R(T(z,u),w,v5),v6) = a(x,L(z,w,v5) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,11285,a,b,12035,a)].">
      <j1 rule="hyper" parents="63 11285 12035"/>
    </justification>
  </clause>

  <clause id="12039">
    <literal><![CDATA[
      a(x,R(y,z,u) * (y \ 1),w) = a(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(969(a,1),12035(a,2,2))].">
      <j1 rule="para" parents="969 12035"/>
    </justification>
  </clause>

  <clause id="12040">
    <literal><![CDATA[
      a(x,L(y,y,z) * (y \ z),u) = a(x,z * a(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(8527(a,1),12035(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8527 12035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12041">
    <literal><![CDATA[
      a(x,y \ R(y,z,u),w) = a(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(978(a,1),12039(a,1,2))].">
      <j1 rule="para" parents="978 12039"/>
    </justification>
  </clause>

  <clause id="12042">
    <literal><![CDATA[
      a(x,(y / (z \ 1)) / z,u) = a(x,y * a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(4412(a,1),12040(a,1,2))].">
      <j1 rule="para" parents="4412 12040"/>
    </justification>
  </clause>

  <clause id="12043">
    <literal><![CDATA[
      a(x,y \ (z / (y \ 1)),u) = a(x,z * a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11195,a(flip),b,12042,a)].">
      <j1 rule="hyper" parents="63 11195 12042"/>
    </justification>
  </clause>

  <clause id="12044">
    <literal><![CDATA[
      a(x,y \ ((y \ 1) \ z),u) = a(x,z * a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11209,a(flip),b,12043,a)].">
      <j1 rule="hyper" parents="63 11209 12043"/>
    </justification>
  </clause>

  <clause id="12045">
    <literal><![CDATA[
      a(x,(y \ 1) \ (y \ z),u) = a(x,y \ ((y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,11312,a,b,12044,a)].">
      <j1 rule="hyper" parents="316 11312 12044"/>
    </justification>
  </clause>

  <clause id="12046">
    <literal><![CDATA[
      a(x,y \ ((y \ 1) \ (y * z)),u) = a(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),12045(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 12045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12047">
    <literal><![CDATA[
      L(a(x,y,z),u,R(w,w,(v5 \ 1) \ v6) \ (v5 \ v6)) = L(a(x,y,z),u,((v5 \ 1) \ v6) * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,11618,a(flip),b,11644,a),flip(a)].">
      <j1 rule="hyper" parents="316 11618 11644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12048">
    <literal><![CDATA[
      L(a(x,y,z),u,R(w,w,v5 \ v6) \ (v5 \ v6)) = L(a(x,y,z),u,((v5 \ 1) \ v6) * w)
    ]]></literal>
    <justification jstring="[para(4789(a,1),12047(a,1,3,1))].">
      <j1 rule="para" parents="4789 12047"/>
    </justification>
  </clause>

  <clause id="12049">
    <literal><![CDATA[
      L(a(x,y,z),u,((w \ 1) \ v5) * v6) = L(a(x,y,z),u,(w \ v5) * (v6 \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,4659,a(flip),b,12048,a),flip(a)].">
      <j1 rule="hyper" parents="63 4659 12048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12050">
    <literal><![CDATA[
      L(a(x,y,z),u,((w \ 1) \ v5) * v6) = L(a(x,y,z),u,(w \ v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,11618,a(flip),b,12049,a),flip(a)].">
      <j1 rule="hyper" parents="316 11618 12049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12051">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * (v5 * K(v5 \ 1,v5 * w))))) = a(x,y,z \ (u * L(w / (v5 \ 1),v5,v5)))
    ]]></literal>
    <justification jstring="[para(10207(a,1),11755(a,1,3,2,2))].">
      <j1 rule="para" parents="10207 11755"/>
    </justification>
  </clause>

  <clause id="12052">
    <literal><![CDATA[
      a(x,y,a((z * z) \ u,u,L(w,v5,(z * z) \ u))) = a(x,y,a((z * z) \ u,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,12001,a(flip),b,12006,a),flip(a)].">
      <j1 rule="hyper" parents="316 12001 12006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12054">
    <literal><![CDATA[
      a(x,y,a((z * z) \ u,u,L(w,v5,(z * z) \ u))) = a(x,y,a(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,12010,a(flip),b,12052,a),flip(a)].">
      <j1 rule="hyper" parents="316 12010 12052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12056">
    <literal><![CDATA[
      a(x,y,a((z * z) \ u,u,L(w,v5,u))) = a(x,y,a(w,u,u))
    ]]></literal>
    <justification jstring="[para(5764(a,1),12054(a,1,3))].">
      <j1 rule="para" parents="5764 12054"/>
    </justification>
  </clause>

  <clause id="12057">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),w,w)) = a(x,y,a(z,w,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12010,a(flip),b,12056,a)].">
      <j1 rule="hyper" parents="63 12010 12056"/>
    </justification>
  </clause>

  <clause id="12059">
    <literal><![CDATA[
      T(a(x \ 1,x,y) * (z * L(y,x,x \ 1)),K(y,z)) = L(z,L(y,x,x),a(x \ 1,x,y)) * y
    ]]></literal>
    <justification jstring="[para(10977(a,1),12026(a,2,1))].">
      <j1 rule="para" parents="10977 12026"/>
    </justification>
  </clause>

  <clause id="12060">
    <literal><![CDATA[
      a(x,y,T(z / R(u,w,v5),u) * v6) = a(x,y,(L(u,w,v5) \ z) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,8684,a(flip),b,12028,a),flip(a)].">
      <j1 rule="hyper" parents="63 8684 12028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12061">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) \ v5) * v6) = a(x,y,(L(z,u,w) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(2838(a,1),12060(a,1,3,1))].">
      <j1 rule="para" parents="2838 12060"/>
    </justification>
  </clause>

  <clause id="12062">
    <literal><![CDATA[
      a(x,y,(z \ (a(z,z \ 1,u) \ z)) * w) = a(x,y,(L(z,z \ 1,u) \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11369,a,b,12061,a)].">
      <j1 rule="hyper" parents="63 11369 12061"/>
    </justification>
  </clause>

  <clause id="12063">
    <literal><![CDATA[
      a(x,y,(R(L(z,u,w),v5,v6) \ v7) * v8) = a(x,y,(L(L(z,v5,v6),u,w) \ v7) * v8)
    ]]></literal>
    <justification jstring="[para(30(a,1),12061(a,2,3,1,1))].">
      <j1 rule="para" parents="30 12061"/>
    </justification>
  </clause>

  <clause id="12064">
    <literal><![CDATA[
      a(x,y,(R(L(z \ u,w,v5),z,z \ 1) \ v6) * v7) = a(x,y,(L((1 / z) * u,w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[para(894(a,1),12061(a,2,3,1,1))].">
      <j1 rule="para" parents="894 12061"/>
    </justification>
  </clause>

  <clause id="12065">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ v5) * (v6 * (a(v6,v7,R(z,u,w) \ v5) \ v7))) = a(x,y,L(R(z,u,w) \ v5,v7,v6) * (v6 * v7))
    ]]></literal>
    <justification jstring="[para(8534(a,1),12061(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8534 12061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12066">
    <literal><![CDATA[
      a(x,y,(z \ (a(z,z \ 1,u) \ z)) * w) = a(x,y,a(u,z \ 1,z) * w)
    ]]></literal>
    <justification jstring="[para(7384(a,1),12062(a,2,3,1))].">
      <j1 rule="para" parents="7384 12062"/>
    </justification>
  </clause>

  <clause id="12067">
    <literal><![CDATA[
      a(x,y,(a(z,z \ 1,u) \ 1) * w) = a(x,y,a(u,z \ 1,z) * w)
    ]]></literal>
    <justification jstring="[para(8429(a,1),12066(a,1,3,1))].">
      <j1 rule="para" parents="8429 12066"/>
    </justification>
  </clause>

  <clause id="12068">
    <literal><![CDATA[
      a(x,y,a(z,u \ 1,u) * w) = a(x,y,a(u,u \ 1,z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5564,a(flip),b,12067,a),flip(a)].">
      <j1 rule="hyper" parents="63 5564 12067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12069">
    <literal><![CDATA[
      a(x,y,a(z,u \ 1,u) * w) = a(x,y,a(u,u,z) * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,7579,a(flip),b,12068,a),flip(a)].">
      <j1 rule="hyper" parents="316 7579 12068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12070">
    <literal><![CDATA[
      a(x,y,((z \ u) \ (u * (1 / z))) * w) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10575,a,b,12069,a)].">
      <j1 rule="hyper" parents="63 10575 12069"/>
    </justification>
  </clause>

  <clause id="12071">
    <literal><![CDATA[
      a(x,y,((z \ u) \ (u * (z \ 1))) * w) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6069,a(flip),b,12070,a)].">
      <j1 rule="hyper" parents="63 6069 12070"/>
    </justification>
  </clause>

  <clause id="12072">
    <literal><![CDATA[
      a(x,y,(L(R(z,u,w),v5,v6) \ v7) * v8) = a(x,y,(L(L(z,u,w),v5,v6) \ v7) * v8)
    ]]></literal>
    <justification jstring="[para(29(a,1),12063(a,1,3,1,1))].">
      <j1 rule="para" parents="29 12063"/>
    </justification>
  </clause>

  <clause id="12073">
    <literal><![CDATA[
      a(x,y,(L(T(z * (u \ 1),u),w,v5) \ v6) * v7) = a(x,y,(L(L(u \ z,u,u),w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[para(622(a,2),12072(a,1,3,1,1,1))].">
      <j1 rule="para" parents="622 12072"/>
    </justification>
  </clause>

  <clause id="12074">
    <literal><![CDATA[
      a(x,y,(L(R((z \ 1) \ u,z \ 1,z \ 1),w,v5) \ v6) * v7) = a(x,y,(L((z \ (z \ 1)) \ ((1 / z) * u),w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[para(1593(a,1),12072(a,2,3,1,1,1))].">
      <j1 rule="para" parents="1593 12072"/>
    </justification>
  </clause>

  <clause id="12075">
    <literal><![CDATA[
      R(x,y,((T(z,u) * w) \ ((T(z,u) * u) * w)) * v5) = R(x,y,L(u,z,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,4697,a(flip),b,12030,a),flip(a)].">
      <j1 rule="hyper" parents="316 4697 12030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12077">
    <literal><![CDATA[
      R(x,y,((z * u) \ ((z * w) * u)) * v5) = R(x,y,L(w,z,u) * v5)
    ]]></literal>
    <justification jstring="[para(3187(a,1),12075(a,1,3,1))].">
      <j1 rule="para" parents="3187 12075"/>
    </justification>
  </clause>

  <clause id="12078">
    <literal><![CDATA[
      R(x,y,R(z,u,w) * v5) = R(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,4795,a(flip),b,12077,a)].">
      <j1 rule="hyper" parents="63 4795 12077"/>
    </justification>
  </clause>

  <clause id="12080">
    <literal><![CDATA[
      R(x,y,L(z,u,w) * L(v5,v5,R(z,u,w))) = R(x,y,R(z,u,w) / (v5 \ 1))
    ]]></literal>
    <justification jstring="[para(1445(a,1),12078(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1445 12078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12081">
    <literal><![CDATA[
      a(x,y,z * (R(u,u,L(w,v5,v6) * v7) * (L(w,v5,v6) * v7))) = a(x,y,(u \ (R(w,v5,v6) * v7)) * z)
    ]]></literal>
    <justification jstring="[para(12078(a,1),9693(a,1,3,2,1))].">
      <j1 rule="para" parents="12078 9693"/>
    </justification>
  </clause>

  <clause id="12082">
    <literal><![CDATA[
      R(x,y,L(z,u,w) * L(v5,v5,R(z,u,w))) = R(x,y,(v5 \ 1) \ R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,4680,a(flip),b,12080,a),flip(a)].">
      <j1 rule="hyper" parents="316 4680 12080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12083">
    <literal><![CDATA[
      R(x,y,L(z,u,w) * L(v5,v5,R(z,u,w))) = R(x,y,v5 \ R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,4789,a(flip),b,12082,a),flip(a)].">
      <j1 rule="hyper" parents="316 4789 12082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12084">
    <literal><![CDATA[
      R(x,y,L(z,u,w) * L(v5,v5,L(z,u,w))) = R(x,y,v5 \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(4628(a,1),12083(a,1,3,2))].">
      <j1 rule="para" parents="4628 12083"/>
    </justification>
  </clause>

  <clause id="12085">
    <literal><![CDATA[
      R(x,y,L(z,u,w) / (v5 \ 1)) = R(x,y,v5 \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(1445(a,1),12084(a,1,3))].">
      <j1 rule="para" parents="1445 12084"/>
    </justification>
  </clause>

  <clause id="12086">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ L(u,w,v5)) = R(x,y,z \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,4680,a(flip),b,12085,a)].">
      <j1 rule="hyper" parents="63 4680 12085"/>
    </justification>
  </clause>

  <clause id="12087">
    <literal><![CDATA[
      R(x,y,z \ R(u,w,v5)) = R(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,4789,a(flip),b,12086,a),flip(a)].">
      <j1 rule="hyper" parents="63 4789 12086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12088">
    <literal><![CDATA[
      a(x,y,z \ (u * L(w / (v5 \ 1),v5,v5))) = a(x,y,z \ (u * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5517,a(flip),b,12051,a),flip(a)].">
      <j1 rule="hyper" parents="63 5517 12051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12090">
    <literal><![CDATA[
      T(a(x \ 1,x,y) * (z * L(y,x,x \ 1)),K(y,z)) = L(z,L(y,x,x),a(x,x,y)) * y
    ]]></literal>
    <justification jstring="[para(7848(a,1),12059(a,2,1))].">
      <j1 rule="para" parents="7848 12059"/>
    </justification>
  </clause>

  <clause id="12091">
    <literal><![CDATA[
      T(a(x \ 1,x,y) * (z * L(y,x,x \ 1)),K(y,z)) = a(x,x,y) * (z * L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,5448,a(flip),b,12090,a),flip(a)].">
      <j1 rule="hyper" parents="316 5448 12090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12092">
    <literal><![CDATA[
      a(x \ 1,x,y) * (z * L(y,x,x \ 1)) = a(x,x,y) * (z * L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,5365,a(flip),b,12091,a)].">
      <j1 rule="hyper" parents="63 5365 12091"/>
    </justification>
  </clause>

  <clause id="12093">
    <literal><![CDATA[
      (x * a(y \ 1,y,z)) \ ((x * z) / (a(y \ 1,y,z) \ z)) = (a(y,y,z) * (x * L(z,y,y))) \ (x * z)
    ]]></literal>
    <justification jstring="[para(12092(a,1),9726(a,2,1))].">
      <j1 rule="para" parents="12092 9726"/>
    </justification>
  </clause>

  <clause id="12094">
    <literal><![CDATA[
      a(x,y,(R(L(z \ u,w,v5),z,z) \ v6) * v7) = a(x,y,(L((1 / z) * u,w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[para(573(a,1),12064(a,1,3,1,1))].">
      <j1 rule="para" parents="573 12064"/>
    </justification>
  </clause>

  <clause id="12095">
    <literal><![CDATA[
      a(x,y,(L(L(z \ u,z,z),w,v5) \ v6) * v7) = a(x,y,(L((1 / z) * u,w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,12063,a(flip),b,12094,a)].">
      <j1 rule="hyper" parents="63 12063 12094"/>
    </justification>
  </clause>

  <clause id="12096">
    <literal><![CDATA[
      a(x,y,(L(L(z \ u,z,z),w,v5) \ v6) * v7) = a(x,y,(L(u * (z \ 1),w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,5555,a(flip),b,12073,a),flip(a)].">
      <j1 rule="hyper" parents="63 5555 12073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12098">
    <literal><![CDATA[
      a(x,y,(L((1 / z) * u,w,v5) \ v6) * v7) = a(x,y,(L(u * (z \ 1),w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,12095,a(flip),b,12096,a)].">
      <j1 rule="hyper" parents="63 12095 12096"/>
    </justification>
  </clause>

  <clause id="12099">
    <literal><![CDATA[
      (K(x,(K(x \ 1,x) \ y) \ 1) / x) * (((((x \ 1) * x) \ y) \ 1) * x) = (x \ ((x \ 1) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(272(a,2),10310(a,1,1,1,2,1,1))].">
      <j1 rule="para" parents="272 10310"/>
    </justification>
  </clause>

  <clause id="12101">
    <literal><![CDATA[
      a(x * (y * ((T(z,u) \ 1) * (T(z,u) \ 1))),w,v5) = a((y * x) * ((z \ 1) * (z \ 1)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,4194,a(flip),b,10605,a),flip(a)].">
      <j1 rule="hyper" parents="316 4194 10605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12103">
    <literal><![CDATA[
      a(x * (y * ((T(z,u) \ 1) * (T(z,u) \ 1))),w,v5) = a(y * (x * ((z \ 1) * (z \ 1))),w,v5)
    ]]></literal>
    <justification jstring="[para(32(a,1),12101(a,2,1))].">
      <j1 rule="para" parents="32 12101"/>
    </justification>
  </clause>

  <clause id="12104">
    <literal><![CDATA[
      a(x * (y * ((T(z,u) \ 1) * (T(z,u) \ 1))),w,v5) = a(x * ((z * z) \ y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,11101,a(flip),b,12103,a),flip(a)].">
      <j1 rule="hyper" parents="316 11101 12103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12105">
    <literal><![CDATA[
      a(x * ((T(y,z) * T(y,z)) \ u),w,v5) = a(u * ((y * y) \ x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11101,a(flip),b,12104,a)].">
      <j1 rule="hyper" parents="63 11101 12104"/>
    </justification>
  </clause>

  <clause id="12106">
    <literal><![CDATA[
      a(((x * T(x,y)) \ z) * u,w,v5) = a(z * ((x * x) \ u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10516,a(flip),b,12105,a)].">
      <j1 rule="hyper" parents="63 10516 12105"/>
    </justification>
  </clause>

  <clause id="12108">
    <literal><![CDATA[
      a(((x * x) \ y) * z,u,w) = a(y * ((x * x) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10507,a(flip),b,12106,a)].">
      <j1 rule="hyper" parents="63 10507 12106"/>
    </justification>
  </clause>

  <clause id="12109">
    <literal><![CDATA[
      x * (K((y \ z) * u,x) * K(x * ((y \ z) * u),w)) = T(((z \ y) \ u) * x,w) / ((z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(6210(a,1),10619(a,1,2,2))].">
      <j1 rule="para" parents="6210 10619"/>
    </justification>
  </clause>

  <clause id="12110">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u \ R(w,v5,v6)) \ L(w,v5,v6)) = a(x,y,(R(w,v5,v6) / u) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5476,a(flip),b,10650,a),flip(a)].">
      <j1 rule="hyper" parents="316 5476 10650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12112">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u \ R(w,v5,v6)) \ L(w,v5,v6)) = a(x,y,(u \ R(w,v5,v6)) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5543,a(flip),b,12110,a),flip(a)].">
      <j1 rule="hyper" parents="316 5543 12110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12113">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u \ L(w,v5,v6)) \ L(w,v5,v6)) = a(x,y,(u \ R(w,v5,v6)) * z)
    ]]></literal>
    <justification jstring="[para(7482(a,1),12112(a,1,3,1))].">
      <j1 rule="para" parents="7482 12112"/>
    </justification>
  </clause>

  <clause id="12114">
    <literal><![CDATA[
      a(x,y,T((L(z,u,w) / v5) * v6,v6 \ v5)) = a(x,y,(v5 \ R(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[para(3740(a,1),12113(a,1,3))].">
      <j1 rule="para" parents="3740 12113"/>
    </justification>
  </clause>

  <clause id="12115">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) / v5) * v6) = a(x,y,(v5 \ R(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(5556,a,12114,a)].">
      <j1 rule="hyper" parents="5556 12114"/>
    </justification>
  </clause>

  <clause id="12117">
    <literal><![CDATA[
      a(x,y,(z \ R(u,w,v5)) * v6) = a(x,y,(z \ L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5543,a(flip),b,12115,a),flip(a)].">
      <j1 rule="hyper" parents="63 5543 12115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12118">
    <literal><![CDATA[
      a(x,y,(z \ L(K(u,w) * v5,v6,v7)) * v8) = a(x,y,v8 * (z \ R(v5,v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7973,a(flip),b,12117,a),flip(a)].">
      <j1 rule="hyper" parents="63 7973 12117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12120">
    <literal><![CDATA[
      a(x,y,z * (u \ R(w,v5,v6))) = a(x,y,z * (u \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7976,a(flip),b,12118,a),flip(a)].">
      <j1 rule="hyper" parents="63 7976 12118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12121">
    <literal><![CDATA[
      a(x,y,R(z,z,u \ R(w,v5,v6)) * (u \ L(w,v5,v6))) = a(x,y,z \ (u \ R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5844,a(flip),b,12120,a),flip(a)].">
      <j1 rule="hyper" parents="63 5844 12120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12123">
    <literal><![CDATA[
      a(x,y,R(z,z,u \ L(w,v5,v6)) * (u \ L(w,v5,v6))) = a(x,y,z \ (u \ R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(12087(a,1),12121(a,1,3,1))].">
      <j1 rule="para" parents="12087 12121"/>
    </justification>
  </clause>

  <clause id="12124">
    <literal><![CDATA[
      a(x,y,z \ (u \ R(w,v5,v6))) = a(x,y,z \ (u \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5844,a(flip),b,12123,a),flip(a)].">
      <j1 rule="hyper" parents="63 5844 12123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12125">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ ((w \ 1) \ v5)))) = a(x,y,z \ (u \ L(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11665,a,b,12124,a)].">
      <j1 rule="hyper" parents="63 11665 12124"/>
    </justification>
  </clause>

  <clause id="12126">
    <literal><![CDATA[
      a(x,y,z \ (L(R(u,u,L(w,v5,v6)),v7,u) \ L(w,v5,v6))) = a(x,y,z \ (u * R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8089,a(flip),b,12124,a),flip(a)].">
      <j1 rule="hyper" parents="63 8089 12124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12127">
    <literal><![CDATA[
      a(x,y,z \ (R(u / w,w,u \ R(v5,v6,v7)) \ L(v5,v6,v7))) = a(x,y,z \ (w * (u \ R(v5,v6,v7))))
    ]]></literal>
    <justification jstring="[para(490(a,1),12124(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="490 12124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12128">
    <literal><![CDATA[
      a(x,y,z \ (L(u \ w,u,w \ R(v5,v6,v7)) \ L(v5,v6,v7))) = a(x,y,z \ T((R(v5,v6,v7) / w) * u,u \ w))
    ]]></literal>
    <justification jstring="[para(3740(a,1),12124(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3740 12124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12129">
    <literal><![CDATA[
      a(x,y,z \ (u * R(w,v5,v6))) = a(x,y,z \ (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8087,a(flip),b,12126,a),flip(a)].">
      <j1 rule="hyper" parents="63 8087 12126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12130">
    <literal><![CDATA[
      a(x,y,(z * L(T(u,w),z,w)) \ (z * L(T(u,w * z),w,z))) = a(x,y,a(w,w \ (L(u,z,w) * w),z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9639,a(flip),b,12129,a),flip(a)].">
      <j1 rule="hyper" parents="63 9639 12129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12131">
    <literal><![CDATA[
      a(x,y,z \ (u * L(K(w,v5) * v6,v7,v8))) = a(x,y,z \ (R(v6,v7,v8) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7901,a(flip),b,12129,a),flip(a)].">
      <j1 rule="hyper" parents="63 7901 12129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12132">
    <literal><![CDATA[
      a(x,y,((T(z,u) * w) * v5) \ ((z * w) * L(v5,z,w))) = a(x,y,a(v5,z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6054,a(flip),b,12129,a),flip(a)].">
      <j1 rule="hyper" parents="63 6054 12129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12133">
    <literal><![CDATA[
      a(x,y,z \ (R(u,w,v5) * v6)) = a(x,y,z \ (L(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,7903,a(flip),b,12131,a),flip(a)].">
      <j1 rule="hyper" parents="63 7903 12131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12134">
    <literal><![CDATA[
      a(x,y,z \ (u * (R(w,v5,v5) * T(v5,v5 \ 1)))) = a(x,y,z \ (L(v5 * w,v5 \ 1,v5) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6029,a,b,12133,a)].">
      <j1 rule="hyper" parents="63 6029 12133"/>
    </justification>
  </clause>

  <clause id="12135">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,w * u) * v5)) = a(x,y,z \ ((w * ((u * w) \ 1)) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,6686,a(flip),b,12133,a),flip(a)].">
      <j1 rule="hyper" parents="63 6686 12133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12136">
    <literal><![CDATA[
      a(x,y,((T(z,u) * w) * v5) \ (w * (T(z,w) * v5))) = a(x,y,a(v5,z,w))
    ]]></literal>
    <justification jstring="[para(3285(a,1),12132(a,1,3,2))].">
      <j1 rule="para" parents="3285 12132"/>
    </justification>
  </clause>

  <clause id="12137">
    <literal><![CDATA[
      a(x,y,((T(z,u) * w) * v5) \ (w * (z * v5))) = a(x,y,a(v5,z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5773,a(flip),b,12136,a)].">
      <j1 rule="hyper" parents="63 5773 12136"/>
    </justification>
  </clause>

  <clause id="12139">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ (u * (z * w))) = a(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5632,a(flip),b,12137,a)].">
      <j1 rule="hyper" parents="63 5632 12137"/>
    </justification>
  </clause>

  <clause id="12140">
    <literal><![CDATA[
      a(x,y,(z * (T(u \ z,u) * w)) \ (u * ((u \ z) * ((u \ z) * w)))) = a(x,y,a((u \ z) * w,u \ z,u))
    ]]></literal>
    <justification jstring="[para(6265(a,1),12139(a,1,3,1))].">
      <j1 rule="para" parents="6265 12139"/>
    </justification>
  </clause>

  <clause id="12141">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,w * u) * v5)) = a(x,y,z \ (v5 * (w * (u * w))))
    ]]></literal>
    <justification jstring="[hyper(316,a,6353,a(flip),b,12135,a),flip(a)].">
      <j1 rule="hyper" parents="316 6353 12135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12142">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,w * u) * v5)) = a(x,y,z \ (L(u,w,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,6794,a(flip),b,12141,a),flip(a)].">
      <j1 rule="hyper" parents="316 6794 12141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12143">
    <literal><![CDATA[
      a(x,y,z \ (u * L(w,v5,v5 * w))) = a(x,y,z \ (L(w,v5,v5) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,12142,a)].">
      <j1 rule="hyper" parents="63 5490 12142"/>
    </justification>
  </clause>

  <clause id="12144">
    <literal><![CDATA[
      a(x,y,z \ (u * (R(w,v5,v5) * T(v5,v5 \ 1)))) = a(x,y,z \ (u * L(v5 * w,v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,11753,a(flip),b,12134,a),flip(a)].">
      <j1 rule="hyper" parents="316 11753 12134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12145">
    <literal><![CDATA[
      a(x,y,z \ (u * (R(w,v5,v5) * T(v5,v5 \ 1)))) = a(x,y,z \ (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,11754,a(flip),b,12144,a),flip(a)].">
      <j1 rule="hyper" parents="316 11754 12144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12146">
    <literal><![CDATA[
      a(x,y,z \ (u * R(w * v5,v5 \ 1,v5))) = a(x,y,z \ (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(1043(a,1),12145(a,1,3,2,2))].">
      <j1 rule="para" parents="1043 12145"/>
    </justification>
  </clause>

  <clause id="12147">
    <literal><![CDATA[
      a(x,y,z \ (u * L(w * v5,v5 \ 1,v5))) = a(x,y,z \ (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12129,a(flip),b,12146,a)].">
      <j1 rule="hyper" parents="63 12129 12146"/>
    </justification>
  </clause>

  <clause id="12148">
    <literal><![CDATA[
      a(x,y,(z \ (1 / u)) * (w * ((u * z) \ K(u,u \ 1)))) = a(x,y,(w * (z \ u)) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,6020,a(flip),b,10669,a),flip(a)].">
      <j1 rule="hyper" parents="316 6020 10669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12149">
    <literal><![CDATA[
      a(x,y,(z * (u \ w)) * (u * w)) = a(x,y,(u \ w) * ((u * w) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7210,a(flip),b,12148,a),flip(a)].">
      <j1 rule="hyper" parents="63 7210 12148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12151">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((z * u) * w)) = a(x,y,(u * z) * (w * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5623,a,b,12149,a),flip(a)].">
      <j1 rule="hyper" parents="63 5623 12149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12152">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w \ (u \ w),v5) * (v5 * (w / (u * w))))) = a(x,y,z \ (v5 * a(u \ 1,u,w)))
    ]]></literal>
    <justification jstring="[para(10957(a,1),10856(a,1,3,2,1))].">
      <j1 rule="para" parents="10957 10856"/>
    </justification>
  </clause>

  <clause id="12164">
    <literal><![CDATA[
      (x \ (x / y)) \ ((y \ x) \ ((y \ x) * y)) = (x / y) \ (x * ((y \ x) \ ((y \ x) * y)))
    ]]></literal>
    <justification jstring="[para(1641(a,1),11390(a,1,1))].">
      <j1 rule="para" parents="1641 11390"/>
    </justification>
  </clause>

  <clause id="12165">
    <literal><![CDATA[
      (x / y) \ (x * ((y \ x) \ ((y \ x) * y))) = (x \ (x / y)) \ y
    ]]></literal>
    <justification jstring="[para(9(a,1),12164(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 12164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12166">
    <literal><![CDATA[
      (x \ (x / y)) \ y = (x / y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),12165(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 12165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12168">
    <literal><![CDATA[
      x \ ((((x \ (y \ L(y,z,u))) \ L(y,z,u)) * K(x \ 1,x)) / y) = a(x \ (y \ L(y,z,u)),x,y)
    ]]></literal>
    <justification jstring="[para(4840(a,1),11552(a,1,2,1))].">
      <j1 rule="para" parents="4840 11552"/>
    </justification>
  </clause>

  <clause id="12169">
    <literal><![CDATA[
      a(x,y,z * (L(u,u,L(w,v5,v6) * v7) * (L(w,v5,v6) * v7))) = a(x,y,(u \ (R(w,v5,v6) * v7)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11760,a(flip),b,12081,a)].">
      <j1 rule="hyper" parents="63 11760 12081"/>
    </justification>
  </clause>

  <clause id="12170">
    <literal><![CDATA[
      (K(x,y \ K(x \ 1,x)) / x) * (((((x \ 1) * x) \ y) \ 1) * x) = (x \ ((x \ 1) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(425(a,1),12099(a,1,1,1,2))].">
      <j1 rule="para" parents="425 12099"/>
    </justification>
  </clause>

  <clause id="12171">
    <literal><![CDATA[
      (K(x,y \ 1) / x) * (((((x \ 1) * x) \ y) \ 1) * x) = (x \ ((x \ 1) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(3989(a,1),12170(a,1,1,1))].">
      <j1 rule="para" parents="3989 12170"/>
    </justification>
  </clause>

  <clause id="12172">
    <literal><![CDATA[
      (K(x,y \ 1) / x) * (((K(x \ 1,x) \ y) \ 1) * x) = (x \ ((x \ 1) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(272(a,2),12171(a,1,2,1,1,1))].">
      <j1 rule="para" parents="272 12171"/>
    </justification>
  </clause>

  <clause id="12175">
    <literal><![CDATA[
      (K(x,y \ 1) / x) * ((y \ K(x \ 1,x)) * x) = (x \ ((x \ 1) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(425(a,1),12172(a,1,2,1))].">
      <j1 rule="para" parents="425 12172"/>
    </justification>
  </clause>

  <clause id="12176">
    <literal><![CDATA[
      L(x \ K(y \ 1,y),y,y \ 1) = (y \ ((y \ 1) \ x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,10311,a(flip),b,12175,a)].">
      <j1 rule="hyper" parents="63 10311 12175"/>
    </justification>
  </clause>

  <clause id="12177">
    <literal><![CDATA[
      (x \ ((x \ 1) \ y)) \ 1 = (x \ 1) * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,4865,a(flip),b,12176,a),flip(a)].">
      <j1 rule="hyper" parents="63 4865 12176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12178">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ 1 = x \ ((x \ 1) \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(39,a,8346,a,b,12177,a)].">
      <j1 rule="hyper" parents="39 8346 12177"/>
    </justification>
  </clause>

  <clause id="12179">
    <literal><![CDATA[
      (x \ 1) * (y * (x / (y * x))) = ((y \ 1) * (y * x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,11170,a,b,12178,a)].">
      <j1 rule="hyper" parents="316 11170 12178"/>
    </justification>
  </clause>

  <clause id="12180">
    <literal><![CDATA[
      (x \ 1) * (x * (y \ ((y \ 1) \ (x \ 1)))) = ((y \ 1) * (y * x)) \ 1
    ]]></literal>
    <justification jstring="[para(12178(a,1),8314(a,1,2,2))].">
      <j1 rule="para" parents="12178 8314"/>
    </justification>
  </clause>

  <clause id="12181">
    <literal><![CDATA[
      x * (y \ ((y \ 1) \ (x \ 1))) = y * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(34,a,12179,a,b,12180,a),flip(a)].">
      <j1 rule="hyper" parents="34 12179 12180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12182">
    <literal><![CDATA[
      T(((x \ y) \ z) * u,w) / ((x \ y) \ z) = T(((y \ x) * z) * u,w) / ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10618,a(flip),b,12109,a),flip(a)].">
      <j1 rule="hyper" parents="63 10618 12109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12183">
    <literal><![CDATA[
      T(T(((x \ y) * 1) * z,u) / ((x \ y) * 1),x \ y) = T(z * ((y \ x) \ 1),u) / ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(12182(a,1),3735(a,1,1))].">
      <j1 rule="para" parents="12182 3735"/>
    </justification>
  </clause>

  <clause id="12184">
    <literal><![CDATA[
      a(x,y,z \ (R(u / w,w,u \ L(v5,v6,v7)) \ L(v5,v6,v7))) = a(x,y,z \ (w * (u \ R(v5,v6,v7))))
    ]]></literal>
    <justification jstring="[para(12087(a,1),12127(a,1,3,2,1))].">
      <j1 rule="para" parents="12087 12127"/>
    </justification>
  </clause>

  <clause id="12185">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w \ (u \ w),v5) * (v5 * ((u * w) \ w)))) = a(x,y,z \ (v5 * a(u \ 1,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5609,a(flip),b,12152,a)].">
      <j1 rule="hyper" parents="63 5609 12152"/>
    </justification>
  </clause>

  <clause id="12186">
    <literal><![CDATA[
      a(x \ (y \ L(y,z,u)),x,y) = x \ ((((x \ 1) \ y) * K(x \ 1,x)) / y)
    ]]></literal>
    <justification jstring="[para(9755(a,1),12168(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9755 12168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12187">
    <literal><![CDATA[
      a(x \ (y \ L(y,z,u)),x,y) = x \ (((1 / x) \ y) / y)
    ]]></literal>
    <justification jstring="[para(2257(a,1),12186(a,2,2,1))].">
      <j1 rule="para" parents="2257 12186"/>
    </justification>
  </clause>

  <clause id="12189">
    <literal><![CDATA[
      a(x \ (y \ L(y,z,u)),x,y) = a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,8706,a(flip),b,12187,a),flip(a)].">
      <j1 rule="hyper" parents="316 8706 12187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12190">
    <literal><![CDATA[
      ((x \ L(x,y,z)) / u) * (u * x) = a(u \ 1,u,x) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(12189(a,1),2404(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12189 2404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12191">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (a(u \ 1,u,x) \ L(x,y,z)) = L(x,u,u \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(133,a,12190,a(flip),b,1606,a)].">
      <j1 rule="hyper" parents="133 12190 1606"/>
    </justification>
  </clause>

  <clause id="12193">
    <literal><![CDATA[
      a(x,y,z * ((L(u,w,v5) * v6) / (T(v7,u * v6) \ 1))) = a(x,y,(v7 \ (R(u,w,v5) * v6)) * z)
    ]]></literal>
    <justification jstring="[para(10314(a,1),12169(a,1,3,2))].">
      <j1 rule="para" parents="10314 12169"/>
    </justification>
  </clause>

  <clause id="12194">
    <literal><![CDATA[
      a(x,y,z * ((T(u,w * v5) \ 1) \ (L(w,v6,v7) * v5))) = a(x,y,(u \ (R(w,v6,v7) * v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5481,a(flip),b,12193,a)].">
      <j1 rule="hyper" parents="63 5481 12193"/>
    </justification>
  </clause>

  <clause id="12195">
    <literal><![CDATA[
      a(x,y,(T(z,u * w) \ (L(u,v5,v6) * w)) * v7) = a(x,y,(z \ (R(u,v5,v6) * w)) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,6701,a(flip),b,12194,a)].">
      <j1 rule="hyper" parents="63 6701 12194"/>
    </justification>
  </clause>

  <clause id="12196">
    <literal><![CDATA[
      a(x,y,(z \ (R(u,w,v5) * v6)) * v7) = a(x,y,(z \ (L(u,w,v5) * v6)) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,5545,a(flip),b,12195,a),flip(a)].">
      <j1 rule="hyper" parents="63 5545 12195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12198">
    <literal><![CDATA[
      a(x,y,(z \ (L(u \ 1,u,w) * u)) * v5) = a(x,y,v5 * (z \ a(u \ 1,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8863,a(flip),b,12196,a),flip(a)].">
      <j1 rule="hyper" parents="63 8863 12196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12199">
    <literal><![CDATA[
      a(x,y,(z \ ((u \ 1) * L(u,u,w))) * v5) = a(x,y,v5 * (z \ a(u \ 1,u,w)))
    ]]></literal>
    <justification jstring="[para(4442(a,1),12198(a,1,3,1,2))].">
      <j1 rule="para" parents="4442 12198"/>
    </justification>
  </clause>

  <clause id="12200">
    <literal><![CDATA[
      a(x,y,(z \ (L(u,u,w) * u)) * v5) = a(x,y,v5 * (z \ a(u \ 1,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7051,a(flip),b,12199,a)].">
      <j1 rule="hyper" parents="63 7051 12199"/>
    </justification>
  </clause>

  <clause id="12201">
    <literal><![CDATA[
      a(x,y,(z \ (u * L(u,u,w))) * v5) = a(x,y,v5 * (z \ a(u \ 1,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5690,a,b,12200,a)].">
      <j1 rule="hyper" parents="63 5690 12200"/>
    </justification>
  </clause>

  <clause id="12202">
    <literal><![CDATA[
      a(x,y,z * (u \ a(w \ 1,w,v5))) = a(x,y,z * (u \ a(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7419,a(flip),b,12201,a),flip(a)].">
      <j1 rule="hyper" parents="63 7419 12201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12203">
    <literal><![CDATA[
      a(x,y,(z \ (u * ((u * w) \ w))) * v5) = a(x,y,v5 * (z \ a(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8877,a,b,12202,a)].">
      <j1 rule="hyper" parents="63 8877 12202"/>
    </justification>
  </clause>

  <clause id="12204">
    <literal><![CDATA[
      a(x,y,(z \ (u * (w \ (u \ w)))) * v5) = a(x,y,v5 * (z \ a(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11742,a(flip),b,12203,a)].">
      <j1 rule="hyper" parents="63 11742 12203"/>
    </justification>
  </clause>

  <clause id="12205">
    <literal><![CDATA[
      a(x,y,(z \ a(u,u \ 1,w)) * v5) = a(x,y,v5 * (z \ a(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8499,a(flip),b,12204,a)].">
      <j1 rule="hyper" parents="63 8499 12204"/>
    </justification>
  </clause>

  <clause id="12206">
    <literal><![CDATA[
      a(x,y,z * (u \ a(w,w \ 1,v5))) = a(x,y,z * (u \ a(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,12205,a)].">
      <j1 rule="hyper" parents="63 5469 12205"/>
    </justification>
  </clause>

  <clause id="12207">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ (v5 \ (w \ v5))))) = a(x,y,z * (u \ a(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8838,a,b,12206,a)].">
      <j1 rule="hyper" parents="63 8838 12206"/>
    </justification>
  </clause>

  <clause id="12208">
    <literal><![CDATA[
      T(T((x \ y) * z,u) / ((x \ y) * 1),x \ y) = T(z * ((y \ x) \ 1),u) / ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(8(a,1),12183(a,1,1,1,1,1))].">
      <j1 rule="para" parents="8 12183"/>
    </justification>
  </clause>

  <clause id="12209">
    <literal><![CDATA[
      T(T((x \ y) * z,u) / (x \ y),x \ y) = T(z * ((y \ x) \ 1),u) / ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(8(a,1),12208(a,1,1,2))].">
      <j1 rule="para" parents="8 12208"/>
    </justification>
  </clause>

  <clause id="12210">
    <literal><![CDATA[
      T(x * ((y \ z) \ 1),u) / ((y \ z) \ 1) = (z \ y) \ T((z \ y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(377,a,12209,a),flip(a)].">
      <j1 rule="hyper" parents="377 12209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12211">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * z,u) = (y \ x) * T((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,852,a(flip),b,12210,a),flip(a)].">
      <j1 rule="hyper" parents="63 852 12210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12212">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((z \ (((x \ y) \ 1) \ u)) * z) = z * ((y \ x) * T((y \ x) \ (z \ u),z))
    ]]></literal>
    <justification jstring="[para(12211(a,1),3307(a,2,2))].">
      <j1 rule="para" parents="12211 3307"/>
    </justification>
  </clause>

  <clause id="12213">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((z \ (((x \ y) \ 1) \ u)) * z) = (y \ x) * ((z \ ((y \ x) \ u)) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,3306,a(flip),b,12212,a),flip(a)].">
      <j1 rule="hyper" parents="316 3306 12212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12214">
    <literal><![CDATA[
      (x \ y) \ ((z \ ((x \ y) * u)) * z) = (y \ x) * ((z \ ((y \ x) \ u)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1390,a(flip),b,12213,a)].">
      <j1 rule="hyper" parents="63 1390 12213"/>
    </justification>
  </clause>

  <clause id="12215">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ R(v5,v6,v7)))) = a(x,y,z \ (u * (w \ L(v5,v6,v7))))
    ]]></literal>
    <justification jstring="[para(490(a,1),12184(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="490 12184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12216">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ L(w \ 1,w,v5)))) = a(x,y,z \ (u * a(w \ 1,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8906,a(flip),b,12215,a),flip(a)].">
      <j1 rule="hyper" parents="63 8906 12215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12217">
    <literal><![CDATA[
      a(x,y,z \ (u * a(w \ 1,w,v5))) = a(x,y,z \ (u * (w * L(w,w,v5))))
    ]]></literal>
    <justification jstring="[hyper(63,a,9074,a(flip),b,12216,a),flip(a)].">
      <j1 rule="hyper" parents="63 9074 12216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12218">
    <literal><![CDATA[
      a(x,y,z \ (u * a(w \ 1,w,v5))) = a(x,y,z \ (u * a(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,7310,a(flip),b,12217,a),flip(a)].">
      <j1 rule="hyper" parents="316 7310 12217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12219">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w \ (u \ w),v5) * (v5 * ((u * w) \ w)))) = a(x,y,z \ (v5 * a(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,12218,a(flip),b,12185,a),flip(a)].">
      <j1 rule="hyper" parents="316 12218 12185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12220">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w \ (u \ w),v5) * (v5 * (w \ (u \ w))))) = a(x,y,z \ (v5 * a(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11780,a(flip),b,12219,a)].">
      <j1 rule="hyper" parents="63 11780 12219"/>
    </justification>
  </clause>

  <clause id="12221">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w \ (v5 \ w)) * v5))) = a(x,y,z \ (u * a(w,v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5598,a(flip),b,12220,a)].">
      <j1 rule="hyper" parents="63 5598 12220"/>
    </justification>
  </clause>

  <clause id="12222">
    <literal><![CDATA[
      a(x,y,z \ (a(u,u \ 1,w) * v5)) = a(x,y,z \ (v5 * a(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8837,a(flip),b,12221,a)].">
      <j1 rule="hyper" parents="63 8837 12221"/>
    </justification>
  </clause>

  <clause id="12223">
    <literal><![CDATA[
      ((x * y) / (z \ K(u,w))) * L(z \ K(u,w),y,x) = ((x * (y * (K(u,w) / z))) / (1 / z)) * K(w,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10724,a(flip),b,10261,a)].">
      <j1 rule="hyper" parents="63 10724 10261"/>
    </justification>
  </clause>

  <clause id="12224">
    <literal><![CDATA[
      (x / (L(y,z,y) * z)) * L(L(y,z,y) * z,u,w) = (x / (z * y)) * L(z * y,u,w)
    ]]></literal>
    <justification jstring="[para(1649(a,1),10509(a,2,2,1))].">
      <j1 rule="para" parents="1649 10509"/>
    </justification>
  </clause>

  <clause id="12225">
    <literal><![CDATA[
      ((x \ y) / y) \ L(x \ y,z,u) = (y / (y * x)) * L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8995,a(flip),b,12224,a)].">
      <j1 rule="hyper" parents="63 8995 12224"/>
    </justification>
  </clause>

  <clause id="12226">
    <literal><![CDATA[
      ((x \ 1) / ((x \ 1) * y)) * L((x \ 1) * y,z,u) = ((y \ x) / x) \ L(y \ (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(590(a,1),12225(a,1,1)),flip(a)].">
      <j1 rule="para" parents="590 12225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12227">
    <literal><![CDATA[
      x / (a(y,z,u) \ (w \ (a(y,z,u) * (w * x)))) = x \ (w \ ((w * (x * a(y,z,u))) / a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8541,a(flip),b,10634,a),flip(a)].">
      <j1 rule="hyper" parents="63 8541 10634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12228">
    <literal><![CDATA[
      x / (a(y,z,u) \ (w \ (a(y,z,u) * (w * x)))) = a(a(y,z,u),x,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,9441,a(flip),b,12227,a),flip(a)].">
      <j1 rule="hyper" parents="316 9441 12227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12229">
    <literal><![CDATA[
      a(x,y,z \ ((((u \ (u \ w)) * (u * u)) \ v5) \ v6)) = a(x,y,z \ ((L(1 / w,u,u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,7743,a(flip),b,10706,a),flip(a)].">
      <j1 rule="hyper" parents="316 7743 10706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12230">
    <literal><![CDATA[
      a(x,y,z \ ((L(1 / u,w,w) \ v5) \ v6)) = a(x,y,z \ (((w \ (w \ u)) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,7740,a(flip),b,12229,a),flip(a)].">
      <j1 rule="hyper" parents="63 7740 12229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12232">
    <literal><![CDATA[
      L(L(x,y \ (z \ y),z),z * (y \ (z \ y)),z) = z * (z * (L(z,z,z \ y) \ ((y \ (y / z)) * x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10913,a(flip),b,10895,a)].">
      <j1 rule="hyper" parents="63 10913 10895"/>
    </justification>
  </clause>

  <clause id="12234">
    <literal><![CDATA[
      R(x,y,z) \ R(R(x,u,w),y,z) = L(x,y,z) \ R(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8727,a(flip),b,11330,a),flip(a)].">
      <j1 rule="hyper" parents="63 8727 11330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12235">
    <literal><![CDATA[
      (L(R(x,y,z),u,w) \ L(x,u,w)) \ 1 = R(x,u,w) \ R(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,7676,a,b,12234,a)].">
      <j1 rule="hyper" parents="316 7676 12234"/>
    </justification>
  </clause>

  <clause id="12236">
    <literal><![CDATA[
      R(R(x,y,z),u,w) \ R(x,y,z) = L(R(x,u,w),y,z) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,7677,a,b,12235,a)].">
      <j1 rule="hyper" parents="39 7677 12235"/>
    </justification>
  </clause>

  <clause id="12237">
    <literal><![CDATA[
      (L(R(x,y,z),u,w) \ L(x,u,w)) * K(R(x,u,w),v5) = R(R(x,u,w),y,z) \ T(R(x,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(138,a,12236,a(flip),b,3898,a)].">
      <j1 rule="hyper" parents="138 12236 3898"/>
    </justification>
  </clause>

  <clause id="12238">
    <literal><![CDATA[
      R(R(x,y,z \ K(u,w)),v5,v6) \ R(x,y,z \ K(u,w)) = L(R(x,v5,v6),y,z \ 1) \ L(x,y,z \ K(u,w))
    ]]></literal>
    <justification jstring="[para(3805(a,1),12236(a,2,1))].">
      <j1 rule="para" parents="3805 12236"/>
    </justification>
  </clause>

  <clause id="12239">
    <literal><![CDATA[
      (L(R(x,y,z),u,w) \ L(x,u,w)) * K(x,v5) = R(R(x,u,w),y,z) \ T(R(x,u,w),v5)
    ]]></literal>
    <justification jstring="[para(3387(a,1),12237(a,1,2))].">
      <j1 rule="para" parents="3387 12237"/>
    </justification>
  </clause>

  <clause id="12240">
    <literal><![CDATA[
      R(R(x,y,z),u,w) \ T(R(x,y,z),v5) = L(R(x,u,w),y,z) \ L(T(x,v5),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4452,a(flip),b,12239,a),flip(a)].">
      <j1 rule="hyper" parents="63 4452 12239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12242">
    <literal><![CDATA[
      R(R(x,y,z),u,w) \ R(T(x,v5),y,z) = L(R(x,u,w),y,z) \ L(T(x,v5),y,z)
    ]]></literal>
    <justification jstring="[para(27(a,2),12240(a,1,2))].">
      <j1 rule="para" parents="27 12240"/>
    </justification>
  </clause>

  <clause id="12243">
    <literal><![CDATA[
      x * ((x * R(T(y,x),z,u)) \ R(T(y,x),z,u)) = L(R(y,x,x),z,u) \ L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9152,a,b,12242,a)].">
      <j1 rule="hyper" parents="63 9152 12242"/>
    </justification>
  </clause>

  <clause id="12244">
    <literal><![CDATA[
      x * ((x * R(T(y,x),z,u)) \ R(T(y,x),z,u)) = x * ((x * L(y,z,u)) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,9151,a(flip),b,12243,a),flip(a)].">
      <j1 rule="hyper" parents="316 9151 12243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12245">
    <literal><![CDATA[
      x * ((R(y,z,u) * x) \ R(T(y,x),z,u)) = x * ((x * L(y,z,u)) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(252(a,1),12244(a,1,2,1))].">
      <j1 rule="para" parents="252 12244"/>
    </justification>
  </clause>

  <clause id="12246">
    <literal><![CDATA[
      x * ((x * R(y,z,u)) \ R(y,z,u)) = x * ((x * L(y,z,u)) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9300(a,1),12245(a,1,2))].">
      <j1 rule="para" parents="9300 12245"/>
    </justification>
  </clause>

  <clause id="12247">
    <literal><![CDATA[
      (x * R(y,z,u)) \ R(y,z,u) = (x * L(y,z,u)) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(354,a,12246,a),flip(a)].">
      <j1 rule="hyper" parents="354 12246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12249">
    <literal><![CDATA[
      a(x,y,L(a(z,u,L(w \ v5,v5,v5)),a(z,u,L(w \ v5,v5,v5)),u)) = a(x,y,a(L(w,v5,v5) \ v5,u,z))
    ]]></literal>
    <justification jstring="[para(8612(a,2),11341(a,1,3,2))].">
      <j1 rule="para" parents="8612 11341"/>
    </justification>
  </clause>

  <clause id="12250">
    <literal><![CDATA[
      a(x,(y * (z * (u \ T(u \ 1,u)))) \ w,v5) = a(x,(y * z) \ (((u \ 1) * (u \ 1)) \ w),v5)
    ]]></literal>
    <justification jstring="[para(636(a,1),11356(a,1,2,1,2,2,2))].">
      <j1 rule="para" parents="636 11356"/>
    </justification>
  </clause>

  <clause id="12251">
    <literal><![CDATA[
      a(x,(y * z) \ (((u \ 1) * (u \ 1)) \ w),v5) = a(x,(y * (z * (u \ (u \ 1)))) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11767,a(flip),b,12250,a),flip(a)].">
      <j1 rule="hyper" parents="63 11767 12250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12253">
    <literal><![CDATA[
      a(x,(y * z) \ (((u \ 1) * (u \ 1)) \ w),v5) = a(x,(y * (z / (u * u))) \ w,v5)
    ]]></literal>
    <justification jstring="[para(434(a,1),12251(a,2,2,1,2))].">
      <j1 rule="para" parents="434 12251"/>
    </justification>
  </clause>

  <clause id="12254">
    <literal><![CDATA[
      a(x,(y * z) \ (((u \ 1) * (u \ 1)) \ w),v5) = a(x,(y * ((u * u) \ z)) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,11246,a(flip),b,12253,a),flip(a)].">
      <j1 rule="hyper" parents="316 11246 12253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12255">
    <literal><![CDATA[
      a(x,(y * ((z * z) \ u)) \ w,v5) = a(x,(y * u) \ ((z * z) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11725,a(flip),b,12254,a),flip(a)].">
      <j1 rule="hyper" parents="63 11725 12254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12256">
    <literal><![CDATA[
      a(x,(y * z) \ ((y * y) * (y \ z)),u) = a(x,a(y,y,(y * y) \ z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11432,a(flip),b,12255,a),flip(a)].">
      <j1 rule="hyper" parents="63 11432 12255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12257">
    <literal><![CDATA[
      a(x,a(y,y,(y * y) \ z),u) = a(x,a(y,y,y \ z),u)
    ]]></literal>
    <justification jstring="[para(90(a,1),12256(a,1,2)),flip(a)].">
      <j1 rule="para" parents="90 12256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12258">
    <literal><![CDATA[
      a(x,a(y,y,y \ z),u) = a(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(5802(a,1),12257(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5802 12257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12259">
    <literal><![CDATA[
      a(a(x,x,x \ y),L(x \ y,x,x),z) = a(y * (x \ 1),a(x,x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7022,a,b,12258,a)].">
      <j1 rule="hyper" parents="63 7022 12258"/>
    </justification>
  </clause>

  <clause id="12260">
    <literal><![CDATA[
      a(x,a(y,y,z * y),u) = a(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(5478(a,1),12258(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5478 12258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12262">
    <literal><![CDATA[
      a(x,y * z,a(y,z,z)) \ 1 = a(y * z,a(z,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9453,a(flip),b,12260,a)].">
      <j1 rule="hyper" parents="63 9453 12260"/>
    </justification>
  </clause>

  <clause id="12263">
    <literal><![CDATA[
      a(x * y,a(x,y,x * y),z) = a(x * y,a(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9451,a,b,12262,a)].">
      <j1 rule="hyper" parents="63 9451 12262"/>
    </justification>
  </clause>

  <clause id="12264">
    <literal><![CDATA[
      a(a(x,x,x \ y),L(x \ y,x,x),z) = a(y * x,a(x,x,y),z)
    ]]></literal>
    <justification jstring="[hyper(316,a,11932,a(flip),b,12259,a),flip(a)].">
      <j1 rule="hyper" parents="316 11932 12259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12265">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ (L(v5,R(z,u,w) \ v6,R(z,u,w)) * v6)) = L(x,y,(R(z,u,w) \ v6) * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,1679,a(flip),b,11409,a),flip(a)].">
      <j1 rule="hyper" parents="316 1679 11409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12267">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ (L(v5,R(z,u,w) \ v6,L(z,u,w)) * v6)) = L(x,y,(R(z,u,w) \ v6) * v5)
    ]]></literal>
    <justification jstring="[para(4628(a,1),12265(a,1,3,2,1))].">
      <j1 rule="para" parents="4628 12265"/>
    </justification>
  </clause>

  <clause id="12268">
    <literal><![CDATA[
      (x * y) \ ((x * (y * (L(z,u,w) \ z))) / (L(z,u,w) \ z)) = a(L(z,u,w) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7123,a(flip),b,11566,a)].">
      <j1 rule="hyper" parents="63 7123 11566"/>
    </justification>
  </clause>

  <clause id="12269">
    <literal><![CDATA[
      (x * y) \ ((z \ L(z,u,w)) \ (x * (y * (z \ L(z,u,w))))) = a(L(z,u,w) \ z,y,x)
    ]]></literal>
    <justification jstring="[para(9560(a,1),12268(a,1,2))].">
      <j1 rule="para" parents="9560 12268"/>
    </justification>
  </clause>

  <clause id="12270">
    <literal><![CDATA[
      a(L(x,y,z) \ x,u,w) = a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8577,a(flip),b,12269,a),flip(a)].">
      <j1 rule="hyper" parents="63 8577 12269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12271">
    <literal><![CDATA[
      a(L(x \ 1,x,x \ y) \ (x \ 1),z,u) = a((x \ 1) \ (y \ (y / x)),z,u)
    ]]></literal>
    <justification jstring="[para(1603(a,1),12270(a,2,1,2))].">
      <j1 rule="para" parents="1603 12270"/>
    </justification>
  </clause>

  <clause id="12272">
    <literal><![CDATA[
      a(x \ L(x,y,y),z,u) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(4952(a,1),12270(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4952 12270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12273">
    <literal><![CDATA[
      L(a(x,y,L(z,y,x)),u,a(z \ L(z,y,x),w,v5)) = a(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(12270(a,1),11910(a,1,3))].">
      <j1 rule="para" parents="12270 11910"/>
    </justification>
  </clause>

  <clause id="12274">
    <literal><![CDATA[
      a(a(x,y,y),z,u) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,7260,a(flip),b,12272,a)].">
      <j1 rule="hyper" parents="63 7260 12272"/>
    </justification>
  </clause>

  <clause id="12277">
    <literal><![CDATA[
      a(a(x \ y,x,x),z,u) = a(a(x,x,y * x),z,u)
    ]]></literal>
    <justification jstring="[para(8522(a,1),12274(a,2,1))].">
      <j1 rule="para" parents="8522 12274"/>
    </justification>
  </clause>

  <clause id="12278">
    <literal><![CDATA[
      L(a(x,y,L(z,y,x)),u,a(z * L(z,y,x),w,v5)) = a(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,8994,a(flip),b,12273,a)].">
      <j1 rule="hyper" parents="63 8994 12273"/>
    </justification>
  </clause>

  <clause id="12279">
    <literal><![CDATA[
      a(a(x \ y,x,x),z,u) = a((x \ 1) \ (y \ (y / x)),z,u)
    ]]></literal>
    <justification jstring="[para(7296(a,1),12271(a,1,1))].">
      <j1 rule="para" parents="7296 12271"/>
    </justification>
  </clause>

  <clause id="12280">
    <literal><![CDATA[
      a(a(x,x,y * x),z,u) = a((x \ 1) \ (y \ (y / x)),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12277,a(flip),b,12279,a)].">
      <j1 rule="hyper" parents="63 12277 12279"/>
    </justification>
  </clause>

  <clause id="12281">
    <literal><![CDATA[
      a(a(x,x,y * x),z,u) = a(x * (y \ (y / x)),z,u)
    ]]></literal>
    <justification jstring="[para(1695(a,1),12280(a,2,1))].">
      <j1 rule="para" parents="1695 12280"/>
    </justification>
  </clause>

  <clause id="12282">
    <literal><![CDATA[
      a(a(x,x,y * x),z,u) = a(x * (y \ (x \ y)),z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4043,a(flip),b,12281,a),flip(a)].">
      <j1 rule="hyper" parents="316 4043 12281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12283">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(a(u,w,v5),x,L(x,y,z)) = (a(u,w,v5) * L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1459(a,1),11603(a,2,2))].">
      <j1 rule="para" parents="1459 11603"/>
    </justification>
  </clause>

  <clause id="12284">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(a(u,w,v5),x,L(x,y,z)) = (a(u,w,v5) * x) * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,7192,a(flip),b,12283,a),flip(a)].">
      <j1 rule="hyper" parents="316 7192 12283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12286">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(a(u,w,v5),x,L(x,y,z)) = x * (a(u,w,v5) * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,8815,a(flip),b,12284,a),flip(a)].">
      <j1 rule="hyper" parents="316 8815 12284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12287">
    <literal><![CDATA[
      L(a(x,y,z),u,L(u,w,v5)) * (u \ L(u,w,v5)) = u * (a(x,y,z) * L(u \ 1,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5026,a,b,12286,a)].">
      <j1 rule="hyper" parents="63 5026 12286"/>
    </justification>
  </clause>

  <clause id="12288">
    <literal><![CDATA[
      ((x * (y * (K(z,u) / w))) / (1 / w)) * K(u,z) = ((x * y) / (w \ 1)) * L(w \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11500,a(flip),b,12223,a),flip(a)].">
      <j1 rule="hyper" parents="63 11500 12223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12290">
    <literal><![CDATA[
      ((x * (y * (K(z,u) / w))) / (1 / w)) * K(u,z) = (x * (y * (w \ 1))) / (w \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,1465,a(flip),b,12288,a),flip(a)].">
      <j1 rule="hyper" parents="316 1465 12288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12291">
    <literal><![CDATA[
      (x * (y * (K(z,u) / w))) / (K(z,u) / w) = (x * (y * (w \ 1))) / (w \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,10182,a(flip),b,12290,a)].">
      <j1 rule="hyper" parents="63 10182 12290"/>
    </justification>
  </clause>

  <clause id="12292">
    <literal><![CDATA[
      (x * (y * (z \ K(u,w)))) / (z \ K(u,w)) = (x * (y * (z \ 1))) / (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,10788,a(flip),b,12291,a)].">
      <j1 rule="hyper" parents="63 10788 12291"/>
    </justification>
  </clause>

  <clause id="12293">
    <literal><![CDATA[
      (x * (y * (z \ K(u,w)))) / (z \ K(u,w)) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(316,a,964,a(flip),b,12292,a),flip(a)].">
      <j1 rule="hyper" parents="316 964 12292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12294">
    <literal><![CDATA[
      a(x,y,a(L(z \ u,u,u),w,v5)) = a(x,y,a(L(z,u,u) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,11337,a(flip),b,12249,a)].">
      <j1 rule="hyper" parents="63 11337 12249"/>
    </justification>
  </clause>

  <clause id="12295">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((R(u,w,w) \ w) \ (z * L(w,w,u)))) = a(x,y,a(L(u \ w,w,w),u,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,11936,a,b,12294,a)].">
      <j1 rule="hyper" parents="316 11936 12294"/>
    </justification>
  </clause>

  <clause id="12296">
    <literal><![CDATA[
      L((x * (y / (x * y))) \ z,a(x \ 1,x,y),a(x \ 1,x,y) \ 1) = (1 / (x * (y / (x * y)))) * z
    ]]></literal>
    <justification jstring="[para(8865(a,1),10560(a,1,3,1))].">
      <j1 rule="para" parents="8865 10560"/>
    </justification>
  </clause>

  <clause id="12297">
    <literal><![CDATA[
      L((x * (y / (x * y))) \ z,a(x \ 1,x,y),a(x \ 1,x,y)) = (1 / (x * (y / (x * y)))) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,10641,a(flip),b,12296,a)].">
      <j1 rule="hyper" parents="63 10641 12296"/>
    </justification>
  </clause>

  <clause id="12298">
    <literal><![CDATA[
      L((x * (y / (x * y))) \ z,a(x \ 1,x,y),a(x,x,y)) = (1 / (x * (y / (x * y)))) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,7848,a(flip),b,12297,a)].">
      <j1 rule="hyper" parents="63 7848 12297"/>
    </justification>
  </clause>

  <clause id="12299">
    <literal><![CDATA[
      L((x * (y / (x * y))) \ z,a(x,x,y),a(x,x,y)) = (1 / (x * (y / (x * y)))) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,11380,a(flip),b,12298,a)].">
      <j1 rule="hyper" parents="63 11380 12298"/>
    </justification>
  </clause>

  <clause id="12300">
    <literal><![CDATA[
      L((x * (y / (x * y))) \ z,a(x,x,y),a(x,x,y)) = ((x * (y / (x * y))) \ 1) * z
    ]]></literal>
    <justification jstring="[para(2217(a,1),12299(a,2,1))].">
      <j1 rule="para" parents="2217 12299"/>
    </justification>
  </clause>

  <clause id="12301">
    <literal><![CDATA[
      L((x * (y / (x * y))) \ z,a(x,x,y),a(x,x,y)) = (y \ ((x \ 1) * (x * y))) * z
    ]]></literal>
    <justification jstring="[hyper(316,a,11399,a(flip),b,12300,a),flip(a)].">
      <j1 rule="hyper" parents="316 11399 12300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12302">
    <literal><![CDATA[
      a(x,y,L(z,L(R(u,u,w),(u * u) \ w,(u * u) \ w),v5)) = a(x,y,L(z,w * ((u * u) \ (u \ w)),v5))
    ]]></literal>
    <justification jstring="[para(10970(a,1),11000(a,2,3))].">
      <j1 rule="para" parents="10970 11000"/>
    </justification>
  </clause>

  <clause id="12304">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w \ (v5 * v6)),a(z,u,w \ (v5 * v6)),u)) = a(x,y,a(w \ ((v5 \ 1) * v6),u,z))
    ]]></literal>
    <justification jstring="[para(6682(a,1),11339(a,1,3,2))].">
      <j1 rule="para" parents="6682 11339"/>
    </justification>
  </clause>

  <clause id="12305">
    <literal><![CDATA[
      a(x,y,a(z \ ((u \ 1) * w),v5,v6)) = a(x,y,a(z \ (u * w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,11337,a(flip),b,12304,a),flip(a)].">
      <j1 rule="hyper" parents="63 11337 12304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12306">
    <literal><![CDATA[
      a(x,y,a(z \ ((z \ 1) * u),w,v5)) = a(x,y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(9(a,1),12305(a,2,3,1))].">
      <j1 rule="para" parents="9 12305"/>
    </justification>
  </clause>

  <clause id="12307">
    <literal><![CDATA[
      a(x,y,a((z \ 1) \ u,w,v5)) = a(x,y,a(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),12306(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="10 12306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12308">
    <literal><![CDATA[
      a(x,y,a((z * z) \ u,w,v5)) = a(x,y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(6787(a,1),12306(a,1,3))].">
      <j1 rule="para" parents="6787 12306"/>
    </justification>
  </clause>

  <clause id="12309">
    <literal><![CDATA[
      a(x,y,a(z * (z * u),w,v5)) = a(x,y,a(L(u,z,z),w,v5))
    ]]></literal>
    <justification jstring="[para(18(a,2),12308(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="18 12308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12310">
    <literal><![CDATA[
      a(x,y,a(L(z \ u,z,z),w,v5)) = a(x,y,a(z * u,w,v5))
    ]]></literal>
    <justification jstring="[para(102(a,2),12308(a,1,3,1))].">
      <j1 rule="para" parents="102 12308"/>
    </justification>
  </clause>

  <clause id="12311">
    <literal><![CDATA[
      a(x,y,a(L(L(z \ u,w,v5),z,z),v6,v7)) = a(x,y,a(L(z * u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(1356(a,1),12309(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1356 12309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12312">
    <literal><![CDATA[
      a(x,y,a(z * (u \ 1),w,v5)) = a(x,y,a(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(4651(a,1),12310(a,1,3))].">
      <j1 rule="para" parents="4651 12310"/>
    </justification>
  </clause>

  <clause id="12315">
    <literal><![CDATA[
      L(x,y \ (z \ y),(y \ (z \ y)) \ 1) = x * (((z * a(z \ y,z,z)) * ((y \ (y / z)) * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(146,a,11472,a)].">
      <j1 rule="hyper" parents="146 11472"/>
    </justification>
  </clause>

  <clause id="12316">
    <literal><![CDATA[
      T(a(x,R(y,z,u),L(y,z,u)) \ x,R(y,z,u)) = K(y,w) * (R(T(y,w),z,u) \ (x / (R(y,z,u) \ 1)))
    ]]></literal>
    <justification jstring="[para(5746(a,1),11661(a,1,1,1))].">
      <j1 rule="para" parents="5746 11661"/>
    </justification>
  </clause>

  <clause id="12317">
    <literal><![CDATA[
      a(x,y,z * (((u * (w \ v5)) * a(u * (w \ v5),v6,v6)) * v7)) = a(x,y,z * (L(u * (v5 / w),v6,v6) * v7))
    ]]></literal>
    <justification jstring="[para(3150(a,1),11761(a,1,3,2,1,2))].">
      <j1 rule="para" parents="3150 11761"/>
    </justification>
  </clause>

  <clause id="12318">
    <literal><![CDATA[
      (((x * y) / x) * x) * (L(z,u,w) * L(z \ 1,u,w)) = (x * (L(z,u,w) * L(z \ 1,u,w))) * y
    ]]></literal>
    <justification jstring="[hyper(316,a,114,a(flip),b,11950,a),flip(a)].">
      <j1 rule="hyper" parents="316 114 11950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12319">
    <literal><![CDATA[
      (x * (L(y,z,u) * L(y \ 1,z,u))) * w = (x * w) * (L(y,z,u) * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(630,a,12318,a),flip(a)].">
      <j1 rule="hyper" parents="630 12318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12321">
    <literal><![CDATA[
      (x * (L(y,z,u) * L(y \ 1,z,u))) * w = x * (w * (L(y,z,u) * L(y \ 1,z,u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,6319,a(flip),b,12319,a),flip(a)].">
      <j1 rule="hyper" parents="316 6319 12319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12322">
    <literal><![CDATA[
      x * (y * (L(z,u,w) * L(z \ 1,u,w))) = (x * (z \ L(L(z,u,w),u,w))) * y
    ]]></literal>
    <justification jstring="[para(9957(a,1),12321(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9957 12321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12323">
    <literal><![CDATA[
      (x * (y \ L(L(y,z,u),z,u))) * w = x * (w * (y \ L(L(y,z,u),z,u)))
    ]]></literal>
    <justification jstring="[para(9957(a,1),12322(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9957 12322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12324">
    <literal><![CDATA[
      (x * a(y \ 1,y,z)) \ ((x * z) / (a(y \ 1,y,z) \ z)) = a(a(y,y,z),L(z,y,y),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,7614,a(flip),b,12093,a),flip(a)].">
      <j1 rule="hyper" parents="316 7614 12093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12325">
    <literal><![CDATA[
      (x * a(y \ 1,y,z)) \ ((x * z) / L(z,y,y \ 1)) = a(a(y,y,z),L(z,y,y),x)
    ]]></literal>
    <justification jstring="[para(2406(a,1),12324(a,1,2,2))].">
      <j1 rule="para" parents="2406 12324"/>
    </justification>
  </clause>

  <clause id="12326">
    <literal><![CDATA[
      (x * a(y \ 1,y,z)) \ (z * (L(z,y,y \ 1) \ x)) = a(a(y,y,z),L(z,y,y),x)
    ]]></literal>
    <justification jstring="[para(4390(a,1),12325(a,1,2))].">
      <j1 rule="para" parents="4390 12325"/>
    </justification>
  </clause>

  <clause id="12327">
    <literal><![CDATA[
      a(a(x,x,x \ y),L(x \ y,x,x),z) = (z * a(x \ 1,x,x \ y)) \ ((x \ y) * (((1 / x) * y) \ z))
    ]]></literal>
    <justification jstring="[para(887(a,1),12326(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="887 12326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12328">
    <literal><![CDATA[
      a(x,y,a(z,z \ (L(u,w,z) * z),w)) = a(x,y,(w * L(T(u,z),w,z)) \ (L(u,z,w) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6337,a(flip),b,12130,a),flip(a)].">
      <j1 rule="hyper" parents="63 6337 12130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12330">
    <literal><![CDATA[
      a(x,y,a(z,z \ (L(u,w,z) * z),w)) = a(x,y,(w * L(u,w,z)) \ (L(u,z,w) * w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5688,a(flip),b,12328,a),flip(a)].">
      <j1 rule="hyper" parents="316 5688 12328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12332">
    <literal><![CDATA[
      a(x,y,a(z,T(L(u,w,z),z),w)) = a(x,y,(w * L(u,w,z)) \ (L(u,z,w) * w))
    ]]></literal>
    <justification jstring="[para(22(a,2),12330(a,1,3,2))].">
      <j1 rule="para" parents="22 12330"/>
    </justification>
  </clause>

  <clause id="12333">
    <literal><![CDATA[
      a(x,y,(z * L(u,z,w)) \ (L(u,w,z) * z)) = a(x,y,a(w,L(u,z,w),z))
    ]]></literal>
    <justification jstring="[para(3465(a,1),12332(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3465 12332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12335">
    <literal><![CDATA[
      a(x,y,L(z,L(R(u,u,w),(u * u) \ w,(u * u) \ w),v5)) = a(x,y,L(z,(u \ w) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,9024,a(flip),b,12302,a),flip(a)].">
      <j1 rule="hyper" parents="316 9024 12302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12337">
    <literal><![CDATA[
      a(x,y,L(z,L(R(u,u,w),(u * u) \ w,w),v5)) = a(x,y,L(z,(u \ w) * w,v5))
    ]]></literal>
    <justification jstring="[para(10994(a,1),12335(a,1,3))].">
      <j1 rule="para" parents="10994 12335"/>
    </justification>
  </clause>

  <clause id="12339">
    <literal><![CDATA[
      a(x,y,L(z,L(L(u,u,w),(u * u) \ w,w),v5)) = a(x,y,L(z,(u \ w) * w,v5))
    ]]></literal>
    <justification jstring="[para(10997(a,1),12337(a,1,3))].">
      <j1 rule="para" parents="10997 12337"/>
    </justification>
  </clause>

  <clause id="12340">
    <literal><![CDATA[
      T(a(x,L(y,z,u),L(y,z,u)) \ x,R(y,z,u)) = K(y,w) * (R(T(y,w),z,u) \ (x / (R(y,z,u) \ 1)))
    ]]></literal>
    <justification jstring="[para(11325(a,1),12316(a,1,1,1))].">
      <j1 rule="para" parents="11325 12316"/>
    </justification>
  </clause>

  <clause id="12341">
    <literal><![CDATA[
      a(x,y,z * (R(u * (w \ v5),v6,v6) * v7)) = a(x,y,z * (L(u * (v5 / w),v6,v6) * v7))
    ]]></literal>
    <justification jstring="[para(2381(a,1),12317(a,1,3,2,1))].">
      <j1 rule="para" parents="2381 12317"/>
    </justification>
  </clause>

  <clause id="12342">
    <literal><![CDATA[
      a(x,y,z * (L(u * (w / v5),v6,v6) * v7)) = a(x,y,z * (L(u * (v5 \ w),v6,v6) * v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,11760,a(flip),b,12341,a),flip(a)].">
      <j1 rule="hyper" parents="63 11760 12341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12343">
    <literal><![CDATA[
      a(x,y,z * (L(u * (w \ 1),w,w) * v5)) = a(x,y,z * (v5 * L((1 / w) * u,w,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11959,a(flip),b,12342,a),flip(a)].">
      <j1 rule="hyper" parents="63 11959 12342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12344">
    <literal><![CDATA[
      a(x,y,z * (L(u * (w \ 1),w,w) * v5)) = a(x,y,z * (v5 * L((w \ 1) * u,w,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,7053,a(flip),b,12343,a),flip(a)].">
      <j1 rule="hyper" parents="316 7053 12343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12345">
    <literal><![CDATA[
      a(x,y,z * (L(u * (w \ 1),w,w) * v5)) = a(x,y,z * (v5 * L(u * w,w,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,9738,a(flip),b,12344,a),flip(a)].">
      <j1 rule="hyper" parents="316 9738 12344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12346">
    <literal><![CDATA[
      a(x,y,z * (L(u * (w \ 1),w,w) * v5)) = a(x,y,z * (v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,9022,a(flip),b,12345,a),flip(a)].">
      <j1 rule="hyper" parents="316 9022 12345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12347">
    <literal><![CDATA[
      (x * a(y \ 1,y,y \ z)) \ ((y \ z) * (((1 / y) * z) \ x)) = a(z * y,a(y,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12264,a(flip),b,12327,a),flip(a)].">
      <j1 rule="hyper" parents="63 12264 12327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12348">
    <literal><![CDATA[
      (x * (((y \ z) / z) * y)) \ ((y \ z) * (((1 / y) * z) \ x)) = a(z * y,a(y,y,z),x)
    ]]></literal>
    <justification jstring="[para(8864(a,1),12347(a,1,1,2))].">
      <j1 rule="para" parents="8864 12347"/>
    </justification>
  </clause>

  <clause id="12349">
    <literal><![CDATA[
      T(a(x,L(y,z,u),L(y,z,u)) \ x,y) = K(y,w) * (R(T(y,w),z,u) \ (x / (R(y,z,u) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(2852,a,12340,a)].">
      <j1 rule="hyper" parents="2852 12340"/>
    </justification>
  </clause>

  <clause id="12351">
    <literal><![CDATA[
      K(x,y) * (R(T(x,y),z,u) \ (w / (R(x,z,u) \ 1))) = L(x,z,u) \ (w / (L(x,z,u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,11660,a(flip),b,12349,a),flip(a)].">
      <j1 rule="hyper" parents="63 11660 12349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12352">
    <literal><![CDATA[
      R(x,y,z) \ (u / (R(x,y,z) \ 1)) = L(x,y,z) \ (u / (L(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,3410,a(flip),b,12351,a)].">
      <j1 rule="hyper" parents="63 3410 12351"/>
    </justification>
  </clause>

  <clause id="12353">
    <literal><![CDATA[
      T(x,y) * L(R(L(y,z,u),x,L(L(y,z,u),w,v5)),w,v5) = T(x * L(L(y,w,v5),z,u),L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(29(a,1),10746(a,1,2))].">
      <j1 rule="para" parents="29 10746"/>
    </justification>
  </clause>

  <clause id="12355">
    <literal><![CDATA[
      L(x,a(y,z,u) \ 1,a(y,z,u) \ w) * w = (x * (a(y,z,u) \ 1)) * ((a(y,z,u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10482,a(flip),b,11041,a),flip(a)].">
      <j1 rule="hyper" parents="316 10482 11041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12356">
    <literal><![CDATA[
      a(x,(y * z) \ ((u * u) \ (y * (w * (z * (u * u))))),v5) = a(x,L(w,z * (u * u),y),v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,11213,a(flip),b,11357,a),flip(a)].">
      <j1 rule="hyper" parents="316 11213 11357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12358">
    <literal><![CDATA[
      a(x,(y * z) \ T(y * (u * z),w * w),v5) = a(x,L(u,z * (w * w),y),v5)
    ]]></literal>
    <justification jstring="[para(833(a,1),12356(a,1,2,2))].">
      <j1 rule="para" parents="833 12356"/>
    </justification>
  </clause>

  <clause id="12359">
    <literal><![CDATA[
      a(x,L(y,z * (u * u),w),v5) = a(x,(w * z) \ (w * (y * z)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11203,a(flip),b,12358,a),flip(a)].">
      <j1 rule="hyper" parents="63 11203 12358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12361">
    <literal><![CDATA[
      a(x,L(T(y,z),z,u),w) = a(x,L(y,z * (v5 * v5),u),w)
    ]]></literal>
    <justification jstring="[para(247(a,1),12359(a,2,2)),flip(a)].">
      <j1 rule="para" parents="247 12359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12362">
    <literal><![CDATA[
      a(x,L(y,z * (u * u),w),v5) = a(x,L(y,z,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11213,a(flip),b,12361,a),flip(a)].">
      <j1 rule="hyper" parents="63 11213 12361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12364">
    <literal><![CDATA[
      a(x,L(y,z \ 1,u),w) = a(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(229(a,1),12362(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="229 12362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12365">
    <literal><![CDATA[
      a(x,L(y,(z \ 1) \ u,w),v5) = a(x,L(y,z \ u,w),v5)
    ]]></literal>
    <justification jstring="[para(10965(a,1),12362(a,1,2))].">
      <j1 rule="para" parents="10965 12362"/>
    </justification>
  </clause>

  <clause id="12366">
    <literal><![CDATA[
      a(x,y,L(a(z \ 1,u,w),a(z,u,w),u) * v5) = a(x,y,v5 * (u \ (z \ (((z \ 1) * (u * w)) / w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,5839,a(flip),b,11382,a)].">
      <j1 rule="hyper" parents="63 5839 11382"/>
    </justification>
  </clause>

  <clause id="12367">
    <literal><![CDATA[
      a(x,y,L(z,u * (w * ((v5 * v5) \ ((v5 * v5) \ u))),v6)) = a(x,y,L(z,L(w,u / (v5 * v5),u / (v5 * v5)),v6))
    ]]></literal>
    <justification jstring="[para(11024(a,1),11483(a,1,3))].">
      <j1 rule="para" parents="11024 11483"/>
    </justification>
  </clause>

  <clause id="12368">
    <literal><![CDATA[
      a(x,y,(z * (T(u \ z,u) * w)) \ (u * L(w,u \ z,u \ z))) = a(x,y,a((u \ z) * w,u \ z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6345,a(flip),b,12140,a)].">
      <j1 rule="hyper" parents="63 6345 12140"/>
    </justification>
  </clause>

  <clause id="12369">
    <literal><![CDATA[
      a(x,y,(z * ((u \ z) * w)) \ (u * L(w,u \ z,u \ z))) = a(x,y,a((u \ z) * w,u \ z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5946,a(flip),b,12368,a)].">
      <j1 rule="hyper" parents="63 5946 12368"/>
    </justification>
  </clause>

  <clause id="12371">
    <literal><![CDATA[
      T(x,y) * L(L(R(y,x,L(L(y,z,u),w,v5)),z,u),w,v5) = T(x * L(L(y,w,v5),z,u),L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(29(a,1),12353(a,1,2,1))].">
      <j1 rule="para" parents="29 12353"/>
    </justification>
  </clause>

  <clause id="12372">
    <literal><![CDATA[
      a(x,y,L(z,u * (w * ((v5 * v5) \ ((v5 * v5) \ u))),v6)) = a(x,y,L(z,L(w,(v5 * v5) \ u,(v5 * v5) \ u),v6))
    ]]></literal>
    <justification jstring="[para(10851(a,1),12367(a,2,3,2))].">
      <j1 rule="para" parents="10851 12367"/>
    </justification>
  </clause>

  <clause id="12373">
    <literal><![CDATA[
      T(x,y) * L(L(R(y,x,L(L(y,z,u),w,v5)),z,u),w,v5) = T(x * L(L(y,w,v5),z,u),y)
    ]]></literal>
    <justification jstring="[hyper(316,a,4308,a(flip),b,12371,a),flip(a)].">
      <j1 rule="hyper" parents="316 4308 12371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12375">
    <literal><![CDATA[
      T(x,y) * L(L(R(y,x,y),z,u),w,v5) = T(x * L(L(y,w,v5),z,u),y)
    ]]></literal>
    <justification jstring="[para(5214(a,1),12373(a,1,2,1))].">
      <j1 rule="para" parents="5214 12373"/>
    </justification>
  </clause>

  <clause id="12377">
    <literal><![CDATA[
      x * T(y * L(L(x,z,u),w,v5),x) = (y * x) * L(L(x,w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(12375(a,1),3444(a,1,2))].">
      <j1 rule="para" parents="12375 3444"/>
    </justification>
  </clause>

  <clause id="12378">
    <literal><![CDATA[
      (x * L(L(y,z,u),w,v5)) * y = (x * y) * L(L(y,w,v5),z,u)
    ]]></literal>
    <justification jstring="[hyper(290,a,12377,a)].">
      <j1 rule="hyper" parents="290 12377"/>
    </justification>
  </clause>

  <clause id="12379">
    <literal><![CDATA[
      (x * L(L(x,y,z),u,w)) \ (v5 \ ((v5 * x) * L(L(x,y,z),u,w))) = a(v5,L(L(x,u,w),y,z),x)
    ]]></literal>
    <justification jstring="[para(12378(a,1),8466(a,1,2,2))].">
      <j1 rule="para" parents="12378 8466"/>
    </justification>
  </clause>

  <clause id="12380">
    <literal><![CDATA[
      a(x,L(L(y,z,u),w,v5),y) = a(x,y,L(L(y,w,v5),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8444,a,b,12379,a),flip(a)].">
      <j1 rule="hyper" parents="63 8444 12379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12381">
    <literal><![CDATA[
      a(x,y,L(z,u * (w * ((v5 * v5) \ ((v5 * v5) \ u))),v6)) = a(x,y,L(z,L(w,(v5 * v5) \ u,u),v6))
    ]]></literal>
    <justification jstring="[para(10994(a,1),12372(a,2,3))].">
      <j1 rule="para" parents="10994 12372"/>
    </justification>
  </clause>

  <clause id="12382">
    <literal><![CDATA[
      a(x,y,L(z,(u * ((w * w) \ v5)) * v5,v6)) = a(x,y,L(z,L(u,(w * w) \ v5,v5),v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,9697,a(flip),b,12381,a)].">
      <j1 rule="hyper" parents="63 9697 12381"/>
    </justification>
  </clause>

  <clause id="12385">
    <literal><![CDATA[
      a(x,y,L(z,(u * w) * ((v5 * v5) \ w),v6)) = a(x,y,L(z,L(u,(v5 * v5) \ w,w),v6))
    ]]></literal>
    <justification jstring="[para(11136(a,1),12382(a,1,3))].">
      <j1 rule="para" parents="11136 12382"/>
    </justification>
  </clause>

  <clause id="12386">
    <literal><![CDATA[
      a(x,y,L(z,L(u,(w * w) \ v5,v5),v6)) = a(x,y,L(z,v5 * (u * v5),v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,9024,a(flip),b,12385,a),flip(a)].">
      <j1 rule="hyper" parents="63 9024 12385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12388">
    <literal><![CDATA[
      a(x,y,L(z,L(u,(w * w) \ v5,v5),v6)) = a(x,y,L(z,L(u,v5,v5),v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,10979,a(flip),b,12386,a),flip(a)].">
      <j1 rule="hyper" parents="316 10979 12386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12389">
    <literal><![CDATA[
      a(x,y,L(z,L(L(u,u,w),w,w),v5)) = a(x,y,L(z,(u \ w) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,12339,a(flip),b,12388,a),flip(a)].">
      <j1 rule="hyper" parents="63 12339 12388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12396">
    <literal><![CDATA[
      L(R(x,y,z),R(x,y,z) * L(x \ L(x,u,w),y,z),v5) \ R(x,y,z) = a(v5,L(x,y,z),L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,2548,a(flip),b,11334,a),flip(a)].">
      <j1 rule="hyper" parents="316 2548 11334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12397">
    <literal><![CDATA[
      L(x * a(L(y,z,u) \ y,x,w),w,L(y,z,u) \ y) = L(x,L(y,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,9320,a(flip),b,11646,a),flip(a)].">
      <j1 rule="hyper" parents="316 9320 11646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12398">
    <literal><![CDATA[
      L(x * a(y \ L(y,z,u),x,w),w,L(y,z,u) \ y) = L(x,L(y,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[para(12270(a,1),12397(a,1,1,2))].">
      <j1 rule="para" parents="12270 12397"/>
    </justification>
  </clause>

  <clause id="12399">
    <literal><![CDATA[
      L(x * a(y \ L(y,z,u),x,w),w,y \ L(y,z,u)) = L(x,L(y,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9212,a(flip),b,12398,a)].">
      <j1 rule="hyper" parents="63 9212 12398"/>
    </justification>
  </clause>

  <clause id="12400">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,w) = L(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9741,a(flip),b,12399,a),flip(a)].">
      <j1 rule="hyper" parents="63 9741 12399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12401">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,w \ L(w,v5,v6)) = L(x,y \ L(y,z,u),L(w,v5,v6) \ w)
    ]]></literal>
    <justification jstring="[hyper(316,a,9212,a,b,12400,a),flip(a)].">
      <j1 rule="hyper" parents="316 9212 12400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12402">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,w) = L(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11941,a,b,12400,a)].">
      <j1 rule="hyper" parents="63 11941 12400"/>
    </justification>
  </clause>

  <clause id="12403">
    <literal><![CDATA[
      L(x * (L(y,z,u) \ y),y \ L(y,z,u),x) = 1 / ((L(y,z,u) \ y) \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,9895,a(flip),b,12400,a),flip(a)].">
      <j1 rule="hyper" parents="63 9895 12400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12404">
    <literal><![CDATA[
      x \ L(x,y \ L(y,z,u),L(y,z,u) \ y) = a(x,L(y,z,u) \ y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,12400,a(flip),b,11945,a)].">
      <j1 rule="hyper" parents="133 12400 11945"/>
    </justification>
  </clause>

  <clause id="12405">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ L(u,x \ L(x,y,z),x \ L(x,y,z)) = u * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,12400,a(flip),b,8971,a)].">
      <j1 rule="hyper" parents="133 12400 8971"/>
    </justification>
  </clause>

  <clause id="12406">
    <literal><![CDATA[
      L(x * (L(y,z,u) \ y),y \ L(y,z,u),x) \ 1 = (L(y,z,u) \ y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(12400(a,1),9885(a,1,1))].">
      <j1 rule="para" parents="12400 9885"/>
    </justification>
  </clause>

  <clause id="12407">
    <literal><![CDATA[
      L(x \ L(x,y \ L(y,z,u),w),x,(y * L(y,z,u)) * w) = a(x,L(y,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[para(12400(a,1),11947(a,1,1,2))].">
      <j1 rule="para" parents="12400 11947"/>
    </justification>
  </clause>

  <clause id="12409">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,L(w,v5,v6) \ w) = L(x,y \ L(y,z,u),w * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,8367,a(flip),b,12402,a)].">
      <j1 rule="hyper" parents="63 8367 12402"/>
    </justification>
  </clause>

  <clause id="12412">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ L(u,x \ L(x,y,z),L(x,y,z) \ x) = u * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,12401,a(flip),b,8971,a)].">
      <j1 rule="hyper" parents="133 12401 8971"/>
    </justification>
  </clause>

  <clause id="12413">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),L(w,v5,v6) \ w) = L(x,y \ L(y,z,u),w * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,12400,a(flip),b,12409,a)].">
      <j1 rule="hyper" parents="63 12400 12409"/>
    </justification>
  </clause>

  <clause id="12414">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),w \ L(w,v5,v6)) = L(x,y \ L(y,z,u),w * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,9212,a(flip),b,12413,a)].">
      <j1 rule="hyper" parents="63 9212 12413"/>
    </justification>
  </clause>

  <clause id="12415">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ L(u,x \ L(x,y,z),x * L(x,y,z)) = u * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(12414(a,1),12405(a,1,2))].">
      <j1 rule="para" parents="12414 12405"/>
    </justification>
  </clause>

  <clause id="12417">
    <literal><![CDATA[
      a(x,L(y,z,u) \ y,y * L(y,z,u)) = a(x,y \ L(y,z,u),y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8370,a(flip),b,12404,a),flip(a)].">
      <j1 rule="hyper" parents="63 8370 12404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12418">
    <literal><![CDATA[
      x * a(x,y \ L(y,z,u),y * L(y,z,u)) = L(x,L(y,z,u) \ y,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(12417(a,1),11945(a,1,2))].">
      <j1 rule="para" parents="12417 11945"/>
    </justification>
  </clause>

  <clause id="12420">
    <literal><![CDATA[
      x * a(x,y \ L(y,z,u),y * L(y,z,u)) = L(x,y \ L(y,z,u),y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,12409,a(flip),b,12418,a),flip(a)].">
      <j1 rule="hyper" parents="316 12409 12418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12426">
    <literal><![CDATA[
      L(L(x,y,z \ L(u,w,v5)) \ x,x,(z \ L(u,w,v5)) * y) = a(z \ R(u,w,v5),y,L(x,y,z \ R(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9146,a(flip),b,11888,a)].">
      <j1 rule="hyper" parents="63 9146 11888"/>
    </justification>
  </clause>

  <clause id="12427">
    <literal><![CDATA[
      a(x,y,L(L(z * a(u,w,u),v5,1 / v6),1 / v6,v5)) = a(x,y,v5 \ ((v6 \ 1) \ (((v6 \ a(u,w,u)) * z) * v5)))
    ]]></literal>
    <justification jstring="[para(7900(a,1),11907(a,2,3,2))].">
      <j1 rule="para" parents="7900 11907"/>
    </justification>
  </clause>

  <clause id="12441">
    <literal><![CDATA[
      a(x,y,z \ (L(u \ w,u,w \ R(v5,v6,v7)) \ L(v5,v6,v7))) = a(x,y,z \ ((R(v5,v6,v7) / w) * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5487,a(flip),b,12128,a),flip(a)].">
      <j1 rule="hyper" parents="316 5487 12128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12443">
    <literal><![CDATA[
      a(x,y,z \ (L(u \ w,u,w \ R(v5,v6,v7)) \ L(v5,v6,v7))) = a(x,y,z \ ((w \ R(v5,v6,v7)) * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5627,a(flip),b,12441,a),flip(a)].">
      <j1 rule="hyper" parents="316 5627 12441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12444">
    <literal><![CDATA[
      a(x,y,z \ (L(u \ w,u,w \ L(v5,v6,v7)) \ L(v5,v6,v7))) = a(x,y,z \ ((w \ R(v5,v6,v7)) * u))
    ]]></literal>
    <justification jstring="[para(7482(a,1),12443(a,1,3,2,1))].">
      <j1 rule="para" parents="7482 12443"/>
    </justification>
  </clause>

  <clause id="12445">
    <literal><![CDATA[
      a(x,y,z \ T((L(u,w,v5) / v6) * v7,v7 \ v6)) = a(x,y,z \ ((v6 \ R(u,w,v5)) * v7))
    ]]></literal>
    <justification jstring="[para(3740(a,1),12444(a,1,3,2))].">
      <j1 rule="para" parents="3740 12444"/>
    </justification>
  </clause>

  <clause id="12446">
    <literal><![CDATA[
      a(x,y,z \ ((L(u,w,v5) / v6) * v7)) = a(x,y,z \ ((v6 \ R(u,w,v5)) * v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,5487,a(flip),b,12445,a)].">
      <j1 rule="hyper" parents="63 5487 12445"/>
    </justification>
  </clause>

  <clause id="12448">
    <literal><![CDATA[
      a(x,y,z \ ((u \ R(w,v5,v6)) * v7)) = a(x,y,z \ ((u \ L(w,v5,v6)) * v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,5627,a(flip),b,12446,a),flip(a)].">
      <j1 rule="hyper" parents="63 5627 12446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12449">
    <literal><![CDATA[
      a(x,y,z \ ((u \ L(u,u,w)) * v5)) = a(x,y,z \ (a(u,u,w) * v5))
    ]]></literal>
    <justification jstring="[para(7329(a,1),12448(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="7329 12448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12450">
    <literal><![CDATA[
      a(x,y,z \ (a(u,u,w) * v5)) = a(x,y,z \ (v5 * a(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7327,a(flip),b,12449,a),flip(a)].">
      <j1 rule="hyper" parents="63 7327 12449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12451">
    <literal><![CDATA[
      L(R(x,y,z),u,w \ 1) \ L(x,u,w \ K(v5,v6)) = R(R(x,u,w),y,z) \ R(x,u,w \ K(v5,v6))
    ]]></literal>
    <justification jstring="[para(4736(a,1),12238(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4736 12238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12452">
    <literal><![CDATA[
      L(R(x,y,z),u,w \ 1) \ L(x,u,w \ K(v5,v6)) = R(R(x,u,w),y,z) \ R(x,u,w)
    ]]></literal>
    <justification jstring="[para(4736(a,1),12451(a,2,2))].">
      <j1 rule="para" parents="4736 12451"/>
    </justification>
  </clause>

  <clause id="12454">
    <literal><![CDATA[
      L(R(x,y,z),u,w \ 1) \ L(x,u,w \ K(v5,v6)) = L(R(x,y,z),u,w) \ L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,12236,a(flip),b,12452,a),flip(a)].">
      <j1 rule="hyper" parents="316 12236 12452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12456">
    <literal><![CDATA[
      L(R(x,y,z),u,w \ 1) \ L(x,u,w \ 1) = L(R(x,y,z),u,w) \ L(x,u,w)
    ]]></literal>
    <justification jstring="[para(180(a,1),12454(a,1,2,3,2))].">
      <j1 rule="para" parents="180 12454"/>
    </justification>
  </clause>

  <clause id="12457">
    <literal><![CDATA[
      L(R(x,y,z),L(R(x,y,z),u,w),v5) \ R(x,y,z) = a(v5,L(x,y,z),L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(8387(a,1),12396(a,1,1,2))].">
      <j1 rule="para" parents="8387 12396"/>
    </justification>
  </clause>

  <clause id="12458">
    <literal><![CDATA[
      L(R(x,y,z),L(L(x,y,z),u,w),v5) \ R(x,y,z) = a(v5,L(x,y,z),L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(10997(a,1),12457(a,1,1))].">
      <j1 rule="para" parents="10997 12457"/>
    </justification>
  </clause>

  <clause id="12460">
    <literal><![CDATA[
      a(x \ R(y,z,u),w,L(v5,w,x \ R(y,z,u))) = a(x \ L(y,z,u),w,L(v5,w,x \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11885,a(flip),b,12426,a),flip(a)].">
      <j1 rule="hyper" parents="63 11885 12426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12461">
    <literal><![CDATA[
      a(x \ R(y,z,u),w,L(v5,w,x \ L(y,z,u))) = a(x \ L(y,z,u),w,L(v5,w,x \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(7482(a,1),12460(a,1,3))].">
      <j1 rule="para" parents="7482 12460"/>
    </justification>
  </clause>

  <clause id="12462">
    <literal><![CDATA[
      a(x,y,L(L(z * a(u,w,u),v5,1 / v6),1 / v6,v5)) = a(x,y,v5 \ (v6 \ (((v6 \ a(u,w,u)) * z) * v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,6743,a(flip),b,12427,a),flip(a)].">
      <j1 rule="hyper" parents="316 6743 12427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12463">
    <literal><![CDATA[
      a(x,y,L(L(z * a(u,w,u),v5,v6 \ 1),1 / v6,v5)) = a(x,y,v5 \ (v6 \ (((v6 \ a(u,w,u)) * z) * v5)))
    ]]></literal>
    <justification jstring="[para(1577(a,1),12462(a,1,3,1))].">
      <j1 rule="para" parents="1577 12462"/>
    </justification>
  </clause>

  <clause id="12464">
    <literal><![CDATA[
      a(x,y,L(L(z * a(u,w,u),v5,v6 \ 1),v6 \ 1,v5)) = a(x,y,v5 \ (v6 \ (((v6 \ a(u,w,u)) * z) * v5)))
    ]]></literal>
    <justification jstring="[para(7641(a,1),12463(a,1,3))].">
      <j1 rule="para" parents="7641 12463"/>
    </justification>
  </clause>

  <clause id="12465">
    <literal><![CDATA[
      a(x,y,L(L(z * a(u,w,u),v5,v6 \ 1),v6,v5)) = a(x,y,v5 \ (v6 \ (((v6 \ a(u,w,u)) * z) * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7519,a(flip),b,12464,a)].">
      <j1 rule="hyper" parents="63 7519 12464"/>
    </justification>
  </clause>

  <clause id="12466">
    <literal><![CDATA[
      a(x,y,z \ (u \ (((u \ a(w,v5,w)) * v6) * z))) = a(x,y,L(L(v6 * a(w,v5,w),u,z),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5762,a(flip),b,12465,a),flip(a)].">
      <j1 rule="hyper" parents="63 5762 12465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12467">
    <literal><![CDATA[
      a(x,y,z \ (u \ (((u \ a(w,v5,w)) * v6) * z))) = a(x,y,L(L(v6,u,z),z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,8082,a(flip),b,12466,a),flip(a)].">
      <j1 rule="hyper" parents="316 8082 12466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12471">
    <literal><![CDATA[
      L(T(x,y),T(x,y) \ 1,T(x,y) * T(z,x)) = T((z * x) * (x \ 1),K(x,y)) \ ((1 / (1 / T(x,y))) * T(z,x))
    ]]></literal>
    <justification jstring="[para(4255(a,2),10511(a,2,1))].">
      <j1 rule="para" parents="4255 10511"/>
    </justification>
  </clause>

  <clause id="12472">
    <literal><![CDATA[
      ((x * (y * z)) * (1 / ((1 / a(x,z,y)) * K(y,z)))) \ (x * (y * z)) = 1 / (1 / (((x * z) * y) \ (x * (y * z))))
    ]]></literal>
    <justification jstring="[para(10180(a,1),10563(a,1,1,2,2))].">
      <j1 rule="para" parents="10180 10563"/>
    </justification>
  </clause>

  <clause id="12473">
    <literal><![CDATA[
      (x * (y * (z \ L(z,u,w)))) \ (((z \ L(z,u,w)) * x) * y) = 1 * a(x,z \ L(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(5018(a,1),10564(a,2,1))].">
      <j1 rule="para" parents="5018 10564"/>
    </justification>
  </clause>

  <clause id="12475">
    <literal><![CDATA[
      a(x \ L(x,y,z),z,u) = a(z,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(131,a,12473,a(flip),b,9982,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 12473 9982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12477">
    <literal><![CDATA[
      L(a(x,y,z),u * L(u,w,v5),L(u,w,v5)) * u = (L(u,w,v5) \ 1) * (((L(u,w,v5) \ 1) \ u) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(11604(a,1),10718(a,1,1))].">
      <j1 rule="para" parents="11604 10718"/>
    </justification>
  </clause>

  <clause id="12478">
    <literal><![CDATA[
      a(x,y,(L(z,(u \ 1) \ w,(u \ 1) \ w) * (u \ w)) * v5) = a(x,y,(((u \ w) * (u * u)) \ z) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5996,a(flip),b,10967,a)].">
      <j1 rule="hyper" parents="63 5996 10967"/>
    </justification>
  </clause>

  <clause id="12480">
    <literal><![CDATA[
      a(x,y,(((z \ u) * (z * z)) \ w) * v5) = a(x,y,(((z \ 1) \ u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11711,a(flip),b,12478,a),flip(a)].">
      <j1 rule="hyper" parents="63 11711 12478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12481">
    <literal><![CDATA[
      a(x,y,(((z \ 1) \ u) \ w) * v5) = a(x,y,v5 * ((z \ u) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6747,a(flip),b,12480,a),flip(a)].">
      <j1 rule="hyper" parents="63 6747 12480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12483">
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) \ w) \ v5)) = a(x,y,z * ((u \ w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,12481,a)].">
      <j1 rule="hyper" parents="63 5469 12481"/>
    </justification>
  </clause>

  <clause id="12484">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w \ K(v5,v6))) \ v7)) = a(x,y,(((u \ 1) \ w) \ v7) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11086,a(flip),b,12481,a),flip(a)].">
      <j1 rule="hyper" parents="63 11086 12481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12485">
    <literal><![CDATA[
      a(x,y,((z * (u \ (z \ u))) \ w) * v5) = a(x,y,v5 * ((z \ (u \ (z \ u))) \ w))
    ]]></literal>
    <justification jstring="[para(4734(a,1),12481(a,1,3,1,1))].">
      <j1 rule="para" parents="4734 12481"/>
    </justification>
  </clause>

  <clause id="12486">
    <literal><![CDATA[
      a(x,y,((z \ u) \ (u * w)) \ (L(z,z,u) \ w)) = a(x,y,(L(z,z,u) \ w) * ((z \ u) \ (u * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9684,a(flip),b,12483,a)].">
      <j1 rule="hyper" parents="63 9684 12483"/>
    </justification>
  </clause>

  <clause id="12487">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w \ K(v5,v6))) \ v7)) = a(x,y,z * ((u \ w) \ v7))
    ]]></literal>
    <justification jstring="[hyper(316,a,12481,a(flip),b,12484,a),flip(a)].">
      <j1 rule="hyper" parents="316 12481 12484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12488">
    <literal><![CDATA[
      a(x,y,z * ((R(1 / u,u,w \ K(v5,v6)) \ w) \ v7)) = a(x,y,z * ((u * (w \ K(v5,v6))) \ v7))
    ]]></literal>
    <justification jstring="[para(369(a,1),12487(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="369 12487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12489">
    <literal><![CDATA[
      a(x,y,z * ((R(1 / u,u,w \ K(v5,v6)) \ w) \ v7)) = a(x,y,z * ((u * (w \ 1)) \ v7))
    ]]></literal>
    <justification jstring="[hyper(316,a,10500,a(flip),b,12488,a),flip(a)].">
      <j1 rule="hyper" parents="316 10500 12488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12491">
    <literal><![CDATA[
      a(x,y,z * ((R(1 / u,u,w) \ w) \ v5)) = a(x,y,z * ((u * (w \ 1)) \ v5))
    ]]></literal>
    <justification jstring="[para(4736(a,1),12489(a,1,3,2,1,1))].">
      <j1 rule="para" parents="4736 12489"/>
    </justification>
  </clause>

  <clause id="12492">
    <literal><![CDATA[
      a(x,y,z * ((u * (w \ 1)) \ v5)) = a(x,y,z * ((u * w) \ v5))
    ]]></literal>
    <justification jstring="[para(369(a,1),12491(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="369 12491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12493">
    <literal><![CDATA[
      a(x,y,(((z * (u \ 1)) \ w) \ 1) \ (u \ (z \ w))) = a(x,y,((u \ 1) \ (z \ w)) * ((z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,11403,a,b,12492,a)].">
      <j1 rule="hyper" parents="63 11403 12492"/>
    </justification>
  </clause>

  <clause id="12494">
    <literal><![CDATA[
      a(x,y,(((z * (u \ 1)) \ w) \ 1) \ (u \ (z \ w))) = a(x,y,(u \ (z \ w)) * ((z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(316,a,6698,a(flip),b,12493,a),flip(a)].">
      <j1 rule="hyper" parents="316 6698 12493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12495">
    <literal><![CDATA[
      (x * (L(y,z,u) \ R(L(y,z,u),w,v5))) / x = R(y,z,u) \ R(R(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(8722(a,1),11331(a,1,1,2))].">
      <j1 rule="para" parents="8722 11331"/>
    </justification>
  </clause>

  <clause id="12496">
    <literal><![CDATA[
      (x * (L(y,z,u) \ L(R(y,w,v5),z,u))) / x = R(y,z,u) \ R(R(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(29(a,1),12495(a,1,1,2,2))].">
      <j1 rule="para" parents="29 12495"/>
    </justification>
  </clause>

  <clause id="12497">
    <literal><![CDATA[
      R(x,y,z) \ R(R(x,y,z),u,w) = L(x,y,z) \ L(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(267,a,12496,a),flip(a)].">
      <j1 rule="hyper" parents="267 12496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12498">
    <literal><![CDATA[
      (R(x,y,y) * a(x,y,y)) \ L(R(x,y,y) * a(x,y,y),z,u) = L(x \ L(x,z,u),a(x,y,y),a(x,y,y))
    ]]></literal>
    <justification jstring="[para(2377(a,1),11989(a,1,2,1,1))].">
      <j1 rule="para" parents="2377 11989"/>
    </justification>
  </clause>

  <clause id="12499">
    <literal><![CDATA[
      (R(x,y,y) * a(x,y,y)) \ L(R(x,y,y) * a(x,y,y),z,u) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,8712,a(flip),b,12498,a),flip(a)].">
      <j1 rule="hyper" parents="316 8712 12498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12501">
    <literal><![CDATA[
      R(a(x,y,y) * x,y,y) \ L(R(x,y,y) * a(x,y,y),z,u) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[para(6968(a,2),12499(a,1,1))].">
      <j1 rule="para" parents="6968 12499"/>
    </justification>
  </clause>

  <clause id="12502">
    <literal><![CDATA[
      R(R(x,y,y),y,y) \ L(R(x,y,y) * a(x,y,y),z,u) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[para(2377(a,1),12501(a,1,1,1))].">
      <j1 rule="para" parents="2377 12501"/>
    </justification>
  </clause>

  <clause id="12503">
    <literal><![CDATA[
      R(R(x,y,y),y,y) \ L(R(a(x,y,y) * x,y,y),z,u) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[para(6968(a,2),12502(a,1,2,1))].">
      <j1 rule="para" parents="6968 12502"/>
    </justification>
  </clause>

  <clause id="12504">
    <literal><![CDATA[
      R(R(x,y,y),y,y) \ L(R(R(x,y,y),y,y),z,u) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[para(2377(a,1),12503(a,1,2,1,1))].">
      <j1 rule="para" parents="2377 12503"/>
    </justification>
  </clause>

  <clause id="12505">
    <literal><![CDATA[
      L(R(x,y,y) \ L(R(x,y,y),z,u),y,y) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8381,a(flip),b,12504,a)].">
      <j1 rule="hyper" parents="63 8381 12504"/>
    </justification>
  </clause>

  <clause id="12506">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,u),u,u) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8381(a,1),12505(a,1,1))].">
      <j1 rule="para" parents="8381 12505"/>
    </justification>
  </clause>

  <clause id="12507">
    <literal><![CDATA[
      L((x * y) \ L(x * y,z,u),y,y) = y \ (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,9578,a,b,12506,a),flip(a)].">
      <j1 rule="hyper" parents="41 9578 12506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12508">
    <literal><![CDATA[
      L((x * y) \ L(x * y,z,u),x,x) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,9576,a,b,12506,a),flip(a)].">
      <j1 rule="hyper" parents="41 9576 12506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12510">
    <literal><![CDATA[
      x \ (((x \ 1) \ y) * L(((x \ 1) \ y) \ x,z,u)) = L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(9597(a,1),12507(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9597 12507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12511">
    <literal><![CDATA[
      x \ ((y / x) \ L(y,z,u)) = L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(9749(a,1),12510(a,1,2))].">
      <j1 rule="para" parents="9749 12510"/>
    </justification>
  </clause>

  <clause id="12512">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),x,x) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(152,a,12511,a)].">
      <j1 rule="hyper" parents="152 12511"/>
    </justification>
  </clause>

  <clause id="12513">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,u) \ 1 = L(x \ L(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10036,a,b,12511,a)].">
      <j1 rule="hyper" parents="63 10036 12511"/>
    </justification>
  </clause>

  <clause id="12514">
    <literal><![CDATA[
      L((x \ (y \ 1)) \ L(x \ (y \ 1),z,u),y \ 1,y \ 1) = (y \ 1) \ (((x \ y) / y) \ L(x \ (y \ 1),z,u))
    ]]></literal>
    <justification jstring="[para(590(a,1),12511(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="590 12511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12515">
    <literal><![CDATA[
      (x / y) * (y * (((y \ x) * y) \ L((y \ x) * y,z,u))) = x * L(x \ L(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[para(12511(a,1),10118(a,2,2))].">
      <j1 rule="para" parents="12511 10118"/>
    </justification>
  </clause>

  <clause id="12516">
    <literal><![CDATA[
      T((x / (y \ L(y,z,u))) * L(y \ L(y,z,u),x,x),y \ L(y,z,u)) = (y \ L(y,z,u)) \ ((y / x) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(390,a,12512,a(flip),b,1436,a)].">
      <j1 rule="hyper" parents="390 12512 1436"/>
    </justification>
  </clause>

  <clause id="12517">
    <literal><![CDATA[
      ((x \ 1) / y) \ L(x \ 1,z,u) = y * L(x \ L(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[para(1067(a,1),12512(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1067 12512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12518">
    <literal><![CDATA[
      x \ ((x / (y \ L(y,z,u))) * L(y \ L(y,z,u),x,x)) = (x * (y \ L(y,z,u))) \ ((y / x) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12512(a,1),7109(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12512 7109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12519">
    <literal><![CDATA[
      ((L(x,y,z) \ 1) / u) \ L(L(x,y,z) \ 1,y,z) = u * L((L(x,y,z) \ 1) \ (x \ 1),u,u)
    ]]></literal>
    <justification jstring="[para(9873(a,1),12512(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9873 12512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12520">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,u) \ 1 = L(L(x,y,z) \ x,u,u)
    ]]></literal>
    <justification jstring="[hyper(39,a,5041,a,b,12513,a)].">
      <j1 rule="hyper" parents="39 5041 12513"/>
    </justification>
  </clause>

  <clause id="12521">
    <literal><![CDATA[
      L(x \ (y * L(y \ x,z,u)),w,w) \ 1 = L(L(x \ y,z,u) \ (x \ y),w,w)
    ]]></literal>
    <justification jstring="[para(1252(a,1),12520(a,1,1,1))].">
      <j1 rule="para" parents="1252 12520"/>
    </justification>
  </clause>

  <clause id="12522">
    <literal><![CDATA[
      ((x \ 1) / y) \ L(x \ 1,z,u) = (x / y) \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,12512,a(flip),b,12517,a),flip(a)].">
      <j1 rule="hyper" parents="316 12512 12517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12523">
    <literal><![CDATA[
      (x / y) * (y * (x \ L(x,z,u))) = x * L(x \ L(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[para(8968(a,1),12515(a,1,2,2))].">
      <j1 rule="para" parents="8968 12515"/>
    </justification>
  </clause>

  <clause id="12524">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * T(y / x,x) = y * L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6521,a,b,12523,a)].">
      <j1 rule="hyper" parents="63 6521 12523"/>
    </justification>
  </clause>

  <clause id="12527">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * (x \ y) = y * L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(116(a,1),12524(a,1,2))].">
      <j1 rule="para" parents="116 12524"/>
    </justification>
  </clause>

  <clause id="12528">
    <literal><![CDATA[
      (x * (a(y \ 1,y,z) \ 1)) * (x \ z) = z * L(z \ L(z,y,y \ 1),x,x)
    ]]></literal>
    <justification jstring="[para(5087(a,2),12527(a,1,1,2))].">
      <j1 rule="para" parents="5087 12527"/>
    </justification>
  </clause>

  <clause id="12529">
    <literal><![CDATA[
      (x * (a(y \ 1,y,z) \ 1)) * (x \ z) = a(y \ 1,y,L(z,x,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(316,a,7212,a(flip),b,12528,a),flip(a)].">
      <j1 rule="hyper" parents="316 7212 12528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12530">
    <literal><![CDATA[
      ((L(x,y,z) \ 1) / u) \ L(L(x,y,z) \ 1,y,z) = u * L(x \ L(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[para(2095(a,1),12519(a,2,2,1))].">
      <j1 rule="para" parents="2095 12519"/>
    </justification>
  </clause>

  <clause id="12531">
    <literal><![CDATA[
      ((L(x,y,z) \ 1) / u) \ L(L(x,y,z) \ 1,y,z) = (x / u) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,12512,a(flip),b,12530,a),flip(a)].">
      <j1 rule="hyper" parents="316 12512 12530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12532">
    <literal><![CDATA[
      (L(x,y,z) / u) \ L(L(x,y,z),y,z) = (x / u) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12522,a(flip),b,12531,a)].">
      <j1 rule="hyper" parents="63 12522 12531"/>
    </justification>
  </clause>

  <clause id="12533">
    <literal><![CDATA[
      x \ ((x / (y \ L(y,z,u))) * L(y \ L(y,z,u),x,x)) = a(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,9766,a(flip),b,12518,a),flip(a)].">
      <j1 rule="hyper" parents="316 9766 12518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12534">
    <literal><![CDATA[
      x \ (((y \ L(y,z,u)) \ x) * L(y \ L(y,z,u),x,x)) = a(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5015(a,1),12533(a,1,2,1))].">
      <j1 rule="para" parents="5015 12533"/>
    </justification>
  </clause>

  <clause id="12535">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ v5) * (v6 * (a(v6,v7,R(z,u,w) \ v5) \ v7))) = a(x,y,v6 * (v7 * (R(z,u,w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5472,a(flip),b,12065,a),flip(a)].">
      <j1 rule="hyper" parents="316 5472 12065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12536">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ v5) * (v6 * (a(v6,v7,L(z,u,w) \ v5) \ v7))) = a(x,y,v6 * (v7 * (R(z,u,w) \ v5)))
    ]]></literal>
    <justification jstring="[para(9541(a,1),12535(a,1,3,2,2,1))].">
      <j1 rule="para" parents="9541 12535"/>
    </justification>
  </clause>

  <clause id="12537">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ v5,v6,v7) * (v7 * v6)) = a(x,y,v7 * (v6 * (R(z,u,w) \ v5)))
    ]]></literal>
    <justification jstring="[para(8534(a,1),12536(a,1,3))].">
      <j1 rule="para" parents="8534 12536"/>
    </justification>
  </clause>

  <clause id="12538">
    <literal><![CDATA[
      a(x,y,z * (u * (R(w,v5,v6) \ v7))) = a(x,y,z * (u * (L(w,v5,v6) \ v7)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5472,a(flip),b,12537,a),flip(a)].">
      <j1 rule="hyper" parents="63 5472 12537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12539">
    <literal><![CDATA[
      a(x,y,a(z,z \ u,R(w,v5,v6) \ v7) * ((z \ u) * (L(w,v5,v6) \ v7))) = a(x,y,z \ (u * (R(w,v5,v6) \ v7)))
    ]]></literal>
    <justification jstring="[para(8458(a,1),12538(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8458 12538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12540">
    <literal><![CDATA[
      a(x,y,a(z,z \ u,L(w,v5,v6) \ v7) * ((z \ u) * (L(w,v5,v6) \ v7))) = a(x,y,z \ (u * (R(w,v5,v6) \ v7)))
    ]]></literal>
    <justification jstring="[para(9541(a,1),12539(a,1,3,1))].">
      <j1 rule="para" parents="9541 12539"/>
    </justification>
  </clause>

  <clause id="12541">
    <literal><![CDATA[
      a(x,y,z \ (u * (R(w,v5,v6) \ v7))) = a(x,y,z \ (u * (L(w,v5,v6) \ v7)))
    ]]></literal>
    <justification jstring="[para(8458(a,1),12540(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8458 12540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12542">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ ((v5 * w) \ w)))) = a(x,y,z \ (u * (L(v5,w,w) \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11484,a,b,12541,a)].">
      <j1 rule="hyper" parents="63 11484 12541"/>
    </justification>
  </clause>

  <clause id="12543">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ (w \ (v5 \ w))))) = a(x,y,z \ (u * (L(v5,w,w) \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10103,a(flip),b,12542,a)].">
      <j1 rule="hyper" parents="63 10103 12542"/>
    </justification>
  </clause>

  <clause id="12544">
    <literal><![CDATA[
      a(x,y,z \ (u * L(w \ v5,v5,v5))) = a(x,y,z \ (u * (L(w,v5,v5) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11752,a(flip),b,12543,a)].">
      <j1 rule="hyper" parents="63 11752 12543"/>
    </justification>
  </clause>

  <clause id="12546">
    <literal><![CDATA[
      L(T(x,y),T(x,y) \ 1,T(x,y) * T(z,x)) = T(R(z,x,x),K(x,y)) \ ((1 / (1 / T(x,y))) * T(z,x))
    ]]></literal>
    <justification jstring="[para(565(a,1),12471(a,2,1,1))].">
      <j1 rule="para" parents="565 12471"/>
    </justification>
  </clause>

  <clause id="12547">
    <literal><![CDATA[
      L(T(x,y),T(x,y) \ 1,T(x,y) * T(z,x)) = R(T(z,K(x,y)),x,x) \ ((1 / (1 / T(x,y))) * T(z,x))
    ]]></literal>
    <justification jstring="[para(27(a,2),12546(a,2,1))].">
      <j1 rule="para" parents="27 12546"/>
    </justification>
  </clause>

  <clause id="12548">
    <literal><![CDATA[
      L(T(x,y),T(x,y) \ 1,T(x,y) * T(z,x)) = R(T(z,K(x,y)),x,x) \ (T(1 / (1 / x),y) * T(z,x))
    ]]></literal>
    <justification jstring="[para(2417(a,1),12547(a,2,2,1))].">
      <j1 rule="para" parents="2417 12547"/>
    </justification>
  </clause>

  <clause id="12549">
    <literal><![CDATA[
      L(T(x,y),T(x,y) \ 1,T(x,y) * T(z,x)) = R(T(z,K(x,y)),x,x) \ (K(x,y) * (z * (1 / (1 / x))))
    ]]></literal>
    <justification jstring="[para(7497(a,1),12548(a,2,2))].">
      <j1 rule="para" parents="7497 12548"/>
    </justification>
  </clause>

  <clause id="12550">
    <literal><![CDATA[
      L(T(x,y),T(x,y) \ 1,T(x,y) * T(z,x)) = K(x,y) * (R(z,x,x) \ (z * (1 / (1 / x))))
    ]]></literal>
    <justification jstring="[hyper(316,a,10434,a(flip),b,12549,a),flip(a)].">
      <j1 rule="hyper" parents="316 10434 12549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12551">
    <literal><![CDATA[
      ((x * (y * z)) * (1 / ((a(x,z,y) \ 1) * K(y,z)))) \ (x * (y * z)) = 1 / (1 / (((x * z) * y) \ (x * (y * z))))
    ]]></literal>
    <justification jstring="[para(2276(a,1),12472(a,1,1,2,2,1))].">
      <j1 rule="para" parents="2276 12472"/>
    </justification>
  </clause>

  <clause id="12552">
    <literal><![CDATA[
      L((x \ (y \ 1)) \ L(x \ (y \ 1),z,u),y \ 1,y \ 1) = (y \ 1) \ (y \ (x \ (y * L(y \ x,z,u))))
    ]]></literal>
    <justification jstring="[para(9779(a,1),12514(a,2,2))].">
      <j1 rule="para" parents="9779 12514"/>
    </justification>
  </clause>

  <clause id="12553">
    <literal><![CDATA[
      L(x \ ((y \ 1) * L((y \ 1) \ x,z,u)),y \ 1,y \ 1) = (y \ 1) \ (y \ (x \ (y * L(y \ x,z,u))))
    ]]></literal>
    <justification jstring="[para(1252(a,1),12552(a,1,1))].">
      <j1 rule="para" parents="1252 12552"/>
    </justification>
  </clause>

  <clause id="12554">
    <literal><![CDATA[
      L(x \ (y * L(y \ x,z,u)),y \ 1,y \ 1) = (y \ 1) \ (y \ (x \ (y * L(y \ x,z,u))))
    ]]></literal>
    <justification jstring="[para(1350(a,1),12553(a,1,1,2))].">
      <j1 rule="para" parents="1350 12553"/>
    </justification>
  </clause>

  <clause id="12555">
    <literal><![CDATA[
      (x \ 1) \ (x \ (y \ (x * L(x \ y,z,u)))) = L(y \ (x * L(x \ y,z,u)),x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8942,a(flip),b,12554,a),flip(a)].">
      <j1 rule="hyper" parents="63 8942 12554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12556">
    <literal><![CDATA[
      (x \ 1) \ (x \ (y \ (x * L(x \ y,z,u)))) = L(y \ (x * L(x \ y,z,u)),x,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,7807,a(flip),b,12555,a),flip(a)].">
      <j1 rule="hyper" parents="316 7807 12555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12557">
    <literal><![CDATA[
      ((x * (y * z)) * (1 / (a(x,z,y) \ K(y,z)))) \ (x * (y * z)) = 1 / (1 / (((x * z) * y) \ (x * (y * z))))
    ]]></literal>
    <justification jstring="[para(3780(a,1),12551(a,1,1,2,2))].">
      <j1 rule="para" parents="3780 12551"/>
    </justification>
  </clause>

  <clause id="12558">
    <literal><![CDATA[
      ((x * (y * z)) * (K(z,y) * a(x,z,y))) \ (x * (y * z)) = 1 / (1 / (((x * z) * y) \ (x * (y * z))))
    ]]></literal>
    <justification jstring="[para(2973(a,1),12557(a,1,1,2))].">
      <j1 rule="para" parents="2973 12557"/>
    </justification>
  </clause>

  <clause id="12559">
    <literal><![CDATA[
      ((x * (y * T(z,y))) * a(x,z,y)) \ (x * (y * z)) = 1 / (1 / (((x * z) * y) \ (x * (y * z))))
    ]]></literal>
    <justification jstring="[para(10189(a,1),12558(a,1,1))].">
      <j1 rule="para" parents="10189 12558"/>
    </justification>
  </clause>

  <clause id="12560">
    <literal><![CDATA[
      ((x * (y * z)) * a(x,y,z)) \ (x * (z * y)) = 1 / (1 / (((x * y) * z) \ (x * (z * y))))
    ]]></literal>
    <justification jstring="[para(114(a,1),12559(a,1,1,1,2))].">
      <j1 rule="para" parents="114 12559"/>
    </justification>
  </clause>

  <clause id="12561">
    <literal><![CDATA[
      1 / (1 / (((x * y) * z) \ (x * (z * y)))) = ((x * y) * z) \ (x * (z * y))
    ]]></literal>
    <justification jstring="[para(89(a,1),12560(a,1,1)),flip(a)].">
      <j1 rule="para" parents="89 12560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12562">
    <literal><![CDATA[
      ((x / y) * L(((x / y) \ z) * K(z,y),u,w)) \ T(z,y) = (x / T(y,z)) \ (L(z / (x / y),u,w) \ T(z,y))
    ]]></literal>
    <justification jstring="[para(11113(a,1),10430(a,1,1))].">
      <j1 rule="para" parents="11113 10430"/>
    </justification>
  </clause>

  <clause id="12563">
    <literal><![CDATA[
      (x / T(y,z)) \ (L(z / (x / y),u,w) \ T(z,y)) = ((x / y) * L((x / y) \ T(z,y),u,w)) \ T(z,y)
    ]]></literal>
    <justification jstring="[para(3846(a,1),12562(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3846 12562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12564">
    <literal><![CDATA[
      T((x / y) * L((x / y) \ z,u,w),y) \ T(z,y) = (x / T(y,z)) \ (L(z / (x / y),u,w) \ T(z,y))
    ]]></literal>
    <justification jstring="[para(4881(a,2),12563(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4881 12563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12565">
    <literal><![CDATA[
      T((x \ y) * L((x \ y) \ z,u,w),x) \ T(z,x) = (y / T(x,z)) \ (L(z / (y / x),u,w) \ T(z,x))
    ]]></literal>
    <justification jstring="[para(4979(a,1),12564(a,1,1,1))].">
      <j1 rule="para" parents="4979 12564"/>
    </justification>
  </clause>

  <clause id="12566">
    <literal><![CDATA[
      (x / T(y,z)) \ (L(z / (x / y),u,w) \ T(z,y)) = (y \ (x * L(x \ (z * y),u,w))) \ T(z,y)
    ]]></literal>
    <justification jstring="[para(7600(a,1),12565(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7600 12565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12567">
    <literal><![CDATA[
      T((x / y) \ (L(z / (x / y),u,w) \ z),K(y,z)) = (y \ (x * L(x \ (z * y),u,w))) \ T(z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10512,a,b,12566,a)].">
      <j1 rule="hyper" parents="63 10512 12566"/>
    </justification>
  </clause>

  <clause id="12568">
    <literal><![CDATA[
      T((x \ y) \ (L(z / (x \ y),u,w) \ z),K(x,z)) = (x \ (y * L(y \ (z * x),u,w))) \ T(z,x)
    ]]></literal>
    <justification jstring="[para(11084(a,1),12567(a,1,1))].">
      <j1 rule="para" parents="11084 12567"/>
    </justification>
  </clause>

  <clause id="12569">
    <literal><![CDATA[
      (x \ (y * L(y \ (z * x),u,w))) \ T(z,x) = (x \ y) \ (L(z / (x \ y),u,w) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6508,a(flip),b,12568,a),flip(a)].">
      <j1 rule="hyper" parents="63 6508 12568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12571">
    <literal><![CDATA[
      a(x,y,z \ ((((u * T(w,w \ u)) * (w \ 1)) \ v5) \ v6)) = a(x,y,z \ (((w * (u * (w \ 1))) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,10707,a(flip),b,10703,a),flip(a)].">
      <j1 rule="hyper" parents="316 10707 10703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12573">
    <literal><![CDATA[
      a(x,y,z \ ((((u \ 1) * (w * u)) \ v5) \ v6)) = a(x,y,z \ (((u * (w * (u \ 1))) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,11713,a(flip),b,12571,a)].">
      <j1 rule="hyper" parents="63 11713 12571"/>
    </justification>
  </clause>

  <clause id="12575">
    <literal><![CDATA[
      a(x,y,z \ (((u * (w * (u \ 1))) \ v5) \ v6)) = a(x,y,z \ ((R(w,u,u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,10700,a(flip),b,12573,a),flip(a)].">
      <j1 rule="hyper" parents="63 10700 12573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12576">
    <literal><![CDATA[
      a(x,y,z \ ((((u * (w \ 1)) * w) \ v5) \ v6)) = a(x,y,z \ ((R(u,w,w) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,10672,a,b,12575,a)].">
      <j1 rule="hyper" parents="63 10672 12575"/>
    </justification>
  </clause>

  <clause id="12577">
    <literal><![CDATA[
      a(x,y,z \ (((R(u \ w,u,u) * u) \ v5) \ v6)) = a(x,y,z \ ((R(w,u,u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,10702,a,b,12576,a)].">
      <j1 rule="hyper" parents="63 10702 12576"/>
    </justification>
  </clause>

  <clause id="12578">
    <literal><![CDATA[
      T(x * (y * L(y \ (x \ z),u,w)),v5) \ T(z,v5) = T(x * y,v6) \ T(L(z / (x * y),u,w) \ z,v6)
    ]]></literal>
    <justification jstring="[para(7214(a,1),11555(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7214 11555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12579">
    <literal><![CDATA[
      T(x * (y * L(y \ (x \ z),u,w)),v5) \ T(z,v5) = (x * y) \ (L(z / (x * y),u,w) \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,11556,a(flip),b,12578,a),flip(a)].">
      <j1 rule="hyper" parents="316 11556 12578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12581">
    <literal><![CDATA[
      T(((x \ L(x,y,z)) \ u) * L(x \ L(x,y,z),u,u),x \ L(x,y,z)) = (x \ L(x,y,z)) \ ((x / u) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5015(a,1),12516(a,1,1,1))].">
      <j1 rule="para" parents="5015 12516"/>
    </justification>
  </clause>

  <clause id="12582">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ u) * L(x \ L(x,y,z),u,u) = (x \ L(x,y,z)) \ ((x / u) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(5024,a,12581,a)].">
      <j1 rule="hyper" parents="5024 12581"/>
    </justification>
  </clause>

  <clause id="12584">
    <literal><![CDATA[
      x \ ((y \ L(y,z,u)) \ ((y / x) \ L(y,z,u))) = a(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12582(a,1),12534(a,1,2))].">
      <j1 rule="para" parents="12582 12534"/>
    </justification>
  </clause>

  <clause id="12585">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) \ ((x / y) * (L(1 / y,z,u) \ 1)) = x \ ((y \ L(y,z,u)) \ ((x / y) * L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(9563(a,1),10128(a,2,2))].">
      <j1 rule="para" parents="9563 10128"/>
    </justification>
  </clause>

  <clause id="12586">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) \ ((x / y) * (L(1 / y,z,u) \ 1)) = a(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,8799,a(flip),b,12585,a),flip(a)].">
      <j1 rule="hyper" parents="316 8799 12585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12587">
    <literal><![CDATA[
      (x * (((y \ z) / z) * y)) \ ((x / (y \ z)) * (L(1 / (y \ z),y,z \ (y \ z)) \ 1)) = a(y \ z,(y \ z) \ L(y \ z,y,z \ (y \ z)),x)
    ]]></literal>
    <justification jstring="[para(1656(a,1),12586(a,1,1,2))].">
      <j1 rule="para" parents="1656 12586"/>
    </justification>
  </clause>

  <clause id="12588">
    <literal><![CDATA[
      a(x,y,z \ (u * T((w * (v5 \ v6)) * v7,z \ u))) = a(x,y,z \ (u * ((w * (v6 / v5)) * v7)))
    ]]></literal>
    <justification jstring="[para(8570(a,1),10132(a,1,3))].">
      <j1 rule="para" parents="8570 10132"/>
    </justification>
  </clause>

  <clause id="12589">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * (v5 / v6)) * v7))) = a(x,y,z \ (u * ((w * (v6 \ v5)) * v7)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5495,a(flip),b,12588,a),flip(a)].">
      <j1 rule="hyper" parents="63 5495 12588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12591">
    <literal><![CDATA[
      T(K(x,y) * (a(z,u,w) * y),x * y) = L(a(z,u,w) * y,(a(z,u,w) * y) \ (x * y),a(z,u,w) * y)
    ]]></literal>
    <justification jstring="[para(2761(a,1),10595(a,1,1))].">
      <j1 rule="para" parents="2761 10595"/>
    </justification>
  </clause>

  <clause id="12592">
    <literal><![CDATA[
      T(x * (K(y,x) * a(z,u,w)),y * x) = L(a(z,u,w) * x,(a(z,u,w) * x) \ (y * x),a(z,u,w) * x)
    ]]></literal>
    <justification jstring="[para(3135(a,1),12591(a,1,1))].">
      <j1 rule="para" parents="3135 12591"/>
    </justification>
  </clause>

  <clause id="12593">
    <literal><![CDATA[
      L(a(x,y,z) * u,(a(x,y,z) * u) \ (w * u),a(x,y,z) * u) = L(u,w,u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6122,a(flip),b,12592,a),flip(a)].">
      <j1 rule="hyper" parents="63 6122 12592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12594">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z) \ w,a(x,y,z) * u) = L(u,w,u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11360,a(flip),b,12593,a)].">
      <j1 rule="hyper" parents="63 11360 12593"/>
    </justification>
  </clause>

  <clause id="12596">
    <literal><![CDATA[
      L(a(x,y,z) * u,w,a(x,y,z) * u) = L(u,w,u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6121,a(flip),b,12594,a)].">
      <j1 rule="hyper" parents="63 6121 12594"/>
    </justification>
  </clause>

  <clause id="12598">
    <literal><![CDATA[
      T((x * (a(y,z,u) * w)) / x,x * w) = L(w,x,w) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5305,a,b,12596,a)].">
      <j1 rule="hyper" parents="63 5305 12596"/>
    </justification>
  </clause>

  <clause id="12599">
    <literal><![CDATA[
      L(x * a(y,z,u),w,x * a(y,z,u)) = L(x,w,x) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5306,a(flip),b,12598,a)].">
      <j1 rule="hyper" parents="63 5306 12598"/>
    </justification>
  </clause>

  <clause id="12600">
    <literal><![CDATA[
      L(x * a(y,x,x),z,x) = L(x,z,x) * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8471,a(flip),b,12599,a)].">
      <j1 rule="hyper" parents="63 8471 12599"/>
    </justification>
  </clause>

  <clause id="12601">
    <literal><![CDATA[
      R(T(a(x,y,z) \ 1,u),w * K(v5,v6),(w * K(v5,v6)) \ u) = u \ ((w * (a(x,y,z) \ K(v5,v6))) * (K(v6,v5) * (w \ u)))
    ]]></literal>
    <justification jstring="[para(10176(a,1),11080(a,2,2,2))].">
      <j1 rule="para" parents="10176 11080"/>
    </justification>
  </clause>

  <clause id="12602">
    <literal><![CDATA[
      L(x,((T(y,T(z * u,w)) * u) \ (y * (z * u))) \ v5,v6) = L(x,R(z,u,T(y,T(z * u,w))) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,10821,a(flip),b,11435,a)].">
      <j1 rule="hyper" parents="63 10821 11435"/>
    </justification>
  </clause>

  <clause id="12604">
    <literal><![CDATA[
      L(x,R(y,z,T(u,T(y * z,w))) \ v5,v6) = L(x,((u * z) \ (u * (y * z))) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,10950,a(flip),b,12602,a),flip(a)].">
      <j1 rule="hyper" parents="63 10950 12602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12606">
    <literal><![CDATA[
      L(x,R(y,z,T(u,T(y * z,w))) \ v5,v6) = L(x,L(T(y,z),z,u) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(247(a,1),12604(a,2,2,1))].">
      <j1 rule="para" parents="247 12604"/>
    </justification>
  </clause>

  <clause id="12607">
    <literal><![CDATA[
      L(x,R(y,z,T(u,T(y * z,w))) \ v5,v6) = L(x,L(y,z,u) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,10813,a(flip),b,12606,a),flip(a)].">
      <j1 rule="hyper" parents="316 10813 12606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12609">
    <literal><![CDATA[
      L(x,R(y,z,u) \ w,v5) = L(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(4679(a,1),12607(a,1,2,1))].">
      <j1 rule="para" parents="4679 12607"/>
    </justification>
  </clause>

  <clause id="12610">
    <literal><![CDATA[
      L(x,L(R(y,z,u),w,v5) \ R(y,z,u),v6) = L(x,L(y,z,u) \ L(R(y,z,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,12400,a,b,12609,a)].">
      <j1 rule="hyper" parents="63 12400 12609"/>
    </justification>
  </clause>

  <clause id="12611">
    <literal><![CDATA[
      L(a(x,y,R(z,u,w) \ v5) \ 1,L(z,u,w) \ v5,y) = (R(z,u,w) \ v5) \ L(R(z,u,w) \ v5,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9997,a(flip),b,12609,a),flip(a)].">
      <j1 rule="hyper" parents="63 9997 12609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12612">
    <literal><![CDATA[
      L(x,L(y,z,u) \ (L(w,R(y,z,u) \ v5,R(y,z,u)) * v5),v6) = L(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(714(a,1),12609(a,1,2)),flip(a)].">
      <j1 rule="para" parents="714 12609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12614">
    <literal><![CDATA[
      R(x,y,z) \ L(u,L(x,y,z) \ 1,L(x,y,z)) = (R(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[para(12609(a,1),4633(a,1,2))].">
      <j1 rule="para" parents="12609 4633"/>
    </justification>
  </clause>

  <clause id="12615">
    <literal><![CDATA[
      x * L(y,L(z,u,w) \ x,L(z,u,w)) = R(z,u,w) * ((R(z,u,w) \ x) * y)
    ]]></literal>
    <justification jstring="[para(12609(a,1),4631(a,1,2))].">
      <j1 rule="para" parents="12609 4631"/>
    </justification>
  </clause>

  <clause id="12616">
    <literal><![CDATA[
      (x * y) * L(z,L(x,y,y) \ (x * y),L(x,y,y)) = R(x,y,y) * (L(y,y,L(x,y,y)) * z)
    ]]></literal>
    <justification jstring="[para(12609(a,1),7262(a,1,2))].">
      <j1 rule="para" parents="12609 7262"/>
    </justification>
  </clause>

  <clause id="12617">
    <literal><![CDATA[
      L(x,L(y,z,u) \ L(R(y,z,u),w,v5),v6) = L(x,L(y \ L(y,w,v5),z,u),v6)
    ]]></literal>
    <justification jstring="[para(8381(a,1),12609(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8381 12609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12618">
    <literal><![CDATA[
      L(L(x,L(y,z,u) \ w,v5) \ x,x,R(y,z,u) \ w) = a(v5,R(y,z,u) \ w,x)
    ]]></literal>
    <justification jstring="[para(12609(a,1),9998(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12609 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12619">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ (L(v5,L(z,u,w) \ v6,L(z,u,w)) * v6)) = L(x,y,(R(z,u,w) \ v6) * v5)
    ]]></literal>
    <justification jstring="[para(12609(a,1),12267(a,1,3,2,1))].">
      <j1 rule="para" parents="12609 12267"/>
    </justification>
  </clause>

  <clause id="12620">
    <literal><![CDATA[
      R(x,y,z) * ((R(x,y,z) \ u) * w) = L(x,y,z) * ((L(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,405,a(flip),b,12615,a),flip(a)].">
      <j1 rule="hyper" parents="63 405 12615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12621">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ u) * (K(R(x,y,z),R(x,y,z) \ u) * w)) = T(R(x,y,z),R(x,y,z) \ u) * ((R(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3133,a(flip),b,12620,a),flip(a)].">
      <j1 rule="hyper" parents="63 3133 12620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12623">
    <literal><![CDATA[
      L(L(x,L(y,z,u) \ w,v5) \ x,x,L(y,z,u) \ w) = a(v5,R(y,z,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11407,a(flip),b,12618,a)].">
      <j1 rule="hyper" parents="63 11407 12618"/>
    </justification>
  </clause>

  <clause id="12624">
    <literal><![CDATA[
      a(x,R(y,z,u) \ w,v5) = a(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,9998,a,b,12623,a),flip(a)].">
      <j1 rule="hyper" parents="63 9998 12623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12625">
    <literal><![CDATA[
      a(R(x,y,z),R(u,w,v5) \ v6,v7) = a(L(x,y,z),L(u,w,v5) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,4643,a(flip),b,12624,a),flip(a)].">
      <j1 rule="hyper" parents="316 4643 12624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12626">
    <literal><![CDATA[
      L(x,L(y,z,u) \ L(R(y,z,u),w,v5),v6) = L(x,L(y \ L(y,w,v5),z,u) \ 1,v6)
    ]]></literal>
    <justification jstring="[para(8395(a,1),12610(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8395 12610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12627">
    <literal><![CDATA[
      L(x,L(y \ L(y,z,u),w,v5) \ 1,v6) = L(x,L(y \ L(y,z,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,12617,a(flip),b,12626,a),flip(a)].">
      <j1 rule="hyper" parents="63 12617 12626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12628">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),L(x \ L(x,y,z),u,w),v5) = (v5 * (1 / L(x \ L(x,y,z),u,w))) \ v5
    ]]></literal>
    <justification jstring="[hyper(63,a,2674,a(flip),b,12627,a),flip(a)].">
      <j1 rule="hyper" parents="63 2674 12627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12629">
    <literal><![CDATA[
      (x * y) * L(z,x * (L(x,y,y) \ y),L(x,y,y)) = R(x,y,y) * (L(y,y,L(x,y,y)) * z)
    ]]></literal>
    <justification jstring="[para(1129(a,1),12616(a,1,2,2))].">
      <j1 rule="para" parents="1129 12616"/>
    </justification>
  </clause>

  <clause id="12630">
    <literal><![CDATA[
      R(x,y,y) * (L(y,y,L(x,y,y)) * z) = L(x,y,y) * ((x * (L(x,y,y) \ y)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1144,a(flip),b,12629,a),flip(a)].">
      <j1 rule="hyper" parents="63 1144 12629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12631">
    <literal><![CDATA[
      L(x,y,y) * ((x * (L(x,y,y) \ y)) * z) = R(x,y,y) * (L(y,y,x) * z)
    ]]></literal>
    <justification jstring="[para(7159(a,1),12630(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7159 12630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12632">
    <literal><![CDATA[
      R(x,y,y) * (L(y,y,x) * z) = L(x,y,y) * (R(y,y,x) * z)
    ]]></literal>
    <justification jstring="[para(4662(a,1),12631(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4662 12631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12633">
    <literal><![CDATA[
      (x * y) / ((L(x,y,y) * (R(y,y,x) * z)) / z) = a(L(x,y,y),L(y,y,x),z)
    ]]></literal>
    <justification jstring="[para(12632(a,1),9721(a,1,2,1))].">
      <j1 rule="para" parents="12632 9721"/>
    </justification>
  </clause>

  <clause id="12634">
    <literal><![CDATA[
      L(x,y,(L(z,u,w) \ v5) * T(v6,v5)) = L(x,y,(R(z,u,w) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(714(a,1),12619(a,1,3))].">
      <j1 rule="para" parents="714 12619"/>
    </justification>
  </clause>

  <clause id="12635">
    <literal><![CDATA[
      L(x,y,(R(z,u,w) \ v5) * v6) = L(x,y,(L(z,u,w) \ v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,1679,a(flip),b,12634,a),flip(a)].">
      <j1 rule="hyper" parents="63 1679 12634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12637">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w) \ v5) \ 1,L(z,u,w) \ v5,y) = (R(z,u,w) \ v5) \ L(R(z,u,w) \ v5,y,x)
    ]]></literal>
    <justification jstring="[para(9541(a,1),12611(a,1,1,1))].">
      <j1 rule="para" parents="9541 12611"/>
    </justification>
  </clause>

  <clause id="12638">
    <literal><![CDATA[
      L(x,L(y,z,u) \ (L(w,R(y,z,u) \ v5,R(y,z,u)) * v5),v6) = L(x,(R(y,z,u) \ v5) * w,v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,10808,a(flip),b,12612,a),flip(a)].">
      <j1 rule="hyper" parents="316 10808 12612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12640">
    <literal><![CDATA[
      L(x,L(y,z,u) \ (L(w,R(y,z,u) \ v5,L(y,z,u)) * v5),v6) = L(x,(R(y,z,u) \ v5) * w,v6)
    ]]></literal>
    <justification jstring="[para(4628(a,1),12638(a,1,2,2,1))].">
      <j1 rule="para" parents="4628 12638"/>
    </justification>
  </clause>

  <clause id="12641">
    <literal><![CDATA[
      L(x,L(y,z,u) \ (L(w,L(y,z,u) \ v5,L(y,z,u)) * v5),v6) = L(x,(R(y,z,u) \ v5) * w,v6)
    ]]></literal>
    <justification jstring="[para(12609(a,1),12640(a,1,2,2,1))].">
      <j1 rule="para" parents="12609 12640"/>
    </justification>
  </clause>

  <clause id="12642">
    <literal><![CDATA[
      L(x,(L(y,z,u) \ w) * T(v5,w),v6) = L(x,(R(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(714(a,1),12641(a,1,2))].">
      <j1 rule="para" parents="714 12641"/>
    </justification>
  </clause>

  <clause id="12643">
    <literal><![CDATA[
      L(x,(R(y,z,u) \ w) * v5,v6) = L(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,10808,a(flip),b,12642,a),flip(a)].">
      <j1 rule="hyper" parents="63 10808 12642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12645">
    <literal><![CDATA[
      L(x,(L(y,z,u) \ (L(w,R(y,z,u) \ v5,R(y,z,u)) * v5)) * v6,v7) = L(x,((R(y,z,u) \ v5) * T(w,v5)) * v6,v7)
    ]]></literal>
    <justification jstring="[para(714(a,1),12643(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="714 12643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12646">
    <literal><![CDATA[
      L(x,(R(y,z,u) \ (w * v5)) / v5,v6) = L(x,(L(y,z,u) \ w) * a(R(y,z,u),R(y,z,u) \ w,v5),v6)
    ]]></literal>
    <justification jstring="[para(8485(a,2),12643(a,1,2))].">
      <j1 rule="para" parents="8485 12643"/>
    </justification>
  </clause>

  <clause id="12647">
    <literal><![CDATA[
      L(L(x,(L(y,z,u) \ w) * v5,v6) \ x,x,(R(y,z,u) \ w) * v5) = a(v6,(R(y,z,u) \ w) * v5,x)
    ]]></literal>
    <justification jstring="[para(12643(a,1),9998(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12643 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12648">
    <literal><![CDATA[
      L(L(x,(L(y,z,u) \ w) * v5,v6) \ x,x,(L(y,z,u) \ w) * v5) = a(v6,(R(y,z,u) \ w) * v5,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12635,a(flip),b,12647,a)].">
      <j1 rule="hyper" parents="63 12635 12647"/>
    </justification>
  </clause>

  <clause id="12649">
    <literal><![CDATA[
      a(x,(R(y,z,u) \ w) * v5,v6) = a(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,9998,a,b,12648,a),flip(a)].">
      <j1 rule="hyper" parents="63 9998 12648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12650">
    <literal><![CDATA[
      a(x,(L(T(y,z),u,w) \ v5) * v6,v7) = a(x,v6 * (R(y,u,w) \ v5),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,11275,a(flip),b,12649,a),flip(a)].">
      <j1 rule="hyper" parents="63 11275 12649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12651">
    <literal><![CDATA[
      a(x,y * (R(z,u,w) \ v5),v6) = a(x,y * (L(z,u,w) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,11276,a(flip),b,12650,a),flip(a)].">
      <j1 rule="hyper" parents="63 11276 12650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12652">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),L(x \ L(x,y,z),u,w),v5) = (v5 * (L(x \ L(x,y,z),u,w) \ 1)) \ v5
    ]]></literal>
    <justification jstring="[para(5019(a,1),12628(a,2,1,2))].">
      <j1 rule="para" parents="5019 12628"/>
    </justification>
  </clause>

  <clause id="12653">
    <literal><![CDATA[
      (R(x,y,z) \ u) \ L(R(x,y,z) \ u,w,v5) = (L(x,y,z) \ u) \ L(L(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,9997,a(flip),b,12637,a),flip(a)].">
      <j1 rule="hyper" parents="63 9997 12637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12654">
    <literal><![CDATA[
      (R(x,y,z) \ u) \ L(R(x,y,z) \ u,w,v5) = L(x,y,z) \ (u * L(u \ L(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,1252,a(flip),b,12653,a),flip(a)].">
      <j1 rule="hyper" parents="316 1252 12653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12655">
    <literal><![CDATA[
      L(x,(L(y,z,u) \ (w \ v5)) * a(R(y,z,u),R(y,z,u) \ (w \ v5),w),v6) = L(x,w \ (R(y,z,u) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,10962,a(flip),b,12646,a),flip(a)].">
      <j1 rule="hyper" parents="63 10962 12646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12656">
    <literal><![CDATA[
      L(x,(L(y,z,u) \ (w \ v5)) * a(L(y,z,u),L(y,z,u) \ (w \ v5),w),v6) = L(x,w \ (R(y,z,u) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(12625(a,1),12655(a,1,2,2))].">
      <j1 rule="para" parents="12625 12655"/>
    </justification>
  </clause>

  <clause id="12657">
    <literal><![CDATA[
      L(x,(L(y,z,u) \ ((w \ v5) * w)) / w,v6) = L(x,w \ (R(y,z,u) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(8485(a,2),12656(a,1,2))].">
      <j1 rule="para" parents="8485 12656"/>
    </justification>
  </clause>

  <clause id="12658">
    <literal><![CDATA[
      L(x,y \ (R(z,u,w) \ v5),v6) = L(x,y \ (L(z,u,w) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,10962,a(flip),b,12657,a),flip(a)].">
      <j1 rule="hyper" parents="63 10962 12657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12660">
    <literal><![CDATA[
      L(x,y \ (L(z,u,w) \ (v5 * z)),v6) = L(x,y \ (z * (R(z,u,w) \ v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,10880,a(flip),b,12658,a),flip(a)].">
      <j1 rule="hyper" parents="63 10880 12658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12661">
    <literal><![CDATA[
      L(x,y \ (z * (R(z,u,w) \ v5)),v6) = L(x,y \ (z * (L(z,u,w) \ v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,10881,a(flip),b,12660,a),flip(a)].">
      <j1 rule="hyper" parents="63 10881 12660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12662">
    <literal><![CDATA[
      L(x,y \ (a(L(z,u,w),u,w) \ u),v5) = L(x,y \ (z * (L(z,u,w) \ u)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11411,a,b,12661,a)].">
      <j1 rule="hyper" parents="63 11411 12661"/>
    </justification>
  </clause>

  <clause id="12663">
    <literal><![CDATA[
      L(x,(L(y,z,u) \ (L(w,R(y,z,u) \ v5,R(y,z,u)) * v5)) * v6,v7) = L(x,v6 * ((R(y,z,u) \ v5) * w),v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,10907,a(flip),b,12645,a),flip(a)].">
      <j1 rule="hyper" parents="316 10907 12645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12665">
    <literal><![CDATA[
      L(x,(L(y,z,u) \ (L(w,R(y,z,u) \ v5,L(y,z,u)) * v5)) * v6,v7) = L(x,v6 * ((R(y,z,u) \ v5) * w),v7)
    ]]></literal>
    <justification jstring="[para(4628(a,1),12663(a,1,2,1,2,1))].">
      <j1 rule="para" parents="4628 12663"/>
    </justification>
  </clause>

  <clause id="12666">
    <literal><![CDATA[
      L(x,(L(y,z,u) \ (L(w,L(y,z,u) \ v5,L(y,z,u)) * v5)) * v6,v7) = L(x,v6 * ((R(y,z,u) \ v5) * w),v7)
    ]]></literal>
    <justification jstring="[para(12609(a,1),12665(a,1,2,1,2,1))].">
      <j1 rule="para" parents="12609 12665"/>
    </justification>
  </clause>

  <clause id="12667">
    <literal><![CDATA[
      L(x,((L(y,z,u) \ w) * T(v5,w)) * v6,v7) = L(x,v6 * ((R(y,z,u) \ w) * v5),v7)
    ]]></literal>
    <justification jstring="[para(714(a,1),12666(a,1,2,1))].">
      <j1 rule="para" parents="714 12666"/>
    </justification>
  </clause>

  <clause id="12668">
    <literal><![CDATA[
      L(x,y * ((R(z,u,w) \ v5) * v6),v7) = L(x,y * ((L(z,u,w) \ v5) * v6),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,10907,a(flip),b,12667,a),flip(a)].">
      <j1 rule="hyper" parents="63 10907 12667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12670">
    <literal><![CDATA[
      L(x,y * ((L(z,z,u) \ u) * z),w) = L(x,L(u,z,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10924,a(flip),b,12668,a),flip(a)].">
      <j1 rule="hyper" parents="63 10924 12668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12671">
    <literal><![CDATA[
      L(x,R(y,z,z) * u,w) = L(x,L(y,z,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10926,a(flip),b,12670,a)].">
      <j1 rule="hyper" parents="63 10926 12670"/>
    </justification>
  </clause>

  <clause id="12672">
    <literal><![CDATA[
      L(x,y * ((z \ 1) * (u * z)),w) = L(x,L(u,z,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10921,a,b,12671,a)].">
      <j1 rule="hyper" parents="63 10921 12671"/>
    </justification>
  </clause>

  <clause id="12673">
    <literal><![CDATA[
      L(x,L(y,z,z) * (y * u),w) = L(x,y * (R(y,z,z) * u),w)
    ]]></literal>
    <justification jstring="[para(1166(a,1),12671(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1166 12671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12674">
    <literal><![CDATA[
      a(x,y,L(z,L(1 / u,w * u,w * u),v5)) = a(x,y,L(z,L(w,u,u) * (w * u),v5))
    ]]></literal>
    <justification jstring="[para(12672(a,1),11003(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12672 11003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12675">
    <literal><![CDATA[
      L(x,y * (R(y,z,z) * u),w) = L(x,y * (L(y,z,z) * u),w)
    ]]></literal>
    <justification jstring="[para(1124(a,1),12673(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1124 12673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12676">
    <literal><![CDATA[
      L(x,y * R(y * z,z \ 1,z),u) = L(x,y * (L(y,z,z) * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10949,a,b,12675,a)].">
      <j1 rule="hyper" parents="63 10949 12675"/>
    </justification>
  </clause>

  <clause id="12677">
    <literal><![CDATA[
      L(x,y * (L(y,z,z) * u),w) = L(x,y * (u * R(y,z,z)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10863,a,b,12675,a),flip(a)].">
      <j1 rule="hyper" parents="63 10863 12675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12678">
    <literal><![CDATA[
      a(x,y,L(z,L(1 / u,w * u,w * u),v5)) = a(x,y,L(z,w * (L(w,u,u) * u),v5))
    ]]></literal>
    <justification jstring="[para(1124(a,1),12674(a,2,3,2))].">
      <j1 rule="para" parents="1124 12674"/>
    </justification>
  </clause>

  <clause id="12679">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ L(a(z,y,L(x,y,z)),u,w) = L((L(x,y,z) \ x) \ a(z,y,L(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(11885(a,1),11887(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11885 11887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12680">
    <literal><![CDATA[
      R(T(a(x,y,z) \ 1,u),w * K(v5,v6),(w * K(v5,v6)) \ u) = u \ ((w * (a(x,y,z) \ 1)) * (w \ u))
    ]]></literal>
    <justification jstring="[para(10249(a,1),12601(a,2,2))].">
      <j1 rule="para" parents="10249 12601"/>
    </justification>
  </clause>

  <clause id="12681">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u * K(w,v5),(u * K(w,v5)) \ v6) = v6 \ ((u * (a(x,y,z) \ 1)) * (u \ v6))
    ]]></literal>
    <justification jstring="[para(4997(a,1),12680(a,1,1))].">
      <j1 rule="para" parents="4997 12680"/>
    </justification>
  </clause>

  <clause id="12683">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u * K(w,v5),u \ v6) = v6 \ ((u * (a(x,y,z) \ 1)) * (u \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,4755,a(flip),b,12681,a)].">
      <j1 rule="hyper" parents="63 4755 12681"/>
    </justification>
  </clause>

  <clause id="12686">
    <literal><![CDATA[
      x \ ((y * (a(z,u,w) \ 1)) * (y \ x)) = R(a(z,u,w) \ 1,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10734,a(flip),b,12683,a),flip(a)].">
      <j1 rule="hyper" parents="63 10734 12683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12687">
    <literal><![CDATA[
      a(x / (L(y,z,z) * K(u,w)),L(y,z,z),a(z,z,y)) = ((x / L(y * K(u,w),z,z)) * y) \ (a(z,z,y) * (x * K(w,u)))
    ]]></literal>
    <justification jstring="[para(4837(a,2),6776(a,2,1,1,2))].">
      <j1 rule="para" parents="4837 6776"/>
    </justification>
  </clause>

  <clause id="12695">
    <literal><![CDATA[
      L((x \ 1) \ (y / x),z,u) \ (L((x \ 1) \ (y / x),z,u) / (1 / (x \ 1))) = L(x \ 1,(x \ 1) \ 1,L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(1354(a,2),7528(a,1,2,1))].">
      <j1 rule="para" parents="1354 7528"/>
    </justification>
  </clause>

  <clause id="12696">
    <literal><![CDATA[
      a(x,y,L((((z \ 1) \ u) \ L((z \ 1) \ u,w,v5)) \ (z \ u),v6,v7)) = a(x,y,L(L(1 / ((z \ 1) \ u),w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(316,a,2655,a(flip),b,7757,a),flip(a)].">
      <j1 rule="hyper" parents="316 2655 7757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12697">
    <literal><![CDATA[
      a(x,y,L((((z \ 1) \ u) \ L((z \ 1) \ u,w,v5)) \ (z \ u),v6,v7)) = a(x,y,L(L(((z \ 1) \ u) \ 1,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(316,a,5645,a(flip),b,12696,a),flip(a)].">
      <j1 rule="hyper" parents="316 5645 12696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12698">
    <literal><![CDATA[
      a(x,y,L((((z \ 1) \ u) \ L((z \ 1) \ u,w,v5)) \ (z \ u),v6,v7)) = a(x,y,L(L((z \ 1) \ u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(316,a,5891,a(flip),b,12697,a),flip(a)].">
      <j1 rule="hyper" parents="316 5891 12697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12699">
    <literal><![CDATA[
      a(x,y,L(((z \ 1) \ (u * L(u \ (z \ 1),w,v5))) \ (z \ u),v6,v7)) = a(x,y,L(L((z \ 1) \ u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(1252(a,1),12698(a,1,3,1,1))].">
      <j1 rule="para" parents="1252 12698"/>
    </justification>
  </clause>

  <clause id="12700">
    <literal><![CDATA[
      a(x,y,L((z \ (u * L(u \ z,w,v5))) \ (z \ u),v6,v7)) = a(x,y,L(L((z \ 1) \ u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(9495(a,1),12699(a,1,3,1,1))].">
      <j1 rule="para" parents="9495 12699"/>
    </justification>
  </clause>

  <clause id="12701">
    <literal><![CDATA[
      a(x,y,L(L(1 / (z \ u),w,v5) \ 1,v6,v7)) = a(x,y,L(L((z \ 1) \ u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(5127(a,1),12700(a,1,3,1))].">
      <j1 rule="para" parents="5127 12700"/>
    </justification>
  </clause>

  <clause id="12702">
    <literal><![CDATA[
      a(x,y,L(L(1 / (z \ u),w,v5),v6,v7)) = a(x,y,L(L((z \ 1) \ u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,2655,a(flip),b,12701,a)].">
      <j1 rule="hyper" parents="63 2655 12701"/>
    </justification>
  </clause>

  <clause id="12703">
    <literal><![CDATA[
      a(x,y,L(L((z \ 1) \ u,w,v5),v6,v7)) = a(x,y,L(L((z \ u) \ 1,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,5645,a(flip),b,12702,a),flip(a)].">
      <j1 rule="hyper" parents="63 5645 12702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12704">
    <literal><![CDATA[
      a(x,y,L(L((z \ 1) \ u,w,v5),v6,v7)) = a(x,y,L(L(z \ u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(316,a,5891,a(flip),b,12703,a),flip(a)].">
      <j1 rule="hyper" parents="316 5891 12703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12705">
    <literal><![CDATA[
      a(x,y,L(L(z \ (u \ w),z,u),v5,v6)) = a(x,y,L((u * (z \ 1)) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,12024,a(flip),b,12704,a),flip(a)].">
      <j1 rule="hyper" parents="63 12024 12704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12706">
    <literal><![CDATA[
      a(x,y,L((z * (u \ 1)) \ w,v5,v6)) = a(x,y,L((z * u) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(298(a,1),12705(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="298 12705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12707">
    <literal><![CDATA[
      a(x,y,L((z * (u \ 1)) \ w,v5,v6)) = a(x,y,L((u * z) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,6255,a,b,12706,a),flip(a)].">
      <j1 rule="hyper" parents="316 6255 12706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12708">
    <literal><![CDATA[
      a(x,y,L((z * (u \ ((w \ 1) * (w * u)))) \ v5,v6,v7)) = a(x,y,L(((w * (u / (w * u))) * z) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(11398(a,1),12707(a,1,3,1,1,2))].">
      <j1 rule="para" parents="11398 12707"/>
    </justification>
  </clause>

  <clause id="12709">
    <literal><![CDATA[
      T(x * a(y \ (z \ ((z * x) * y)),x,x),x * ((z \ ((z * x) * y)) / y)) = 1 / (((z \ ((z * x) * y)) / y) \ a(z,x,y))
    ]]></literal>
    <justification jstring="[para(1813(a,1),8491(a,1,1,2))].">
      <j1 rule="para" parents="1813 8491"/>
    </justification>
  </clause>

  <clause id="12710">
    <literal><![CDATA[
      a(x,y,z) \ (a(u,u \ w,a(x,y,z)) * ((u \ w) * a(x,y,z))) = (a(x,y,z) \ 1) \ (u \ (w * (a(x,y,z) \ 1)))
    ]]></literal>
    <justification jstring="[para(2534(a,1),8565(a,1,2,1))].">
      <j1 rule="para" parents="2534 8565"/>
    </justification>
  </clause>

  <clause id="12711">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u \ (w * (a(x,y,z) \ 1))) = a(x,y,z) \ (u \ (w * a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(8458(a,1),12710(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8458 12710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12713">
    <literal><![CDATA[
      a(x,y,z) \ (u \ (((a(w,v5,a(x,y,z) \ 1) \ v5) * w) * a(x,y,z))) = (a(x,y,z) \ 1) \ (u \ (w * (T(v5,w) * (a(x,y,z) \ 1))))
    ]]></literal>
    <justification jstring="[para(8667(a,1),12711(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8667 12711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12717">
    <literal><![CDATA[
      R(x,x,y \ (z \ (u \ (z * (y * u))))) \ (y \ (z \ ((z * (y * u)) / u))) = x \ L(L(u \ L(u,y,z),x,x),u,z * y)
    ]]></literal>
    <justification jstring="[para(4774(a,1),9360(a,1,1))].">
      <j1 rule="para" parents="4774 9360"/>
    </justification>
  </clause>

  <clause id="12718">
    <literal><![CDATA[
      x \ (y \ ((y * (x * (L(z,u,w) \ z))) / (L(z,u,w) \ z))) = a(z \ L(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8577,a(flip),b,9562,a),flip(a)].">
      <j1 rule="hyper" parents="63 8577 9562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12719">
    <literal><![CDATA[
      x \ (y \ ((z \ L(z,u,w)) \ (y * (x * (z \ L(z,u,w)))))) = a(z \ L(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[para(9560(a,1),12718(a,1,2,2))].">
      <j1 rule="para" parents="9560 12718"/>
    </justification>
  </clause>

  <clause id="12720">
    <literal><![CDATA[
      (x * y) * (L(L(R(y,z,u),x,x) \ L(y,x,x),x * y,x * y) \ 1) = (1 / x) \ R(L(y,x,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(12456(a,1),9781(a,1,2,1,1))].">
      <j1 rule="para" parents="12456 9781"/>
    </justification>
  </clause>

  <clause id="12721">
    <literal><![CDATA[
      (L(x,y,y) / (y * x)) \ L(R(x,z,u),y,y) = (1 / y) \ R(L(x,y,y \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9780,a(flip),b,12720,a)].">
      <j1 rule="hyper" parents="63 9780 12720"/>
    </justification>
  </clause>

  <clause id="12722">
    <literal><![CDATA[
      (L(x,y,y) / (y * x)) \ L(R(x,z,u),y,y) = (1 / y) \ L(R(x,z,u),y,y \ 1)
    ]]></literal>
    <justification jstring="[para(29(a,1),12721(a,2,2))].">
      <j1 rule="para" parents="29 12721"/>
    </justification>
  </clause>

  <clause id="12723">
    <literal><![CDATA[
      (L(x,y,y) / (y * x)) \ L(R(x,z,u),y,y) = y * R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,886,a(flip),b,12722,a),flip(a)].">
      <j1 rule="hyper" parents="316 886 12722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12724">
    <literal><![CDATA[
      L(a(x,y,L(a(z,u,w),v5,v6)) \ y,x,L(a(z,u,w),v5,v6)) = L(T(y,L(a(z,u,w),v5,v6)),L(a(z,u,w),v5,v6),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,247,a(flip),b,9796,a),flip(a)].">
      <j1 rule="hyper" parents="316 247 9796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12725">
    <literal><![CDATA[
      L(a(x,y,L(a(z,u,w),v5,v6)) \ y,x,L(a(z,u,w),v5,v6)) = L(y,L(a(z,u,w),v5,v6),x)
    ]]></literal>
    <justification jstring="[para(2436(a,1),12724(a,2,1))].">
      <j1 rule="para" parents="2436 12724"/>
    </justification>
  </clause>

  <clause id="12726">
    <literal><![CDATA[
      L((1 / a(x,y,z)) * K(z,y),(x * (z * y)) \ ((x * y) * z),x * (z * y)) = 1 / (1 / (((x * y) * z) \ (x * (z * y))))
    ]]></literal>
    <justification jstring="[para(10180(a,1),10562(a,1,1))].">
      <j1 rule="para" parents="10180 10562"/>
    </justification>
  </clause>

  <clause id="12727">
    <literal><![CDATA[
      x \ (L(x,y,a(z,u,y)) * L(L(x,y,a(z,u,y)) \ x,w,v5)) = a(x,y,a(z,u,y)) \ L(a(x,y,a(z,u,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(11689(a,1),11691(a,2,2,1))].">
      <j1 rule="para" parents="11689 11691"/>
    </justification>
  </clause>

  <clause id="12728">
    <literal><![CDATA[
      a(x / (L(y,z,z) * K(u,w)),L(y,z,z),a(z,z,y)) = (y * ((L(y,z,z) \ x) * K(w,u))) \ (a(z,z,y) * (x * K(w,u)))
    ]]></literal>
    <justification jstring="[para(6435(a,1),12687(a,2,1))].">
      <j1 rule="para" parents="6435 12687"/>
    </justification>
  </clause>

  <clause id="12729">
    <literal><![CDATA[
      L((x \ 1) \ (y / x),z,u) \ (L((x \ 1) \ (y / x),z,u) / x) = L(x \ 1,(x \ 1) \ 1,L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(80(a,1),12695(a,1,2,2))].">
      <j1 rule="para" parents="80 12695"/>
    </justification>
  </clause>

  <clause id="12731">
    <literal><![CDATA[
      T(x * a(y \ (z \ ((z * x) * y)),x,x),x * (z \ (((z * x) * y) / y))) = 1 / (((z \ ((z * x) * y)) / y) \ a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10656,a(flip),b,12709,a)].">
      <j1 rule="hyper" parents="63 10656 12709"/>
    </justification>
  </clause>

  <clause id="12732">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ (z \ (u \ ((u * (z * y)) / y))) = x \ L(L(y \ L(y,z,u),x,x),y,u * z)
    ]]></literal>
    <justification jstring="[para(9364(a,1),12717(a,1,1))].">
      <j1 rule="para" parents="9364 12717"/>
    </justification>
  </clause>

  <clause id="12733">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ (z \ (u \ ((u * (z * y)) / y))) = (x \ 1) * (z \ (u \ ((u * (z * y)) / y)))
    ]]></literal>
    <justification jstring="[hyper(316,a,9371,a(flip),b,12732,a),flip(a)].">
      <j1 rule="hyper" parents="316 9371 12732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12734">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) * K(z,y),(x * (z * y)) \ ((x * y) * z),x * (z * y)) = 1 / (1 / (((x * y) * z) \ (x * (z * y))))
    ]]></literal>
    <justification jstring="[para(2276(a,1),12726(a,1,1,1))].">
      <j1 rule="para" parents="2276 12726"/>
    </justification>
  </clause>

  <clause id="12735">
    <literal><![CDATA[
      a(x / (L(y,z,z) * K(u,w)),L(y,z,z),a(z,z,y)) = ((y * ((L(y,z,z) \ x) * K(w,u))) \ (a(z,z,y) * x)) * K(w,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,3932,a(flip),b,12728,a),flip(a)].">
      <j1 rule="hyper" parents="316 3932 12728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12736">
    <literal><![CDATA[
      T(x * a(y \ (z \ ((z * x) * y)),x,x),x * (z \ (z * x))) = 1 / (((z \ ((z * x) * y)) / y) \ a(z,x,y))
    ]]></literal>
    <justification jstring="[para(11(a,1),12731(a,1,2,2,2))].">
      <j1 rule="para" parents="11 12731"/>
    </justification>
  </clause>

  <clause id="12737">
    <literal><![CDATA[
      T(x * a(y \ (z \ ((z * x) * y)),x,x),x * x) = 1 / (((z \ ((z * x) * y)) / y) \ a(z,x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),12736(a,1,2,2))].">
      <j1 rule="para" parents="9 12736"/>
    </justification>
  </clause>

  <clause id="12739">
    <literal><![CDATA[
      1 / (((x \ ((x * y) * z)) / z) \ a(x,y,z)) = L(y,y,y) * a(z \ (x \ ((x * y) * z)),y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5334,a(flip),b,12737,a),flip(a)].">
      <j1 rule="hyper" parents="63 5334 12737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12741">
    <literal><![CDATA[
      L(x * a(y \ (z \ ((z * x) * y)),x,x),x,x) = 1 / (((z \ ((z * x) * y)) / y) \ a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,12600,a,b,12739,a)].">
      <j1 rule="hyper" parents="316 12600 12739"/>
    </justification>
  </clause>

  <clause id="12742">
    <literal><![CDATA[
      L(x * a(y \ (z \ ((z * x) * y)),x,x),x,x) = (a(z,x,y) / ((z \ ((z * x) * y)) / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,5298,a(flip),b,12741,a),flip(a)].">
      <j1 rule="hyper" parents="316 5298 12741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12743">
    <literal><![CDATA[
      (1 / (a(x,y,z) / ((x \ ((x * y) * z)) / z))) * K((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,a(x,y,z) / ((x \ ((x * y) * z)) / z)) = L(y * a(z \ (x \ ((x * y) * z)),y,y),y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,3079,a,b,12742,a)].">
      <j1 rule="hyper" parents="316 3079 12742"/>
    </justification>
  </clause>

  <clause id="12744">
    <literal><![CDATA[
      T((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,1 / (a(x,y,z) / ((x \ ((x * y) * z)) / z))) = L(y * a(z \ (x \ ((x * y) * z)),y,y),y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,286,a,b,12742,a)].">
      <j1 rule="hyper" parents="316 286 12742"/>
    </justification>
  </clause>

  <clause id="12745">
    <literal><![CDATA[
      L(a(x,y,z) \ K(z,y),(x * (z * y)) \ ((x * y) * z),x * (z * y)) = 1 / (1 / (((x * y) * z) \ (x * (z * y))))
    ]]></literal>
    <justification jstring="[para(3780(a,1),12734(a,1,1))].">
      <j1 rule="para" parents="3780 12734"/>
    </justification>
  </clause>

  <clause id="12746">
    <literal><![CDATA[
      L(a(x,y,z) \ K(z,y),K(y,z) * a(x,y,z),x * (z * y)) = 1 / (1 / (((x * y) * z) \ (x * (z * y))))
    ]]></literal>
    <justification jstring="[para(10561(a,1),12745(a,1,2))].">
      <j1 rule="para" parents="10561 12745"/>
    </justification>
  </clause>

  <clause id="12747">
    <literal><![CDATA[
      L(a(x,y,z) \ K(z,y),a(x,y,z),x * (z * y)) = 1 / (1 / (((x * y) * z) \ (x * (z * y))))
    ]]></literal>
    <justification jstring="[hyper(63,a,10791,a(flip),b,12746,a)].">
      <j1 rule="hyper" parents="63 10791 12746"/>
    </justification>
  </clause>

  <clause id="12749">
    <literal><![CDATA[
      (K(x,y) * (z * (x * y))) / ((z * y) * T(x,y)) = 1 / (1 / (((z * y) * x) \ (z * (x * y))))
    ]]></literal>
    <justification jstring="[hyper(63,a,10646,a(flip),b,12747,a)].">
      <j1 rule="hyper" parents="63 10646 12747"/>
    </justification>
  </clause>

  <clause id="12750">
    <literal><![CDATA[
      K(x,y) * ((z * (x * y)) / ((z * y) * T(x,y))) = 1 / (1 / (((z * y) * x) \ (z * (x * y))))
    ]]></literal>
    <justification jstring="[hyper(63,a,660,a(flip),b,12749,a)].">
      <j1 rule="hyper" parents="63 660 12749"/>
    </justification>
  </clause>

  <clause id="12751">
    <literal><![CDATA[
      1 / (1 / (((x * y) * z) \ (x * (z * y)))) = K(z,y) * ((x * y) \ ((x * (y * z)) / z))
    ]]></literal>
    <justification jstring="[para(8120(a,1),12750(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8120 12750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12752">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * (y * z)) / z) = 1 / (1 / (((x * y) * z) \ (x * (z * y))))
    ]]></literal>
    <justification jstring="[hyper(316,a,10217,a(flip),b,12751,a)].">
      <j1 rule="hyper" parents="316 10217 12751"/>
    </justification>
  </clause>

  <clause id="12753">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * (y * z)) / z) = ((x * y) * z) \ (x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(316,a,12561,a(flip),b,12752,a),flip(a)].">
      <j1 rule="hyper" parents="316 12561 12752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12754">
    <literal><![CDATA[
      T(x,y) \ (z \ ((z * (x * y)) / y)) = ((z * x) * y) \ (z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,10426,a(flip),b,12753,a)].">
      <j1 rule="hyper" parents="63 10426 12753"/>
    </justification>
  </clause>

  <clause id="12755">
    <literal><![CDATA[
      a(x / (L(y,z,z) * K(u,w)),L(y,z,z),a(z,z,y)) = K(u,w) * (((y * (L(y,z,z) \ x)) \ (a(z,z,y) * x)) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,10338,a(flip),b,12735,a),flip(a)].">
      <j1 rule="hyper" parents="316 10338 12735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12756">
    <literal><![CDATA[
      T((x * (L(x,y,y) \ z)) \ (a(y,y,x) * z),K(u,w)) = a(z / (L(x,y,y) * K(u,w)),L(x,y,y),a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,4111,a(flip),b,12755,a)].">
      <j1 rule="hyper" parents="316 4111 12755"/>
    </justification>
  </clause>

  <clause id="12757">
    <literal><![CDATA[
      T((x * (L(x,y,y) \ z)) \ (a(y,y,x) * z),K(u,w)) = a(z / L(x * K(u,w),y,y),L(x,y,y),a(y,y,x))
    ]]></literal>
    <justification jstring="[para(4837(a,2),12756(a,2,1,2))].">
      <j1 rule="para" parents="4837 12756"/>
    </justification>
  </clause>

  <clause id="12758">
    <literal><![CDATA[
      T((x * (L(x,y,y) \ z)) \ (a(y,y,x) * z),K(u,w)) = a(L(x * K(u,w),y,y) \ z,L(x,y,y),a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,1813,a(flip),b,12757,a),flip(a)].">
      <j1 rule="hyper" parents="316 1813 12757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12759">
    <literal><![CDATA[
      T((x * (L(x,y,y) \ z)) \ (a(y,y,x) * z),K(u,w)) = a(K(w,u) * (L(x,y,y) \ z),L(x,y,y),a(y,y,x))
    ]]></literal>
    <justification jstring="[para(10244(a,1),12758(a,2,1))].">
      <j1 rule="para" parents="10244 12758"/>
    </justification>
  </clause>

  <clause id="12760">
    <literal><![CDATA[
      T((x * (L(x,y,y) \ z)) \ (a(y,y,x) * z),K(u,w)) = a(L(x,y,y) \ z,L(x,y,y),a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,1806,a(flip),b,12759,a),flip(a)].">
      <j1 rule="hyper" parents="316 1806 12759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12762">
    <literal><![CDATA[
      R(x,y / (y / z),y / (y / z)) \ (x * (y / (y / z))) = y / (y / L(z,y / (y / z),L(x,y / (y / z),z)))
    ]]></literal>
    <justification jstring="[para(1589(a,1),6590(a,2,2,2,3))].">
      <j1 rule="para" parents="1589 6590"/>
    </justification>
  </clause>

  <clause id="12764">
    <literal><![CDATA[
      R(x,y / (y / z),y / (y / z)) \ (x * (y / (y / z))) = y / (y / L(z,y / (y / z),L(x,z,z)))
    ]]></literal>
    <justification jstring="[para(10804(a,1),12762(a,2,2,2,3))].">
      <j1 rule="para" parents="10804 12762"/>
    </justification>
  </clause>

  <clause id="12765">
    <literal><![CDATA[
      R(x,y / (y / z),y / (y / z)) \ (x * (y / (y / z))) = y / (y / L(z,z,L(x,z,z)))
    ]]></literal>
    <justification jstring="[para(10804(a,1),12764(a,2,2,2))].">
      <j1 rule="para" parents="10804 12764"/>
    </justification>
  </clause>

  <clause id="12767">
    <literal><![CDATA[
      L(x / (x / y),y,L(z,y,y)) = R(z,x / (x / y),x / (x / y)) \ (z * (x / (x / y)))
    ]]></literal>
    <justification jstring="[hyper(316,a,6582,a,b,12765,a)].">
      <j1 rule="hyper" parents="316 6582 12765"/>
    </justification>
  </clause>

  <clause id="12769">
    <literal><![CDATA[
      L(x / (x / y),y,L(z,y,y)) = R(z,x / (x / y),y) \ (z * (x / (x / y)))
    ]]></literal>
    <justification jstring="[para(4682(a,1),12767(a,2,1))].">
      <j1 rule="para" parents="4682 12767"/>
    </justification>
  </clause>

  <clause id="12771">
    <literal><![CDATA[
      L(x / (x / y),y,L(z,y,y)) = R(z,(x / y) \ x,y) \ (z * (x / (x / y)))
    ]]></literal>
    <justification jstring="[para(10739(a,1),12769(a,2,1))].">
      <j1 rule="para" parents="10739 12769"/>
    </justification>
  </clause>

  <clause id="12772">
    <literal><![CDATA[
      L(x / (x / y),y,L(z,y,y)) = R(z,y,y) \ (z * (x / (x / y)))
    ]]></literal>
    <justification jstring="[para(83(a,1),12771(a,2,1,2))].">
      <j1 rule="para" parents="83 12771"/>
    </justification>
  </clause>

  <clause id="12773">
    <literal><![CDATA[
      R(x,y,y) \ (x * (z / (z / y))) = L(z / (z / y),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7184,a(flip),b,12772,a),flip(a)].">
      <j1 rule="hyper" parents="63 7184 12772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12774">
    <literal><![CDATA[
      L(T(x,y),T(x,y) \ 1,T(x,y) * T(z,x)) = K(x,y) * L(1 / (1 / x),x,z)
    ]]></literal>
    <justification jstring="[para(12773(a,1),12550(a,2,2))].">
      <j1 rule="para" parents="12773 12550"/>
    </justification>
  </clause>

  <clause id="12775">
    <literal><![CDATA[
      L(T(x,y),T(x,y) \ 1,T(x,y) * T(z,x)) = L(K(x,y) * (1 / (1 / x)),x,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,4850,a,b,12774,a),flip(a)].">
      <j1 rule="hyper" parents="316 4850 12774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12776">
    <literal><![CDATA[
      L(T(x,y),T(x,y) \ 1,T(x,y) * T(z,x)) = L(1 / (K(y,x) / x),x,z)
    ]]></literal>
    <justification jstring="[para(10262(a,1),12775(a,2,1))].">
      <j1 rule="para" parents="10262 12775"/>
    </justification>
  </clause>

  <clause id="12777">
    <literal><![CDATA[
      L(T(x,y),T(x,y) \ 1,K(x,y) * (z * x)) = L(1 / (K(y,x) / x),x,z)
    ]]></literal>
    <justification jstring="[para(2864(a,2),12776(a,1,3))].">
      <j1 rule="para" parents="2864 12776"/>
    </justification>
  </clause>

  <clause id="12778">
    <literal><![CDATA[
      L(T(x,y),T(x,y) \ 1,z * x) = L(1 / (K(y,x) / x),x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1575,a(flip),b,12777,a)].">
      <j1 rule="hyper" parents="63 1575 12777"/>
    </justification>
  </clause>

  <clause id="12780">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),y,z) = L(T(y,x),y \ 1,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10801,a(flip),b,12778,a),flip(a)].">
      <j1 rule="hyper" parents="63 10801 12778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12782">
    <literal><![CDATA[
      R(x * K(y \ L(y,z,u),T(w,x)),y \ L(y,z,u),T(w,x)) = (w * (x * (y \ L(y,z,u)))) / T((y \ L(y,z,u)) * w,x)
    ]]></literal>
    <justification jstring="[para(11513(a,2),6648(a,2,2))].">
      <j1 rule="para" parents="11513 6648"/>
    </justification>
  </clause>

  <clause id="12783">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ ((x \ (x / y)) \ ((x \ (x / y)) \ 1)) = (y * a(y \ x,y,y)) \ ((x / y) \ (x * (1 / (x \ (x / y)))))
    ]]></literal>
    <justification jstring="[para(701(a,1),7355(a,2,2))].">
      <j1 rule="para" parents="701 7355"/>
    </justification>
  </clause>

  <clause id="12784">
    <literal><![CDATA[
      (x * ((x * y) \ y)) * a(1 / ((x * y) \ y),x * ((x * y) \ y),x * ((x * y) \ y)) = 1 / (x \ (1 / ((x * y) \ y)))
    ]]></literal>
    <justification jstring="[para(11141(a,1),7357(a,2,2,2))].">
      <j1 rule="para" parents="11141 7357"/>
    </justification>
  </clause>

  <clause id="12785">
    <literal><![CDATA[
      (x * ((x * y) \ y)) * a(1 / ((x * y) \ y),x * ((x * y) \ y),a(y,x,x)) = 1 / (x \ (1 / ((x * y) \ y)))
    ]]></literal>
    <justification jstring="[para(7359(a,1),12784(a,1,2))].">
      <j1 rule="para" parents="7359 12784"/>
    </justification>
  </clause>

  <clause id="12786">
    <literal><![CDATA[
      (x * ((x * y) \ y)) * a(1 / ((x * y) \ y),a(x,x,y),a(y,x,x)) = 1 / (x \ (1 / ((x * y) \ y)))
    ]]></literal>
    <justification jstring="[para(11426(a,1),12785(a,1,2))].">
      <j1 rule="para" parents="11426 12785"/>
    </justification>
  </clause>

  <clause id="12787">
    <literal><![CDATA[
      (x * ((x * y) \ y)) * a(((x * y) \ y) \ 1,a(x,x,y),a(y,x,x)) = 1 / (x \ (1 / ((x * y) \ y)))
    ]]></literal>
    <justification jstring="[para(1808(a,1),12786(a,1,2))].">
      <j1 rule="para" parents="1808 12786"/>
    </justification>
  </clause>

  <clause id="12788">
    <literal><![CDATA[
      (x * ((x * y) \ y)) * a((x * y) \ y,a(x,x,y),a(y,x,x)) = 1 / (x \ (1 / ((x * y) \ y)))
    ]]></literal>
    <justification jstring="[para(7226(a,1),12787(a,1,2))].">
      <j1 rule="para" parents="7226 12787"/>
    </justification>
  </clause>

  <clause id="12789">
    <literal><![CDATA[
      1 / (x \ (1 / ((x * y) \ y))) = (x * ((x * y) \ y)) * 1
    ]]></literal>
    <justification jstring="[para(6978(a,1),12788(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6978 12788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12790">
    <literal><![CDATA[
      1 / (x \ (1 / ((x * y) \ y))) = x * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(316,a,8,a(flip),b,12789,a),flip(a)].">
      <j1 rule="hyper" parents="316 8 12789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12792">
    <literal><![CDATA[
      (x * ((x * y) \ y)) \ 1 = x \ (1 / ((x * y) \ y))
    ]]></literal>
    <justification jstring="[hyper(204,a,12790,a)].">
      <j1 rule="hyper" parents="204 12790"/>
    </justification>
  </clause>

  <clause id="12793">
    <literal><![CDATA[
      x \ (1 / ((x * (x \ y)) \ (x \ y))) = (x * (y \ (x \ y))) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),12792(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12794">
    <literal><![CDATA[
      (x * (y \ (x \ y))) \ 1 = x \ (1 / (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[para(10(a,1),12793(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12795">
    <literal><![CDATA[
      (x \ y) \ (y * (x \ 1)) = x \ (1 / (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9236,a(flip),b,12794,a)].">
      <j1 rule="hyper" parents="63 9236 12794"/>
    </justification>
  </clause>

  <clause id="12797">
    <literal><![CDATA[
      a(x,y,(z \ (1 / (u \ (z \ u)))) * w) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[para(12795(a,1),12071(a,1,3,1))].">
      <j1 rule="para" parents="12795 12071"/>
    </justification>
  </clause>

  <clause id="12798">
    <literal><![CDATA[
      a(x,y,(z \ ((u \ (z \ u)) \ 1)) * w) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5694,a(flip),b,12797,a)].">
      <j1 rule="hyper" parents="63 5694 12797"/>
    </justification>
  </clause>

  <clause id="12799">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ (u \ w)))) = a(x,y,a(u,u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5884,a(flip),b,12798,a)].">
      <j1 rule="hyper" parents="63 5884 12798"/>
    </justification>
  </clause>

  <clause id="12800">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * ((z \ (u \ (z \ u))) \ (w * (v5 \ (z \ (u \ (z \ u))))))) = a(x,y,(v5 * T(v5 \ w,z \ (u \ (z \ u)))) * (v5 \ (z \ (u \ (z \ u)))))
    ]]></literal>
    <justification jstring="[para(963(a,1),12799(a,1,3)),flip(a)].">
      <j1 rule="para" parents="963 12799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12804">
    <literal><![CDATA[
      R(a(x,y,z) / x,L(x,u,w),x \ a(x,y,z)) \ L(x,u,w) = L(x,u,w) * ((a(x,y,z) * (x \ L(x,u,w))) \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(4680(a,1),8717(a,1,1))].">
      <j1 rule="para" parents="4680 8717"/>
    </justification>
  </clause>

  <clause id="12805">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ (w \ 1)) * (a(w,v5,v6) \ (a(w,v5,v6) / w)) = (((a(w,v5,v6) / w) / a(w,v5,v6)) / u) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(3243(a,1),9429(a,1,1))].">
      <j1 rule="para" parents="3243 9429"/>
    </justification>
  </clause>

  <clause id="12808">
    <literal><![CDATA[
      a(x,y,(L((z \ (z \ 1)) \ ((1 / z) * u),w,v5) \ v6) * v7) = a(x,y,(L(R((z \ 1) \ u,z \ 1,z),w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[para(1033(a,1),12074(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1033 12074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12809">
    <literal><![CDATA[
      a(x,y,(L((z \ (z \ 1)) \ ((1 / z) * u),w,v5) \ v6) * v7) = a(x,y,(L(L((z \ 1) \ u,z \ 1,z),w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,12072,a(flip),b,12808,a),flip(a)].">
      <j1 rule="hyper" parents="316 12072 12808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12810">
    <literal><![CDATA[
      a(x,y,(L((z \ (z \ 1)) \ ((1 / z) * u),w,v5) \ v6) * v7) = a(x,y,(L(z * u,w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[para(474(a,1),12809(a,2,3,1,1,1))].">
      <j1 rule="para" parents="474 12809"/>
    </justification>
  </clause>

  <clause id="12812">
    <literal><![CDATA[
      R(x * K(y \ L(y,z,u),T(w,x)),y \ L(y,z,u),T(w,x)) = L(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,7897,a(flip),b,12782,a),flip(a)].">
      <j1 rule="hyper" parents="316 7897 12782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12813">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),T(w,x)) = L(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(5033(a,1),12812(a,1,1))].">
      <j1 rule="para" parents="5033 12812"/>
    </justification>
  </clause>

  <clause id="12814">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),w) = L(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(4739,a,12813,a)].">
      <j1 rule="hyper" parents="4739 12813"/>
    </justification>
  </clause>

  <clause id="12816">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ u,x \ L(x,y,z),L(x,y,z)) = (u * (L(x,y,z) \ 1)) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,9534,a(flip),b,12814,a),flip(a)].">
      <j1 rule="hyper" parents="63 9534 12814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12817">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),w \ 1) = R(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1033,a(flip),b,12814,a),flip(a)].">
      <j1 rule="hyper" parents="63 1033 12814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12819">
    <literal><![CDATA[
      L(x \ L(x,y \ L(y,z,u),w),x,(y \ L(y,z,u)) * w) = a(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(12814(a,1),3422(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12814 3422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12820">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * L(x,x \ L(x,y,z),u)) = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(12814(a,1),9568(a,1,2,2))].">
      <j1 rule="para" parents="12814 9568"/>
    </justification>
  </clause>

  <clause id="12821">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),w \ 1) = L(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,12814,a(flip),b,12817,a),flip(a)].">
      <j1 rule="hyper" parents="316 12814 12817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12822">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) * (u * (x \ R(x,y,z))) = L(u,x \ L(x,y,z),x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9851,a,b,12821,a)].">
      <j1 rule="hyper" parents="63 9851 12821"/>
    </justification>
  </clause>

  <clause id="12823">
    <literal><![CDATA[
      L((x \ 1) * (L(y,z,u) \ y),y \ L(y,z,u),x) = 1 / ((L(y,z,u) \ y) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,12403,a(flip),b,12821,a),flip(a)].">
      <j1 rule="hyper" parents="63 12403 12821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12824">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ u,x \ L(x,y,z),L(x,y,z)) = (x \ 1) \ ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2098,a(flip),b,12821,a),flip(a)].">
      <j1 rule="hyper" parents="63 2098 12821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12825">
    <literal><![CDATA[
      L((x \ 1) * (L(y,z,u) \ y),y \ L(y,z,u),x) \ 1 = (L(y,z,u) \ y) \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(12821(a,1),12406(a,1,1))].">
      <j1 rule="para" parents="12821 12406"/>
    </justification>
  </clause>

  <clause id="12827">
    <literal><![CDATA[
      L(x \ L(x,y \ L(y,z,u),w),x,(y * L(y,z,u)) * w) = a(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11934,a(flip),b,12819,a)].">
      <j1 rule="hyper" parents="63 11934 12819"/>
    </justification>
  </clause>

  <clause id="12828">
    <literal><![CDATA[
      a(x,L(y,z,u) \ y,w) = a(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,12407,a(flip),b,12827,a)].">
      <j1 rule="hyper" parents="63 12407 12827"/>
    </justification>
  </clause>

  <clause id="12832">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) * (u * (x \ R(x,y,z))) = L(u,x \ L(x,y,z),x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,7482,a(flip),b,12822,a),flip(a)].">
      <j1 rule="hyper" parents="316 7482 12822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12833">
    <literal><![CDATA[
      (x * (L(y,z,u) \ 1)) / (y \ 1) = (y \ 1) \ ((L(y,z,u) \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12816,a(flip),b,12824,a)].">
      <j1 rule="hyper" parents="63 12816 12824"/>
    </justification>
  </clause>

  <clause id="12834">
    <literal><![CDATA[
      (x * (L(1 / y,z,u) \ 1)) / y = (y \ 1) \ ((L(y,z,u) \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7612,a,b,12833,a)].">
      <j1 rule="hyper" parents="63 7612 12833"/>
    </justification>
  </clause>

  <clause id="12835">
    <literal><![CDATA[
      ((x \ 1) \ ((L(x,x,y) \ 1) * z)) \ (z * a(y,x,x)) = a(z,a(y,x,x),x)
    ]]></literal>
    <justification jstring="[para(12834(a,1),7347(a,1,1))].">
      <j1 rule="para" parents="12834 7347"/>
    </justification>
  </clause>

  <clause id="12836">
    <literal><![CDATA[
      ((x \ 1) \ ((L(x,x,y) \ 1) * z)) \ (z * a(y,x,x)) = a(z,x,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,7011,a(flip),b,12835,a),flip(a)].">
      <j1 rule="hyper" parents="316 7011 12835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12837">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) * (u * (x \ R(x,y,z))) = L(u,x \ L(x,y,z),x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,12414,a(flip),b,12832,a),flip(a)].">
      <j1 rule="hyper" parents="316 12414 12832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12838">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (u * (x \ R(x,y,z))) = L(u,x \ L(x,y,z),x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7653,a(flip),b,12837,a)].">
      <j1 rule="hyper" parents="63 7653 12837"/>
    </justification>
  </clause>

  <clause id="12839">
    <literal><![CDATA[
      L((x \ 1) * (L(y,z,u) \ y),y \ L(y,z,u),x) = ((L(y,z,u) \ y) \ (1 / (x \ 1))) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,11549,a(flip),b,12823,a),flip(a)].">
      <j1 rule="hyper" parents="316 11549 12823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12840">
    <literal><![CDATA[
      L((x \ 1) * (L(y,z,u) \ y),y \ L(y,z,u),x) = ((L(y,z,u) \ y) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(80(a,1),12839(a,2,1,2))].">
      <j1 rule="para" parents="80 12839"/>
    </justification>
  </clause>

  <clause id="12842">
    <literal><![CDATA[
      (((L(x,y,z) \ x) \ u) \ 1) \ 1 = (L(x,y,z) \ x) \ ((u \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(12840(a,1),12825(a,1,1))].">
      <j1 rule="para" parents="12840 12825"/>
    </justification>
  </clause>

  <clause id="12847">
    <literal><![CDATA[
      (x * a(x \ y,x,x)) \ ((y / x) \ (y * (1 / (y \ (y / x))))) = 1 / (y \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,634,a(flip),b,12783,a),flip(a)].">
      <j1 rule="hyper" parents="63 634 12783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12851">
    <literal><![CDATA[
      R(a(x,y,z) / x,L(x,u,w),x * a(x,y,z)) \ L(x,u,w) = L(x,u,w) * ((a(x,y,z) * (x \ L(x,u,w))) \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(4809(a,1),12804(a,1,1))].">
      <j1 rule="para" parents="4809 12804"/>
    </justification>
  </clause>

  <clause id="12852">
    <literal><![CDATA[
      L(x,y,z) * ((a(x,u,w) * (x \ L(x,y,z))) \ L(x,y,z)) = (x \ a(x,u,w)) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(7787(a,1),12851(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7787 12851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12854">
    <literal><![CDATA[
      L(x \ 1,y,z) * L((x \ ((L(x,y,z) \ x) \ 1)) \ u,w,v5) = (L(x,y,z) \ 1) * L((x \ (L(x,y,z) \ x)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(1065(a,1),5086(a,1,1))].">
      <j1 rule="para" parents="1065 5086"/>
    </justification>
  </clause>

  <clause id="12855">
    <literal><![CDATA[
      L(x \ 1,y,z) * L((x \ (x \ L(x,y,z))) \ u,w,v5) = (L(x,y,z) \ 1) * L((x \ (L(x,y,z) \ x)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(5076(a,1),12854(a,1,2,1,1,2))].">
      <j1 rule="para" parents="5076 12854"/>
    </justification>
  </clause>

  <clause id="12856">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * L((x \ (L(x,y,z) \ x)) \ u,w,v5) = L(x \ 1,y,z) * L(L(x \ 1,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(1065(a,1),12855(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1065 12855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12857">
    <literal><![CDATA[
      L(x \ 1,y,z) * L(L(x \ 1,y,z) \ u,w,v5) = (L(x,y,z) \ 1) * L((L(x,y,z) \ 1) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(1003(a,1),12856(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1003 12856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12858">
    <literal><![CDATA[
      L(x \ 1,y,z) * L(L(x \ 1,y,z) \ u,w,v5) = L(x,y,z) * L(L(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,1350,a(flip),b,12857,a),flip(a)].">
      <j1 rule="hyper" parents="316 1350 12857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12864">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ ((a(y,z,u) \ x) * w) = x \ (((a(y,z,u) \ x) * w) / (a(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(2274(a,1),7221(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2274 7221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12865">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ ((a(y,z,u) \ x) * w) = x \ ((a(y,z,u) \ w) \ (w * (a(y,z,u) \ x)))
    ]]></literal>
    <justification jstring="[para(7500(a,1),12864(a,2,2))].">
      <j1 rule="para" parents="7500 12864"/>
    </justification>
  </clause>

  <clause id="12866">
    <literal><![CDATA[
      (1 \ (L(x \ R(x,y,z),u,w) * ((x \ R(x,y,z)) \ 1))) \ 1 = L(R(x,y,z) \ x,u,w) \ (1 \ ((x \ R(x,y,z)) \ 1))
    ]]></literal>
    <justification jstring="[para(66(a,1),7655(a,2,1,1))].">
      <j1 rule="para" parents="66 7655"/>
    </justification>
  </clause>

  <clause id="12867">
    <literal><![CDATA[
      (1 \ (L(x \ R(x,y,z),u,w) * ((x \ R(x,y,z)) \ 1))) \ 1 = L(R(x,y,z) \ x,u,w) \ (1 \ (R(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(7650(a,1),12866(a,2,2,2))].">
      <j1 rule="para" parents="7650 12866"/>
    </justification>
  </clause>

  <clause id="12868">
    <literal><![CDATA[
      (1 \ (L(x \ R(x,y,z),u,w) * ((x \ R(x,y,z)) \ 1))) \ 1 = L(R(x,y,z) \ x,u,w) \ (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(66(a,1),12867(a,2,2))].">
      <j1 rule="para" parents="66 12867"/>
    </justification>
  </clause>

  <clause id="12869">
    <literal><![CDATA[
      L(R(x,y,z) \ x,u,w) \ (R(x,y,z) \ x) = L(x \ R(x,y,z),u,w) \ (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1904,a(flip),b,12868,a),flip(a)].">
      <j1 rule="hyper" parents="63 1904 12868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12882">
    <literal><![CDATA[
      L(a(x,y,z * K(x * y,z)) \ y,x,z * K(x * y,z)) = (z * (K(x * y,z) * x)) \ (((x * (y * z)) / (x * y)) * (x * y))
    ]]></literal>
    <justification jstring="[para(3075(a,1),8642(a,2,1))].">
      <j1 rule="para" parents="3075 8642"/>
    </justification>
  </clause>

  <clause id="12884">
    <literal><![CDATA[
      (x \ y) / (a(z,(x \ 1) \ y,a(u,w,v5)) * (x \ y)) = a(a(u,w,v5),(x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12228,a(flip),b,8753,a),flip(a)].">
      <j1 rule="hyper" parents="63 12228 8753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12885">
    <literal><![CDATA[
      (x / ((a(y,z,u) \ 1) \ w)) * (w * (a(y,z,u) * a(y,z,u))) = w * ((((a(y,z,u) \ 1) \ w) \ x) * (a(y,z,u) * a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,9660,a(flip),b,9510,a),flip(a)].">
      <j1 rule="hyper" parents="316 9660 9510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12886">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * ((1 / u) * ((L(x,y,z) \ x) \ ((1 / u) \ (L(x,y,z) \ x)))) = (L(x,y,z) \ x) / (u \ 1)
    ]]></literal>
    <justification jstring="[para(83(a,1),11550(a,1,1,2))].">
      <j1 rule="para" parents="83 11550"/>
    </justification>
  </clause>

  <clause id="12887">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * ((1 / u) * ((x \ L(x,y,z)) \ ((1 / u) \ (x \ L(x,y,z))))) = (L(x,y,z) \ x) / (u \ 1)
    ]]></literal>
    <justification jstring="[para(9062(a,1),12886(a,1,2,2))].">
      <j1 rule="para" parents="9062 12886"/>
    </justification>
  </clause>

  <clause id="12888">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * ((1 / u) * ((x \ L(x,y,z)) \ ((x / u) \ L(x,y,z)))) = (L(x,y,z) \ x) / (u \ 1)
    ]]></literal>
    <justification jstring="[para(9752(a,1),12887(a,1,2,2,2))].">
      <j1 rule="para" parents="9752 12887"/>
    </justification>
  </clause>

  <clause id="12889">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * a(u,u,x * L(x,y,z)) = (L(x,y,z) \ x) / (u \ 1)
    ]]></literal>
    <justification jstring="[para(9785(a,1),12888(a,1,2))].">
      <j1 rule="para" parents="9785 12888"/>
    </justification>
  </clause>

  <clause id="12890">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * a(u,u,x * L(x,y,z)) = (1 / u) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,11548,a(flip),b,12889,a),flip(a)].">
      <j1 rule="hyper" parents="316 11548 12889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12891">
    <literal><![CDATA[
      x * (a(x,x,y * L(y,z,u)) * (L(y,z,u) \ y)) = (1 / x) \ (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8507,a(flip),b,12890,a)].">
      <j1 rule="hyper" parents="63 8507 12890"/>
    </justification>
  </clause>

  <clause id="12894">
    <literal><![CDATA[
      L(a(x,y,z * K(x * y,z)) \ y,x,z * K(x * y,z)) = (z * (x * K(y * x,z))) \ (((x * (y * z)) / (x * y)) * (x * y))
    ]]></literal>
    <justification jstring="[para(3640(a,1),12882(a,2,1,2))].">
      <j1 rule="para" parents="3640 12882"/>
    </justification>
  </clause>

  <clause id="12897">
    <literal><![CDATA[
      L(a(x,y,z * K(x * y,z)) \ y,x,z * K(x * y,z)) = (z * (x * K(y * x,z))) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(12(a,1),12894(a,2,2))].">
      <j1 rule="para" parents="12 12894"/>
    </justification>
  </clause>

  <clause id="12899">
    <literal><![CDATA[
      L(a(x,y,z * K(x * y,z)) \ y,x,z * K(x * y,z)) = K(z,y * x) * ((z * x) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(316,a,10225,a(flip),b,12897,a),flip(a)].">
      <j1 rule="hyper" parents="316 10225 12897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12902">
    <literal><![CDATA[
      L(a(x,y,z) \ y,x,z * K(x * y,z)) = K(z,y * x) * ((z * x) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(5467(a,1),12899(a,1,1,1))].">
      <j1 rule="para" parents="5467 12899"/>
    </justification>
  </clause>

  <clause id="12904">
    <literal><![CDATA[
      K(x,y * z) * ((x * z) \ (z * (y * x))) = L(a(z,y,x) \ y,z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1676,a(flip),b,12902,a),flip(a)].">
      <j1 rule="hyper" parents="63 1676 12902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12906">
    <literal><![CDATA[
      K(x,L(a(y,z,u) \ 1,w,v5) * v6) * ((x * L(a(y,z,u) \ 1,w,v5)) \ (L(a(y,z,u) \ 1,w,v5) * (v6 * x))) = L(a(L(a(y,z,u) \ 1,w,v5),v6,x) \ v6,L(a(y,z,u) \ 1,w,v5),x)
    ]]></literal>
    <justification jstring="[para(5005(a,2),12904(a,1,1,2))].">
      <j1 rule="para" parents="5005 12904"/>
    </justification>
  </clause>

  <clause id="12908">
    <literal><![CDATA[
      a(x,y,L(L(a(z,u,w) \ u,z,w),v5,v6)) = a(x,y,L((w * z) \ (z * (u * w)),v5,v6))
    ]]></literal>
    <justification jstring="[para(12904(a,1),5554(a,1,3,1))].">
      <j1 rule="para" parents="12904 5554"/>
    </justification>
  </clause>

  <clause id="12915">
    <literal><![CDATA[
      R((x * y) \ (L(x,z,u) * y),w,(y * x) \ (y * L(x,z,u))) = (x * y) \ (L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(5165(a,1),5195(a,1,1))].">
      <j1 rule="para" parents="5165 5195"/>
    </justification>
  </clause>

  <clause id="12917">
    <literal><![CDATA[
      R(x \ ((x / y) * L(y,z,u)),w,(x * y) \ (x * L(y,z,u))) = (y * x) \ (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(7107(a,1),12915(a,1,1))].">
      <j1 rule="para" parents="7107 12915"/>
    </justification>
  </clause>

  <clause id="12918">
    <literal><![CDATA[
      R(x \ ((x / y) * L(y,z,u)),w,x \ ((x / y) * L(y,z,u))) = (y * x) \ (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(7109(a,1),12917(a,1,3))].">
      <j1 rule="para" parents="7109 12917"/>
    </justification>
  </clause>

  <clause id="12919">
    <literal><![CDATA[
      R(x \ ((x / y) * L(y,z,u)),w,x \ ((x / y) * L(y,z,u))) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,7107,a(flip),b,12918,a),flip(a)].">
      <j1 rule="hyper" parents="316 7107 12918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12920">
    <literal><![CDATA[
      (x \ ((x / y) * L(y,z,u))) \ x = x * (((x / y) * L(y,z,u)) \ x)
    ]]></literal>
    <justification jstring="[para(12919(a,1),5142(a,1,1))].">
      <j1 rule="para" parents="12919 5142"/>
    </justification>
  </clause>

  <clause id="12921">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) \ u = u * (((u / x) * L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,7102,a,b,12920,a)].">
      <j1 rule="hyper" parents="63 7102 12920"/>
    </justification>
  </clause>

  <clause id="12923">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) \ x = x \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(133,a,9281,a(flip),b,12921,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 9281 12921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12925">
    <literal><![CDATA[
      L((x * y) \ L(x * y,z,u),y * x,w) \ w = w * (((w / (x * y)) * L(x * y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(10797(a,1),12921(a,1,1))].">
      <j1 rule="para" parents="10797 12921"/>
    </justification>
  </clause>

  <clause id="12926">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) \ u = u \ (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(4325(a,2),12923(a,1,1))].">
      <j1 rule="para" parents="4325 12923"/>
    </justification>
  </clause>

  <clause id="12928">
    <literal><![CDATA[
      x \ ((L(y,z,u) \ y) * (L(L(y,z,u) \ y,y,u * z) \ x)) = ((x / (L(y,z,u) \ y)) * a(u,z,L(y,z,u))) \ x
    ]]></literal>
    <justification jstring="[para(11885(a,1),12923(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11885 12923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12938">
    <literal><![CDATA[
      x * (((x / (y * z)) * L(y * z,u,w)) \ x) = (z * y) * (L(z * y,u,w) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9284,a(flip),b,12925,a),flip(a)].">
      <j1 rule="hyper" parents="63 9284 12925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12939">
    <literal><![CDATA[
      x * (x \ ((y * z) * (L(y * z,u,w) \ x))) = (z * y) * (L(z * y,u,w) \ x)
    ]]></literal>
    <justification jstring="[para(12923(a,1),12938(a,1,2))].">
      <j1 rule="para" parents="12923 12938"/>
    </justification>
  </clause>

  <clause id="12940">
    <literal><![CDATA[
      (x * y) * (L(x * y,z,u) \ w) = (y * x) * (L(y * x,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(270,a,12939,a)].">
      <j1 rule="hyper" parents="270 12939"/>
    </justification>
  </clause>

  <clause id="12942">
    <literal><![CDATA[
      K(x,y) * ((x * y) * (L(x * y,z,u) \ w)) = (x * y) * (L(y * x,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(139,a,12940,a,b,3060,a)].">
      <j1 rule="hyper" parents="139 12940 3060"/>
    </justification>
  </clause>

  <clause id="12943">
    <literal><![CDATA[
      (x * y) * (L(x * y,z,u) \ ((y * x) * w)) = (y * x) * ((y * x) * (L(y * x,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(1129(a,1),12940(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1129 12940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12944">
    <literal><![CDATA[
      (x * y) * ((y * x) * (L(x * y,z,u) \ w)) = (y * x) * ((y * x) * (L(y * x,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(139,a,12942,a(flip),b,6236,a)].">
      <j1 rule="hyper" parents="139 12942 6236"/>
    </justification>
  </clause>

  <clause id="12945">
    <literal><![CDATA[
      L(x * y,z,u) \ ((y * x) * w) = (y * x) * (L(x * y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(34,a,12943,a,b,12944,a)].">
      <j1 rule="hyper" parents="34 12943 12944"/>
    </justification>
  </clause>

  <clause id="12946">
    <literal><![CDATA[
      x \ ((L(y,z,u) \ y) * (L(L(y,z,u) \ y,y,u * z) \ x)) = (((L(y,z,u) \ y) \ x) * a(u,z,L(y,z,u))) \ x
    ]]></literal>
    <justification jstring="[para(6483(a,1),12928(a,2,1,1))].">
      <j1 rule="para" parents="6483 12928"/>
    </justification>
  </clause>

  <clause id="12953">
    <literal><![CDATA[
      (x * L(a(x,y,x) \ y,z,u)) * x = (x * L(x \ ((x * (y * x)) / x),z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,4339,a(flip),b,6201,a),flip(a)].">
      <j1 rule="hyper" parents="63 4339 6201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12954">
    <literal><![CDATA[
      (L(x,y,x) * L(y,z,u)) * x = (x * L(x \ ((x * (y * x)) / x),z,u)) * x
    ]]></literal>
    <justification jstring="[para(6148(a,1),12953(a,1,1))].">
      <j1 rule="para" parents="6148 12953"/>
    </justification>
  </clause>

  <clause id="12955">
    <literal><![CDATA[
      (x * L(x \ ((x * (y * x)) / x),z,u)) * x = (x * L(y,z,u)) * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4403,a(flip),b,12954,a),flip(a)].">
      <j1 rule="hyper" parents="63 4403 12954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12956">
    <literal><![CDATA[
      L(((x * (y * x)) / x) * x,z,u) = (x * L(y,z,u)) * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1348,a(flip),b,12955,a)].">
      <j1 rule="hyper" parents="63 1348 12955"/>
    </justification>
  </clause>

  <clause id="12957">
    <literal><![CDATA[
      (x * L(y,z,u)) * L(x,y,x) = L(x * (y * x),z,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),12956(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 12956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12958">
    <literal><![CDATA[
      (x * L(y,z,u)) * L(x,y,x) = x * (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(316,a,1359,a(flip),b,12957,a),flip(a)].">
      <j1 rule="hyper" parents="316 1359 12957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12960">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(463,a,12958,a)].">
      <j1 rule="hyper" parents="463 12958"/>
    </justification>
  </clause>

  <clause id="12961">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10977,a,b,12960,a)].">
      <j1 rule="hyper" parents="63 10977 12960"/>
    </justification>
  </clause>

  <clause id="12962">
    <literal><![CDATA[
      (L(x,y,x) * L(y,z,u)) \ L(y,z,u) = L(y,z,u) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12960(a,1),8164(a,1,1,1))].">
      <j1 rule="para" parents="12960 8164"/>
    </justification>
  </clause>

  <clause id="12963">
    <literal><![CDATA[
      (x * (R(y,z,u) * x)) / x = L(x,y,x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,12961,a(flip),b,1621,a),flip(a)].">
      <j1 rule="hyper" parents="138 12961 1621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12964">
    <literal><![CDATA[
      ((x * (R(y,z,u) * x)) / x) \ R(y,z,u) = (L(x,y,x) * L(y,z,u)) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(12963(a,2),12247(a,1,1))].">
      <j1 rule="para" parents="12963 12247"/>
    </justification>
  </clause>

  <clause id="12965">
    <literal><![CDATA[
      ((x * (R(y,z,u) * x)) / x) \ R(y,z,u) = L(y,z,u) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,12962,a(flip),b,12964,a),flip(a)].">
      <j1 rule="hyper" parents="316 12962 12964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12966">
    <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,8169,a(flip),b,12965,a)].">
      <j1 rule="hyper" parents="63 8169 12965"/>
    </justification>
  </clause>

  <clause id="12967">
    <literal><![CDATA[
      K(x,x \ R(y,z,u)) * (L(y,z,u) \ (x \ L(y,z,u))) = T(R(y,z,u) \ (R(y,z,u) / x),K(x,R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(12966(a,1),6196(a,1,2))].">
      <j1 rule="para" parents="12966 6196"/>
    </justification>
  </clause>

  <clause id="12968">
    <literal><![CDATA[
      ((L(x,y,z) \ (u \ L(x,y,z))) * w) * a(R(x,y,z),R(x,y,z) \ (u \ R(x,y,z)),w) = R(x,y,z) \ ((u \ R(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[para(12966(a,1),8437(a,1,1,1))].">
      <j1 rule="para" parents="12966 8437"/>
    </justification>
  </clause>

  <clause id="12969">
    <literal><![CDATA[
      T(R(x,y,z) \ (R(x,y,z) / u),K(u,R(x,y,z))) = K(u,u \ x) * (L(x,y,z) \ (u \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(3539(a,1),12967(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3539 12967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12970">
    <literal><![CDATA[
      T(R(x,y,z) \ (R(x,y,z) / u),K(u,R(x,y,z))) = T(L(x,y,z) \ (L(x,y,z) / u),K(u,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,7809,a(flip),b,12969,a),flip(a)].">
      <j1 rule="hyper" parents="316 7809 12969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12972">
    <literal><![CDATA[
      R(x,y,z) \ (R(x,y,z) / u) = L(x,y,z) \ (L(x,y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(40,a,1954,a,b,12970,a),flip(a)].">
      <j1 rule="hyper" parents="40 1954 12970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12973">
    <literal><![CDATA[
      L(x \ y,x,x) \ (L(x \ y,x,x) / z) = ((x \ 1) * y) \ (((x \ 1) * y) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9714,a(flip),b,12972,a),flip(a)].">
      <j1 rule="hyper" parents="63 9714 12972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12974">
    <literal><![CDATA[
      ((L(x,y,z) \ (u \ L(x,y,z))) * w) * a(R(x,y,z),L(x,y,z) \ (u \ L(x,y,z)),w) = R(x,y,z) \ ((u \ R(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[para(12966(a,1),12968(a,1,2,2))].">
      <j1 rule="para" parents="12966 12968"/>
    </justification>
  </clause>

  <clause id="12975">
    <literal><![CDATA[
      ((L(x,y,z) \ (u \ L(x,y,z))) * w) * a(L(x,y,z),L(x,y,z) \ (u \ L(x,y,z)),w) = R(x,y,z) \ ((u \ R(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[para(4643(a,1),12974(a,1,2))].">
      <j1 rule="para" parents="4643 12974"/>
    </justification>
  </clause>

  <clause id="12976">
    <literal><![CDATA[
      R(x,y,z) \ ((u \ R(x,y,z)) * w) = L(x,y,z) \ ((u \ L(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8437,a(flip),b,12975,a),flip(a)].">
      <j1 rule="hyper" parents="63 8437 12975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12977">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (((w \ v5) * (w * w)) * (v6 * (w \ v5)))) * (w * w))) = a(x,y,z \ (u \ L(v6,(w \ v5) * (w * w),(w \ 1) \ v5)))
    ]]></literal>
    <justification jstring="[para(837(a,1),6391(a,1,3,2))].">
      <j1 rule="para" parents="837 6391"/>
    </justification>
  </clause>

  <clause id="12978">
    <literal><![CDATA[
      a(x \ (L(y,x \ (z * (T(u,w) * v5)),x) * (z * (u * v5))),v6,v7) = a((x \ (z * (T(u,w) * v5))) * y,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,3145,a(flip),b,7840,a),flip(a)].">
      <j1 rule="hyper" parents="316 3145 7840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12980">
    <literal><![CDATA[
      a(x \ (L(y,x \ ((z * u) * w),x) * (w * (z * u))),v5,v6) = a((x \ (w * (T(z,v7) * u))) * y,v5,v6)
    ]]></literal>
    <justification jstring="[para(11010(a,1),12978(a,1,1,2,1))].">
      <j1 rule="para" parents="11010 12978"/>
    </justification>
  </clause>

  <clause id="12981">
    <literal><![CDATA[
      a(x \ (x * ((x \ ((y * z) * u)) * w)),v5,v6) = a((x \ (u * (T(y,v7) * z))) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,4613,a(flip),b,12980,a)].">
      <j1 rule="hyper" parents="63 4613 12980"/>
    </justification>
  </clause>

  <clause id="12983">
    <literal><![CDATA[
      a((x \ (y * (T(z,u) * w))) * v5,v6,v7) = a((x \ ((z * w) * y)) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(9(a,1),12981(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 12981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12985">
    <literal><![CDATA[
      a(((x * y) \ ((x * z) * y)) * u,w,v5) = a(L(z,x,y) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(3286(a,2),12983(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3286 12983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12986">
    <literal><![CDATA[
      a(R(x,y,z) * u,w,v5) = a(L(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11391,a(flip),b,12985,a)].">
      <j1 rule="hyper" parents="63 11391 12985"/>
    </justification>
  </clause>

  <clause id="12987">
    <literal><![CDATA[
      a(L(x,y,z) * u,w,v5) = a(u * R(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,2771,a,b,12986,a),flip(a)].">
      <j1 rule="hyper" parents="63 2771 12986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12989">
    <literal><![CDATA[
      a(x * R(y,z,u),w,v5) = a(x * L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,2771,a,b,12987,a),flip(a)].">
      <j1 rule="hyper" parents="63 2771 12987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12990">
    <literal><![CDATA[
      a(x * R(L(y,z,u),w,v5),v6,v7) = a(x * L(L(y,w,v5),z,u),v6,v7)
    ]]></literal>
    <justification jstring="[para(30(a,1),12989(a,2,1,2))].">
      <j1 rule="para" parents="30 12989"/>
    </justification>
  </clause>

  <clause id="12991">
    <literal><![CDATA[
      a(x * L(R(y,z,u),w,v5),v6,v7) = a(x * L(L(y,z,u),w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(29(a,1),12990(a,1,1,2))].">
      <j1 rule="para" parents="29 12990"/>
    </justification>
  </clause>

  <clause id="12997">
    <literal><![CDATA[
      (x * (y * ((a(z,u,w) * a(z,u,w)) \ v5))) \ ((x * y) * ((a(z,u,w) * a(z,u,w)) \ v5)) = a(x,(a(z,u,w) * a(z,u,w)) \ y,v5)
    ]]></literal>
    <justification jstring="[para(9264(a,1),9266(a,1,2))].">
      <j1 rule="para" parents="9264 9266"/>
    </justification>
  </clause>

  <clause id="12998">
    <literal><![CDATA[
      (x * (y * ((a(z,u,w) * a(z,u,w)) \ v5))) \ ((((a(z,u,w) * a(z,u,w)) \ x) * y) * v5) = a((a(z,u,w) * a(z,u,w)) \ x,y,v5)
    ]]></literal>
    <justification jstring="[para(7034(a,1),9267(a,1,1,2))].">
      <j1 rule="para" parents="7034 9267"/>
    </justification>
  </clause>

  <clause id="12999">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * (u \ K(u,u \ 1))) \ (x \ R(x,y,z)) = (x \ R(x,y,z)) \ ((x \ R(x,y,z)) / (u \ 1))
    ]]></literal>
    <justification jstring="[para(3603(a,1),9621(a,1,1,2,2))].">
      <j1 rule="para" parents="3603 9621"/>
    </justification>
  </clause>

  <clause id="13000">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * (1 / u)) \ (x \ R(x,y,z)) = (x \ R(x,y,z)) \ ((x \ R(x,y,z)) / (u \ 1))
    ]]></literal>
    <justification jstring="[para(1087(a,1),12999(a,1,1,2))].">
      <j1 rule="para" parents="1087 12999"/>
    </justification>
  </clause>

  <clause id="13002">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ ((x \ R(x,y,z)) / (u \ 1)) = (x \ R(x,y,z)) \ ((1 / u) \ (x \ R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9620,a(flip),b,13000,a),flip(a)].">
      <j1 rule="hyper" parents="63 9620 13000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13003">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ ((x \ R(x,y,z)) / (u \ 1)) = (x \ R(x,y,z)) \ ((x / u) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(9770(a,1),13002(a,2,2))].">
      <j1 rule="para" parents="9770 13002"/>
    </justification>
  </clause>

  <clause id="13004">
    <literal><![CDATA[
      (x \ R(x,y,z)) / (u \ 1) = (x / u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(47,a,13003,a)].">
      <j1 rule="hyper" parents="47 13003"/>
    </justification>
  </clause>

  <clause id="13006">
    <literal><![CDATA[
      (L(x,y,z) \ L(R(x,u,w),y,z)) / (v5 \ 1) = (L(x,y,z) / v5) \ R(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29(a,1),13004(a,1,1,2))].">
      <j1 rule="para" parents="29 13004"/>
    </justification>
  </clause>

  <clause id="13007">
    <literal><![CDATA[
      (L(x,y,z) \ L(R(x,u,w),y,z)) / (v5 \ 1) = (L(x,y,z) / v5) \ L(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(29(a,1),13006(a,2,2))].">
      <j1 rule="para" parents="29 13006"/>
    </justification>
  </clause>

  <clause id="13008">
    <literal><![CDATA[
      (x * y) \ T(a(z,u,w) * x,(a(z,u,w) * x) \ (x * y)) = (y * x) \ (a(z,u,w) * x)
    ]]></literal>
    <justification jstring="[para(12(a,1),10594(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 10594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13010">
    <literal><![CDATA[
      (x * y) \ T(a(z,u,w) * x,a(z,u,w) \ y) = (y * x) \ (a(z,u,w) * x)
    ]]></literal>
    <justification jstring="[para(10397(a,1),13008(a,1,2))].">
      <j1 rule="para" parents="10397 13008"/>
    </justification>
  </clause>

  <clause id="13011">
    <literal><![CDATA[
      (x * y) \ T(a(z,u,w) * x,y) = (y * x) \ (a(z,u,w) * x)
    ]]></literal>
    <justification jstring="[para(5249(a,1),13010(a,1,2))].">
      <j1 rule="para" parents="5249 13010"/>
    </justification>
  </clause>

  <clause id="13013">
    <literal><![CDATA[
      L(((x * x) * y) \ L((x * x) * y,z,u),(x * x) * y,w) = a(w,y,y * L(y,z,u)) \ (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11982(a,1),11995(a,2,2))].">
      <j1 rule="para" parents="11982 11995"/>
    </justification>
  </clause>

  <clause id="13014">
    <literal><![CDATA[
      L(((x * x) * y) \ L((x * x) * y,z,u),(x * x) * y,w) = L(y \ L(y,z,u),y,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10038,a(flip),b,13013,a),flip(a)].">
      <j1 rule="hyper" parents="316 10038 13013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13016">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,y * a(z,u,w)) = a((v5 * v5) * x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,10884,a(flip),b,13014,a),flip(a)].">
      <j1 rule="hyper" parents="63 10884 13014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13024">
    <literal><![CDATA[
      a((x * x) * y,z,a(u,w,v5)) = a(y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5385,a(flip),b,13016,a),flip(a)].">
      <j1 rule="hyper" parents="63 5385 13016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13025">
    <literal><![CDATA[
      a(x * (y * (z * z)),u,a(w,v5,v6)) = a(x * y,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,2789,a(flip),b,13024,a)].">
      <j1 rule="hyper" parents="63 2789 13024"/>
    </justification>
  </clause>

  <clause id="13026">
    <literal><![CDATA[
      a((x \ 1) \ y,z,a(u,w,v5)) = a(x \ y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,2787,a(flip),b,13024,a)].">
      <j1 rule="hyper" parents="63 2787 13024"/>
    </justification>
  </clause>

  <clause id="13027">
    <literal><![CDATA[
      a(x \ (L(x \ 1,y,z) \ (x \ 1)),u,a(w,v5,v6)) = a(L(x \ 1,y,z) \ 1,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(1003(a,1),13026(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1003 13026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13028">
    <literal><![CDATA[
      a(x \ y,(x \ 1) \ y,a(z,u,w)) \ a(z,u,w) = L(a(z,u,w),(x \ 1) \ y,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(13026(a,1),4950(a,1,1))].">
      <j1 rule="para" parents="13026 4950"/>
    </justification>
  </clause>

  <clause id="13030">
    <literal><![CDATA[
      a((x \ 1) * y,z,a(u,w,v5)) = a(y * x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,10687,a(flip),b,13025,a),flip(a)].">
      <j1 rule="hyper" parents="63 10687 13025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13031">
    <literal><![CDATA[
      a(x * (y \ 1),z,a(u,w,v5)) = a(x * y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(229(a,1),13025(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="229 13025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13032">
    <literal><![CDATA[
      a(x \ (L(x \ 1,y,z) \ (x \ 1)),u,a(w,v5,v6)) = a(L(x \ 1,y,z),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,7226,a(flip),b,13027,a),flip(a)].">
      <j1 rule="hyper" parents="316 7226 13027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13033">
    <literal><![CDATA[
      a(x \ (L(x,y,z) \ x),u,a(w,v5,v6)) = a(L(x \ 1,y,z),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(7090(a,1),13032(a,1,1,2))].">
      <j1 rule="para" parents="7090 13032"/>
    </justification>
  </clause>

  <clause id="13034">
    <literal><![CDATA[
      a(L(x \ 1,y,z),u,a(w,v5,v6)) = a(L(x,y,z) \ 1,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(1003(a,1),13033(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1003 13033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13035">
    <literal><![CDATA[
      a(L(x \ 1,y,z),u,a(w,v5,v6)) = a(L(x,y,z),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,7226,a(flip),b,13034,a),flip(a)].">
      <j1 rule="hyper" parents="316 7226 13034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13036">
    <literal><![CDATA[
      T(R(x,y,z),R(x,y,z) \ u) * ((R(x,y,z) \ u) * w) = L(x,y,z) * ((L(x,y,z) \ u) * (K(x,x \ u) * w))
    ]]></literal>
    <justification jstring="[para(3576(a,1),12621(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3576 12621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13038">
    <literal><![CDATA[
      T(R(x,y,z),R(x,y,z) \ u) * ((R(x,y,z) \ u) * w) = L(x,y,z) * ((L(x,y,z) \ (x * (u / x))) * w)
    ]]></literal>
    <justification jstring="[para(10193(a,1),13036(a,2,2))].">
      <j1 rule="para" parents="10193 13036"/>
    </justification>
  </clause>

  <clause id="13039">
    <literal><![CDATA[
      T(R(x,y,z),R(x,y,z) \ u) * ((R(x,y,z) \ u) * w) = L(x,y,z) * ((u / L(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[para(4437(a,1),13038(a,2,2,1))].">
      <j1 rule="para" parents="4437 13038"/>
    </justification>
  </clause>

  <clause id="13040">
    <literal><![CDATA[
      R(x,y,z) * ((u / R(x,y,z)) * w) = L(x,y,z) * ((u / L(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3175,a(flip),b,13039,a)].">
      <j1 rule="hyper" parents="63 3175 13039"/>
    </justification>
  </clause>

  <clause id="13041">
    <literal><![CDATA[
      L(R(x,y,z) \ u,R(x,y,z),R(x,y,z) \ 1) * R(x,y,z) = L(x,y,z) * ((1 / L(x,y,z)) * ((x \ u) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3247,a,b,13040,a)].">
      <j1 rule="hyper" parents="63 3247 13040"/>
    </justification>
  </clause>

  <clause id="13042">
    <literal><![CDATA[
      L(R(x,y,z) \ u,R(x,y,z),R(x,y,z) \ 1) * R(x,y,z) = L(x,y,z) * T((1 / L(x,y,z)) * u,x)
    ]]></literal>
    <justification jstring="[para(7536(a,1),13041(a,2,2))].">
      <j1 rule="para" parents="7536 13041"/>
    </justification>
  </clause>

  <clause id="13043">
    <literal><![CDATA[
      L(R(x,y,z) \ u,R(x,y,z),R(x,y,z) \ 1) * R(x,y,z) = ((1 / L(x,y,z)) * u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,4313,a(flip),b,13042,a),flip(a)].">
      <j1 rule="hyper" parents="316 4313 13042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13044">
    <literal><![CDATA[
      ((1 / R(x,y,z)) * u) * R(x,y,z) = ((1 / L(x,y,z)) * u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(887(a,1),13043(a,1,1))].">
      <j1 rule="para" parents="887 13043"/>
    </justification>
  </clause>

  <clause id="13045">
    <literal><![CDATA[
      ((1 / L(x / y,y,x)) * z) * L(x / y,y,x) = ((y * (x \ 1)) * z) * ((y * (x \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2667,a(flip),b,13044,a),flip(a)].">
      <j1 rule="hyper" parents="63 2667 13044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13046">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(w,(v5 \ v6) * (v5 * v5),(v5 \ 1) \ v6))) = a(x,y,z \ (u \ (((v5 \ v6) * (v5 * v5)) * (w * (v5 \ v6)))))
    ]]></literal>
    <justification jstring="[hyper(63,a,5813,a(flip),b,12977,a),flip(a)].">
      <j1 rule="hyper" parents="63 5813 12977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13048">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(w,(v5 \ v6) * (v5 * v5),(v5 \ 1) \ v6))) = a(x,y,z \ (u \ ((w * (v5 \ v6)) * (v5 \ v6))))
    ]]></literal>
    <justification jstring="[hyper(316,a,7733,a(flip),b,13046,a),flip(a)].">
      <j1 rule="hyper" parents="316 7733 13046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13050">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(w,(v5 \ v6) * (v5 * v5),(v5 \ 1) \ v6))) = a(x,y,z \ (u \ L(w,v5 \ v6,v5 \ v6)))
    ]]></literal>
    <justification jstring="[hyper(316,a,6390,a(flip),b,13048,a),flip(a)].">
      <j1 rule="hyper" parents="316 6390 13048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13051">
    <literal><![CDATA[
      a(x,(a(y,z,u) * a(y,z,u)) \ w,v5) = a(x,w,(a(y,z,u) * a(y,z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,14,a,b,12997,a),flip(a)].">
      <j1 rule="hyper" parents="63 14 12997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13052">
    <literal><![CDATA[
      a(x,(a(y,z,u) * a(y,z,u)) \ w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,5802,a(flip),b,13051,a),flip(a)].">
      <j1 rule="hyper" parents="316 5802 13051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13054">
    <literal><![CDATA[
      a(x,y * ((a(z,u,w) * a(z,u,w)) \ v5),v6) = a(x,y * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,11297,a(flip),b,13052,a)].">
      <j1 rule="hyper" parents="63 11297 13052"/>
    </justification>
  </clause>

  <clause id="13055">
    <literal><![CDATA[
      a(x,y \ (a(z,u,w) \ 1),v5) = a(x,y \ a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(5453(a,1),13052(a,1,2))].">
      <j1 rule="para" parents="5453 13052"/>
    </justification>
  </clause>

  <clause id="13056">
    <literal><![CDATA[
      a(x,L(y \ 1,y,z),u) = a(x,y \ a(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(7321(a,1),13055(a,1,2))].">
      <j1 rule="para" parents="7321 13055"/>
    </justification>
  </clause>

  <clause id="13057">
    <literal><![CDATA[
      a(x,L(y \ 1,y,z),u) = a(x,L(y,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(7300(a,2),13056(a,2,2))].">
      <j1 rule="para" parents="7300 13056"/>
    </justification>
  </clause>

  <clause id="13058">
    <literal><![CDATA[
      a(x,y * (a(z,u,w) \ 1),v5) = a(x,y * a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11250,a(flip),b,13054,a)].">
      <j1 rule="hyper" parents="63 11250 13054"/>
    </justification>
  </clause>

  <clause id="13059">
    <literal><![CDATA[
      a(x,y * (a(z,u,w) * a(z,u,w)),v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(183(a,1),13054(a,1,2)),flip(a)].">
      <j1 rule="para" parents="183 13054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13060">
    <literal><![CDATA[
      a(x,y * ((a(z,u,w) \ 1) \ v5),v6) = a(x,y * (a(z,u,w) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(6304(a,1),13054(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6304 13054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13061">
    <literal><![CDATA[
      a(x,a(y,z,u) \ 1,w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(229(a,1),13059(a,1,2)),flip(a)].">
      <j1 rule="para" parents="229 13059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13062">
    <literal><![CDATA[
      (x * ((a(y,z,u) \ 1) * w)) \ (((a(y,z,u) \ 1) * x) * w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5056,a,b,13061,a)].">
      <j1 rule="hyper" parents="63 5056 13061"/>
    </justification>
  </clause>

  <clause id="13064">
    <literal><![CDATA[
      a(x,(a(y,z,u) \ 1) * w,v5) = a(x,w * a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11190,a,b,13058,a)].">
      <j1 rule="hyper" parents="63 11190 13058"/>
    </justification>
  </clause>

  <clause id="13065">
    <literal><![CDATA[
      a(x,y * a(z,z,y),u) = a(x,L(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(5093(a,1),13058(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5093 13058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13066">
    <literal><![CDATA[
      a(x,a(y,z,u) \ u,w) = a(x,u * a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(6859(a,1),13058(a,1,2))].">
      <j1 rule="para" parents="6859 13058"/>
    </justification>
  </clause>

  <clause id="13067">
    <literal><![CDATA[
      a(x,y \ ((y \ 1) \ z),u) = a(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12044,a,b,13065,a)].">
      <j1 rule="hyper" parents="63 12044 13065"/>
    </justification>
  </clause>

  <clause id="13068">
    <literal><![CDATA[
      a(x,L(y * z,y,y),u) = a(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12046,a(flip),b,13067,a),flip(a)].">
      <j1 rule="hyper" parents="63 12046 13067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13069">
    <literal><![CDATA[
      R(x,L(y * z,y,y),y \ z) = a(x,(y \ 1) \ z,y \ z) * x
    ]]></literal>
    <justification jstring="[para(13068(a,1),11680(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13068 11680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13070">
    <literal><![CDATA[
      a(x,y * a(z,y,y),u) = a(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(7297(a,1),13066(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7297 13066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13071">
    <literal><![CDATA[
      a(x,L(y \ 1,y,z) \ 1,u) = a(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8049,a,b,13070,a)].">
      <j1 rule="hyper" parents="63 8049 13070"/>
    </justification>
  </clause>

  <clause id="13072">
    <literal><![CDATA[
      a(x,L(y \ z,y \ z,y),u) = a(x,(z \ y) \ 1,u)
    ]]></literal>
    <justification jstring="[para(356(a,1),13071(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="356 13071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13073">
    <literal><![CDATA[
      R(x,L(y * z,y,y),y \ z) = R(x,(y \ 1) \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,6379,a(flip),b,13069,a),flip(a)].">
      <j1 rule="hyper" parents="316 6379 13069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13074">
    <literal><![CDATA[
      R(x * K(y * z,x),(y \ 1) \ z,y \ z) = (L(y * z,y,y) * x) * (L(y * z,y,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,11681,a(flip),b,13073,a),flip(a)].">
      <j1 rule="hyper" parents="63 11681 13073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13075">
    <literal><![CDATA[
      (L(x * y,x,x) * z) * (L(x * y,x,x) \ 1) = (((x \ 1) \ y) * z) * (((x \ 1) \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,8145,a(flip),b,13074,a),flip(a)].">
      <j1 rule="hyper" parents="63 8145 13074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13076">
    <literal><![CDATA[
      (x * (y * ((a(z,u,w) * a(z,u,w)) \ v5))) \ ((x * ((a(z,u,w) * a(z,u,w)) \ y)) * v5) = a((a(z,u,w) * a(z,u,w)) \ x,y,v5)
    ]]></literal>
    <justification jstring="[para(9263(a,1),12998(a,1,2,1))].">
      <j1 rule="para" parents="9263 12998"/>
    </justification>
  </clause>

  <clause id="13077">
    <literal><![CDATA[
      (x * (y * ((a(z,u,w) * a(z,u,w)) \ v5))) \ ((x * y) * ((a(z,u,w) * a(z,u,w)) \ v5)) = a((a(z,u,w) * a(z,u,w)) \ x,y,v5)
    ]]></literal>
    <justification jstring="[para(9264(a,1),13076(a,1,2))].">
      <j1 rule="para" parents="9264 13076"/>
    </justification>
  </clause>

  <clause id="13078">
    <literal><![CDATA[
      a((a(x,y,z) * a(x,y,z)) \ u,w,v5) = a(u,w,(a(x,y,z) * a(x,y,z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,14,a,b,13077,a),flip(a)].">
      <j1 rule="hyper" parents="63 14 13077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13079">
    <literal><![CDATA[
      a((a(x,y,z) * a(x,y,z)) \ u,w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,5802,a(flip),b,13078,a),flip(a)].">
      <j1 rule="hyper" parents="316 5802 13078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13081">
    <literal><![CDATA[
      a(x * ((a(y,z,u) * a(y,z,u)) \ w),v5,v6) = a(x * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,3225,a(flip),b,13079,a)].">
      <j1 rule="hyper" parents="63 3225 13079"/>
    </justification>
  </clause>

  <clause id="13082">
    <literal><![CDATA[
      a(x * (a(y,z,u) * a(y,z,u)),w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,1811,a(flip),b,13079,a),flip(a)].">
      <j1 rule="hyper" parents="63 1811 13079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13084">
    <literal><![CDATA[
      a(L(a(x,y,z) \ u,a(x,y,z),a(x,y,z)),w,v5) = a(a(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(102(a,2),13079(a,1,1))].">
      <j1 rule="para" parents="102 13079"/>
    </justification>
  </clause>

  <clause id="13085">
    <literal><![CDATA[
      a((a(x,y,z) \ 1) \ u,w,v5) = a(a(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(6304(a,1),13079(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6304 13079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13086">
    <literal><![CDATA[
      a((a(x,y,y) \ 1) \ y,z,u) = a(L(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,7315,a(flip),b,13082,a)].">
      <j1 rule="hyper" parents="63 7315 13082"/>
    </justification>
  </clause>

  <clause id="13087">
    <literal><![CDATA[
      a(a(x,y,z) \ 1,u,w) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(229(a,1),13082(a,1,1)),flip(a)].">
      <j1 rule="para" parents="229 13082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13088">
    <literal><![CDATA[
      a(x * (y \ (x \ y)),z,u) = a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8183,a,b,13087,a)].">
      <j1 rule="hyper" parents="63 8183 13087"/>
    </justification>
  </clause>

  <clause id="13089">
    <literal><![CDATA[
      a(a(x,a(y,z,x),u),w,v5) = a(a(u,x,a(y,z,x)),w,v5)
    ]]></literal>
    <justification jstring="[para(9447(a,1),13087(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9447 13087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13090">
    <literal><![CDATA[
      a(a(x,x,y * x),z,u) = a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12282,a,b,13088,a)].">
      <j1 rule="hyper" parents="63 12282 13088"/>
    </justification>
  </clause>

  <clause id="13091">
    <literal><![CDATA[
      a(x * y,a(y,y,x * y),z) = a(a(x,y,y),x * y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7009,a(flip),b,13090,a)].">
      <j1 rule="hyper" parents="63 7009 13090"/>
    </justification>
  </clause>

  <clause id="13094">
    <literal><![CDATA[
      a(a(x,y,y) * y,z,u) = a(L(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6891,a(flip),b,13086,a)].">
      <j1 rule="hyper" parents="63 6891 13086"/>
    </justification>
  </clause>

  <clause id="13095">
    <literal><![CDATA[
      a(L(x \ y,x \ y,x),z,u) = a(1 / (y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(7372(a,1),13094(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7372 13094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13096">
    <literal><![CDATA[
      a(L(x \ y,x \ y,x),z,u) = a((y \ x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,1813,a(flip),b,13095,a),flip(a)].">
      <j1 rule="hyper" parents="316 1813 13095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13097">
    <literal><![CDATA[
      a(L(x \ (x * y),y,x),z,u) = a(((x * y) \ x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),13096(a,1,1,2))].">
      <j1 rule="para" parents="9 13096"/>
    </justification>
  </clause>

  <clause id="13098">
    <literal><![CDATA[
      a((a(x,x \ 1,y) \ 1) \ y,z,u) = a(L(y,x \ 1,x),z,u)
    ]]></literal>
    <justification jstring="[para(1384(a,1),13085(a,2,1))].">
      <j1 rule="para" parents="1384 13085"/>
    </justification>
  </clause>

  <clause id="13099">
    <literal><![CDATA[
      a((a(x \ 1,x,y) \ 1) \ y,z,u) = a(L(y,x,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(2406(a,1),13085(a,2,1))].">
      <j1 rule="para" parents="2406 13085"/>
    </justification>
  </clause>

  <clause id="13100">
    <literal><![CDATA[
      a(a(x,y,y),x * y,z) = a(x * y,a(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12260,a(flip),b,13091,a),flip(a)].">
      <j1 rule="hyper" parents="63 12260 13091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13101">
    <literal><![CDATA[
      a(L(x,x,y),z,u) = a(((y * x) \ y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),13097(a,1,1,1))].">
      <j1 rule="para" parents="9 13097"/>
    </justification>
  </clause>

  <clause id="13102">
    <literal><![CDATA[
      a(L(x,x,y),z,u) = a((y \ (x \ y)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,11171,a(flip),b,13101,a),flip(a)].">
      <j1 rule="hyper" parents="316 11171 13101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13103">
    <literal><![CDATA[
      a((x \ (y \ x)) \ 1,z,u) = a(x \ ((y \ 1) \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3325,a(flip),b,13102,a),flip(a)].">
      <j1 rule="hyper" parents="63 3325 13102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13104">
    <literal><![CDATA[
      a(x \ ((y \ 1) \ x),x \ (y \ x),z) \ z = L(z,x \ (y \ x),(x \ (y \ x)) \ 1)
    ]]></literal>
    <justification jstring="[para(13103(a,1),2406(a,1,1))].">
      <j1 rule="para" parents="13103 2406"/>
    </justification>
  </clause>

  <clause id="13105">
    <literal><![CDATA[
      a(x * a(y,y \ 1,x),z,u) = a(L(x,y \ 1,y),z,u)
    ]]></literal>
    <justification jstring="[para(6890(a,1),13098(a,1,1))].">
      <j1 rule="para" parents="6890 13098"/>
    </justification>
  </clause>

  <clause id="13106">
    <literal><![CDATA[
      a(x * a(y,y \ 1,x),z,u) = a(L(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,8844,a(flip),b,13105,a),flip(a)].">
      <j1 rule="hyper" parents="316 8844 13105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13107">
    <literal><![CDATA[
      a((x \ 1) \ (x \ y),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(9941(a,1),13106(a,1,1))].">
      <j1 rule="para" parents="9941 13106"/>
    </justification>
  </clause>

  <clause id="13108">
    <literal><![CDATA[
      a(L(x * y,x,x),z,u) = a((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),13107(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 13107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13109">
    <literal><![CDATA[
      a(L(x * y,y,y),z,u) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2791,a,b,13108,a)].">
      <j1 rule="hyper" parents="63 2791 13108"/>
    </justification>
  </clause>

  <clause id="13110">
    <literal><![CDATA[
      a(x * a(y \ 1,y,x),z,u) = a(L(x,y,y \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(6890(a,1),13099(a,1,1))].">
      <j1 rule="para" parents="6890 13099"/>
    </justification>
  </clause>

  <clause id="13111">
    <literal><![CDATA[
      a(x \ ((1 / x) \ y),z,u) = a(L(y,x,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(8789(a,1),13110(a,1,1))].">
      <j1 rule="para" parents="8789 13110"/>
    </justification>
  </clause>

  <clause id="13112">
    <literal><![CDATA[
      a(x \ ((x \ 1) \ y),z,u) = a(L(y,x,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4178,a(flip),b,13111,a)].">
      <j1 rule="hyper" parents="63 4178 13111"/>
    </justification>
  </clause>

  <clause id="13113">
    <literal><![CDATA[
      a(x \ ((x \ 1) \ y),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4650,a(flip),b,13112,a),flip(a)].">
      <j1 rule="hyper" parents="316 4650 13112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13114">
    <literal><![CDATA[
      a(L((x \ 1) * y,x,x),z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),13113(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 13113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13115">
    <literal><![CDATA[
      a(L(x * (y \ 1),y,y),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2791,a,b,13114,a)].">
      <j1 rule="hyper" parents="63 2791 13114"/>
    </justification>
  </clause>

  <clause id="13116">
    <literal><![CDATA[
      x \ ((x / (y \ 1)) * (y \ (K(y * x,y \ 1) * L(K(y * x,y \ 1) \ y,z,u)))) = L(x \ ((y \ K(y * x,y \ 1)) \ x),z,u)
    ]]></literal>
    <justification jstring="[para(1252(a,1),5139(a,1,2,2))].">
      <j1 rule="para" parents="1252 5139"/>
    </justification>
  </clause>

  <clause id="13117">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) * ((L(x,y,z) \ u) \ (u * L(u \ (L(x,y,z) \ u),w,v5))) = L(L(x,y,z) \ 1,w,v5) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4279(a,1),5182(a,1,1))].">
      <j1 rule="para" parents="4279 5182"/>
    </justification>
  </clause>

  <clause id="13118">
    <literal><![CDATA[
      K(x \ 1,x) * ((L(x,y,z) \ u) \ (u * L(u \ (L(x,y,z) \ u),w,v5))) = L(L(x,y,z) \ 1,w,v5) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3788(a,1),13117(a,1,1))].">
      <j1 rule="para" parents="3788 13117"/>
    </justification>
  </clause>

  <clause id="13121">
    <literal><![CDATA[
      K(x \ 1,x) * (L(x,y,z) * L(L(x,y,z) \ 1,u,w)) = L(L(x,y,z) \ 1,u,w) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4988(a,1),13118(a,1,2))].">
      <j1 rule="para" parents="4988 13118"/>
    </justification>
  </clause>

  <clause id="13122">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,u,w) * L(x,y,z) = K(x \ 1,x) * L(x * L(x \ 1,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(2133(a,1),13121(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2133 13121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13123">
    <literal><![CDATA[
      L(K(x \ 1,x) * (x * L(x \ 1,y,z)),u,w) = L(L(x,u,w) \ 1,y,z) * L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,4850,a,b,13122,a)].">
      <j1 rule="hyper" parents="316 4850 13122"/>
    </justification>
  </clause>

  <clause id="13124">
    <literal><![CDATA[
      L(x * (K(x \ 1,x) * L(x \ 1,y,z)),u,w) = L(L(x,u,w) \ 1,y,z) * L(x,u,w)
    ]]></literal>
    <justification jstring="[para(1227(a,1),13123(a,1,1))].">
      <j1 rule="para" parents="1227 13123"/>
    </justification>
  </clause>

  <clause id="13125">
    <literal><![CDATA[
      L(x * L(T(x \ 1,x),y,z),u,w) = L(L(x,u,w) \ 1,y,z) * L(x,u,w)
    ]]></literal>
    <justification jstring="[para(4289(a,1),13124(a,1,1,2))].">
      <j1 rule="para" parents="4289 13124"/>
    </justification>
  </clause>

  <clause id="13126">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,u,w) * L(x,y,z) = L(L(x \ 1,u,w) * x,y,z)
    ]]></literal>
    <justification jstring="[para(251(a,1),13125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="251 13125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13127">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * L(L(x,y,z),u,w) = L(L(x \ 1,u,w) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4442,a(flip),b,13126,a)].">
      <j1 rule="hyper" parents="63 4442 13126"/>
    </justification>
  </clause>

  <clause id="13128">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * L(L(x,y,z),u,w) = L((x \ 1) * L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(4442(a,1),13127(a,2,1))].">
      <j1 rule="para" parents="4442 13127"/>
    </justification>
  </clause>

  <clause id="13129">
    <literal><![CDATA[
      K(x,x \ y) \ ((K(x,x \ y) / ((x \ y) / z)) * L((x \ y) / z,u,w)) = ((y / x) / z) \ L(K(x,x \ y) * ((x \ y) / z),u,w)
    ]]></literal>
    <justification jstring="[para(4850(a,2),7119(a,2,2))].">
      <j1 rule="para" parents="4850 7119"/>
    </justification>
  </clause>

  <clause id="13130">
    <literal><![CDATA[
      (x * L(L(y,z,u) \ y,w,v5)) \ x = x \ (L(L(y,z,u) \ y,w,v5) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,166,a(flip),b,8176,a)].">
      <j1 rule="hyper" parents="63 166 8176"/>
    </justification>
  </clause>

  <clause id="13134">
    <literal><![CDATA[
      x \ (y \ ((L(L(z,u,w) \ z,x,y) * (y * x)) / (L(z,u,w) \ z))) = L(a(y,x,z * L(z,u,w)) \ 1,a(y,x,L(z,u,w) \ z),x)
    ]]></literal>
    <justification jstring="[para(2652(a,1),8698(a,2,1,1))].">
      <j1 rule="para" parents="2652 8698"/>
    </justification>
  </clause>

  <clause id="13135">
    <literal><![CDATA[
      a(x,y,a(R(z,u,u),R(z,u,u) * L(u,u,z),R(z,u,u) * L(u,u,z))) = a(x,y,a(z * u,z * u,L(u,u,z)))
    ]]></literal>
    <justification jstring="[para(7155(a,1),8834(a,2,3,2))].">
      <j1 rule="para" parents="7155 8834"/>
    </justification>
  </clause>

  <clause id="13136">
    <literal><![CDATA[
      a(x,y,a(R(z,u,u),R(z,u,u) * L(u,u,z),R(z,u,u) * L(u,u,z))) = a(x,y,a(z * u,z * u,u))
    ]]></literal>
    <justification jstring="[para(9944(a,1),13135(a,2,3))].">
      <j1 rule="para" parents="9944 13135"/>
    </justification>
  </clause>

  <clause id="13137">
    <literal><![CDATA[
      a(x,y,a(R(z,u,u),z * u,R(z,u,u) * L(u,u,z))) = a(x,y,a(z * u,z * u,u))
    ]]></literal>
    <justification jstring="[para(7155(a,1),13136(a,1,3,2))].">
      <j1 rule="para" parents="7155 13136"/>
    </justification>
  </clause>

  <clause id="13139">
    <literal><![CDATA[
      a(x,y,a(R(z,u,u),z * u,z * u)) = a(x,y,a(z * u,z * u,u))
    ]]></literal>
    <justification jstring="[para(7155(a,1),13137(a,1,3,3))].">
      <j1 rule="para" parents="7155 13137"/>
    </justification>
  </clause>

  <clause id="13140">
    <literal><![CDATA[
      a(x,y,a(z,u * z,L(u,z,z))) = a(x,y,a(u * z,u * z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11320,a(flip),b,13139,a)].">
      <j1 rule="hyper" parents="63 11320 13139"/>
    </justification>
  </clause>

  <clause id="13141">
    <literal><![CDATA[
      a(x,y,a(z,u * z,L(u,z,z))) = a(x,y,a(z,z * u,z * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,11274,a(flip),b,13140,a),flip(a)].">
      <j1 rule="hyper" parents="316 11274 13140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13145">
    <literal><![CDATA[
      a(x,T(1 / (1 / y),z),L(1 / (1 / y),u,w)) \ T(1 / (1 / y),z) = L(1 / (K(z,y) / y),L(T(1 / (1 / y),z),u,w),x)
    ]]></literal>
    <justification jstring="[para(5503(a,1),10019(a,1,1))].">
      <j1 rule="para" parents="5503 10019"/>
    </justification>
  </clause>

  <clause id="13147">
    <literal><![CDATA[
      a(x,T(1 / (1 / y),z),L((1 / y) \ 1,u,w)) \ T(1 / (1 / y),z) = L(1 / (K(z,y) / y),L(T(1 / (1 / y),z),u,w),x)
    ]]></literal>
    <justification jstring="[para(5515(a,1),13145(a,1,1))].">
      <j1 rule="para" parents="5515 13145"/>
    </justification>
  </clause>

  <clause id="13148">
    <literal><![CDATA[
      a(x,T(1 / (1 / y),z),L(y,u,w)) \ T(1 / (1 / y),z) = L(1 / (K(z,y) / y),L(T(1 / (1 / y),z),u,w),x)
    ]]></literal>
    <justification jstring="[para(83(a,1),13147(a,1,1,3,1))].">
      <j1 rule="para" parents="83 13147"/>
    </justification>
  </clause>

  <clause id="13149">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),L(T(1 / (1 / y),x),z,u),w) = a(w,1 / (1 / y),L(y,z,u)) \ T(1 / (1 / y),x)
    ]]></literal>
    <justification jstring="[para(11194(a,1),13148(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11194 13148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13151">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),L(T(1 / (1 / y),x),z,u),w) = a(w,y,L(y,z,u)) \ T(1 / (1 / y),x)
    ]]></literal>
    <justification jstring="[para(11197(a,1),13149(a,2,1))].">
      <j1 rule="para" parents="11197 13149"/>
    </justification>
  </clause>

  <clause id="13152">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),L(T(1 / (1 / y),x),z,u),w) = T(a(w,y,L(y,z,u)) \ (1 / (1 / y)),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,5316,a,b,13151,a),flip(a)].">
      <j1 rule="hyper" parents="316 5316 13151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13154">
    <literal><![CDATA[
      (x \ K(y,z)) \ (K(z,y) * ((x * L(x \ K(y,z),u,w)) * v5)) = ((x \ K(y,z)) \ v5) * ((x \ K(y,z)) \ L(x \ K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(10294(a,1),10515(a,1,2,2,1))].">
      <j1 rule="para" parents="10294 10515"/>
    </justification>
  </clause>

  <clause id="13155">
    <literal><![CDATA[
      (x \ K(y,z)) \ (K(z,y) * (K(y,z) * (u * (x \ L(x,w,v5))))) = ((x \ K(y,z)) \ u) * ((x \ K(y,z)) \ L(x \ K(y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(9802(a,1),13154(a,1,2,2))].">
      <j1 rule="para" parents="9802 13154"/>
    </justification>
  </clause>

  <clause id="13156">
    <literal><![CDATA[
      ((x \ K(y,z)) \ u) * ((x \ K(y,z)) \ L(x \ K(y,z),w,v5)) = (x \ K(y,z)) \ (u * (x \ L(x,w,v5)))
    ]]></literal>
    <justification jstring="[para(2995(a,1),13155(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2995 13155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13157">
    <literal><![CDATA[
      ((x \ K(y,z)) \ u) * (x \ (K(y,z) * L(K(y,z) \ x,w,v5))) = (x \ K(y,z)) \ (u * (x \ L(x,w,v5)))
    ]]></literal>
    <justification jstring="[para(1252(a,1),13156(a,1,2))].">
      <j1 rule="para" parents="1252 13156"/>
    </justification>
  </clause>

  <clause id="13159">
    <literal><![CDATA[
      (x \ K(y,z)) \ (u * (x \ L(x,w,v5))) = ((x \ K(y,z)) \ u) * (x \ L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(4842(a,1),13157(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4842 13157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13166">
    <literal><![CDATA[
      ((K(x,y) * ((T(x,y) \ z) * u)) \ w) * (K(x,y) * ((T(x,y) \ z) * u)) = w * K(K(y,x) * (u \ ((T(x,y) \ z) \ w)),(x \ z) * u)
    ]]></literal>
    <justification jstring="[para(6562(a,1),11057(a,2,2))].">
      <j1 rule="para" parents="6562 11057"/>
    </justification>
  </clause>

  <clause id="13167">
    <literal><![CDATA[
      a(x,y,z * (K(u,K(w,v5)) * ((((v6 \ a(v7,v8,v7)) * v9) * v10) * v11))) = a(x,y,z * (v11 * (((a(v7,v8,v7) * v9) * (v6 \ K(u,K(w,v5)))) * v10)))
    ]]></literal>
    <justification jstring="[para(656(a,1),11445(a,1,3,2))].">
      <j1 rule="para" parents="656 11445"/>
    </justification>
  </clause>

  <clause id="13168">
    <literal><![CDATA[
      a(x,y,z) \ (u \ (((a(w,v5,a(x,y,z) \ 1) \ v5) * w) * a(x,y,z))) = (a(x,y,z) \ 1) \ (u \ (w * T(v5 * (a(x,y,z) \ 1),w)))
    ]]></literal>
    <justification jstring="[para(5340(a,2),12713(a,2,2,2,2))].">
      <j1 rule="para" parents="5340 12713"/>
    </justification>
  </clause>

  <clause id="13177">
    <literal><![CDATA[
      L(x \ ((y \ K(y * x,y \ 1)) \ x),z,u) = x \ ((x / (y \ 1)) * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(4842(a,1),13116(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4842 13116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13178">
    <literal><![CDATA[
      x \ ((x / (y \ 1)) * (y \ L(y,z,u))) = L(x \ (x / (y \ 1)),z,u)
    ]]></literal>
    <justification jstring="[para(4206(a,1),13177(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4206 13177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13180">
    <literal><![CDATA[
      K(x,x \ y) \ ((K(x,x \ y) / ((x \ y) / z)) * L((x \ y) / z,u,w)) = ((y / x) / z) \ L((y / x) / z,u,w)
    ]]></literal>
    <justification jstring="[para(2776(a,1),13129(a,2,2,1))].">
      <j1 rule="para" parents="2776 13129"/>
    </justification>
  </clause>

  <clause id="13181">
    <literal><![CDATA[
      K(x,x \ y) \ ((K(x,x \ y) / ((x \ y) / z)) * L((x \ y) / z,u,w)) = (z \ (y / x)) \ L(z \ (y / x),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,5190,a(flip),b,13180,a),flip(a)].">
      <j1 rule="hyper" parents="316 5190 13180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13182">
    <literal><![CDATA[
      K(x,x \ y) \ ((K(x,x \ y) / (z \ (x \ y))) * L(z \ (x \ y),u,w)) = (z \ (y / x)) \ L(z \ (y / x),u,w)
    ]]></literal>
    <justification jstring="[para(10724(a,1),13181(a,1,2))].">
      <j1 rule="para" parents="10724 13181"/>
    </justification>
  </clause>

  <clause id="13183">
    <literal><![CDATA[
      K(x,x \ y) \ (K(x,x \ y) * ((z \ (x \ y)) \ L(z \ (x \ y),u,w))) = (z \ (y / x)) \ L(z \ (y / x),u,w)
    ]]></literal>
    <justification jstring="[para(1461(a,1),13182(a,1,2))].">
      <j1 rule="para" parents="1461 13182"/>
    </justification>
  </clause>

  <clause id="13184">
    <literal><![CDATA[
      (x \ (y / z)) \ L(x \ (y / z),u,w) = (x \ (z \ y)) \ L(x \ (z \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(322,a,13183,a),flip(a)].">
      <j1 rule="hyper" parents="322 13183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13186">
    <literal><![CDATA[
      (x \ (y \ 1)) \ L(x \ (y \ 1),x,y) = a(y,x,x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,11840,a(flip),b,13184,a),flip(a)].">
      <j1 rule="hyper" parents="63 11840 13184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13187">
    <literal><![CDATA[
      (x \ (y \ 1)) \ ((y * x) \ 1) = a(y,x,x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(298(a,1),13186(a,1,2))].">
      <j1 rule="para" parents="298 13186"/>
    </justification>
  </clause>

  <clause id="13188">
    <literal><![CDATA[
      ((x * y) \ 1) \ (y \ (x \ 1)) = a(x,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(39,a,11473,a,b,13187,a(flip))].">
      <j1 rule="hyper" parents="39 11473 13187"/>
    </justification>
  </clause>

  <clause id="13189">
    <literal><![CDATA[
      a(x,y,((z * u) \ (u \ (z \ 1))) * w) = a(x,y,w * a(z,u,u \ z))
    ]]></literal>
    <justification jstring="[para(13188(a,1),6701(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="13188 6701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13190">
    <literal><![CDATA[
      a(x,y,((z * u) \ (u \ z)) * w) = a(x,y,w * a(z,u,u \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5880,a(flip),b,13189,a)].">
      <j1 rule="hyper" parents="63 5880 13189"/>
    </justification>
  </clause>

  <clause id="13191">
    <literal><![CDATA[
      a(x,y,((z * u) \ (u \ z)) * w) = a(x,y,w * a(z,u,z * u))
    ]]></literal>
    <justification jstring="[para(9946(a,1),13190(a,2,3,2))].">
      <j1 rule="para" parents="9946 13190"/>
    </justification>
  </clause>

  <clause id="13192">
    <literal><![CDATA[
      a(x,y,(z * (u \ (z \ u))) * w) = a(x,y,w * a(u,z,u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7699,a(flip),b,13191,a)].">
      <j1 rule="hyper" parents="63 7699 13191"/>
    </justification>
  </clause>

  <clause id="13193">
    <literal><![CDATA[
      a(x,y,z * a(u,w,u * w)) = a(x,y,a(u,w,w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8184,a(flip),b,13192,a),flip(a)].">
      <j1 rule="hyper" parents="63 8184 13192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13194">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * (w \ u))) = a(x,y,a(u,w,w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9947,a,b,13193,a)].">
      <j1 rule="hyper" parents="63 9947 13193"/>
    </justification>
  </clause>

  <clause id="13195">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * L(w,u * z,u \ z)) = a(x,y,(z / u) * ((((u \ z) * u) * u) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,10929,a(flip),b,13194,a),flip(a)].">
      <j1 rule="hyper" parents="63 10929 13194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13196">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * L(w,u * z,u \ z)) = a(x,y,(L(u \ z,u,u) * w) * (z / u))
    ]]></literal>
    <justification jstring="[hyper(316,a,7507,a(flip),b,13195,a),flip(a)].">
      <j1 rule="hyper" parents="316 7507 13195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13197">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * L(w,u * z,u \ z)) = a(x,y,(L(u \ z,u,u) * w) * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5481,a(flip),b,13196,a),flip(a)].">
      <j1 rule="hyper" parents="316 5481 13196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13198">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * L(w,u * z,u \ z)) = a(x,y,((u \ z) * w) * L(u \ z,u,u))
    ]]></literal>
    <justification jstring="[para(4403(a,1),13197(a,2,3))].">
      <j1 rule="para" parents="4403 13197"/>
    </justification>
  </clause>

  <clause id="13199">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * L(w,u * z,u \ z)) = a(x,y,((u \ z) * w) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5867,a(flip),b,13198,a),flip(a)].">
      <j1 rule="hyper" parents="316 5867 13198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13200">
    <literal><![CDATA[
      x \ (y \ ((L(L(z,u,w) \ z,x,y) * (y * x)) / (L(z,u,w) \ z))) = L(a(y,x,z * L(z,u,w)) \ 1,a(y,x,z * L(z,u,w)),x)
    ]]></literal>
    <justification jstring="[para(2652(a,1),13134(a,2,2))].">
      <j1 rule="para" parents="2652 13134"/>
    </justification>
  </clause>

  <clause id="13201">
    <literal><![CDATA[
      x * K(K(y,z) * (u \ ((T(z,y) \ w) \ x)),(z \ w) * u) = (((z \ w) * u) \ x) * (K(z,y) * ((T(z,y) \ w) * u))
    ]]></literal>
    <justification jstring="[para(2902(a,1),13166(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2902 13166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13202">
    <literal><![CDATA[
      x * K(K(y,z) * (u \ ((T(z,y) \ w) \ x)),(z \ w) * u) = (((z \ w) * u) \ x) * ((z \ w) * u)
    ]]></literal>
    <justification jstring="[para(2902(a,1),13201(a,2,2))].">
      <j1 rule="para" parents="2902 13201"/>
    </justification>
  </clause>

  <clause id="13205">
    <literal><![CDATA[
      x * K(K(y,z) * ((u \ (w \ T(z,y))) * x),(z \ w) * u) = (((z \ w) * u) \ x) * ((z \ w) * u)
    ]]></literal>
    <justification jstring="[para(10731(a,1),13202(a,1,2))].">
      <j1 rule="para" parents="10731 13202"/>
    </justification>
  </clause>

  <clause id="13206">
    <literal><![CDATA[
      ((x \ (y * z)) \ u) * (x \ (y * z)) = (((x \ y) * z) \ u) * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11849,a(flip),b,13205,a)].">
      <j1 rule="hyper" parents="63 11849 13205"/>
    </justification>
  </clause>

  <clause id="13207">
    <literal><![CDATA[
      (((x \ y) \ z) \ u) * ((x \ y) \ z) = (((y \ x) * z) \ u) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8126,a,b,13206,a)].">
      <j1 rule="hyper" parents="63 8126 13206"/>
    </justification>
  </clause>

  <clause id="13208">
    <literal><![CDATA[
      (((x \ y) * x) \ z) * ((x \ y) * x) = (T(y,x) \ z) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8134,a(flip),b,13207,a),flip(a)].">
      <j1 rule="hyper" parents="63 8134 13207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13209">
    <literal><![CDATA[
      a(x,y,z * (u * (((a(w,v5,w) * v6) * (v7 \ K(v8,K(v9,v10)))) * v11))) = a(x,y,z * ((((v7 \ a(w,v5,w)) * v6) * v11) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5500,a(flip),b,13167,a),flip(a)].">
      <j1 rule="hyper" parents="63 5500 13167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13211">
    <literal><![CDATA[
      a(x,y,z * (u * ((a(w,v5,w) * (v6 * (v7 \ K(v8,K(v9,v10))))) * v11))) = a(x,y,z * ((((v7 \ a(w,v5,w)) * v6) * v11) * u))
    ]]></literal>
    <justification jstring="[para(4540(a,1),13209(a,1,3,2,2,1))].">
      <j1 rule="para" parents="4540 13209"/>
    </justification>
  </clause>

  <clause id="13212">
    <literal><![CDATA[
      a(x,y,z * (u * (a(w,v5,w) * ((v6 * (v7 \ K(v8,K(v9,v10)))) * v11)))) = a(x,y,z * ((((v7 \ a(w,v5,w)) * v6) * v11) * u))
    ]]></literal>
    <justification jstring="[para(4540(a,1),13211(a,1,3,2,2))].">
      <j1 rule="para" parents="4540 13211"/>
    </justification>
  </clause>

  <clause id="13213">
    <literal><![CDATA[
      a(x,y,(z * ((u * (w \ K(v5,K(v6,v7)))) * v8)) * v9) = a(x,y,v9 * ((((w \ a(v10,v11,v10)) * u) * v8) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8073,a(flip),b,13212,a)].">
      <j1 rule="hyper" parents="63 8073 13212"/>
    </justification>
  </clause>

  <clause id="13215">
    <literal><![CDATA[
      a(x,y,z * ((((u \ a(w,v5,w)) * v6) * v7) * v8)) = a(x,y,(v8 * ((v6 * u) * v7)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11731,a(flip),b,13213,a),flip(a)].">
      <j1 rule="hyper" parents="63 11731 13213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13217">
    <literal><![CDATA[
      a(x,y,z) \ (u \ (((a(w,v5,a(x,y,z) \ 1) \ v5) * w) * a(x,y,z))) = (a(x,y,z) \ 1) \ (u \ ((v5 * (a(x,y,z) \ 1)) * w))
    ]]></literal>
    <justification jstring="[para(114(a,1),13168(a,2,2,2))].">
      <j1 rule="para" parents="114 13168"/>
    </justification>
  </clause>

  <clause id="13218">
    <literal><![CDATA[
      a(x,y,z) \ (u \ (((a(w,v5,a(x,y,z)) \ v5) * w) * a(x,y,z))) = (a(x,y,z) \ 1) \ (u \ ((v5 * (a(x,y,z) \ 1)) * w))
    ]]></literal>
    <justification jstring="[para(2534(a,1),13217(a,1,2,2,1,1,1))].">
      <j1 rule="para" parents="2534 13217"/>
    </justification>
  </clause>

  <clause id="13219">
    <literal><![CDATA[
      a(x,y,z) \ (u \ (w * (T(v5,w) * a(x,y,z)))) = (a(x,y,z) \ 1) \ (u \ ((v5 * (a(x,y,z) \ 1)) * w))
    ]]></literal>
    <justification jstring="[para(8667(a,1),13218(a,1,2,2))].">
      <j1 rule="para" parents="8667 13218"/>
    </justification>
  </clause>

  <clause id="13220">
    <literal><![CDATA[
      a(x,y,z) \ (u \ (w * T(v5 * a(x,y,z),w))) = (a(x,y,z) \ 1) \ (u \ ((v5 * (a(x,y,z) \ 1)) * w))
    ]]></literal>
    <justification jstring="[para(5317(a,2),13219(a,1,2,2,2))].">
      <j1 rule="para" parents="5317 13219"/>
    </justification>
  </clause>

  <clause id="13221">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u \ ((w * (a(x,y,z) \ 1)) * v5)) = a(x,y,z) \ (u \ ((w * a(x,y,z)) * v5))
    ]]></literal>
    <justification jstring="[para(114(a,1),13220(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="114 13220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13222">
    <literal><![CDATA[
      x \ (y \ ((L(L(z,u,w) \ z,x,y) * (y * x)) / (L(z,u,w) \ z))) = x \ (y \ ((y * (x * (z * L(z,u,w)))) / (z * L(z,u,w))))
    ]]></literal>
    <justification jstring="[hyper(316,a,8541,a(flip),b,13200,a),flip(a)].">
      <j1 rule="hyper" parents="316 8541 13200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13223">
    <literal><![CDATA[
      x \ (y \ ((y * (x * (L(z,u,w) \ z))) / (L(z,u,w) \ z))) = x \ (y \ ((y * (x * (z * L(z,u,w)))) / (z * L(z,u,w))))
    ]]></literal>
    <justification jstring="[para(6503(a,1),13222(a,1,2,2,1))].">
      <j1 rule="para" parents="6503 13222"/>
    </justification>
  </clause>

  <clause id="13224">
    <literal><![CDATA[
      x \ (y \ ((y * (x * (z * L(z,u,w)))) / (z * L(z,u,w)))) = a(z \ L(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12718,a(flip),b,13223,a),flip(a)].">
      <j1 rule="hyper" parents="63 12718 13223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13225">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * v5) * T(v6,(a(x,y,z) \ v5) * L(a(x,y,z),u,w)) = v6 * (((v5 / a(x,y,z)) * L(a(x,y,z),u,w)) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(2276(a,1),5351(a,1,2,2,1))].">
      <j1 rule="para" parents="2276 5351"/>
    </justification>
  </clause>

  <clause id="13226">
    <literal><![CDATA[
      (x * ((L(y,z,u) \ y) * w)) / (x * ((w * (K(v5,v6) * (v7 * v7))) * (v7 \ (v7 \ K(v6,v5))))) = L(L(y,z,u) \ y,w * (K(v5,v6) * (v7 * v7)),x)
    ]]></literal>
    <justification jstring="[para(7072(a,1),11784(a,1,2))].">
      <j1 rule="para" parents="7072 11784"/>
    </justification>
  </clause>

  <clause id="13227">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * v5) * T(v6,(a(x,y,z) \ v5) * a(x,y,z)) = v6 * (((v5 / a(x,y,z)) * L(a(x,y,z),u,w)) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(6514(a,1),13225(a,1,2))].">
      <j1 rule="para" parents="6514 13225"/>
    </justification>
  </clause>

  <clause id="13228">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * v5) * T(v6,v5) = v6 * (((v5 / a(x,y,z)) * L(a(x,y,z),u,w)) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(2274(a,1),13227(a,1,2,2))].">
      <j1 rule="para" parents="2274 13227"/>
    </justification>
  </clause>

  <clause id="13230">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * v5) * T(v6,v5) = v6 * (v5 * L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(1436(a,1),13228(a,2,2))].">
      <j1 rule="para" parents="1436 13228"/>
    </justification>
  </clause>

  <clause id="13231">
    <literal><![CDATA[
      (x * ((L(y,z,u) \ y) * w)) / (x * (w * ((K(v5,v6) * (v7 * v7)) * (v7 \ (v7 \ K(v6,v5)))))) = L(L(y,z,u) \ y,w * (K(v5,v6) * (v7 * v7)),x)
    ]]></literal>
    <justification jstring="[para(7072(a,1),13226(a,1,2,2))].">
      <j1 rule="para" parents="7072 13226"/>
    </justification>
  </clause>

  <clause id="13232">
    <literal><![CDATA[
      (x * ((L(y,z,u) \ y) * w)) / (x * (w * (K(v5,v6) * ((v7 * v7) * (v7 \ (v7 \ K(v6,v5))))))) = L(L(y,z,u) \ y,w * (K(v5,v6) * (v7 * v7)),x)
    ]]></literal>
    <justification jstring="[para(406(a,1),13231(a,1,2,2,2))].">
      <j1 rule="para" parents="406 13231"/>
    </justification>
  </clause>

  <clause id="13233">
    <literal><![CDATA[
      (x * ((L(y,z,u) \ y) * w)) / (x * (w * (K(v5,v6) * (v7 * (v7 * (v7 \ (v7 \ K(v6,v5)))))))) = L(L(y,z,u) \ y,w * (K(v5,v6) * (v7 * v7)),x)
    ]]></literal>
    <justification jstring="[para(7072(a,1),13232(a,1,2,2,2,2))].">
      <j1 rule="para" parents="7072 13232"/>
    </justification>
  </clause>

  <clause id="13234">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u * (K(w,v5) * (v6 * v6)),v7) = (v7 * ((L(x,y,z) \ x) * u)) / (v7 * (u * (K(w,v5) * K(v5,w))))
    ]]></literal>
    <justification jstring="[para(76(a,1),13233(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="76 13233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13236">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u * (K(w,v5) * (v6 * v6)),v7) = (v7 * ((L(x,y,z) \ x) * u)) / (v7 * u)
    ]]></literal>
    <justification jstring="[para(2972(a,1),13234(a,2,2,2))].">
      <j1 rule="para" parents="2972 13234"/>
    </justification>
  </clause>

  <clause id="13237">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u * (K(w,v5) * (v6 * v6)),v7) = L(L(x,y,z) \ x,u,v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,6657,a(flip),b,13236,a),flip(a)].">
      <j1 rule="hyper" parents="316 6657 13236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13238">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u * (w * w),v5) = L(L(x,y,z) \ x,u,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10824,a(flip),b,13237,a)].">
      <j1 rule="hyper" parents="63 10824 13237"/>
    </justification>
  </clause>

  <clause id="13239">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u \ 1,w) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(229(a,1),13238(a,1,2)),flip(a)].">
      <j1 rule="para" parents="229 13238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13240">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,x \ u) * u = (L(x,y,z) \ 1) * ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(13239(a,1),11570(a,1,1))].">
      <j1 rule="para" parents="13239 11570"/>
    </justification>
  </clause>

  <clause id="13241">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(x,y,z) \ u) \ u = (u / (L(x,y,z) \ 1)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(13239(a,1),11747(a,1,1))].">
      <j1 rule="para" parents="13239 11747"/>
    </justification>
  </clause>

  <clause id="13242">
    <literal><![CDATA[
      (x \ 1) * (L(L(x,y,z) \ x,x,u) * u) = ((x \ 1) * (L(x \ 1,y,z) \ (x \ 1))) * u
    ]]></literal>
    <justification jstring="[para(13239(a,1),11583(a,1,2,1))].">
      <j1 rule="para" parents="13239 11583"/>
    </justification>
  </clause>

  <clause id="13243">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) * u = (L(x,y,z) \ 1) * ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(9094(a,1),13240(a,1,1))].">
      <j1 rule="para" parents="9094 13240"/>
    </justification>
  </clause>

  <clause id="13244">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ u) = (u / x) * (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,9107,a(flip),b,13243,a),flip(a)].">
      <j1 rule="hyper" parents="63 9107 13243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13245">
    <literal><![CDATA[
      x * ((L(x,y,z) \ 1) * ((x \ 1) \ u)) = (x * (L(x,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[para(13243(a,1),11582(a,1,2))].">
      <j1 rule="para" parents="13243 11582"/>
    </justification>
  </clause>

  <clause id="13246">
    <literal><![CDATA[
      (x / (y \ 1)) * (L(y,z,u) \ 1) = (x / y) * (L(1 / y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,6622,a(flip),b,13244,a)].">
      <j1 rule="hyper" parents="63 6622 13244"/>
    </justification>
  </clause>

  <clause id="13247">
    <literal><![CDATA[
      (L(x,y,y \ 1) \ 1) * ((x \ 1) \ z) = (z / x) * (y \ ((1 / y) \ x))
    ]]></literal>
    <justification jstring="[para(9931(a,1),13244(a,2,2))].">
      <j1 rule="para" parents="9931 13244"/>
    </justification>
  </clause>

  <clause id="13249">
    <literal><![CDATA[
      (x / (L(y,z,u) \ 1)) * (y \ 1) = y * ((L(1 / y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11571,a(flip),b,13241,a),flip(a)].">
      <j1 rule="hyper" parents="63 11571 13241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13250">
    <literal><![CDATA[
      (x * ((L(1 / x,y,z) \ 1) \ u)) / (x \ 1) = u / (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(136,a,11571,a(flip),b,13241,a(flip))].">
      <j1 rule="hyper" parents="136 11571 13241"/>
    </justification>
  </clause>

  <clause id="13251">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ ((x \ 1) * u) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10075,a,b,13249,a)].">
      <j1 rule="hyper" parents="63 10075 13249"/>
    </justification>
  </clause>

  <clause id="13252">
    <literal><![CDATA[
      (x / L(y,z,u)) * L(L(y,z,u),z,u) = y * ((L(1 / y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9893,a,b,13249,a)].">
      <j1 rule="hyper" parents="63 9893 13249"/>
    </justification>
  </clause>

  <clause id="13253">
    <literal><![CDATA[
      (x / (1 / L(y,z,u))) * (1 / y) = y * ((L(1 / y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5177,a,b,13249,a)].">
      <j1 rule="hyper" parents="63 5177 13249"/>
    </justification>
  </clause>

  <clause id="13255">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ (x * u) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9631,a,b,13251,a)].">
      <j1 rule="hyper" parents="63 9631 13251"/>
    </justification>
  </clause>

  <clause id="13256">
    <literal><![CDATA[
      x * ((L(1 / x,y,z) \ 1) \ (u * (L(x,y,z) \ x))) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9666,a(flip),b,13253,a),flip(a)].">
      <j1 rule="hyper" parents="63 9666 13253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13257">
    <literal><![CDATA[
      L(L(x,y,z),y,z) * (L(x,y,z) \ u) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4585,a,b,13252,a)].">
      <j1 rule="hyper" parents="63 4585 13252"/>
    </justification>
  </clause>

  <clause id="13258">
    <literal><![CDATA[
      x * ((((1 / x) * a(1 / x,a(y,z,1 / x),u)) \ 1) \ (w * (L(x,a(y,z,1 / x),u) \ x))) = L(w,x,x \ L(x,a(y,z,1 / x),u))
    ]]></literal>
    <justification jstring="[para(9466(a,2),13256(a,1,2,1,1))].">
      <j1 rule="para" parents="9466 13256"/>
    </justification>
  </clause>

  <clause id="13260">
    <literal><![CDATA[
      (x \ 1) * (L(L(x,y,z) \ x,x,u) * u) = (L(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[para(7088(a,1),13242(a,2,1))].">
      <j1 rule="para" parents="7088 13242"/>
    </justification>
  </clause>

  <clause id="13261">
    <literal><![CDATA[
      (x \ 1) * ((y / x) * (L(1 / x,z,u) \ 1)) = (L(x,z,u) \ 1) * y
    ]]></literal>
    <justification jstring="[para(9107(a,1),13260(a,1,2))].">
      <j1 rule="para" parents="9107 13260"/>
    </justification>
  </clause>

  <clause id="13262">
    <literal><![CDATA[
      (x \ 1) * ((L(x,y,z) \ x) * z) = (L(x,y,z) \ 1) * z
    ]]></literal>
    <justification jstring="[para(9861(a,1),13260(a,1,2,1))].">
      <j1 rule="para" parents="9861 13260"/>
    </justification>
  </clause>

  <clause id="13263">
    <literal><![CDATA[
      (L(x,x,y) \ 1) * y = (x \ 1) * R(y,x,x)
    ]]></literal>
    <justification jstring="[para(7295(a,1),13262(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7295 13262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13264">
    <literal><![CDATA[
      a(x,y,z \ (((R(u,w,w) * w) \ v5) \ v6)) = a(x,y,z \ ((((L(w,w,u) \ 1) * u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(13263(a,2),10698(a,1,3,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13263 10698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13265">
    <literal><![CDATA[
      (x \ 1) \ ((L(x,y,z) \ 1) * u) = (u / x) * (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,13261,a)].">
      <j1 rule="hyper" parents="144 13261"/>
    </justification>
  </clause>

  <clause id="13266">
    <literal><![CDATA[
      (x \ 1) \ ((L(x,y,z) \ 1) * u) = (L(x,y,z) \ 1) * ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,13244,a,b,13265,a),flip(a)].">
      <j1 rule="hyper" parents="316 13244 13265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13267">
    <literal><![CDATA[
      ((x / y) * (L(1 / y,y,z) \ 1)) \ (x * a(z,y,y)) = a(x,y,a(z,y,y))
    ]]></literal>
    <justification jstring="[para(13265(a,1),12836(a,1,1))].">
      <j1 rule="para" parents="13265 12836"/>
    </justification>
  </clause>

  <clause id="13268">
    <literal><![CDATA[
      a(x,y,z \ (((R(u,w,w) * w) \ v5) \ v6)) = a(x,y,z \ (((u * L(w,w,u)) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,10698,a(flip),b,13264,a),flip(a)].">
      <j1 rule="hyper" parents="316 10698 13264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13269">
    <literal><![CDATA[
      a(x,y,z \ (((R(u,w,w) * w) \ v5) \ v6)) = a(x,y,z \ (((u / (w \ 1)) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(1445(a,1),13268(a,2,3,2,1,1))].">
      <j1 rule="para" parents="1445 13268"/>
    </justification>
  </clause>

  <clause id="13270">
    <literal><![CDATA[
      a(x,y,z \ (((R(u,w,w) * w) \ v5) \ v6)) = a(x,y,z \ ((((w \ 1) \ u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,5926,a(flip),b,13269,a),flip(a)].">
      <j1 rule="hyper" parents="316 5926 13269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13271">
    <literal><![CDATA[
      a(x,y,z \ (((R(u,w,w) * w) \ v5) \ v6)) = a(x,y,z \ (((w \ u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,11929,a(flip),b,13270,a),flip(a)].">
      <j1 rule="hyper" parents="316 11929 13270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13272">
    <literal><![CDATA[
      a(x,y,z \ (((u \ (u \ w)) \ v5) \ v6)) = a(x,y,z \ ((R(w,u,u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,12577,a(flip),b,13271,a),flip(a)].">
      <j1 rule="hyper" parents="63 12577 13271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13273">
    <literal><![CDATA[
      a(x,y,z \ ((L(1 / u,w,w) \ v5) \ v6)) = a(x,y,z \ ((R(u,w,w) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,12230,a,b,13272,a)].">
      <j1 rule="hyper" parents="63 12230 13272"/>
    </justification>
  </clause>

  <clause id="13274">
    <literal><![CDATA[
      a(x,y,z \ (((a(u,u,w) * w) \ v5) \ v6)) = a(x,y,z \ ((R(w,u,u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,11931,a(flip),b,13273,a)].">
      <j1 rule="hyper" parents="63 11931 13273"/>
    </justification>
  </clause>

  <clause id="13275">
    <literal><![CDATA[
      x * ((((1 / x) * a(1 / x,a(y,z,x),u)) \ 1) \ (w * (L(x,a(y,z,1 / x),u) \ x))) = L(w,x,x \ L(x,a(y,z,1 / x),u))
    ]]></literal>
    <justification jstring="[para(2535(a,1),13258(a,1,2,1,1,2,2))].">
      <j1 rule="para" parents="2535 13258"/>
    </justification>
  </clause>

  <clause id="13276">
    <literal><![CDATA[
      x * ((((1 / x) * a(x \ 1,a(y,z,x),u)) \ 1) \ (w * (L(x,a(y,z,1 / x),u) \ x))) = L(w,x,x \ L(x,a(y,z,1 / x),u))
    ]]></literal>
    <justification jstring="[para(1808(a,1),13275(a,1,2,1,1,2))].">
      <j1 rule="para" parents="1808 13275"/>
    </justification>
  </clause>

  <clause id="13277">
    <literal><![CDATA[
      x * ((((1 / x) * a(x,a(y,z,x),u)) \ 1) \ (w * (L(x,a(y,z,1 / x),u) \ x))) = L(w,x,x \ L(x,a(y,z,1 / x),u))
    ]]></literal>
    <justification jstring="[para(11106(a,1),13276(a,1,2,1,1,2))].">
      <j1 rule="para" parents="11106 13276"/>
    </justification>
  </clause>

  <clause id="13278">
    <literal><![CDATA[
      x * (((a(x,a(y,z,x),u) / x) \ 1) \ (w * (L(x,a(y,z,1 / x),u) \ x))) = L(w,x,x \ L(x,a(y,z,1 / x),u))
    ]]></literal>
    <justification jstring="[para(8428(a,1),13277(a,1,2,1,1))].">
      <j1 rule="para" parents="8428 13277"/>
    </justification>
  </clause>

  <clause id="13279">
    <literal><![CDATA[
      x * ((a(y,x,a(z,u,x)) * x) \ (w * (L(x,a(z,u,1 / x),y) \ x))) = L(w,x,x \ L(x,a(z,u,1 / x),y))
    ]]></literal>
    <justification jstring="[para(11130(a,1),13278(a,1,2,1))].">
      <j1 rule="para" parents="11130 13278"/>
    </justification>
  </clause>

  <clause id="13280">
    <literal><![CDATA[
      x * ((a(y,x,a(z,u,x)) * x) \ (w * (L(x,a(z,u,x),y) \ x))) = L(w,x,x \ L(x,a(z,u,1 / x),y))
    ]]></literal>
    <justification jstring="[para(2535(a,1),13279(a,1,2,2,2,1,2))].">
      <j1 rule="para" parents="2535 13279"/>
    </justification>
  </clause>

  <clause id="13281">
    <literal><![CDATA[
      x * ((a(y,x,a(z,u,x)) * x) \ (w * a(y,x,a(z,u,x)))) = L(w,x,x \ L(x,a(z,u,1 / x),y))
    ]]></literal>
    <justification jstring="[para(9472(a,1),13280(a,1,2,2,2))].">
      <j1 rule="para" parents="9472 13280"/>
    </justification>
  </clause>

  <clause id="13282">
    <literal><![CDATA[
      L(x,y,y \ L(y,a(z,u,1 / y),w)) = y * L(y \ x,y,a(w,y,a(z,u,y)))
    ]]></literal>
    <justification jstring="[para(2299(a,2),13281(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2299 13281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13283">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,x,a(u,w,x))) = L(y,x,x \ L(x,a(u,w,x),z))
    ]]></literal>
    <justification jstring="[para(2535(a,1),13282(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="2535 13282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13284">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,x,a(u,w,x))) = L(y,x,a(x,a(u,w,x),z))
    ]]></literal>
    <justification jstring="[para(9468(a,1),13283(a,2,3))].">
      <j1 rule="para" parents="9468 13283"/>
    </justification>
  </clause>

  <clause id="13285">
    <literal><![CDATA[
      ((x * (a(y,z,u) \ 1)) * w) / (w * T(x,u \ L(u,z,y))) = R((a(y,z,u) \ 1) * K(x,w),T(x,u \ L(u,z,y)),w)
    ]]></literal>
    <justification jstring="[para(4992(a,1),5221(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4992 5221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13286">
    <literal><![CDATA[
      ((x * (a(y,z,u) \ 1)) * w) / (w * T(x,u \ L(u,z,y))) = R(a(y,z,u) \ K(x,w),T(x,u \ L(u,z,y)),w)
    ]]></literal>
    <justification jstring="[para(3780(a,1),13285(a,2,1))].">
      <j1 rule="para" parents="3780 13285"/>
    </justification>
  </clause>

  <clause id="13287">
    <literal><![CDATA[
      ((x * (a(y,z,u) \ 1)) * w) / (w * T(x,u \ L(u,z,y))) = R(a(y,z,u) \ K(x,w),x,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,10738,a(flip),b,13286,a),flip(a)].">
      <j1 rule="hyper" parents="316 10738 13286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13289">
    <literal><![CDATA[
      ((x * (a(y,z,u) \ 1)) * w) / (w * x) = R(a(y,z,u) \ K(x,w),x,w)
    ]]></literal>
    <justification jstring="[para(4992(a,1),13287(a,1,2,2))].">
      <j1 rule="para" parents="4992 13287"/>
    </justification>
  </clause>

  <clause id="13290">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) * R(a(y,z,u) \ K(w,x),w,x) = L(a(y,z,u) \ 1,w,x)
    ]]></literal>
    <justification jstring="[para(13289(a,1),9065(a,1,2))].">
      <j1 rule="para" parents="13289 9065"/>
    </justification>
  </clause>

  <clause id="13291">
    <literal><![CDATA[
      R(K(x,a(y,z,u) \ w) * (a(y,z,u) \ K(w,x)),w,x) = L(a(y,z,u) \ 1,w,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1028,a,b,13290,a)].">
      <j1 rule="hyper" parents="63 1028 13290"/>
    </justification>
  </clause>

  <clause id="13292">
    <literal><![CDATA[
      R(K(x,y) * (a(z,u,w) \ K(y,x)),y,x) = L(a(z,u,w) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(5290(a,1),13291(a,1,1,1))].">
      <j1 rule="para" parents="5290 13291"/>
    </justification>
  </clause>

  <clause id="13293">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u,w) = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(2980(a,1),13292(a,1,1))].">
      <j1 rule="para" parents="2980 13292"/>
    </justification>
  </clause>

  <clause id="13295">
    <literal><![CDATA[
      x \ ((y * (a(z,u,w) \ 1)) * (y \ x)) = L(a(z,u,w) \ 1,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12686,a,b,13293,a)].">
      <j1 rule="hyper" parents="63 12686 13293"/>
    </justification>
  </clause>

  <clause id="13296">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w * (v5 \ 1)) = R(a(x,y,z) \ 1,u,w * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,1711,a(flip),b,13293,a),flip(a)].">
      <j1 rule="hyper" parents="63 1711 13293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13297">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w \ 1) = R(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1033,a(flip),b,13293,a),flip(a)].">
      <j1 rule="hyper" parents="63 1033 13293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13299">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w \ 1) = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,13293,a(flip),b,13297,a),flip(a)].">
      <j1 rule="hyper" parents="316 13293 13297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13300">
    <literal><![CDATA[
      1 / L(a(x,y,z) \ 1,u,u * (a(x,y,z) \ 1)) = (1 / (u * (a(x,y,z) \ 1))) * u
    ]]></literal>
    <justification jstring="[hyper(209,a,13299,a(flip),b,1604,a(flip))].">
      <j1 rule="hyper" parents="209 13299 1604"/>
    </justification>
  </clause>

  <clause id="13301">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w * (v5 \ 1)) = L(a(x,y,z) \ 1,u,w * v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,13293,a(flip),b,13296,a),flip(a)].">
      <j1 rule="hyper" parents="316 13293 13296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13302">
    <literal><![CDATA[
      1 / L(a(x,y,z) \ 1,u,u * a(x,y,z)) = (1 / (u * (a(x,y,z) \ 1))) * u
    ]]></literal>
    <justification jstring="[para(13301(a,1),13300(a,1,2))].">
      <j1 rule="para" parents="13301 13300"/>
    </justification>
  </clause>

  <clause id="13303">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,u * a(x,y,z)) \ 1 = (1 / (u * (a(x,y,z) \ 1))) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,5002,a(flip),b,13302,a)].">
      <j1 rule="hyper" parents="63 5002 13302"/>
    </justification>
  </clause>

  <clause id="13309">
    <literal><![CDATA[
      L(x,y,z) \ (L(x \ L(x,u,w),x \ L(x,u,w),v5) * v5) = (x \ L(x,u,w)) \ (L(x,y,z) \ (((x \ L(x,u,w)) * (x \ L(x,u,w))) * v5))
    ]]></literal>
    <justification jstring="[para(8380(a,1),8094(a,1,2,1))].">
      <j1 rule="para" parents="8380 8094"/>
    </justification>
  </clause>

  <clause id="13310">
    <literal><![CDATA[
      x * (((L(x,y,y) \ z) * x) \ (a(y,y,x) * ((L(x,y,y) \ z) * L(x,y,y)))) = (z / L(x,y,y)) \ (z * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(4953(a,1),8560(a,1,1))].">
      <j1 rule="para" parents="4953 8560"/>
    </justification>
  </clause>

  <clause id="13311">
    <literal><![CDATA[
      x * (((L(x,y,y) \ z) * x) \ (a(y,y,x) * ((x \ z) * x))) = (z / L(x,y,y)) \ (z * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(4409(a,1),13310(a,1,2,2,2))].">
      <j1 rule="para" parents="4409 13310"/>
    </justification>
  </clause>

  <clause id="13313">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (x \ (((L(y,z,u) / x) \ (y * (L(y,z,u) * L(y,z,u)))) / (y * L(y,z,u)))) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[para(3329(a,1),8909(a,1,2,2,1))].">
      <j1 rule="para" parents="3329 8909"/>
    </justification>
  </clause>

  <clause id="13314">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (x \ (((L(y,z,u) / x) \ (y * (y * L(L(y,z,u),z,u)))) / (y * L(y,z,u)))) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[para(9956(a,1),13313(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="9956 13313"/>
    </justification>
  </clause>

  <clause id="13315">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (x \ (((L(y,z,u) / x) \ L(y * (y * L(y,z,u)),z,u)) / (y * L(y,z,u)))) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[para(1367(a,2),13314(a,1,2,2,1,2))].">
      <j1 rule="para" parents="1367 13314"/>
    </justification>
  </clause>

  <clause id="13316">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (x \ (((L(y,z,u) / x) \ L(L(y * (y * y),z,u),z,u)) / (y * L(y,z,u)))) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[para(1367(a,2),13315(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="1367 13315"/>
    </justification>
  </clause>

  <clause id="13317">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (x \ ((((L(y,z,u) / x) \ L(L(y,z,u),z,u)) * (y * y)) / (y * L(y,z,u)))) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[para(1109(a,1),13316(a,1,2,2,1))].">
      <j1 rule="para" parents="1109 13316"/>
    </justification>
  </clause>

  <clause id="13318">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (x \ ((((y / x) \ L(y,z,u)) * (y * y)) / (y * L(y,z,u)))) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[para(12532(a,1),13317(a,1,2,2,1,1))].">
      <j1 rule="para" parents="12532 13317"/>
    </justification>
  </clause>

  <clause id="13319">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (x \ (((y / x) \ L(y,z,u)) / ((y * L(y,z,u)) / (y * y)))) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[para(676(a,1),13318(a,1,2,2))].">
      <j1 rule="para" parents="676 13318"/>
    </justification>
  </clause>

  <clause id="13320">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (x \ (((y / x) \ L(y,z,u)) / (y * (L(y,z,u) / (y * y))))) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[para(683(a,1),13319(a,1,2,2,2))].">
      <j1 rule="para" parents="683 13319"/>
    </justification>
  </clause>

  <clause id="13321">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (x \ (((y / x) \ L(y,z,u)) / (y * L(y \ 1,z,u)))) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[para(1110(a,1),13320(a,1,2,2,2,2))].">
      <j1 rule="para" parents="1110 13320"/>
    </justification>
  </clause>

  <clause id="13322">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (x \ (((y / x) \ L(y,z,u)) / (y \ L(y,z,u)))) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[para(1064(a,1),13321(a,1,2,2,2))].">
      <j1 rule="para" parents="1064 13321"/>
    </justification>
  </clause>

  <clause id="13323">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (x \ ((y \ L(y,z,u)) \ ((y / x) \ L(y,z,u)))) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[para(5015(a,1),13322(a,1,2,2))].">
      <j1 rule="para" parents="5015 13322"/>
    </justification>
  </clause>

  <clause id="13324">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * a(x,x,y * L(y,z,u)) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[para(12584(a,1),13323(a,1,2))].">
      <j1 rule="para" parents="12584 13323"/>
    </justification>
  </clause>

  <clause id="13325">
    <literal><![CDATA[
      x * (a(x,x,y * L(y,z,u)) * (L(y,z,u) \ y)) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,8412,a(flip),b,13324,a)].">
      <j1 rule="hyper" parents="63 8412 13324"/>
    </justification>
  </clause>

  <clause id="13326">
    <literal><![CDATA[
      (1 / x) \ (L(y,z,u) \ y) = (L(y,z,u) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,12891,a(flip),b,13325,a)].">
      <j1 rule="hyper" parents="63 12891 13325"/>
    </justification>
  </clause>

  <clause id="13328">
    <literal><![CDATA[
      ((L(x,y,z) \ x) / (1 / u)) \ 1 = 1 / ((L(x,y,z) / u) \ x)
    ]]></literal>
    <justification jstring="[hyper(209,a,13326,a(flip),b,11547,a),flip(a)].">
      <j1 rule="hyper" parents="209 13326 11547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13329">
    <literal><![CDATA[
      (L(x,y,z) / (u \ 1)) \ x = u \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(80(a,1),13326(a,1,1)),flip(a)].">
      <j1 rule="para" parents="80 13326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13333">
    <literal><![CDATA[
      x \ (L(R(y,x,x),z,u) \ R(y,x,x)) = (L(y,z,u) * x) \ R(y,x,x)
    ]]></literal>
    <justification jstring="[para(571(a,1),13329(a,1,1)),flip(a)].">
      <j1 rule="para" parents="571 13329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13340">
    <literal><![CDATA[
      (x \ y) * (L(z * (L(z,u,w) \ z),u,w) * L((z * (L(z,u,w) \ z)) \ 1,u,w)) = x \ ((z * L(L(z \ 1,u,w),u,w)) * y)
    ]]></literal>
    <justification jstring="[para(4459(a,1),9881(a,2,2,1,2,1))].">
      <j1 rule="para" parents="4459 9881"/>
    </justification>
  </clause>

  <clause id="13341">
    <literal><![CDATA[
      (x \ y) * (L(z * (L(z,u,w) \ z),u,w) * L((z * (L(z,u,w) \ z)) \ 1,u,w)) = x \ ((z \ L(L(z,u,w),u,w)) * y)
    ]]></literal>
    <justification jstring="[para(1372(a,1),13340(a,2,2,1))].">
      <j1 rule="para" parents="1372 13340"/>
    </justification>
  </clause>

  <clause id="13342">
    <literal><![CDATA[
      (x \ y) * (z * L((z * (L(z,u,w) \ z)) \ 1,u,w)) = x \ ((z \ L(L(z,u,w),u,w)) * y)
    ]]></literal>
    <justification jstring="[para(9863(a,1),13341(a,1,2,1))].">
      <j1 rule="para" parents="9863 13341"/>
    </justification>
  </clause>

  <clause id="13343">
    <literal><![CDATA[
      (x \ y) * (z * L(L(z \ 1,u,w),u,w)) = x \ ((z \ L(L(z,u,w),u,w)) * y)
    ]]></literal>
    <justification jstring="[para(4459(a,1),13342(a,1,2,2,1))].">
      <j1 rule="para" parents="4459 13342"/>
    </justification>
  </clause>

  <clause id="13344">
    <literal><![CDATA[
      x \ ((y \ L(L(y,z,u),z,u)) * w) = (x \ w) * (y \ L(L(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[para(1372(a,1),13343(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1372 13343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13345">
    <literal><![CDATA[
      (x \ L(T(y,z),u,w)) * (T(y,z) \ L(L(y,v5,v6),v5,v6)) = x \ ((y \ L(L(y,v5,v6),v5,v6)) * L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,10280,a,b,13344,a)].">
      <j1 rule="hyper" parents="316 10280 13344"/>
    </justification>
  </clause>

  <clause id="13346">
    <literal><![CDATA[
      (x \ L(T(y,z),u,w)) * (T(y,z) \ L(L(y,v5,v6),v5,v6)) = x \ L(y * (y \ L(L(y,v5,v6),v5,v6)),u,w)
    ]]></literal>
    <justification jstring="[para(10086(a,2),13345(a,2,2))].">
      <j1 rule="para" parents="10086 13345"/>
    </justification>
  </clause>

  <clause id="13347">
    <literal><![CDATA[
      (x \ L(T(y,z),u,w)) * (T(y,z) \ L(L(y,v5,v6),v5,v6)) = x \ L(L(L(y,v5,v6),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),13346(a,2,2,1))].">
      <j1 rule="para" parents="10 13346"/>
    </justification>
  </clause>

  <clause id="13349">
    <literal><![CDATA[
      L(L(x,y,z),y,z) * (u \ L(x,w,v5)) = x * (u \ L(L(L(x,y,z),y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(13347(a,1),10658(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13347 10658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13350">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ L(L(L(x,y,z),y,z),u,w) = x \ L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(375,a,13349,a),flip(a)].">
      <j1 rule="hyper" parents="375 13349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13351">
    <literal><![CDATA[
      L(L(x,y,z) \ L(L(x,y,z),u,w),y,z) = x \ L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2136,a(flip),b,13350,a)].">
      <j1 rule="hyper" parents="63 2136 13350"/>
    </justification>
  </clause>

  <clause id="13353">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),u,w) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2141,a(flip),b,13351,a)].">
      <j1 rule="hyper" parents="63 2141 13351"/>
    </justification>
  </clause>

  <clause id="13354">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,y) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(41,a,9997,a,b,13353,a),flip(a)].">
      <j1 rule="hyper" parents="41 9997 13353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13355">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z))) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(41,a,9863,a,b,13353,a)].">
      <j1 rule="hyper" parents="41 9863 13353"/>
    </justification>
  </clause>

  <clause id="13357">
    <literal><![CDATA[
      x * (y * L(z \ L(z,u,w),y,x)) = (x * y) * (z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,13353,a(flip),b,18,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 13353 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13362">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ 1,u,w) = L(x \ L(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(13353(a,1),9873(a,1,1,1))].">
      <j1 rule="para" parents="13353 9873"/>
    </justification>
  </clause>

  <clause id="13364">
    <literal><![CDATA[
      L(x \ L(x,x * y,z),x,y) = a(z,x * y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,7106,a(flip),b,13354,a)].">
      <j1 rule="hyper" parents="63 7106 13354"/>
    </justification>
  </clause>

  <clause id="13365">
    <literal><![CDATA[
      x \ ((x / y) * L(y,x,z)) = a(z,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,7101,a(flip),b,13354,a)].">
      <j1 rule="hyper" parents="63 7101 13354"/>
    </justification>
  </clause>

  <clause id="13366">
    <literal><![CDATA[
      x \ (y * L(y \ x,x,z)) = a(z,x,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,7100,a(flip),b,13354,a)].">
      <j1 rule="hyper" parents="63 7100 13354"/>
    </justification>
  </clause>

  <clause id="13368">
    <literal><![CDATA[
      (x \ y) \ ((z * x) \ (z * y)) = a(z,x,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1258,a,b,13366,a)].">
      <j1 rule="hyper" parents="63 1258 13366"/>
    </justification>
  </clause>

  <clause id="13369">
    <literal><![CDATA[
      a(x,y,x \ y) = a(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(39,a,9981,a(flip),b,13366,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 9981 13366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13370">
    <literal><![CDATA[
      a(x,y * x,x \ (y * x)) = a(x,y * x,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,5826,a(flip),b,13369,a),flip(a)].">
      <j1 rule="hyper" parents="316 5826 13369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13372">
    <literal><![CDATA[
      ((x * y) \ (x * z)) \ (y \ z) = a(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(39,a,5225,a,b,13368,a(flip))].">
      <j1 rule="hyper" parents="39 5225 13368"/>
    </justification>
  </clause>

  <clause id="13373">
    <literal><![CDATA[
      a(x,y * x,L(y,x,x)) = a(x,y * x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5478,a(flip),b,13370,a),flip(a)].">
      <j1 rule="hyper" parents="63 5478 13370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13375">
    <literal><![CDATA[
      a(x,y,a(z,z * u,z * u)) = a(x,y,a(z,u * z,u))
    ]]></literal>
    <justification jstring="[para(13373(a,1),13141(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13373 13141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13376">
    <literal><![CDATA[
      a(x,y,a(z,u * z,u * z)) = a(x,y,a(u,z * u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8833,a,b,13375,a)].">
      <j1 rule="hyper" parents="63 8833 13375"/>
    </justification>
  </clause>

  <clause id="13378">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ 1 = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(1894(a,1),13362(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1894 13362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13379">
    <literal><![CDATA[
      L(x \ L(x,y,z),u * w,v5) \ 1 = L(L(x,y,z) \ x,w * u,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,10797,a,b,13378,a),flip(a)].">
      <j1 rule="hyper" parents="316 10797 13378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13380">
    <literal><![CDATA[
      x \ (y * ((y \ x) * (L(z,u,w) \ z))) = L(z \ L(z,u,w),y \ x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,101,a,b,13378,a)].">
      <j1 rule="hyper" parents="316 101 13378"/>
    </justification>
  </clause>

  <clause id="13381">
    <literal><![CDATA[
      L(R(x,y,z),u,w) \ R(x,y,z) = L(L(x,u,w) \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8395,a,b,13378,a)].">
      <j1 rule="hyper" parents="63 8395 13378"/>
    </justification>
  </clause>

  <clause id="13382">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(x,u,w) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2148,a,b,13378,a)].">
      <j1 rule="hyper" parents="63 2148 13378"/>
    </justification>
  </clause>

  <clause id="13383">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(x,y,z) = L(L(x,u,w) \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2143,a,b,13378,a)].">
      <j1 rule="hyper" parents="63 2143 13378"/>
    </justification>
  </clause>

  <clause id="13384">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) = (u \ ((u / x) * L(x,y,z))) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,7102,a(flip),b,13378,a),flip(a)].">
      <j1 rule="hyper" parents="63 7102 13378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13390">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ 1 = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(13378(a,1),5041(a,1,1))].">
      <j1 rule="para" parents="13378 5041"/>
    </justification>
  </clause>

  <clause id="13391">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,z * y) = ((z * y) \ ((z * (y * x)) / x)) \ 1
    ]]></literal>
    <justification jstring="[para(7099(a,1),13378(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7099 13378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13392">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ x = x * L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(13378(a,1),7211(a,1,1))].">
      <j1 rule="para" parents="13378 7211"/>
    </justification>
  </clause>

  <clause id="13395">
    <literal><![CDATA[
      R(x,y,z) * L(L(x,u,w) \ x,y,z) = L(1 / R(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(13378(a,1),8675(a,1,2))].">
      <j1 rule="para" parents="13378 8675"/>
    </justification>
  </clause>

  <clause id="13396">
    <literal><![CDATA[
      L(L(x * a(y,z,z),z,y) \ (x * a(y,z,z)),u,w) = L(x \ L(x,z,y),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(9291(a,1),13378(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9291 13378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13398">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,w) = L(x,u,w) * (L(x \ L(x,u,w),y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(13378(a,1),9672(a,1,2))].">
      <j1 rule="para" parents="13378 9672"/>
    </justification>
  </clause>

  <clause id="13399">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),u,w) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(13378(a,1),9883(a,1,1))].">
      <j1 rule="para" parents="13378 9883"/>
    </justification>
  </clause>

  <clause id="13400">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,x,u) = a(u,x,x * L(x,y,z)) * x
    ]]></literal>
    <justification jstring="[para(13378(a,1),10058(a,1,2))].">
      <j1 rule="para" parents="13378 10058"/>
    </justification>
  </clause>

  <clause id="13401">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),L(x \ L(x,y,z),u,w),v5) = (v5 * L(L(x,y,z) \ x,u,w)) \ v5
    ]]></literal>
    <justification jstring="[para(13378(a,1),12652(a,2,1,2))].">
      <j1 rule="para" parents="13378 12652"/>
    </justification>
  </clause>

  <clause id="13403">
    <literal><![CDATA[
      L(a(x,y,z),z,y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,10006,a(flip),b,13399,a)].">
      <j1 rule="hyper" parents="63 10006 13399"/>
    </justification>
  </clause>

  <clause id="13404">
    <literal><![CDATA[
      a(x,y,z) * a(z,a(x,y,z),y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,11611,a,b,13403,a)].">
      <j1 rule="hyper" parents="63 11611 13403"/>
    </justification>
  </clause>

  <clause id="13405">
    <literal><![CDATA[
      L(a(x,y,R(z,u,w) \ v5),L(z,u,w) \ v5,y) = L(R(z,u,w) \ v5,y,x) \ (R(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,12609,a(flip),b,13403,a)].">
      <j1 rule="hyper" parents="63 12609 13403"/>
    </justification>
  </clause>

  <clause id="13406">
    <literal><![CDATA[
      L(a(x,y,(z * u) \ ((z * w) * u)),L(w,z,u),y) = L((z * u) \ ((z * w) * u),y,x) \ ((z * u) \ ((z * w) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10942,a(flip),b,13403,a)].">
      <j1 rule="hyper" parents="63 10942 13403"/>
    </justification>
  </clause>

  <clause id="13407">
    <literal><![CDATA[
      L(a(x,y,z \ R(z,u,w)),z \ L(z,u,w),y) = L(z \ R(z,u,w),y,x) \ (z \ R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9850,a(flip),b,13403,a)].">
      <j1 rule="hyper" parents="63 9850 13403"/>
    </justification>
  </clause>

  <clause id="13408">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),z,y) = L(L(z,y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(13403(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13403 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13409">
    <literal><![CDATA[
      L(a(x,y,z * L(z,u,w)),z \ L(z,u,w),y) = L(z \ L(z,u,w),y,x) \ (z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(5566(a,1),13403(a,1,1))].">
      <j1 rule="para" parents="5566 13403"/>
    </justification>
  </clause>

  <clause id="13410">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * L(a(z,u,w),w,u)) = (a(x,y,a(z,u,w)) * v5) * (L(w,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(13403(a,1),6870(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13403 6870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13411">
    <literal><![CDATA[
      L(a(x,y,z * L(u,w,v5)),z * R(u,w,v5),y) = L(z * R(u,w,v5),y,x) \ (z * R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(7272(a,1),13403(a,1,1))].">
      <j1 rule="para" parents="7272 13403"/>
    </justification>
  </clause>

  <clause id="13412">
    <literal><![CDATA[
      L(a(x,y,z \ L(u,w,v5)),z \ R(u,w,v5),y) = L(z \ R(u,w,v5),y,x) \ (z \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(10648(a,1),13403(a,1,1))].">
      <j1 rule="para" parents="10648 13403"/>
    </justification>
  </clause>

  <clause id="13413">
    <literal><![CDATA[
      L(a(x,y,L(L(y,z,u),w,v5)),y,L(L(y,w,v5),z,u)) = L(y,L(L(y,w,v5),z,u),x) \ y
    ]]></literal>
    <justification jstring="[para(12380(a,1),13403(a,1,1))].">
      <j1 rule="para" parents="12380 13403"/>
    </justification>
  </clause>

  <clause id="13415">
    <literal><![CDATA[
      a(x,a(y,z,x),z) = a(z,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(34,a,9952,a,b,13404,a),flip(a)].">
      <j1 rule="hyper" parents="34 9952 13404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13416">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,z) * (z \ L(z,y,x))) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[para(11625(a,2),13404(a,1,2))].">
      <j1 rule="para" parents="11625 13404"/>
    </justification>
  </clause>

  <clause id="13417">
    <literal><![CDATA[
      x * a(y,x,a(z,y,x)) = L(x,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(139,a,13415,a(flip),b,9468,a)].">
      <j1 rule="hyper" parents="139 13415 9468"/>
    </justification>
  </clause>

  <clause id="13419">
    <literal><![CDATA[
      L(L(a(a(x,y,z),u,T(w,u)),v5,v6),T(w,u),u) = L(((u * a(x,y,z)) \ (a(x,y,z) * (w * u))) \ T(w,u),v5,v6)
    ]]></literal>
    <justification jstring="[para(2355(a,2),13408(a,2,1,1))].">
      <j1 rule="para" parents="2355 13408"/>
    </justification>
  </clause>

  <clause id="13420">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),a(y,z,L(a(x,y,z),u,w)),z) \ L(L(z,y,x) \ z,u,w) = a(y,z,L(a(x,y,z),u,w)) \ 1
    ]]></literal>
    <justification jstring="[para(13408(a,1),11632(a,1,2))].">
      <j1 rule="para" parents="13408 11632"/>
    </justification>
  </clause>

  <clause id="13422">
    <literal><![CDATA[
      L(1 / L(a(x,y,z),u,w),z,y) = L(z \ L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10030,a,b,13390,a)].">
      <j1 rule="hyper" parents="63 10030 13390"/>
    </justification>
  </clause>

  <clause id="13423">
    <literal><![CDATA[
      x \ (y \ (x * ((z \ L(z,u,w)) * T(y,x)))) = L(L(z \ L(z,u,w),x,y),y,x)
    ]]></literal>
    <justification jstring="[para(13390(a,1),10104(a,2,1))].">
      <j1 rule="para" parents="13390 10104"/>
    </justification>
  </clause>

  <clause id="13424">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,y * z) = a(z,y,L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(11884(a,1),13390(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11884 13390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13425">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,z * y) = a(z,y,L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(11885(a,1),13390(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11885 13390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13426">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,u,z)) \ 1) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(13424(a,1),7838(a,1,3))].">
      <j1 rule="para" parents="13424 7838"/>
    </justification>
  </clause>

  <clause id="13427">
    <literal><![CDATA[
      a(x,a(y,z,L(u,z,y)) \ 1,w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(13424(a,1),11429(a,1,2))].">
      <j1 rule="para" parents="13424 11429"/>
    </justification>
  </clause>

  <clause id="13428">
    <literal><![CDATA[
      a(x,a(y,z,L(u,z,y)),w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,13061,a(flip),b,13427,a)].">
      <j1 rule="hyper" parents="63 13061 13427"/>
    </justification>
  </clause>

  <clause id="13429">
    <literal><![CDATA[
      L(K(x,y) * (z \ L(z,u,w)),z,w * u) = K(x,y) * (a(w,u,L(z,u,w)) \ 1)
    ]]></literal>
    <justification jstring="[para(13425(a,1),4850(a,2,2))].">
      <j1 rule="para" parents="13425 4850"/>
    </justification>
  </clause>

  <clause id="13430">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,u,z)) \ 1) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(13425(a,1),11313(a,1,3))].">
      <j1 rule="para" parents="13425 11313"/>
    </justification>
  </clause>

  <clause id="13431">
    <literal><![CDATA[
      L(x,a(y,z,L(u,z,y)) \ 1,w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(13425(a,1),11820(a,1,2))].">
      <j1 rule="para" parents="13425 11820"/>
    </justification>
  </clause>

  <clause id="13433">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,u,z))) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2534,a(flip),b,13430,a)].">
      <j1 rule="hyper" parents="63 2534 13430"/>
    </justification>
  </clause>

  <clause id="13434">
    <literal><![CDATA[
      a(x,y,z \ (L(z \ u,z,w) \ u)) = a(x,y,a(z \ u,z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9173,a(flip),b,13433,a)].">
      <j1 rule="hyper" parents="63 9173 13433"/>
    </justification>
  </clause>

  <clause id="13435">
    <literal><![CDATA[
      L(L(x,L(L(x,y,z),u,w),v5) \ x,y,z) = a(v5,L(x,y,z),L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12458,a(flip),b,13381,a),flip(a)].">
      <j1 rule="hyper" parents="63 12458 13381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13436">
    <literal><![CDATA[
      (L(x,y,z) * u) \ R(x,u,u) = u \ L(L(x,y,z) \ x,u,u)
    ]]></literal>
    <justification jstring="[para(13381(a,1),13333(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13381 13333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13437">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ L(L(z,y,x) \ z,u,w) = a(y,L(z,u,w),a(x,y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(133,a,13383,a(flip),b,9952,a)].">
      <j1 rule="hyper" parents="133 13383 9952"/>
    </justification>
  </clause>

  <clause id="13438">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),L(x,u,w),y) = a(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(13383(a,1),9998(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13383 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13439">
    <literal><![CDATA[
      L(L(L(L(x,y,z),x,u) \ L(x,y,z),w,v5),x,L(L(x,y,z),w,v5)) = a(u,x,L(L(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(13383(a,1),10000(a,1,1))].">
      <j1 rule="para" parents="13383 10000"/>
    </justification>
  </clause>

  <clause id="13440">
    <literal><![CDATA[
      L(L(x * y,z,u) \ (x * y),y * x,w) = (w \ ((w / (y * x)) * L(y * x,z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(6408(a,1),13384(a,1,1))].">
      <j1 rule="para" parents="6408 13384"/>
    </justification>
  </clause>

  <clause id="13441">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w) \ 1,z,y) = L(z \ L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(2434(a,1),13422(a,1,1))].">
      <j1 rule="para" parents="2434 13422"/>
    </justification>
  </clause>

  <clause id="13442">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) = L(a(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(41,a,10015,a,b,13441,a)].">
      <j1 rule="hyper" parents="41 10015 13441"/>
    </justification>
  </clause>

  <clause id="13443">
    <literal><![CDATA[
      a(x,y,z) \ a(z,a(x,y,z),u) = L(a(x,y,z),z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,11615,a,b,13442,a)].">
      <j1 rule="hyper" parents="63 11615 13442"/>
    </justification>
  </clause>

  <clause id="13444">
    <literal><![CDATA[
      x \ (y \ ((y * x) * a(z,u,w))) = L(a(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,9888,a,b,13442,a(flip))].">
      <j1 rule="hyper" parents="39 9888 13442"/>
    </justification>
  </clause>

  <clause id="13445">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) \ 1 = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(39,a,5038,a,b,13442,a(flip))].">
      <j1 rule="hyper" parents="39 5038 13442"/>
    </justification>
  </clause>

  <clause id="13447">
    <literal><![CDATA[
      L(a(x,y,z),x,z * y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,9890,a(flip),b,13442,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 9890 13442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13448">
    <literal><![CDATA[
      L(a(x,a(y,z,x),u),w,v5) \ 1 = L(a(u,x,a(y,z,x)),w,v5)
    ]]></literal>
    <justification jstring="[para(9447(a,1),13442(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9447 13442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13449">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),u,w) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(13442(a,2),9873(a,1,1))].">
      <j1 rule="para" parents="13442 9873"/>
    </justification>
  </clause>

  <clause id="13450">
    <literal><![CDATA[
      x * (y * L(a(z,u,w) \ 1,y,x)) = (a(z,u,w) \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(13442(a,2),9923(a,1,2,2))].">
      <j1 rule="para" parents="13442 9923"/>
    </justification>
  </clause>

  <clause id="13451">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),x,z * y) = L(x \ R(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(13442(a,2),9891(a,1,1))].">
      <j1 rule="para" parents="13442 9891"/>
    </justification>
  </clause>

  <clause id="13452">
    <literal><![CDATA[
      x \ ((x * y) * a(z,u,w)) = y * L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,13445,a(flip),b,9920,a),flip(a)].">
      <j1 rule="hyper" parents="139 13445 9920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13453">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ a(x,y,z) = a(x,y,z) \ L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,13445,a(flip),b,5185,a),flip(a)].">
      <j1 rule="hyper" parents="133 13445 5185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13454">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),u,w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(13445(a,1),9874(a,1,1))].">
      <j1 rule="para" parents="13445 9874"/>
    </justification>
  </clause>

  <clause id="13455">
    <literal><![CDATA[
      x \ (y \ (x * (T(y,x) * a(z,u,w)))) = L(L(a(z,u,w),x,y),y,x)
    ]]></literal>
    <justification jstring="[para(13445(a,1),9992(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13445 9992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13456">
    <literal><![CDATA[
      L(L(L(x \ R(x,y,z),u,w),u,w),x,z * y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3432,a,b,13454,a)].">
      <j1 rule="hyper" parents="63 3432 13454"/>
    </justification>
  </clause>

  <clause id="13457">
    <literal><![CDATA[
      x \ ((1 / x) \ a(y,z,u)) = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,8792,a,b,13454,a)].">
      <j1 rule="hyper" parents="41 8792 13454"/>
    </justification>
  </clause>

  <clause id="13459">
    <literal><![CDATA[
      x * L(a(y,z,u),x,x) = (1 / x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(152,a,13457,a)].">
      <j1 rule="hyper" parents="152 13457"/>
    </justification>
  </clause>

  <clause id="13462">
    <literal><![CDATA[
      L(a(x,y,z),u,u) \ ((u \ a(x,y,z)) * u) = a(u \ a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[para(13457(a,1),11797(a,1,1))].">
      <j1 rule="para" parents="13457 11797"/>
    </justification>
  </clause>

  <clause id="13463">
    <literal><![CDATA[
      L(R(x,y,z) \ x,x,y * z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(9964(a,1),13449(a,1,1))].">
      <j1 rule="para" parents="9964 13449"/>
    </justification>
  </clause>

  <clause id="13464">
    <literal><![CDATA[
      L(R(x,y,L(a(z,u,w),y,y)) \ x,x,(1 / y) \ a(z,u,w)) = a(x,y,L(a(z,u,w),y,y)) \ 1
    ]]></literal>
    <justification jstring="[para(13459(a,1),13463(a,1,3))].">
      <j1 rule="para" parents="13459 13463"/>
    </justification>
  </clause>

  <clause id="13465">
    <literal><![CDATA[
      x \ (y \ (a(z,u,w) * (y * x))) = L(a(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2393,a,b,13444,a)].">
      <j1 rule="hyper" parents="63 2393 13444"/>
    </justification>
  </clause>

  <clause id="13467">
    <literal><![CDATA[
      L(x \ R(x,y,L(a(z,u,w),y,v5)),x,v5 \ ((v5 * y) * a(z,u,w))) = a(x,y,L(a(z,u,w),y,v5))
    ]]></literal>
    <justification jstring="[para(13452(a,2),3422(a,2,3)),flip(a)].">
      <j1 rule="para" parents="13452 3422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13468">
    <literal><![CDATA[
      L(a(x,y,z),u \ (a(x,y,z) \ w),u) = (u \ (a(x,y,z) \ w)) \ (u \ w)
    ]]></literal>
    <justification jstring="[para(76(a,1),13465(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="76 13465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13469">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(38,a,9968,a,b,13443,a),flip(a)].">
      <j1 rule="hyper" parents="38 9968 13443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13470">
    <literal><![CDATA[
      a(x,a(y,y,x),z) = a(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,7280,a,b,13469,a),flip(a)].">
      <j1 rule="hyper" parents="316 7280 13469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13472">
    <literal><![CDATA[
      x * a(y,a(z,u,y),x) = L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,13469,a,b,11689,a)].">
      <j1 rule="hyper" parents="139 13469 11689"/>
    </justification>
  </clause>

  <clause id="13474">
    <literal><![CDATA[
      x * a(y,a(z,u,y),w) = x * a(w,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,13469,a,b,9,a)].">
      <j1 rule="hyper" parents="139 13469 9"/>
    </justification>
  </clause>

  <clause id="13475">
    <literal><![CDATA[
      x * a(y,x,a(z,u,x)) = L(x,a(z,u,x),y)
    ]]></literal>
    <justification jstring="[hyper(139,a,13469,a(flip),b,9468,a)].">
      <j1 rule="hyper" parents="139 13469 9468"/>
    </justification>
  </clause>

  <clause id="13478">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * y = L(y,a(z,u,y),x)
    ]]></literal>
    <justification jstring="[para(13469(a,1),9469(a,1,1))].">
      <j1 rule="para" parents="13469 9469"/>
    </justification>
  </clause>

  <clause id="13479">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * (x \ L(x,w,v5)) = L(x,a(y,z,x),u) \ L(x,w,v5)
    ]]></literal>
    <justification jstring="[para(13469(a,2),9474(a,1,1))].">
      <j1 rule="para" parents="13469 9474"/>
    </justification>
  </clause>

  <clause id="13480">
    <literal><![CDATA[
      x * a(y,a(z,z,y),x) = L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,13470,a,b,11770,a)].">
      <j1 rule="hyper" parents="139 13470 11770"/>
    </justification>
  </clause>

  <clause id="13481">
    <literal><![CDATA[
      a(x,a(y,y,x),z) * z = L(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(13470(a,2),11774(a,1,1))].">
      <j1 rule="para" parents="13470 11774"/>
    </justification>
  </clause>

  <clause id="13482">
    <literal><![CDATA[
      L(x,y * z,a(y,z,y * z)) = x * a(y * z,a(z,z,y),x)
    ]]></literal>
    <justification jstring="[para(12263(a,1),13472(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12263 13472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13485">
    <literal><![CDATA[
      L((a(x,y,a(z,u,y)) \ 1) \ w,a(x,y,a(z,u,y)) \ 1,L(y,a(z,u,y),x)) = R(y,a(x,y,a(z,u,y)),a(x,y,a(z,u,y))) \ ((y * a(x,y,a(z,u,y))) * w)
    ]]></literal>
    <justification jstring="[para(13475(a,1),574(a,1,3))].">
      <j1 rule="para" parents="13475 574"/>
    </justification>
  </clause>

  <clause id="13486">
    <literal><![CDATA[
      L(x,a(y,z,x),u) \ (a(u,x,a(y,z,x)) * w) = L(x \ w,x,a(u,x,a(y,z,x)))
    ]]></literal>
    <justification jstring="[para(13475(a,1),2338(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13475 2338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13487">
    <literal><![CDATA[
      (x \ y) * a(z,x \ y,a(x,y,x * y)) = L(x \ y,a(x,y,x \ y),z)
    ]]></literal>
    <justification jstring="[para(13369(a,1),13475(a,1,2,3))].">
      <j1 rule="para" parents="13369 13475"/>
    </justification>
  </clause>

  <clause id="13488">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),u,w) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,3424,a(flip),b,13456,a),flip(a)].">
      <j1 rule="hyper" parents="41 3424 13456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13490">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,y,x) \ z) = a(x,y,z) * (z \ L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(144,a,13416,a)].">
      <j1 rule="hyper" parents="144 13416"/>
    </justification>
  </clause>

  <clause id="13491">
    <literal><![CDATA[
      (L(x,y,z) * u) \ R(x,u,u) = (u \ 1) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,6669,a(flip),b,13436,a),flip(a)].">
      <j1 rule="hyper" parents="316 6669 13436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13492">
    <literal><![CDATA[
      a(a(x,y,z),L(z,u,w),v5) \ 1 = L(a(v5,z,a(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(10054(a,2),13448(a,1,1))].">
      <j1 rule="para" parents="10054 13448"/>
    </justification>
  </clause>

  <clause id="13494">
    <literal><![CDATA[
      x * a(y * z,a(z,z,y),x) = L(x,y * z,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,9227,a(flip),b,13482,a),flip(a)].">
      <j1 rule="hyper" parents="63 9227 13482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13495">
    <literal><![CDATA[
      ((x * y) * (z \ L(z,u,w))) \ (x * (y * (z \ L(z,u,w)))) = a(x,y,L(z \ L(z,u,w),y,x))
    ]]></literal>
    <justification jstring="[para(13357(a,1),458(a,1,1))].">
      <j1 rule="para" parents="13357 458"/>
    </justification>
  </clause>

  <clause id="13496">
    <literal><![CDATA[
      (x \ y) * L(a(z,u,w) \ 1,x \ y,x) = x \ ((a(z,u,w) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,160,a(flip),b,13450,a),flip(a)].">
      <j1 rule="hyper" parents="133 160 13450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13497">
    <literal><![CDATA[
      a(x * y,z,z * L(z,y,x)) \ (L(z,y,x) \ z) = ((x * y) \ ((x * (y * z)) / z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,10055,a,b,13391,a)].">
      <j1 rule="hyper" parents="63 10055 13391"/>
    </justification>
  </clause>

  <clause id="13498">
    <literal><![CDATA[
      L(x,y,z) \ (x * L(x \ L(x,y,z),x,z * y)) = (L(x,y,z) \ x) \ (((z * y) \ ((z * (y * x)) / x)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,13391,a(flip),b,1253,a),flip(a)].">
      <j1 rule="hyper" parents="133 13391 1253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13500">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,z * y) = (y \ (z \ ((z * (y * x)) / x))) \ 1
    ]]></literal>
    <justification jstring="[para(9350(a,1),13391(a,2,1))].">
      <j1 rule="para" parents="9350 13391"/>
    </justification>
  </clause>

  <clause id="13501">
    <literal><![CDATA[
      L(L(a(x,y,z) \ L(a(x,y,z),u,w),v5,v6),L(a(x,y,z),v5,v6),u) = a(w,u,L(a(x,y,z),v5,v6))
    ]]></literal>
    <justification jstring="[para(13453(a,1),13438(a,1,1,1))].">
      <j1 rule="para" parents="13453 13438"/>
    </justification>
  </clause>

  <clause id="13502">
    <literal><![CDATA[
      x \ (y \ (x * T(y * a(z,u,w),x))) = L(L(a(z,u,w),x,y),y,x)
    ]]></literal>
    <justification jstring="[para(5317(a,2),13455(a,1,2,2,2))].">
      <j1 rule="para" parents="5317 13455"/>
    </justification>
  </clause>

  <clause id="13503">
    <literal><![CDATA[
      (x \ (y \ ((y * (x * z)) / z))) \ 1 = a(y,x,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,11885,a(flip),b,13500,a),flip(a)].">
      <j1 rule="hyper" parents="63 11885 13500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13504">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ z,z,w * u) * v5) = a(x,y,(u \ (w \ ((w * (u * z)) / z))) * v5)
    ]]></literal>
    <justification jstring="[para(13500(a,2),5564(a,1,3,1))].">
      <j1 rule="para" parents="13500 5564"/>
    </justification>
  </clause>

  <clause id="13505">
    <literal><![CDATA[
      x \ (y \ ((y * (x * z)) / z)) = a(y,x,L(z,x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,13503,a),flip(a)].">
      <j1 rule="hyper" parents="39 2301 13503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13506">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),y,x)) \ 1 = a(z \ L(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13224,a(flip),b,13505,a),flip(a)].">
      <j1 rule="hyper" parents="63 13224 13505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13507">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ (a(u,z,L(y,z,u)) \ 1) = (x \ 1) * (z \ (u \ ((u * (z * y)) / y)))
    ]]></literal>
    <justification jstring="[para(13505(a,1),12733(a,1,2))].">
      <j1 rule="para" parents="13505 12733"/>
    </justification>
  </clause>

  <clause id="13508">
    <literal><![CDATA[
      x \ (y \ ((y * a(z,u,w)) * x)) = L(L(a(z,u,w),x,y),y,x)
    ]]></literal>
    <justification jstring="[para(114(a,1),13502(a,1,2,2))].">
      <j1 rule="para" parents="114 13502"/>
    </justification>
  </clause>

  <clause id="13510">
    <literal><![CDATA[
      R(x \ L(x,y,z),u,w) * L((a(z,y,x) \ 1) \ (x \ L(x,y,z)),u,w) = L(1 / R(x \ L(x,y,z),u,w),x,y) \ 1
    ]]></literal>
    <justification jstring="[para(13354(a,1),13395(a,1,2,1,1))].">
      <j1 rule="para" parents="13354 13395"/>
    </justification>
  </clause>

  <clause id="13511">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) \ 1 = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9966,a(flip),b,13451,a),flip(a)].">
      <j1 rule="hyper" parents="63 9966 13451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13512">
    <literal><![CDATA[
      L(R(x,y,z) \ x,u,w) \ 1 = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(13511(a,1),2229(a,1,1))].">
      <j1 rule="para" parents="13511 2229"/>
    </justification>
  </clause>

  <clause id="13513">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * K(x \ a(y,z,u),x) = a(x \ a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4964,a(flip),b,13462,a)].">
      <j1 rule="hyper" parents="63 4964 13462"/>
    </justification>
  </clause>

  <clause id="13514">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * K(x \ 1,x) = a(x \ a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(5287(a,1),13513(a,1,2))].">
      <j1 rule="para" parents="5287 13513"/>
    </justification>
  </clause>

  <clause id="13515">
    <literal><![CDATA[
      (x \ a(x,x,a(y,z,u))) * x = a(x \ a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5282,a(flip),b,13514,a)].">
      <j1 rule="hyper" parents="63 5282 13514"/>
    </justification>
  </clause>

  <clause id="13517">
    <literal><![CDATA[
      (x \ 1) * L(x,x,a(y,z,u)) = a(x \ a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7363,a(flip),b,13515,a)].">
      <j1 rule="hyper" parents="63 7363 13515"/>
    </justification>
  </clause>

  <clause id="13520">
    <literal><![CDATA[
      (x \ y) * a(z,x \ y,a(x,y,y)) = L(x \ y,a(x,y,x \ y),z)
    ]]></literal>
    <justification jstring="[para(7284(a,1),13487(a,1,2))].">
      <j1 rule="para" parents="7284 13487"/>
    </justification>
  </clause>

  <clause id="13521">
    <literal><![CDATA[
      (x \ y) * a(z,x \ y,a(x,y,y)) = L(x \ y,a(x,y,x * y),z)
    ]]></literal>
    <justification jstring="[para(13369(a,1),13520(a,2,2))].">
      <j1 rule="para" parents="13369 13520"/>
    </justification>
  </clause>

  <clause id="13522">
    <literal><![CDATA[
      x \ (y * ((y \ x) * (L(y \ x,z,u) \ (y \ x)))) = (x \ (y * L(y \ x,z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(475(a,1),13380(a,2,1))].">
      <j1 rule="para" parents="475 13380"/>
    </justification>
  </clause>

  <clause id="13523">
    <literal><![CDATA[
      x \ (y \ (x * T(y * (z \ L(z,u,w)),x))) = L(L(z \ L(z,u,w),x,y),y,x)
    ]]></literal>
    <justification jstring="[para(11518(a,2),13423(a,1,2,2,2))].">
      <j1 rule="para" parents="11518 13423"/>
    </justification>
  </clause>

  <clause id="13524">
    <literal><![CDATA[
      L(K(x,y) * (z \ L(z,u,w)),z,w * u) = a(w,u,L(z,u,w)) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2466,a(flip),b,13429,a),flip(a)].">
      <j1 rule="hyper" parents="316 2466 13429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13525">
    <literal><![CDATA[
      T(x,y) \ (z \ ((z * (x * u)) / u)) = a(z,x,L(u,x,z)) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9366,a(flip),b,13524,a)].">
      <j1 rule="hyper" parents="63 9366 13524"/>
    </justification>
  </clause>

  <clause id="13527">
    <literal><![CDATA[
      x \ (y \ ((y * (z \ L(z,u,w))) * x)) = L(L(z \ L(z,u,w),x,y),y,x)
    ]]></literal>
    <justification jstring="[para(114(a,1),13523(a,1,2,2))].">
      <j1 rule="para" parents="114 13523"/>
    </justification>
  </clause>

  <clause id="13528">
    <literal><![CDATA[
      (L(x,a(y,z,x),u) \ w) * a(u,x,a(y,z,x)) = L(x \ w,x,a(u,x,a(y,z,x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7618,a(flip),b,13486,a)].">
      <j1 rule="hyper" parents="63 7618 13486"/>
    </justification>
  </clause>

  <clause id="13529">
    <literal><![CDATA[
      L(x * a(y,z,z),z,y) \ (x * a(y,z,z)) = L(x,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(41,a,13379,a(flip),b,13396,a),flip(a)].">
      <j1 rule="hyper" parents="41 13379 13396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13530">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,w) = L(x,u,w) * L(L(x,u,w) \ x,y,z)
    ]]></literal>
    <justification jstring="[para(13378(a,1),13398(a,2,2))].">
      <j1 rule="para" parents="13378 13398"/>
    </justification>
  </clause>

  <clause id="13531">
    <literal><![CDATA[
      x \ (y * ((y \ x) * (L(y \ x,z,u) \ (y \ x)))) = L(x \ y,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1900,a(flip),b,13522,a),flip(a)].">
      <j1 rule="hyper" parents="316 1900 13522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13532">
    <literal><![CDATA[
      L(L(x \ y,z,u) \ (x \ y),x \ y,x) = L(y \ x,z,u) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,101,a(flip),b,13531,a)].">
      <j1 rule="hyper" parents="63 101 13531"/>
    </justification>
  </clause>

  <clause id="13534">
    <literal><![CDATA[
      L(x,L(L(x,y,z),u,w),v5) \ x = a(v5,x,L(L(x,u,w),y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6901,a(flip),b,13413,a),flip(a)].">
      <j1 rule="hyper" parents="63 6901 13413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13536">
    <literal><![CDATA[
      a(x,L(y,z,u),L(L(y,z,u),w,v5)) = L(a(x,y,L(L(y,w,v5),z,u)),z,u)
    ]]></literal>
    <justification jstring="[para(13534(a,1),13435(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13534 13435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13538">
    <literal><![CDATA[
      a(x * y,z,a(z,y,x)) \ (L(z,y,x) \ z) = ((x * y) \ ((x * (y * z)) / z)) \ 1
    ]]></literal>
    <justification jstring="[para(11826(a,1),13497(a,1,1))].">
      <j1 rule="para" parents="11826 13497"/>
    </justification>
  </clause>

  <clause id="13539">
    <literal><![CDATA[
      (((x * y) \ ((x * (y * z)) / z)) \ 1) \ (L(z,y,x) \ z) = a(x * y,z,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(13538(a,1),2301(a,1,1))].">
      <j1 rule="para" parents="13538 2301"/>
    </justification>
  </clause>

  <clause id="13540">
    <literal><![CDATA[
      ((x \ (y \ ((y * (x * z)) / z))) \ 1) \ (L(z,x,y) \ z) = a(y * x,z,a(z,x,y))
    ]]></literal>
    <justification jstring="[para(9350(a,1),13539(a,1,1,1))].">
      <j1 rule="para" parents="9350 13539"/>
    </justification>
  </clause>

  <clause id="13541">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) \ (L(z,y,x) \ z) = a(x * y,z,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(13503(a,1),13540(a,1,1))].">
      <j1 rule="para" parents="13503 13540"/>
    </justification>
  </clause>

  <clause id="13543">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ (a(u,z,L(y,z,u)) \ 1) = (x \ 1) * (a(u,z,L(y,z,u)) \ 1)
    ]]></literal>
    <justification jstring="[para(13505(a,1),13507(a,2,2))].">
      <j1 rule="para" parents="13505 13507"/>
    </justification>
  </clause>

  <clause id="13545">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),L(x \ L(x,y,z),u,w),v5) = v5 \ (L(L(x,y,z) \ x,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,13130,a(flip),b,13401,a),flip(a)].">
      <j1 rule="hyper" parents="316 13130 13401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13546">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w) \ v5),L(z,u,w) \ v5,y) = L(R(z,u,w) \ v5,y,x) \ (R(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(9541(a,1),13405(a,1,1))].">
      <j1 rule="para" parents="9541 13405"/>
    </justification>
  </clause>

  <clause id="13547">
    <literal><![CDATA[
      L(a(x,y,z \ L(z,u,w)),z \ L(z,u,w),y) = L(z \ R(z,u,w),y,x) \ (z \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(7390(a,1),13407(a,1,1))].">
      <j1 rule="para" parents="7390 13407"/>
    </justification>
  </clause>

  <clause id="13548">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) * (L(w,u,z) \ w) = a(x,y,a(z,u,w)) * (v5 * (L(w,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(13403(a,1),13410(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13403 13410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13549">
    <literal><![CDATA[
      x \ (y \ ((y * (x * (z \ L(z,u,w)))) / (z \ L(z,u,w)))) = a(y,x,L(z \ L(z,u,w),x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,9351,a(flip),b,13495,a)].">
      <j1 rule="hyper" parents="63 9351 13495"/>
    </justification>
  </clause>

  <clause id="13550">
    <literal><![CDATA[
      L(R(x,y,z) \ u,w,v5) \ (R(x,y,z) \ u) = L(L(x,y,z) \ u,w,v5) \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13403,a(flip),b,13546,a),flip(a)].">
      <j1 rule="hyper" parents="63 13403 13546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13551">
    <literal><![CDATA[
      L(a(x,y,z * L(z,u,w)),z \ L(z,u,w),y) = L(z \ R(z,u,w),y,x) \ (z \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(5566(a,1),13547(a,1,1))].">
      <j1 rule="para" parents="5566 13547"/>
    </justification>
  </clause>

  <clause id="13552">
    <literal><![CDATA[
      x \ (y \ ((z \ L(z,u,w)) \ (y * (x * (z \ L(z,u,w)))))) = a(y,x,L(z \ L(z,u,w),x,y))
    ]]></literal>
    <justification jstring="[para(5015(a,1),13549(a,1,2,2))].">
      <j1 rule="para" parents="5015 13549"/>
    </justification>
  </clause>

  <clause id="13553">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,w),y,x)) = a(z \ L(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12719,a(flip),b,13552,a),flip(a)].">
      <j1 rule="hyper" parents="63 12719 13552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13554">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),y,x)) = a(z \ L(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5893,a(flip),b,13553,a)].">
      <j1 rule="hyper" parents="63 5893 13553"/>
    </justification>
  </clause>

  <clause id="13555">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,w) \ 1 = a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(13554(a,1),13506(a,1,1))].">
      <j1 rule="para" parents="13554 13506"/>
    </justification>
  </clause>

  <clause id="13556">
    <literal><![CDATA[
      L(L(a(x,y,L(y,z,u)),w,v5),y,L(L(y,z,u),w,v5)) = a(x,y,L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(10004(a,1),13439(a,1,1,1))].">
      <j1 rule="para" parents="10004 13439"/>
    </justification>
  </clause>

  <clause id="13557">
    <literal><![CDATA[
      a(x,y,L(L(y,z,u),w,v5)) = L(a(x,y,L(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,6975,a(flip),b,13556,a),flip(a)].">
      <j1 rule="hyper" parents="63 6975 13556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13559">
    <literal><![CDATA[
      L(a(x,y,L(y,z,u)),z,u) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,11862,a(flip),b,13557,a),flip(a)].">
      <j1 rule="hyper" parents="63 11862 13557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13560">
    <literal><![CDATA[
      L(a(x,y,L(L(y,z,u),w,v5)),w,v5) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,13454,a,b,13557,a(flip))].">
      <j1 rule="hyper" parents="41 13454 13557"/>
    </justification>
  </clause>

  <clause id="13562">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) = L(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(41,a,13454,a,b,13559,a),flip(a)].">
      <j1 rule="hyper" parents="41 13454 13559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13564">
    <literal><![CDATA[
      L(a(x,y,y) \ 1,z,u) = a(x,y,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(13559(a,1),9873(a,1,1,1))].">
      <j1 rule="para" parents="13559 9873"/>
    </justification>
  </clause>

  <clause id="13565">
    <literal><![CDATA[
      a(x,L(y,z,u),L(y,z,u)) = L(a(x,y,L(y,z,u)),z,u)
    ]]></literal>
    <justification jstring="[para(11863(a,1),13559(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11863 13559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13567">
    <literal><![CDATA[
      (x * y) * a(z,u,L(u,y,x)) = x * (y * a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,13562,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="139 13562 18"/>
    </justification>
  </clause>

  <clause id="13569">
    <literal><![CDATA[
      L(a(x,L(y,z,u) \ y,L(y,z,u) \ y),y,z) = a(x,L(y,z,u) \ y,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(9998(a,2),13562(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9998 13562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13570">
    <literal><![CDATA[
      a(x,y,a(z,u,L(u,w,v5))) = a(x,y,a(u,u,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[para(13562(a,2),11807(a,2,3)),flip(a)].">
      <j1 rule="para" parents="13562 11807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13571">
    <literal><![CDATA[
      a(x,y \ 1,L(y \ 1,z,u)) \ 1 = L(a(x,y \ 1,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(2534(a,1),13564(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2534 13564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13572">
    <literal><![CDATA[
      (x \ L(a(y,x,x) \ 1,z,u)) * x = (x \ 1) * (a(y,x,L(x,z,u)) \ x)
    ]]></literal>
    <justification jstring="[para(13564(a,2),7195(a,1,1,2))].">
      <j1 rule="para" parents="13564 7195"/>
    </justification>
  </clause>

  <clause id="13573">
    <literal><![CDATA[
      L(a(x,y * z,y * z) \ 1,z,y) = a(x,y * z,z \ y) \ 1
    ]]></literal>
    <justification jstring="[para(9926(a,1),13564(a,2,1))].">
      <j1 rule="para" parents="9926 13564"/>
    </justification>
  </clause>

  <clause id="13574">
    <literal><![CDATA[
      a(x,L(y,z,u),L(L(y,z,u),w,v5)) = a(x,y,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,13536,a,b,13560,a)].">
      <j1 rule="hyper" parents="63 13536 13560"/>
    </justification>
  </clause>

  <clause id="13575">
    <literal><![CDATA[
      a(x,L(y,z,u),L(y,z,u)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,13559,a(flip),b,13565,a),flip(a)].">
      <j1 rule="hyper" parents="316 13559 13565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13577">
    <literal><![CDATA[
      a(x,(y \ z) \ 1,L(z \ y,z \ y,z)) = a(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13072,a(flip),b,13575,a)].">
      <j1 rule="hyper" parents="63 13072 13575"/>
    </justification>
  </clause>

  <clause id="13578">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y,z,u)) = a(x,y,y) * x
    ]]></literal>
    <justification jstring="[hyper(138,a,13575,a(flip),b,2376,a),flip(a)].">
      <j1 rule="hyper" parents="138 13575 2376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13579">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),L(z,u,w),v5)) = a(x,y,a(v5,z,z))
    ]]></literal>
    <justification jstring="[para(13575(a,1),7280(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13575 7280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13581">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y,z,u)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2377,a(flip),b,13578,a),flip(a)].">
      <j1 rule="hyper" parents="316 2377 13578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13582">
    <literal><![CDATA[
      R(x / y,L(y,z,u),L(y,z,u)) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,563,a(flip),b,13581,a),flip(a)].">
      <j1 rule="hyper" parents="316 563 13581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13584">
    <literal><![CDATA[
      R(x,L(y \ z,y,z),z * y) = R(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1717,a(flip),b,13581,a)].">
      <j1 rule="hyper" parents="63 1717 13581"/>
    </justification>
  </clause>

  <clause id="13585">
    <literal><![CDATA[
      R(x / L(y,z,u),y,y) = x * (L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,563,a(flip),b,13581,a),flip(a)].">
      <j1 rule="hyper" parents="63 563 13581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13587">
    <literal><![CDATA[
      R(x,y,y) * (y * L(L(y,z,u),z,u)) = (x * L(y,z,u)) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(13581(a,1),9959(a,1,1))].">
      <j1 rule="para" parents="13581 9959"/>
    </justification>
  </clause>

  <clause id="13588">
    <literal><![CDATA[
      (L(x,y,z) * u) * (L(x,y,z) \ 1) = (x * u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,4335,a(flip),b,13582,a)].">
      <j1 rule="hyper" parents="63 4335 13582"/>
    </justification>
  </clause>

  <clause id="13592">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * (x \ 1))) = u * (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,6823,a,b,13585,a)].">
      <j1 rule="hyper" parents="63 6823 13585"/>
    </justification>
  </clause>

  <clause id="13593">
    <literal><![CDATA[
      L(x,y,z) * (u * (L(x,y,z) \ 1)) = x * (u * (x \ 1))
    ]]></literal>
    <justification jstring="[para(13585(a,1),6824(a,1,2))].">
      <j1 rule="para" parents="13585 6824"/>
    </justification>
  </clause>

  <clause id="13594">
    <literal><![CDATA[
      (x / L(y,z,u)) * ((x * (L(y,z,u) \ 1)) \ y) = L(y,y,x / L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13585(a,1),7166(a,1,2,1))].">
      <j1 rule="para" parents="13585 7166"/>
    </justification>
  </clause>

  <clause id="13596">
    <literal><![CDATA[
      R(x,(y * (z \ 1)) \ 1,y * z) = R(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11045,a(flip),b,13584,a)].">
      <j1 rule="hyper" parents="63 11045 13584"/>
    </justification>
  </clause>

  <clause id="13597">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),v5,v5)) = a(x,y,a(z,v5,L(v5,u,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,7280,a,b,13570,a)].">
      <j1 rule="hyper" parents="316 7280 13570"/>
    </justification>
  </clause>

  <clause id="13599">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),L(z,u,w),v5)) = a(x,y,a(z,z,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,7280,a(flip),b,13579,a),flip(a)].">
      <j1 rule="hyper" parents="316 7280 13579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13602">
    <literal><![CDATA[
      (((x \ 1) \ y) * z) * (((x \ 1) \ y) \ 1) = ((x * y) * z) * ((x * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,13075,a(flip),b,13588,a)].">
      <j1 rule="hyper" parents="63 13075 13588"/>
    </justification>
  </clause>

  <clause id="13603">
    <literal><![CDATA[
      a(L(x,L(y,z,u),L(y,z,u)),w,v5) = a((y * x) * (y \ 1),w,v5)
    ]]></literal>
    <justification jstring="[para(13588(a,1),4649(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13588 4649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13604">
    <literal><![CDATA[
      (x / (y \ 1)) * (L(y,z,u) \ 1) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(12(a,1),13592(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 13592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13606">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * (v5 * (L(L(x,y,z) \ x,u,w) \ 1)) = (v5 * ((L(x,y,z) \ x) \ 1)) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,6496,a(flip),b,13593,a),flip(a)].">
      <j1 rule="hyper" parents="316 6496 13593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13607">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ 1,u) = T(u,x \ 1) / (x * (u * (x \ 1)))
    ]]></literal>
    <justification jstring="[para(13593(a,1),5744(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13593 5744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13608">
    <literal><![CDATA[
      L(x,L(y,L(z,u,w),L(z,u,w)),v5) = L(x,z * (y * (z \ 1)),v5)
    ]]></literal>
    <justification jstring="[para(13593(a,1),11006(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13593 11006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13609">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) / (x \ 1) = u / (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(136,a,75,a(flip),b,13604,a),flip(a)].">
      <j1 rule="hyper" parents="136 75 13604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13610">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6622,a,b,13604,a)].">
      <j1 rule="hyper" parents="63 6622 13604"/>
    </justification>
  </clause>

  <clause id="13611">
    <literal><![CDATA[
      (x / y) * (L(1 / y,z,u) \ 1) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13246,a(flip),b,13604,a)].">
      <j1 rule="hyper" parents="63 13246 13604"/>
    </justification>
  </clause>

  <clause id="13613">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) / (y \ 1) = x / (L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,4381,a(flip),b,13609,a)].">
      <j1 rule="hyper" parents="63 4381 13609"/>
    </justification>
  </clause>

  <clause id="13614">
    <literal><![CDATA[
      L(x,y,z) \ (u / (L(x,y,z) \ 1)) = x \ (u / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(133,a,13609,a(flip),b,7087,a(flip))].">
      <j1 rule="hyper" parents="133 13609 7087"/>
    </justification>
  </clause>

  <clause id="13615">
    <literal><![CDATA[
      (x \ 1) \ ((L(x,y,z) \ 1) * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13266,a,b,13610,a)].">
      <j1 rule="hyper" parents="63 13266 13610"/>
    </justification>
  </clause>

  <clause id="13616">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) * u = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13243,a,b,13610,a)].">
      <j1 rule="hyper" parents="63 13243 13610"/>
    </justification>
  </clause>

  <clause id="13617">
    <literal><![CDATA[
      L(x,y,z) * (L(L(x,y,z),y,z) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9894,a,b,13610,a)].">
      <j1 rule="hyper" parents="63 9894 13610"/>
    </justification>
  </clause>

  <clause id="13618">
    <literal><![CDATA[
      (x / y) * (z \ ((1 / z) \ y)) = y * (L(y,z,z \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13247,a(flip),b,13610,a)].">
      <j1 rule="hyper" parents="63 13247 13610"/>
    </justification>
  </clause>

  <clause id="13619">
    <literal><![CDATA[
      (x \ 1) * (x * (L(x,y,z) \ u)) = (L(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(139,a,13610,a(flip),b,13266,a)].">
      <j1 rule="hyper" parents="139 13610 13266"/>
    </justification>
  </clause>

  <clause id="13620">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * u = x * (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(13610(a,1),13245(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13610 13245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13621">
    <literal><![CDATA[
      (x / y) * (y * (L(y,z,u) \ y)) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9101,a(flip),b,13616,a)].">
      <j1 rule="hyper" parents="63 9101 13616"/>
    </justification>
  </clause>

  <clause id="13622">
    <literal><![CDATA[
      x * L(L(y,z,u) \ y,y,x) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6493,a(flip),b,13616,a)].">
      <j1 rule="hyper" parents="63 6493 13616"/>
    </justification>
  </clause>

  <clause id="13624">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) = u \ (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(35,a,6532,a,b,13616,a),flip(a)].">
      <j1 rule="hyper" parents="35 6532 13616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13625">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,z,x * y)
    ]]></literal>
    <justification jstring="[hyper(35,a,6981,a(flip),b,13616,a)].">
      <j1 rule="hyper" parents="35 6981 13616"/>
    </justification>
  </clause>

  <clause id="13626">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) * L(u,v5,v6))) = a(x,y,z * (u * (L(u,v5,v6) \ w)))
    ]]></literal>
    <justification jstring="[para(13616(a,1),9115(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="13616 9115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13627">
    <literal><![CDATA[
      a(x,y,L((z \ u) * L(z,w,v5),v6,v7)) = a(x,y,L(z * (L(z,w,v5) \ u),v6,v7))
    ]]></literal>
    <justification jstring="[para(13616(a,1),9340(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="13616 9340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13628">
    <literal><![CDATA[
      x * (L(x,y,z) \ y) = a(z,y,x) * y
    ]]></literal>
    <justification jstring="[para(9998(a,2),13616(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9998 13616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13629">
    <literal><![CDATA[
      a(x \ ((y \ z) * (L(y \ 1,u,w) \ 1)),v5,v6) = a(x \ (y * (L(y,u,w) \ z)),v5,v6)
    ]]></literal>
    <justification jstring="[para(13616(a,1),11704(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13616 11704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13631">
    <literal><![CDATA[
      x * (L(x,y,z) \ y) = y * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,2290,a(flip),b,13628,a),flip(a)].">
      <j1 rule="hyper" parents="316 2290 13628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13632">
    <literal><![CDATA[
      x \ (y * a(z,y,x)) = L(x,y,z) \ y
    ]]></literal>
    <justification jstring="[hyper(133,a,2290,a(flip),b,13628,a)].">
      <j1 rule="hyper" parents="133 2290 13628"/>
    </justification>
  </clause>

  <clause id="13633">
    <literal><![CDATA[
      a(x,y,z) = y \ (z * (L(z,y,x) \ y))
    ]]></literal>
    <justification jstring="[hyper(133,a,13628,a,b,2290,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 13628 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13634">
    <literal><![CDATA[
      a(x,y,z) * (z \ y) = L(z,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(34,a,6892,a,b,13628,a)].">
      <j1 rule="hyper" parents="34 6892 13628"/>
    </justification>
  </clause>

  <clause id="13635">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,9171,a,b,13628,a(flip))].">
      <j1 rule="hyper" parents="35 9171 13628"/>
    </justification>
  </clause>

  <clause id="13636">
    <literal><![CDATA[
      L(x,y,z) = (a(z,y,x) * y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(13628(a,1),4395(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13628 4395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13637">
    <literal><![CDATA[
      T(a(x,y,z) * y,z) = L(z,y,x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(13628(a,1),4434(a,1,1))].">
      <j1 rule="para" parents="13628 4434"/>
    </justification>
  </clause>

  <clause id="13638">
    <literal><![CDATA[
      L(x,y \ (a(L(z,u,w),u,w) \ u),v5) = L(x,y \ (a(w,u,z) * u),v5)
    ]]></literal>
    <justification jstring="[para(13628(a,1),12662(a,2,2,2))].">
      <j1 rule="para" parents="13628 12662"/>
    </justification>
  </clause>

  <clause id="13639">
    <literal><![CDATA[
      a(x \ R(y,z,u),w,L(v5,w,x \ L(y,z,u))) = a(x \ L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,12461,a,b,13635,a)].">
      <j1 rule="hyper" parents="63 12461 13635"/>
    </justification>
  </clause>

  <clause id="13640">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11884,a,b,13635,a),flip(a)].">
      <j1 rule="hyper" parents="63 11884 13635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13642">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,w) = a(w,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13554,a(flip),b,13635,a)].">
      <j1 rule="hyper" parents="63 13554 13635"/>
    </justification>
  </clause>

  <clause id="13643">
    <literal><![CDATA[
      a(a(x,x,y),z,u) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,11911,a(flip),b,13635,a)].">
      <j1 rule="hyper" parents="63 11911 13635"/>
    </justification>
  </clause>

  <clause id="13644">
    <literal><![CDATA[
      a(x,y,z * a(x,z,y)) = a(x,y,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,11899,a(flip),b,13635,a)].">
      <j1 rule="hyper" parents="63 11899 13635"/>
    </justification>
  </clause>

  <clause id="13645">
    <literal><![CDATA[
      a(x,y,(x * y) \ z) = a(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11865,a(flip),b,13635,a),flip(a)].">
      <j1 rule="hyper" parents="63 11865 13635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13646">
    <literal><![CDATA[
      a(x,y,y * L(y,x,z)) = a(x,y,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10007,a(flip),b,13635,a),flip(a)].">
      <j1 rule="hyper" parents="63 10007 13635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13647">
    <literal><![CDATA[
      x \ (L(y / x,x,z) \ y) = a(z,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9172,a(flip),b,13635,a)].">
      <j1 rule="hyper" parents="63 9172 13635"/>
    </justification>
  </clause>

  <clause id="13648">
    <literal><![CDATA[
      L(L(x,y,z),a(z,y,L(x,y,z)),y) = L(L(x,y,z),y,z) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,13635,a(flip),b,11628,a),flip(a)].">
      <j1 rule="hyper" parents="139 13635 11628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13649">
    <literal><![CDATA[
      a(x,L(x,y,z),L(u,x,L(x,y,z))) = a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(1231(a,1),13635(a,1,3))].">
      <j1 rule="para" parents="1231 13635"/>
    </justification>
  </clause>

  <clause id="13650">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) \ (L(L(z,y,x),u,w) \ v5) = L(L(z,y,x),u,w) \ (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(13635(a,1),6996(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13635 6996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13651">
    <literal><![CDATA[
      a(x \ R(y,z,u),w,L(v5,w,x \ L(y,z,u))) = a(x \ R(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(7482(a,1),13635(a,1,3))].">
      <j1 rule="para" parents="7482 13635"/>
    </justification>
  </clause>

  <clause id="13652">
    <literal><![CDATA[
      L(x,x \ y,z) * (x \ y) = a(z,x \ y,x) \ y
    ]]></literal>
    <justification jstring="[para(13635(a,1),8579(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13635 8579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13653">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,a(z,y,L(x,y,z) \ 1),y) = (x \ 1) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(13635(a,1),11749(a,2,2))].">
      <j1 rule="para" parents="13635 11749"/>
    </justification>
  </clause>

  <clause id="13654">
    <literal><![CDATA[
      L(a(x,y,z),u,a(z * L(z,y,x),w,v5)) = a(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(13635(a,1),12278(a,1,1))].">
      <j1 rule="para" parents="13635 12278"/>
    </justification>
  </clause>

  <clause id="13656">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ 1) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(13635(a,1),13426(a,1,3,1))].">
      <j1 rule="para" parents="13635 13426"/>
    </justification>
  </clause>

  <clause id="13658">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(13635(a,1),13428(a,1,2))].">
      <j1 rule="para" parents="13635 13428"/>
    </justification>
  </clause>

  <clause id="13659">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,z * y) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(13635(a,1),13425(a,2,1))].">
      <j1 rule="para" parents="13635 13425"/>
    </justification>
  </clause>

  <clause id="13660">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(13635(a,1),13433(a,1,3))].">
      <j1 rule="para" parents="13635 13433"/>
    </justification>
  </clause>

  <clause id="13661">
    <literal><![CDATA[
      L(x,a(y,z,u) \ 1,w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(13635(a,1),13431(a,1,2,1))].">
      <j1 rule="para" parents="13635 13431"/>
    </justification>
  </clause>

  <clause id="13662">
    <literal><![CDATA[
      x \ (y \ ((y * (x * z)) / z)) = a(y,x,z) \ 1
    ]]></literal>
    <justification jstring="[para(13635(a,1),13505(a,2,1))].">
      <j1 rule="para" parents="13635 13505"/>
    </justification>
  </clause>

  <clause id="13663">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) \ 1 = a(z \ L(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(13635(a,1),13506(a,1,1))].">
      <j1 rule="para" parents="13635 13506"/>
    </justification>
  </clause>

  <clause id="13664">
    <literal><![CDATA[
      T(x,y) \ (z \ ((z * (x * u)) / u)) = a(z,x,u) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(13635(a,1),13525(a,2,1))].">
      <j1 rule="para" parents="13635 13525"/>
    </justification>
  </clause>

  <clause id="13665">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ (a(u,z,y) \ 1) = (x \ 1) * (a(u,z,L(y,z,u)) \ 1)
    ]]></literal>
    <justification jstring="[para(13635(a,1),13543(a,1,2,1))].">
      <j1 rule="para" parents="13635 13543"/>
    </justification>
  </clause>

  <clause id="13666">
    <literal><![CDATA[
      L(x,y * x,y) \ x = a(y,y * x,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,9977,a,b,13631,a(flip))].">
      <j1 rule="hyper" parents="34 9977 13631"/>
    </justification>
  </clause>

  <clause id="13669">
    <literal><![CDATA[
      a(a(x,y,z),z,u) * (u \ z) = L(u,a(x,y,z),z) \ z
    ]]></literal>
    <justification jstring="[para(6997(a,2),13634(a,2,1))].">
      <j1 rule="para" parents="6997 13634"/>
    </justification>
  </clause>

  <clause id="13670">
    <literal><![CDATA[
      a(a(x,x,y),z,u) = a(u,z,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,7280,a,b,13643,a),flip(a)].">
      <j1 rule="hyper" parents="316 7280 13643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13671">
    <literal><![CDATA[
      a(a(x,y,y),z,u) = a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,12274,a,b,13643,a)].">
      <j1 rule="hyper" parents="63 12274 13643"/>
    </justification>
  </clause>

  <clause id="13672">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,y)) = a(x,a(y,v5,w),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,8984,a,b,13658,a)].">
      <j1 rule="hyper" parents="316 8984 13658"/>
    </justification>
  </clause>

  <clause id="13675">
    <literal><![CDATA[
      a(x,a(x,y,z),u) = a(u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,13469,a(flip),b,13658,a),flip(a)].">
      <j1 rule="hyper" parents="316 13469 13658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13677">
    <literal><![CDATA[
      x * a(y,a(z,u,w),v5) = x * a(y,a(w,u,z),v5)
    ]]></literal>
    <justification jstring="[hyper(139,a,13658,a,b,9,a)].">
      <j1 rule="hyper" parents="139 13658 9"/>
    </justification>
  </clause>

  <clause id="13679">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ L(v5,a(x,a(u,z,y),w),a(x,a(u,z,y),w)) = v5 * (a(x,a(u,z,y),w) \ 1)
    ]]></literal>
    <justification jstring="[para(13658(a,1),5384(a,1,1))].">
      <j1 rule="para" parents="13658 5384"/>
    </justification>
  </clause>

  <clause id="13680">
    <literal><![CDATA[
      a(x,a(x,y,y),z) * z = L(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(13658(a,1),13481(a,1,1))].">
      <j1 rule="para" parents="13658 13481"/>
    </justification>
  </clause>

  <clause id="13681">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(u,x,a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,13469,a,b,13660,a)].">
      <j1 rule="hyper" parents="316 13469 13660"/>
    </justification>
  </clause>

  <clause id="13684">
    <literal><![CDATA[
      a(x,y,(z \ (u \ w)) * ((u * z) \ w)) = a(x,y,a(u,z,w \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(316,a,11319,a,b,13660,a)].">
      <j1 rule="hyper" parents="316 11319 13660"/>
    </justification>
  </clause>

  <clause id="13687">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) = a(x,y,a(v5,w,u * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,8927,a,b,13660,a)].">
      <j1 rule="hyper" parents="316 8927 13660"/>
    </justification>
  </clause>

  <clause id="13688">
    <literal><![CDATA[
      a(x \ y,x,a(x,z,u)) = a(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,9988,a(flip),b,13660,a),flip(a)].">
      <j1 rule="hyper" parents="316 9988 13660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13689">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,13660,a,b,2295,a),flip(a)].">
      <j1 rule="hyper" parents="139 13660 2295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13690">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) = x * a(y,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,13660,a,b,9,a)].">
      <j1 rule="hyper" parents="139 13660 9"/>
    </justification>
  </clause>

  <clause id="13694">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),a(w,u,z),y) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(13660(a,1),8919(a,1,1,2))].">
      <j1 rule="para" parents="13660 8919"/>
    </justification>
  </clause>

  <clause id="13697">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * x = L(x,y,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(13660(a,1),11774(a,1,1))].">
      <j1 rule="para" parents="13660 11774"/>
    </justification>
  </clause>

  <clause id="13698">
    <literal><![CDATA[
      x * a(y,x,a(x,z,u)) = L(x,a(u,z,x),y)
    ]]></literal>
    <justification jstring="[para(13660(a,1),13475(a,1,2))].">
      <j1 rule="para" parents="13660 13475"/>
    </justification>
  </clause>

  <clause id="13699">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * y = L(y,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(13660(a,1),13478(a,1,1))].">
      <j1 rule="para" parents="13660 13478"/>
    </justification>
  </clause>

  <clause id="13702">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w),v5,v6)) = a(x,y,a(v6,v5,a(w,u,z)))
    ]]></literal>
    <justification jstring="[para(13660(a,1),13660(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13660 13660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13705">
    <literal><![CDATA[
      a(a(x,y,y),z,u) = a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,12274,a,b,13670,a)].">
      <j1 rule="hyper" parents="63 12274 13670"/>
    </justification>
  </clause>

  <clause id="13707">
    <literal><![CDATA[
      x * a(a(y,z,z),u,w) = x * a(w,u,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,13671,a,b,9,a)].">
      <j1 rule="hyper" parents="139 13671 9"/>
    </justification>
  </clause>

  <clause id="13708">
    <literal><![CDATA[
      a(a(x,y,y),z,u) * w = w * a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(138,a,13671,a,b,2287,a)].">
      <j1 rule="hyper" parents="138 13671 2287"/>
    </justification>
  </clause>

  <clause id="13709">
    <literal><![CDATA[
      a(x * y,a(y,y,x),z) = a(z,x * y,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,13100,a(flip),b,13671,a)].">
      <j1 rule="hyper" parents="63 13100 13671"/>
    </justification>
  </clause>

  <clause id="13710">
    <literal><![CDATA[
      a(x,a(x,y,z),u) = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,13660,a,b,13675,a),flip(a)].">
      <j1 rule="hyper" parents="316 13660 13675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13711">
    <literal><![CDATA[
      x * a(y,x,a(z,u,x)) = L(x,a(x,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(139,a,13675,a(flip),b,9463,a)].">
      <j1 rule="hyper" parents="139 13675 9463"/>
    </justification>
  </clause>

  <clause id="13712">
    <literal><![CDATA[
      x * a(y,a(z,u,y),x) = L(x,y,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,13681,a,b,11770,a)].">
      <j1 rule="hyper" parents="139 13681 11770"/>
    </justification>
  </clause>

  <clause id="13715">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * w = w * a(a(z,u,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,13705,a,b,2295,a),flip(a)].">
      <j1 rule="hyper" parents="139 13705 2295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13717">
    <literal><![CDATA[
      x * a(y,x,a(x,z,u)) = L(x,a(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(139,a,13710,a(flip),b,9463,a)].">
      <j1 rule="hyper" parents="139 13710 9463"/>
    </justification>
  </clause>

  <clause id="13719">
    <literal><![CDATA[
      L(a(x,y,z),z,x * y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(41,a,13454,a,b,13625,a(flip))].">
      <j1 rule="hyper" parents="41 13454 13625"/>
    </justification>
  </clause>

  <clause id="13720">
    <literal><![CDATA[
      a(x,y,z) \ L(z \ L(z,y,x),z,x * y) = L(z,y,x) * L(z \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(13625(a,2),9725(a,1,1))].">
      <j1 rule="para" parents="13625 9725"/>
    </justification>
  </clause>

  <clause id="13722">
    <literal><![CDATA[
      R(x,a(y,z,u),L(L(u,z,y) \ u,u,z * y)) = R(x,L(u,z,y) \ u,L(u,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(13640(a,2),13581(a,1,2))].">
      <j1 rule="para" parents="13640 13581"/>
    </justification>
  </clause>

  <clause id="13724">
    <literal><![CDATA[
      (x * y) \ (L(z / (x * y),y,x) \ z) = a(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6982,a,b,13645,a)].">
      <j1 rule="hyper" parents="63 6982 13645"/>
    </justification>
  </clause>

  <clause id="13726">
    <literal><![CDATA[
      L(x,(y \ (z \ y)) * z,u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11176,a,b,13661,a)].">
      <j1 rule="hyper" parents="63 11176 13661"/>
    </justification>
  </clause>

  <clause id="13727">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) \ (z / y)) * L(y,x,x) = L(z,y,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,11431,a(flip),b,13680,a)].">
      <j1 rule="hyper" parents="63 11431 13680"/>
    </justification>
  </clause>

  <clause id="13728">
    <literal><![CDATA[
      a(a(x,y,z),x,u) \ x = L(x,a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9440,a,b,13698,a)].">
      <j1 rule="hyper" parents="63 9440 13698"/>
    </justification>
  </clause>

  <clause id="13730">
    <literal><![CDATA[
      L(x,a(x,y,z),z * y) = a(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8723,a(flip),b,13717,a),flip(a)].">
      <j1 rule="hyper" parents="63 8723 13717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13732">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ 1 = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11601,a(flip),b,13659,a),flip(a)].">
      <j1 rule="hyper" parents="63 11601 13659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13733">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ 1 = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10638,a(flip),b,13659,a),flip(a)].">
      <j1 rule="hyper" parents="63 10638 13659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13734">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ 1 = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5386,a(flip),b,13659,a),flip(a)].">
      <j1 rule="hyper" parents="63 5386 13659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13736">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,489,a(flip),b,13659,a)].">
      <j1 rule="hyper" parents="63 489 13659"/>
    </justification>
  </clause>

  <clause id="13737">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * a(w,a(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(139,a,10638,a(flip),b,13659,a(flip))].">
      <j1 rule="hyper" parents="139 10638 13659"/>
    </justification>
  </clause>

  <clause id="13738">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * a(w,u,a(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(139,a,5386,a(flip),b,13659,a(flip))].">
      <j1 rule="hyper" parents="139 5386 13659"/>
    </justification>
  </clause>

  <clause id="13740">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) \ 1 = a(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,13705,a(flip),b,13732,a),flip(a)].">
      <j1 rule="hyper" parents="316 13705 13732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13742">
    <literal><![CDATA[
      L(a(a(x,y,z),u,w),v5,v6) \ 1 = L(a(w,u,a(x,y,z)),v5,v6)
    ]]></literal>
    <justification jstring="[para(13732(a,1),13445(a,1,1,1))].">
      <j1 rule="para" parents="13732 13445"/>
    </justification>
  </clause>

  <clause id="13743">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * a(w,a(u,z,y),x) = 1
    ]]></literal>
    <justification jstring="[hyper(139,a,13658,a,b,13733,a)].">
      <j1 rule="hyper" parents="139 13658 13733"/>
    </justification>
  </clause>

  <clause id="13744">
    <literal><![CDATA[
      (R(x,x,a(y,z,u)) \ ((x \ ((x * x) * a(y,z,u))) * w)) / w = a(y,z,u) * (a(w,a(y,z,u),L(x,x,a(y,z,u))) \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,13733,a,b,8767,a),flip(a)].">
      <j1 rule="hyper" parents="139 13733 8767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13746">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,y) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,13354,a,b,13734,a)].">
      <j1 rule="hyper" parents="63 13354 13734"/>
    </justification>
  </clause>

  <clause id="13747">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,y)) = L(a(x,y,a(w,v5,y)),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13492,a(flip),b,13734,a),flip(a)].">
      <j1 rule="hyper" parents="63 13492 13734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13750">
    <literal><![CDATA[
      x \ (a(y,x,z) \ x) = a(y,x,z) \ 1
    ]]></literal>
    <justification jstring="[para(8532(a,2),13662(a,1,2))].">
      <j1 rule="para" parents="8532 13662"/>
    </justification>
  </clause>

  <clause id="13751">
    <literal><![CDATA[
      x * (a(y,x,z) \ 1) = a(y,x,z) \ x
    ]]></literal>
    <justification jstring="[hyper(152,a,13750,a)].">
      <j1 rule="hyper" parents="152 13750"/>
    </justification>
  </clause>

  <clause id="13752">
    <literal><![CDATA[
      (x / y) * L(y,x,z) = a(z,x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(38,a,13365,a,b,13750,a)].">
      <j1 rule="hyper" parents="38 13365 13750"/>
    </justification>
  </clause>

  <clause id="13754">
    <literal><![CDATA[
      R(x,a(y,x,z),a(y,x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,2630,a,b,13751,a(flip))].">
      <j1 rule="hyper" parents="38 2630 13751"/>
    </justification>
  </clause>

  <clause id="13755">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ u,v5,v6)) = a(x,y,L(u * a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(13751(a,1),5888(a,1,3,1))].">
      <j1 rule="para" parents="13751 5888"/>
    </justification>
  </clause>

  <clause id="13756">
    <literal><![CDATA[
      x \ (L(x,y,z) * y) = a(z,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,4382,a,b,13752,a)].">
      <j1 rule="hyper" parents="63 4382 13752"/>
    </justification>
  </clause>

  <clause id="13757">
    <literal><![CDATA[
      L(x,y,z) * (x \ y) = a(z,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,4325,a,b,13752,a)].">
      <j1 rule="hyper" parents="63 4325 13752"/>
    </justification>
  </clause>

  <clause id="13758">
    <literal><![CDATA[
      a(x,y,y \ (z \ y)) \ y = (z \ L(z,y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,9329,a(flip),b,13752,a),flip(a)].">
      <j1 rule="hyper" parents="63 9329 13752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13759">
    <literal><![CDATA[
      (a(x,y,z) \ y) * z = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(138,a,13752,a(flip),b,1438,a)].">
      <j1 rule="hyper" parents="138 13752 1438"/>
    </justification>
  </clause>

  <clause id="13760">
    <literal><![CDATA[
      L(x,y,z \ ((u \ w) * L(u,w,v5))) = L(x,y,z \ (a(v5,w,u) \ w))
    ]]></literal>
    <justification jstring="[para(13752(a,1),4174(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="13752 4174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13763">
    <literal><![CDATA[
      x \ (L(x,y,a(y,z,u)) * y) = L(y,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,13728,a(flip),b,13756,a),flip(a)].">
      <j1 rule="hyper" parents="316 13728 13756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13764">
    <literal><![CDATA[
      x * (y * a(x,y,a(z,u,w))) = L(x,y,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,9440,a(flip),b,13756,a)].">
      <j1 rule="hyper" parents="139 9440 13756"/>
    </justification>
  </clause>

  <clause id="13765">
    <literal><![CDATA[
      L(L(x,y,z),1 / (1 / x),u) * ((L(x,y,z) \ 1) * x) = a(u,1 / (1 / x),L(x,y,z)) \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(6721(a,1),13757(a,1,2))].">
      <j1 rule="para" parents="6721 13757"/>
    </justification>
  </clause>

  <clause id="13766">
    <literal><![CDATA[
      (x \ 1) * (a(y,z,x) \ z) = L(x \ 1,z,y) * z
    ]]></literal>
    <justification jstring="[para(13757(a,1),7079(a,1,2))].">
      <j1 rule="para" parents="13757 7079"/>
    </justification>
  </clause>

  <clause id="13767">
    <literal><![CDATA[
      (x * a(y,x,a(z,u,w))) * y = x * L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(9440(a,1),13759(a,1,1))].">
      <j1 rule="para" parents="9440 13759"/>
    </justification>
  </clause>

  <clause id="13768">
    <literal><![CDATA[
      (a(x,y,L(a(z,x,y) \ 1,u,w)) \ y) * L(a(z,x,y) \ 1,u,w) = y * L(y \ L(y,x,z),u,w)
    ]]></literal>
    <justification jstring="[para(10015(a,1),13759(a,2,2))].">
      <j1 rule="para" parents="10015 13759"/>
    </justification>
  </clause>

  <clause id="13769">
    <literal><![CDATA[
      L(x,y * (z \ (y \ z)),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10797,a,b,13726,a)].">
      <j1 rule="hyper" parents="63 10797 13726"/>
    </justification>
  </clause>

  <clause id="13771">
    <literal><![CDATA[
      x * (x * (L(x,x,x \ y) \ ((y \ (y / x)) * z))) = L(L(z,y \ (x \ y),x),a(x,x,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12232,a(flip),b,13769,a)].">
      <j1 rule="hyper" parents="63 12232 13769"/>
    </justification>
  </clause>

  <clause id="13772">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,w) = a(w,u,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,2652,a,b,13642,a),flip(a)].">
      <j1 rule="hyper" parents="316 2652 13642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13773">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) * v5 = v5 * a(z \ L(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,13642,a,b,2295,a),flip(a)].">
      <j1 rule="hyper" parents="139 13642 2295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13774">
    <literal><![CDATA[
      x * a(y \ L(y,z,u),w,v5) = x * a(v5,w,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,13642,a,b,9,a)].">
      <j1 rule="hyper" parents="139 13642 9"/>
    </justification>
  </clause>

  <clause id="13775">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,w) * v5 = v5 * a(w,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(138,a,13642,a,b,2287,a)].">
      <j1 rule="hyper" parents="138 13642 2287"/>
    </justification>
  </clause>

  <clause id="13776">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,w) * v5 = a(w,u,x * L(x,y,z)) * v5
    ]]></literal>
    <justification jstring="[hyper(138,a,13642,a,b,11,a)].">
      <j1 rule="hyper" parents="138 13642 11"/>
    </justification>
  </clause>

  <clause id="13777">
    <literal><![CDATA[
      a(x,x \ L(x,y,z),u) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2579,a(flip),b,13642,a)].">
      <j1 rule="hyper" parents="63 2579 13642"/>
    </justification>
  </clause>

  <clause id="13779">
    <literal><![CDATA[
      L(a(x,a(y,z,u),w),v5 * a(x,a(u,z,y),w),v5) \ a(x,a(y,z,u),w) = a(v5,v5 * a(x,a(y,z,u),w),a(x,a(y,z,u),w))
    ]]></literal>
    <justification jstring="[para(13677(a,1),13666(a,1,1,2))].">
      <j1 rule="para" parents="13677 13666"/>
    </justification>
  </clause>

  <clause id="13780">
    <literal><![CDATA[
      (L(x \ 1,y,z) * y) \ R(x \ 1,a(z,y,x) \ y,a(z,y,x) \ y) = (a(z,y,x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(13766(a,1),570(a,1,1))].">
      <j1 rule="para" parents="13766 570"/>
    </justification>
  </clause>

  <clause id="13782">
    <literal><![CDATA[
      a(x,x \ L(x,y,z),z * y) = a(z * y,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,11826,a(flip),b,13777,a),flip(a)].">
      <j1 rule="hyper" parents="316 11826 13777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13783">
    <literal><![CDATA[
      x * a(y,y \ L(y,z,u),x) = L(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,13777,a,b,8241,a)].">
      <j1 rule="hyper" parents="139 13777 8241"/>
    </justification>
  </clause>

  <clause id="13784">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) * w = w * a(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(139,a,13777,a,b,2295,a),flip(a)].">
      <j1 rule="hyper" parents="139 13777 2295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13787">
    <literal><![CDATA[
      L(L(x \ y,z,u) \ (x \ y),x \ y,x) = x \ (L(y / x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(133,a,6574,a(flip),b,13622,a),flip(a)].">
      <j1 rule="hyper" parents="133 6574 13622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13788">
    <literal><![CDATA[
      (L(x,y,z) * u) * L(L(x,w,v5) \ x,x,L(x,y,z) * u) = x * ((L(x,y,z) * u) / L(T(x,u),w,v5))
    ]]></literal>
    <justification jstring="[para(6569(a,2),13622(a,2,2))].">
      <j1 rule="para" parents="6569 13622"/>
    </justification>
  </clause>

  <clause id="13789">
    <literal><![CDATA[
      x * L(L(L(y,z,u) \ y,w,v5),L(y,w,v5),x) = L(y,w,v5) * (L(L(y,w,v5),z,u) \ x)
    ]]></literal>
    <justification jstring="[para(13383(a,1),13622(a,1,2,1))].">
      <j1 rule="para" parents="13383 13622"/>
    </justification>
  </clause>

  <clause id="13790">
    <literal><![CDATA[
      (x \ ((x / y) * L(y,z,u))) \ 1 = x \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,13384,a(flip),b,13624,a)].">
      <j1 rule="hyper" parents="63 13384 13624"/>
    </justification>
  </clause>

  <clause id="13791">
    <literal><![CDATA[
      (x * a(y,y,x)) * (x \ z) = x * (L(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6588,a(flip),b,13611,a)].">
      <j1 rule="hyper" parents="63 6588 13611"/>
    </justification>
  </clause>

  <clause id="13792">
    <literal><![CDATA[
      L(x,y,z) * (L(L(x,y,z),u,w) \ (z * (y * x))) = (z * y) * (L(1 / L(x,y,z),u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(202(a,1),13611(a,1,1)),flip(a)].">
      <j1 rule="para" parents="202 13611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13793">
    <literal><![CDATA[
      ((x / y) / ((L(1 / y,z,u) \ 1) \ 1)) \ (y * (L(y,z,u) \ x)) = a(x / y,L(1 / y,z,u) \ 1,L(1 / y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(13611(a,1),6928(a,1,2))].">
      <j1 rule="para" parents="13611 6928"/>
    </justification>
  </clause>

  <clause id="13794">
    <literal><![CDATA[
      (x * (L(x,x,y) \ z)) \ (z * a(y,x,x)) = a(z,x,a(y,x,x))
    ]]></literal>
    <justification jstring="[para(13611(a,1),13267(a,1,1))].">
      <j1 rule="para" parents="13611 13267"/>
    </justification>
  </clause>

  <clause id="13795">
    <literal><![CDATA[
      x * ((L(1 / x,y,z) \ 1) \ u) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,13250,a,b,13613,a)].">
      <j1 rule="hyper" parents="37 13250 13613"/>
    </justification>
  </clause>

  <clause id="13796">
    <literal><![CDATA[
      R(x,y,z) \ (u / (R(x,y,z) \ 1)) = x \ (u / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,12352,a,b,13614,a)].">
      <j1 rule="hyper" parents="63 12352 13614"/>
    </justification>
  </clause>

  <clause id="13799">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w) \ v5,a(x,y,z),a(x,y,z)) = (L(a(x,y,z),u,w) \ 1) * v5
    ]]></literal>
    <justification jstring="[hyper(38,a,7604,a,b,13615,a)].">
      <j1 rule="hyper" parents="38 7604 13615"/>
    </justification>
  </clause>

  <clause id="13800">
    <literal><![CDATA[
      L(x,y,z) \ L(u,x \ 1,x) = (L(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,7628,a(flip),b,13619,a)].">
      <j1 rule="hyper" parents="63 7628 13619"/>
    </justification>
  </clause>

  <clause id="13801">
    <literal><![CDATA[
      ((L(x,y,z) \ 1) * u) * L((x \ 1) \ 1,y,z) = ((1 / x) * u) * x
    ]]></literal>
    <justification jstring="[para(13800(a,1),9407(a,1,1))].">
      <j1 rule="para" parents="13800 9407"/>
    </justification>
  </clause>

  <clause id="13802">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * u = x * (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6596,a,b,13620,a)].">
      <j1 rule="hyper" parents="63 6596 13620"/>
    </justification>
  </clause>

  <clause id="13804">
    <literal><![CDATA[
      x * (x * (L(x,x,y) \ z)) = (x * a(y,x,x)) * z
    ]]></literal>
    <justification jstring="[para(7290(a,1),13620(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7290 13620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13806">
    <literal><![CDATA[
      a(x,y,(z * (z * (L(z,u,w) \ v5))) * v6) = a(x,y,v6 * (v5 * L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(13620(a,1),8285(a,1,3,1))].">
      <j1 rule="para" parents="13620 8285"/>
    </justification>
  </clause>

  <clause id="13807">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * (w * (L(w,v5,v6) \ v7))))) = a(x,y,z \ (u \ (v7 * L(w \ 1,v5,v6))))
    ]]></literal>
    <justification jstring="[para(13620(a,1),8322(a,1,3,2,2))].">
      <j1 rule="para" parents="13620 8322"/>
    </justification>
  </clause>

  <clause id="13808">
    <literal><![CDATA[
      (x * (x * (L(x,y,z) \ u))) * L(x \ K(u,x),y,z) = R(u,x * (L(x,y,z) \ x),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(13620(a,1),9811(a,1,1))].">
      <j1 rule="para" parents="13620 9811"/>
    </justification>
  </clause>

  <clause id="13809">
    <literal><![CDATA[
      a(x,y,(z * (z * (L(z,u,w) \ v5))) \ v6) = a(x,y,(v5 * L(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[para(13620(a,1),11733(a,1,3,1))].">
      <j1 rule="para" parents="13620 11733"/>
    </justification>
  </clause>

  <clause id="13810">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * x)) = u * (x * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(11(a,1),13621(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 13621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13811">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * (L(L(z,y,x),u,w) \ L(z,y,x))) = L(z,y,x) * (L(L(z,y,x),u,w) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(202(a,1),13621(a,1,1))].">
      <j1 rule="para" parents="202 13621"/>
    </justification>
  </clause>

  <clause id="13812">
    <literal><![CDATA[
      a(x,y,z \ ((u * ((L(u,w,v5) \ u) \ 1)) * (v6 / u))) = a(x,y,z \ (u * (L(u,w,v5) \ v6)))
    ]]></literal>
    <justification jstring="[para(13621(a,1),6353(a,2,3,2))].">
      <j1 rule="para" parents="13621 6353"/>
    </justification>
  </clause>

  <clause id="13813">
    <literal><![CDATA[
      (x / (y * z)) * ((y * z) * T(y * (z / (y * z)),y * z)) = (y * z) * (L(y * z,(y * z) \ z,y) \ x)
    ]]></literal>
    <justification jstring="[para(10610(a,1),13621(a,1,2,2))].">
      <j1 rule="para" parents="10610 13621"/>
    </justification>
  </clause>

  <clause id="13814">
    <literal><![CDATA[
      L(L(x \ 1,x,x \ (y / z)) \ (z * (L(z,u,w) \ z)),(y / z) \ (x \ (y / z)),y / z) = ((y / z) / x) \ (z * (L(z,u,w) \ y))
    ]]></literal>
    <justification jstring="[para(13621(a,1),10893(a,2,2))].">
      <j1 rule="para" parents="13621 10893"/>
    </justification>
  </clause>

  <clause id="13815">
    <literal><![CDATA[
      L(x,y,L(y,z,u)) \ x = a(y,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9909,a(flip),b,13649,a)].">
      <j1 rule="hyper" parents="63 9909 13649"/>
    </justification>
  </clause>

  <clause id="13816">
    <literal><![CDATA[
      a(x,L(x,y,z),u) \ u = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,13815,a)].">
      <j1 rule="hyper" parents="39 2301 13815"/>
    </justification>
  </clause>

  <clause id="13817">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) \ 1 = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,13642,a(flip),b,13663,a),flip(a)].">
      <j1 rule="hyper" parents="316 13642 13663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13818">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) \ 1 = a(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,2579,a(flip),b,13663,a),flip(a)].">
      <j1 rule="hyper" parents="316 2579 13663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13819">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * (u \ x) = L(u,a(y,z,x),x) \ x
    ]]></literal>
    <justification jstring="[para(7009(a,1),13669(a,1,1))].">
      <j1 rule="para" parents="7009 13669"/>
    </justification>
  </clause>

  <clause id="13820">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w),v5,v6)) = a(x,y,a(a(w,u,z),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,13660,a,b,13702,a)].">
      <j1 rule="hyper" parents="316 13660 13702"/>
    </justification>
  </clause>

  <clause id="13821">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (y * x) = y * L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8401,a(flip),b,13767,a)].">
      <j1 rule="hyper" parents="63 8401 13767"/>
    </justification>
  </clause>

  <clause id="13824">
    <literal><![CDATA[
      x * a(x,x \ L(x,y,z),z * y) = L(x,a(x,y,z),z * y)
    ]]></literal>
    <justification jstring="[para(13782(a,2),13717(a,1,2))].">
      <j1 rule="para" parents="13782 13717"/>
    </justification>
  </clause>

  <clause id="13825">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,x,x \ L(x,y,z)) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,13783,a(flip),b,8800,a)].">
      <j1 rule="hyper" parents="139 13783 8800"/>
    </justification>
  </clause>

  <clause id="13826">
    <literal><![CDATA[
      L(x,y \ (1 / z),(y \ (1 / z)) \ L(y \ (1 / z),y,z)) = x * a(y \ (1 / z),(y \ (1 / z)) \ ((z * y) \ K(z,z \ 1)),x)
    ]]></literal>
    <justification jstring="[para(1090(a,1),13783(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1090 13783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13828">
    <literal><![CDATA[
      (L(x,y,z) \ u) * a(x,x \ L(x,w,v5),u) = L(x,y,z) \ L(u,x,x \ L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(13783(a,1),8423(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13783 8423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13829">
    <literal><![CDATA[
      L(L(x,y,z),y,z) * (L(x,y,z) \ u) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13257,a,b,13795,a)].">
      <j1 rule="hyper" parents="63 13257 13795"/>
    </justification>
  </clause>

  <clause id="13830">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ (x * u) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13255,a,b,13795,a)].">
      <j1 rule="hyper" parents="63 13255 13795"/>
    </justification>
  </clause>

  <clause id="13831">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) \ u = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11668,a,b,13795,a)].">
      <j1 rule="hyper" parents="63 11668 13795"/>
    </justification>
  </clause>

  <clause id="13832">
    <literal><![CDATA[
      x * ((x * a(y,x,x)) \ z) = (z / x) * L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7345,a(flip),b,13795,a)].">
      <j1 rule="hyper" parents="63 7345 13795"/>
    </justification>
  </clause>

  <clause id="13833">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((L(1 / x,u,w) \ 1) \ v5)) = L(x,y,z) \ ((v5 / x) * L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(133,a,13795,a(flip),b,1128,a),flip(a)].">
      <j1 rule="hyper" parents="133 13795 1128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13836">
    <literal><![CDATA[
      R(x,y,z) \ T(u / (R(x,y,z) \ 1),R(x,y,z) \ 1) = ((R(x,y,z) \ 1) \ (x \ (u / (x \ 1)))) * (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(13796(a,1),851(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13796 851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13837">
    <literal><![CDATA[
      (x * y) * ((y * x) * (L(x * y,z,u) \ w)) = (L(1 / (y * x),z,u) \ 1) * w
    ]]></literal>
    <justification jstring="[hyper(316,a,12944,a,b,13802,a)].">
      <j1 rule="hyper" parents="316 12944 13802"/>
    </justification>
  </clause>

  <clause id="13839">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * x = u * (x * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,4428,a,b,13810,a)].">
      <j1 rule="hyper" parents="63 4428 13810"/>
    </justification>
  </clause>

  <clause id="13840">
    <literal><![CDATA[
      x \ L(x,x \ L(x,y,z),u) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10029,a(flip),b,13817,a)].">
      <j1 rule="hyper" parents="63 10029 13817"/>
    </justification>
  </clause>

  <clause id="13842">
    <literal><![CDATA[
      L(x,y,z) \ L(x \ L(x,y,z),x,u) = x \ a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,13817,a(flip),b,10035,a),flip(a)].">
      <j1 rule="hyper" parents="133 13817 10035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13844">
    <literal><![CDATA[
      a(x \ y,(x \ y) \ L(x \ y,x,x \ 1),z) = a(z,x \ y,(x \ y) * ((1 / x) * y)) \ 1
    ]]></literal>
    <justification jstring="[para(887(a,1),13818(a,1,1,3,2)),flip(a)].">
      <j1 rule="para" parents="887 13818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13845">
    <literal><![CDATA[
      a((x \ 1) * y,((x \ 1) * y) \ L((x \ 1) * y,z,u),w) = a(w,y * x,(y * x) * L(y * x,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(9733(a,1),13818(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9733 13818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13848">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ (x * u) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(6585(a,1),13830(a,1,1))].">
      <j1 rule="para" parents="6585 13830"/>
    </justification>
  </clause>

  <clause id="13849">
    <literal><![CDATA[
      (x \ y) * (x * (L(x,z,u) \ x)) = (L(x,z,u) \ y) * x
    ]]></literal>
    <justification jstring="[para(1130(a,1),13839(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1130 13839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13850">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ u = ((x \ u) / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,168,a(flip),b,13848,a)].">
      <j1 rule="hyper" parents="63 168 13848"/>
    </justification>
  </clause>

  <clause id="13853">
    <literal><![CDATA[
      (x * L(a(y,z,x),x,z)) \ u = ((x \ u) / x) * L(x,z,y)
    ]]></literal>
    <justification jstring="[para(13403(a,2),13850(a,1,1,2))].">
      <j1 rule="para" parents="13403 13850"/>
    </justification>
  </clause>

  <clause id="13855">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (z * y)) = a(x,y,z) \ K(z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12754,a(flip),b,13664,a)].">
      <j1 rule="hyper" parents="63 12754 13664"/>
    </justification>
  </clause>

  <clause id="13856">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,y,z) \ u)) = L(L(x,y,z),y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,1130,a(flip),b,13617,a),flip(a)].">
      <j1 rule="hyper" parents="63 1130 13617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13857">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,y,z) \ u) = x \ (L(L(x,y,z),y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(133,a,1130,a(flip),b,13617,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 1130 13617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13858">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (a(x,y,z) \ v5) = a(x,y,z) * (L(a(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(13454(a,1),13617(a,1,2,1))].">
      <j1 rule="para" parents="13454 13617"/>
    </justification>
  </clause>

  <clause id="13859">
    <literal><![CDATA[
      L(a(x,y,z),u,a(z * L(z,y,x),w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,13635,a(flip),b,13654,a),flip(a)].">
      <j1 rule="hyper" parents="316 13635 13654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13860">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,x,u) = x * a(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13400,a,b,13784,a)].">
      <j1 rule="hyper" parents="63 13400 13784"/>
    </justification>
  </clause>

  <clause id="13861">
    <literal><![CDATA[
      L((x \ ((x / y) * L(y,z,u))) \ 1,w,v5) = R(x \ (y * (L(y,z,u) \ x)),w,v5)
    ]]></literal>
    <justification jstring="[para(13790(a,1),11953(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13790 11953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13862">
    <literal><![CDATA[
      a(x,a(y,z,z),L(z,z,y)) = a(x,z,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7424,a(flip),b,13794,a)].">
      <j1 rule="hyper" parents="63 7424 13794"/>
    </justification>
  </clause>

  <clause id="13863">
    <literal><![CDATA[
      a(x,a(y,y,z),L(y,y,z)) = a(x,y,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13658,a,b,13862,a)].">
      <j1 rule="hyper" parents="63 13658 13862"/>
    </justification>
  </clause>

  <clause id="13864">
    <literal><![CDATA[
      a(x,a(y,y,z),L(y,y,z)) * y = L(y,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[para(13863(a,2),13478(a,1,1))].">
      <j1 rule="para" parents="13863 13478"/>
    </justification>
  </clause>

  <clause id="13865">
    <literal><![CDATA[
      x \ (L(x,y,a(y,y,z)) * y) = a(x,a(y,y,z),L(y,y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(316,a,13763,a,b,13864,a)].">
      <j1 rule="hyper" parents="316 13763 13864"/>
    </justification>
  </clause>

  <clause id="13866">
    <literal><![CDATA[
      x \ (y \ (L(L(y,z,u),z,u) \ ((y * L(L(y,z,u),z,u)) * x))) = L(x,L(y,z,u),L(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(13857(a,1),9962(a,1,2))].">
      <j1 rule="para" parents="13857 9962"/>
    </justification>
  </clause>

  <clause id="13867">
    <literal><![CDATA[
      x \ (y * L(y \ x,y * x,z)) = a(z,y * x,x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,10115,a(flip),b,13573,a)].">
      <j1 rule="hyper" parents="63 10115 13573"/>
    </justification>
  </clause>

  <clause id="13868">
    <literal><![CDATA[
      x \ (y * L(y \ x,x * y,z)) = a(z,y * x,x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(10797(a,1),13867(a,1,2,2))].">
      <j1 rule="para" parents="10797 13867"/>
    </justification>
  </clause>

  <clause id="13869">
    <literal><![CDATA[
      a(x * y,x * y,L(a(z,u,w),x,y)) = a(a(z,u,w),y * x,x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,11870,a(flip),b,13868,a)].">
      <j1 rule="hyper" parents="63 11870 13868"/>
    </justification>
  </clause>

  <clause id="13870">
    <literal><![CDATA[
      a(x,(y \ z) \ 1,y \ z) = a(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2657,a(flip),b,13577,a)].">
      <j1 rule="hyper" parents="63 2657 13577"/>
    </justification>
  </clause>

  <clause id="13871">
    <literal><![CDATA[
      a(x,y \ z,y \ z) \ x = (x / (z \ y)) / (1 / (z \ y))
    ]]></literal>
    <justification jstring="[para(13870(a,1),10693(a,1,1))].">
      <j1 rule="para" parents="13870 10693"/>
    </justification>
  </clause>

  <clause id="13872">
    <literal><![CDATA[
      T(a(x,y \ z,y \ z) \ x,(z \ y) \ 1) = ((z \ y) \ 1) \ (x / (((z \ y) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(13871(a,2),4232(a,1,1))].">
      <j1 rule="para" parents="13871 4232"/>
    </justification>
  </clause>

  <clause id="13873">
    <literal><![CDATA[
      a(L(x,L(y,z,u),L(y,z,u)),w,v5) = a(L(x,y,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,4649,a(flip),b,13603,a),flip(a)].">
      <j1 rule="hyper" parents="316 4649 13603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13874">
    <literal><![CDATA[
      L(x,L(y,L(z,u,w),L(z,u,w)),v5) = L(x,L(y,z,z),v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,11006,a(flip),b,13608,a),flip(a)].">
      <j1 rule="hyper" parents="316 11006 13608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13875">
    <literal><![CDATA[
      a(x,y,y) * (z * L(y,y,x)) = L(z,y,a(y,y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(38,a,9015,a,b,13865,a)].">
      <j1 rule="hyper" parents="38 9015 13865"/>
    </justification>
  </clause>

  <clause id="13876">
    <literal><![CDATA[
      L(a(x,y \ 1,y) \ 1,z,u) = a(x,y \ 1,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(2655(a,1),13571(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2655 13571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13878">
    <literal><![CDATA[
      a(x,y \ 1,L(y,z,u)) = L(a(x,y \ 1,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(39,a,13442,a(flip),b,13876,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 13442 13876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13879">
    <literal><![CDATA[
      a(x,y,L(z * a(u,z,w * v5),u,v5 * w)) = a(x,y,L(z,w * v5,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8747,a(flip),b,13755,a),flip(a)].">
      <j1 rule="hyper" parents="63 8747 13755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13880">
    <literal><![CDATA[
      a(x,y,L(z * a(u,z,w),u,w)) = a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8746,a(flip),b,13755,a),flip(a)].">
      <j1 rule="hyper" parents="63 8746 13755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13881">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) * u,z,w)) = a(x,y,L(u,w,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5535,a,b,13880,a)].">
      <j1 rule="hyper" parents="63 5535 13880"/>
    </justification>
  </clause>

  <clause id="13883">
    <literal><![CDATA[
      ((1 / L(x,y,z)) * u) * L(x,y,z) = ((1 / x) * u) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,6580,a(flip),b,13801,a)].">
      <j1 rule="hyper" parents="63 6580 13801"/>
    </justification>
  </clause>

  <clause id="13885">
    <literal><![CDATA[
      ((x * (y \ 1)) * z) * ((x * (y \ 1)) \ 1) = ((1 / (y / x)) * z) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13045,a(flip),b,13883,a)].">
      <j1 rule="hyper" parents="63 13045 13883"/>
    </justification>
  </clause>

  <clause id="13886">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,x,x \ L(x,y,z)) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,13795,a,b,13825,a),flip(a)].">
      <j1 rule="hyper" parents="316 13795 13825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13887">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * L(v5,L(x,u,w),L(x,u,w) \ L(L(x,u,w),y,z)) = (v5 / L(x,u,w)) * L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(2136(a,1),13825(a,1,1))].">
      <j1 rule="para" parents="2136 13825"/>
    </justification>
  </clause>

  <clause id="13888">
    <literal><![CDATA[
      (x \ L(x,x,y)) * L(z,x,a(x,x,y)) = (z / x) * L(x,x,y)
    ]]></literal>
    <justification jstring="[para(7488(a,1),13825(a,1,2))].">
      <j1 rule="para" parents="7488 13825"/>
    </justification>
  </clause>

  <clause id="13889">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,x * a(z,y,y),(x * a(z,y,y)) \ L(x * a(z,y,y),y,z)) = (u / (x * a(z,y,y))) * L(x * a(z,y,y),y,z)
    ]]></literal>
    <justification jstring="[para(9291(a,1),13825(a,1,1))].">
      <j1 rule="para" parents="9291 13825"/>
    </justification>
  </clause>

  <clause id="13890">
    <literal><![CDATA[
      (x * L(y,z,u)) * L(y,z,u) = (x * y) * L(L(y,z,u),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9972,a(flip),b,13587,a),flip(a)].">
      <j1 rule="hyper" parents="63 9972 13587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13891">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ 1,u) = a(x,x \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,5700,a(flip),b,13607,a),flip(a)].">
      <j1 rule="hyper" parents="316 5700 13607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13893">
    <literal><![CDATA[
      a(L(x,x,y),L(x \ 1,x,y),z) = a(x,x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13057,a,b,13891,a)].">
      <j1 rule="hyper" parents="63 13057 13891"/>
    </justification>
  </clause>

  <clause id="13895">
    <literal><![CDATA[
      a(L(x,x,y),y \ (x \ y),z) = a(x,x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11376,a(flip),b,13893,a)].">
      <j1 rule="hyper" parents="63 11376 13893"/>
    </justification>
  </clause>

  <clause id="13896">
    <literal><![CDATA[
      a(x \ ((y \ 1) \ x),x \ (y \ x),z) = a(y,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3325,a(flip),b,13895,a)].">
      <j1 rule="hyper" parents="63 3325 13895"/>
    </justification>
  </clause>

  <clause id="13897">
    <literal><![CDATA[
      L(x,y \ (z \ y),(y \ (z \ y)) \ 1) = a(z,z \ 1,x) \ x
    ]]></literal>
    <justification jstring="[para(13896(a,1),13104(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13896 13104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13898">
    <literal><![CDATA[
      L(x,y \ (z \ y),(y \ (z \ y)) \ 1) = L(x,z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1384,a(flip),b,13897,a),flip(a)].">
      <j1 rule="hyper" parents="316 1384 13897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13901">
    <literal><![CDATA[
      L(L(x,y,z),y,z) * a(z,y,x) = L(L(x,y,z),a(z,y,x),y)
    ]]></literal>
    <justification jstring="[para(13635(a,1),13648(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13635 13648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13902">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,a(z,y,L(x,y,z) \ 1),y) = x \ a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,6861,a(flip),b,13653,a),flip(a)].">
      <j1 rule="hyper" parents="316 6861 13653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13903">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,a(z,y,L(x,y,z)),y) = x \ a(z,y,x)
    ]]></literal>
    <justification jstring="[para(2534(a,1),13902(a,1,2))].">
      <j1 rule="para" parents="2534 13902"/>
    </justification>
  </clause>

  <clause id="13904">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,a(z,y,x),y) = x \ a(z,y,x)
    ]]></literal>
    <justification jstring="[para(13635(a,1),13903(a,1,2))].">
      <j1 rule="para" parents="13635 13903"/>
    </justification>
  </clause>

  <clause id="13905">
    <literal><![CDATA[
      a(x,y,(((z * (u \ 1)) \ w) \ 1) \ (u \ (z \ w))) = a(x,y,a(z,u,w \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12494,a,b,13684,a)].">
      <j1 rule="hyper" parents="63 12494 13684"/>
    </justification>
  </clause>

  <clause id="13906">
    <literal><![CDATA[
      L(x \ y,z,u) \ (x \ y) = y \ (L(x / y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13532,a(flip),b,13787,a)].">
      <j1 rule="hyper" parents="63 13532 13787"/>
    </justification>
  </clause>

  <clause id="13907">
    <literal><![CDATA[
      L(R(x,y,z) \ u,w,v5) \ (R(x,y,z) \ u) = u \ (L(L(x,y,z) / u,w,v5) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13550,a,b,13906,a)].">
      <j1 rule="hyper" parents="63 13550 13906"/>
    </justification>
  </clause>

  <clause id="13908">
    <literal><![CDATA[
      L(a(x,y,z \ L(u,w,v5)),z \ R(u,w,v5),y) = R(u,w,v5) \ (L(z / R(u,w,v5),y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13412,a,b,13906,a)].">
      <j1 rule="hyper" parents="63 13412 13906"/>
    </justification>
  </clause>

  <clause id="13909">
    <literal><![CDATA[
      L(a(x,y,z * L(z,u,w)),z \ L(z,u,w),y) = L(z,u,w) \ (L(z / L(z,u,w),y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13409,a,b,13906,a)].">
      <j1 rule="hyper" parents="63 13409 13906"/>
    </justification>
  </clause>

  <clause id="13911">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) \ 1 = y \ (L(x / y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1900,a,b,13906,a)].">
      <j1 rule="hyper" parents="63 1900 13906"/>
    </justification>
  </clause>

  <clause id="13912">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) \ (x \ R(x,y,z)) = x \ (L(R(x,y,z) / x,u,w) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12869,a(flip),b,13906,a)].">
      <j1 rule="hyper" parents="63 12869 13906"/>
    </justification>
  </clause>

  <clause id="13913">
    <literal><![CDATA[
      x \ (L((x \ y) / x,z,u) \ (x \ y)) = ((x \ y) \ (x \ L(y,z,u))) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1909,a(flip),b,13906,a),flip(a)].">
      <j1 rule="hyper" parents="63 1909 13906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13914">
    <literal><![CDATA[
      a(x,y,z \ (L(u / z,w,v5) \ u)) = a(x,y,(u \ z) * L(u \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(13906(a,1),2652(a,1,3))].">
      <j1 rule="para" parents="13906 2652"/>
    </justification>
  </clause>

  <clause id="13915">
    <literal><![CDATA[
      (x \ (L(y / x,z,u) \ y)) * (y \ x) = L(1 / (y \ x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(13906(a,1),6592(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13906 6592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13916">
    <literal><![CDATA[
      x * L(y \ (L(z / y,u,w) \ z),z \ y,x) = (z \ y) * (L(z \ y,u,w) \ x)
    ]]></literal>
    <justification jstring="[para(13906(a,1),13622(a,1,2,1))].">
      <j1 rule="para" parents="13906 13622"/>
    </justification>
  </clause>

  <clause id="13917">
    <literal><![CDATA[
      L(x,y,z) * (x \ a(u,x,x * L(x,y,z))) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(152,a,13842,a)].">
      <j1 rule="hyper" parents="152 13842"/>
    </justification>
  </clause>

  <clause id="13922">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,x,z * y) = L(x,a(x,y,z),z * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,13824,a(flip),b,13860,a),flip(a)].">
      <j1 rule="hyper" parents="316 13824 13860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13923">
    <literal><![CDATA[
      L(x,y,z) * a(u,x,x * L(x,y,z)) = x * L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,13917,a(flip),b,1126,a),flip(a)].">
      <j1 rule="hyper" parents="139 13917 1126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13924">
    <literal><![CDATA[
      L(x,a(x,y,z),z * y) = L(x,y,z) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(13625(a,2),13922(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13625 13922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13925">
    <literal><![CDATA[
      L(x,a(x,y,z),z * y) = L(x,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(316,a,11629,a(flip),b,13924,a),flip(a)].">
      <j1 rule="hyper" parents="316 11629 13924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13926">
    <literal><![CDATA[
      L(x,a(x,y,z),z * y) = x * a(y,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,13475,a,b,13925,a),flip(a)].">
      <j1 rule="hyper" parents="316 13475 13925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13927">
    <literal><![CDATA[
      a(x,y,z) \ R(x,y,z) = L(x,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13730,a(flip),b,13925,a)].">
      <j1 rule="hyper" parents="63 13730 13925"/>
    </justification>
  </clause>

  <clause id="13928">
    <literal><![CDATA[
      R(x,y,z) = a(x,y,z) * L(x,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(139,a,13925,a(flip),b,13730,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 13925 13730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13931">
    <literal><![CDATA[
      R(x,y,z) = L(x,a(z,y,x),y) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(38,a,2275,a,b,13927,a),flip(a)].">
      <j1 rule="hyper" parents="38 2275 13927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13932">
    <literal><![CDATA[
      L(x,a(y,z,x),z) \ R(x,z,y) = a(x,z,y)
    ]]></literal>
    <justification jstring="[para(13927(a,1),2301(a,1,1))].">
      <j1 rule="para" parents="13927 2301"/>
    </justification>
  </clause>

  <clause id="13933">
    <literal><![CDATA[
      L(L(x,a(y,L(x,z,u),L(x,w,v5)),x),w,v5) \ R(L(x,w,v5),L(x,z,u),y) = a(L(x,w,v5),L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(7997(a,1),13932(a,1,1))].">
      <j1 rule="para" parents="7997 13932"/>
    </justification>
  </clause>

  <clause id="13934">
    <literal><![CDATA[
      L(x,y,z) \ ((L(x,a(z,y,x),y) \ L(x,y,z)) * u) = R(x,y,z) \ (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(13932(a,1),12976(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13932 12976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13936">
    <literal><![CDATA[
      a(x * y,z,a(z,y,x)) = a(y,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,13717,a,b,13926,a(flip))].">
      <j1 rule="hyper" parents="34 13717 13926"/>
    </justification>
  </clause>

  <clause id="13937">
    <literal><![CDATA[
      a(x * y,z,a(x,y,z)) = a(y,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,13711,a,b,13926,a(flip))].">
      <j1 rule="hyper" parents="34 13711 13926"/>
    </justification>
  </clause>

  <clause id="13938">
    <literal><![CDATA[
      a(x,a(x,y,z),z * y) = a(y,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,13710,a,b,13936,a)].">
      <j1 rule="hyper" parents="63 13710 13936"/>
    </justification>
  </clause>

  <clause id="13939">
    <literal><![CDATA[
      a(x * y,z,a(z,x,y)) = a(x,z,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2771,a,b,13936,a)].">
      <j1 rule="hyper" parents="63 2771 13936"/>
    </justification>
  </clause>

  <clause id="13941">
    <literal><![CDATA[
      a(x,a(x,y,z),y * z) = a(y,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,13938,a)].">
      <j1 rule="hyper" parents="63 5469 13938"/>
    </justification>
  </clause>

  <clause id="13942">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * a(y,x,z) = y \ R(y,x,z)
    ]]></literal>
    <justification jstring="[para(13939(a,1),8726(a,1,1))].">
      <j1 rule="para" parents="13939 8726"/>
    </justification>
  </clause>

  <clause id="13943">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) \ R(y,x,z) = y * a(y,x,z)
    ]]></literal>
    <justification jstring="[para(13939(a,1),8732(a,1,1))].">
      <j1 rule="para" parents="13939 8732"/>
    </justification>
  </clause>

  <clause id="13945">
    <literal><![CDATA[
      x * (R(x,y,z) \ a(x,y,z)) = a(y,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,8761,a,b,13941,a)].">
      <j1 rule="hyper" parents="63 8761 13941"/>
    </justification>
  </clause>

  <clause id="13946">
    <literal><![CDATA[
      a(x,y,z) \ a(y,x,a(z,y,x)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,13941,a(flip),b,8760,a)].">
      <j1 rule="hyper" parents="133 13941 8760"/>
    </justification>
  </clause>

  <clause id="13947">
    <literal><![CDATA[
      L(x,y,z) * (R(x,u,w) \ a(x,u,w)) = a(u,x,a(w,u,x)) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(13941(a,1),9295(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13941 9295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13948">
    <literal><![CDATA[
      L(a(x,y,a(z,x,y)),y \ L(y,x,z),u) \ u = (y \ R(y,x,z)) * (a(y,x,z) \ u)
    ]]></literal>
    <justification jstring="[para(13941(a,1),10131(a,1,1,1))].">
      <j1 rule="para" parents="13941 10131"/>
    </justification>
  </clause>

  <clause id="13949">
    <literal><![CDATA[
      a(x,y,z) * a(y,x,a(x,y,z)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13689,a(flip),b,13942,a)].">
      <j1 rule="hyper" parents="63 13689 13942"/>
    </justification>
  </clause>

  <clause id="13950">
    <literal><![CDATA[
      1 \ R(x,L(x,y,z),u) = x * a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(6971(a,1),13943(a,1,1))].">
      <j1 rule="para" parents="6971 13943"/>
    </justification>
  </clause>

  <clause id="13951">
    <literal><![CDATA[
      x \ R(x,L(x,y,z),u) = a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(133,a,66,a(flip),b,13950,a(flip))].">
      <j1 rule="hyper" parents="133 66 13950"/>
    </justification>
  </clause>

  <clause id="13954">
    <literal><![CDATA[
      L((x \ (a(y,x,x) \ 1)) * x,z,u) = (x \ 1) * (a(y,x,L(x,z,u)) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1369,a,b,13572,a)].">
      <j1 rule="hyper" parents="63 1369 13572"/>
    </justification>
  </clause>

  <clause id="13955">
    <literal><![CDATA[
      (x / L(y,z,u)) * ((x * (L(y,z,u) \ 1)) \ y) = L(y,y,L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,1586,a(flip),b,13594,a),flip(a)].">
      <j1 rule="hyper" parents="316 1586 13594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13957">
    <literal><![CDATA[
      T(((x * y) * z) * ((x * y) \ 1),x * y) = R(z,(x \ 1) \ y,x \ y)
    ]]></literal>
    <justification jstring="[para(13602(a,1),8144(a,1,1))].">
      <j1 rule="para" parents="13602 8144"/>
    </justification>
  </clause>

  <clause id="13958">
    <literal><![CDATA[
      R(x,(y \ 1) \ z,y \ z) = R(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,625,a(flip),b,13957,a),flip(a)].">
      <j1 rule="hyper" parents="63 625 13957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13959">
    <literal><![CDATA[
      a(x,(y \ 1) \ z,y \ z) = x \ R(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[para(13958(a,1),6378(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13958 6378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13960">
    <literal><![CDATA[
      a(x,(y \ 1) \ z,y \ z) = a(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2380,a(flip),b,13959,a),flip(a)].">
      <j1 rule="hyper" parents="316 2380 13959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13961">
    <literal><![CDATA[
      a(x,y,a(z,u \ w,u \ w)) = a(x,y,a(z,u * w,u * w))
    ]]></literal>
    <justification jstring="[para(13960(a,1),12016(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13960 12016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13962">
    <literal><![CDATA[
      a(x,y,a(z,z * u,z * u)) = a(x,y,a(z,z \ u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7358,a(flip),b,13961,a),flip(a)].">
      <j1 rule="hyper" parents="63 7358 13961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13963">
    <literal><![CDATA[
      a(x,y,a(z,z \ u,u)) = a(x,y,a(z,u * z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13375,a(flip),b,13962,a),flip(a)].">
      <j1 rule="hyper" parents="63 13375 13962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13964">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),z \ v5,z \ v5)) = a(x,y,v5 * (z * (L(z,u,w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11992,a,b,13626,a)].">
      <j1 rule="hyper" parents="63 11992 13626"/>
    </justification>
  </clause>

  <clause id="13965">
    <literal><![CDATA[
      a(x \ R(y,z,u),w,v5) = a(x \ L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,13639,a(flip),b,13651,a),flip(a)].">
      <j1 rule="hyper" parents="63 13639 13651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13968">
    <literal><![CDATA[
      a(x,y,z * L(L(u,w,v5) \ v6,u,u)) = a(x,y,z * (v6 * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5852,a(flip),b,13806,a)].">
      <j1 rule="hyper" parents="63 5852 13806"/>
    </justification>
  </clause>

  <clause id="13969">
    <literal><![CDATA[
      a(x,y,(z \ u) * (w * L(z * u,z,z))) = a(x,y,L(w,z * u,z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9484,a(flip),b,13968,a),flip(a)].">
      <j1 rule="hyper" parents="63 9484 13968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13970">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ v5,z,z) \ v6) = a(x,y,(v5 * L(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5960,a(flip),b,13809,a)].">
      <j1 rule="hyper" parents="63 5960 13809"/>
    </justification>
  </clause>

  <clause id="13972">
    <literal><![CDATA[
      T(((1 / (x / y)) * z) * (x / y),y / x) = R(z,y * (x \ 1),y * x)
    ]]></literal>
    <justification jstring="[para(13885(a,1),8350(a,1,1))].">
      <j1 rule="para" parents="13885 8350"/>
    </justification>
  </clause>

  <clause id="13973">
    <literal><![CDATA[
      R(x,(y \ z) \ 1,y \ z) = R(x,y * (z \ 1),y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10757,a(flip),b,13972,a)].">
      <j1 rule="hyper" parents="63 10757 13972"/>
    </justification>
  </clause>

  <clause id="13974">
    <literal><![CDATA[
      (x * ((y / z) \ 1)) * T(y / z,y \ z) = R(x,z * (y \ 1),z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10756,a,b,13973,a)].">
      <j1 rule="hyper" parents="63 10756 13973"/>
    </justification>
  </clause>

  <clause id="13975">
    <literal><![CDATA[
      ((x \ y) \ (x \ L(y,z,u))) \ 1 = (x \ L(y,z,u)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9188,a(flip),b,13913,a),flip(a)].">
      <j1 rule="hyper" parents="63 9188 13913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13976">
    <literal><![CDATA[
      a(x,y,(z \ L(u,w,v5)) \ (z \ u)) = a(x,y,(z \ u) \ (z \ L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(13975(a,1),2534(a,1,3))].">
      <j1 rule="para" parents="13975 2534"/>
    </justification>
  </clause>

  <clause id="13977">
    <literal><![CDATA[
      a(x,y,z \ (L(z \ u,w,v5) \ u)) = a(x,y,(u \ z) * L(u \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5730,a(flip),b,13914,a)].">
      <j1 rule="hyper" parents="63 5730 13914"/>
    </justification>
  </clause>

  <clause id="13982">
    <literal><![CDATA[
      (x \ 1) * (a(y,x,L(x,z,u)) \ x) = L(L(x \ 1,x,y) * x,z,u)
    ]]></literal>
    <justification jstring="[para(7321(a,1),13954(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7321 13954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13983">
    <literal><![CDATA[
      (x \ 1) * (a(y,x,L(x,z,u)) \ x) = L((x \ 1) * L(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4442(a,1),13982(a,2,1))].">
      <j1 rule="para" parents="4442 13982"/>
    </justification>
  </clause>

  <clause id="13984">
    <literal><![CDATA[
      a(L(x,y,z) \ u,x,x) \ x = (u / L(x,y,z)) * ((u * (L(x,y,z) \ 1)) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,7297,a,b,13955,a)].">
      <j1 rule="hyper" parents="316 7297 13955"/>
    </justification>
  </clause>

  <clause id="13985">
    <literal><![CDATA[
      a(x,y,(z \ u) * (w * (z \ u))) = a(x,y,L(w,z * u,z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9019,a(flip),b,13969,a)].">
      <j1 rule="hyper" parents="63 9019 13969"/>
    </justification>
  </clause>

  <clause id="13986">
    <literal><![CDATA[
      a(x,y,L(z,u \ w,u \ w)) = a(x,y,L(z,u * w,u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5826,a(flip),b,13985,a)].">
      <j1 rule="hyper" parents="63 5826 13985"/>
    </justification>
  </clause>

  <clause id="13988">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),z * v5,z * v5)) = a(x,y,L((z \ v5) * v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6073,a(flip),b,13986,a),flip(a)].">
      <j1 rule="hyper" parents="63 6073 13986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13989">
    <literal><![CDATA[
      a(x,y,L(L(z,u * z,u * z),w,v5)) = a(x,y,L((z \ u) * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,10910,a,b,13988,a)].">
      <j1 rule="hyper" parents="63 10910 13988"/>
    </justification>
  </clause>

  <clause id="13990">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(z \ u,u,w)) = a(x,y,a(u \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,13434,a(flip),b,13977,a),flip(a)].">
      <j1 rule="hyper" parents="63 13434 13977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13991">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ (a(u,z,y) \ 1) = (x \ 1) * (a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(13635(a,1),13665(a,2,2,1))].">
      <j1 rule="para" parents="13635 13665"/>
    </justification>
  </clause>

  <clause id="13992">
    <literal><![CDATA[
      a(x,y,z) \ (a(x,y,z) \ 1) = L(z,y,x) * L(z \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(13659(a,1),13720(a,1,2))].">
      <j1 rule="para" parents="13659 13720"/>
    </justification>
  </clause>

  <clause id="13993">
    <literal><![CDATA[
      a(x,y,z) \ (a(x,y,z) \ 1) = z \ L(L(z,y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,9957,a(flip),b,13992,a),flip(a)].">
      <j1 rule="hyper" parents="316 9957 13992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13994">
    <literal><![CDATA[
      a(x,y,z) * (z \ L(L(z,y,x),y,x)) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,9957,a(flip),b,13992,a)].">
      <j1 rule="hyper" parents="139 9957 13992"/>
    </justification>
  </clause>

  <clause id="13995">
    <literal><![CDATA[
      L(L(x,y,z),y,z) * (a(z,y,x) * a(z,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(39,a,445,a,b,13993,a(flip))].">
      <j1 rule="hyper" parents="39 445 13993"/>
    </justification>
  </clause>

  <clause id="13997">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ x = a(z,y,x) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,13995,a)].">
      <j1 rule="hyper" parents="144 13995"/>
    </justification>
  </clause>

  <clause id="13998">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,a(z,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(132,a,13454,a,b,13995,a),flip(a)].">
      <j1 rule="hyper" parents="132 13454 13995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14000">
    <literal><![CDATA[
      a(x,y,(L(L(z,u,w),u,w) \ v5) * v6) = a(x,y,v6 * (z \ v5))
    ]]></literal>
    <justification jstring="[para(13995(a,1),6737(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="13995 6737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14001">
    <literal><![CDATA[
      a(x,L(L(y,z,u),z,u),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(13995(a,1),13059(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13995 13059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14002">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(13995(a,1),13082(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13995 13082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14004">
    <literal><![CDATA[
      a(x,L((y * z) \ u,z,y),w) = a(x,z \ (y \ u),w)
    ]]></literal>
    <justification jstring="[para(298(a,1),14001(a,1,2,1))].">
      <j1 rule="para" parents="298 14001"/>
    </justification>
  </clause>

  <clause id="14005">
    <literal><![CDATA[
      a(x,y * (L(y,z,u) \ y),w) = a(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(9863(a,1),14001(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9863 14001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14007">
    <literal><![CDATA[
      a(L((x * y) \ z,y,x),u,w) = a(y \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[para(298(a,1),14002(a,1,1,1))].">
      <j1 rule="para" parents="298 14002"/>
    </justification>
  </clause>

  <clause id="14009">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ 1 = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(144,a,13998,a)].">
      <j1 rule="hyper" parents="144 13998"/>
    </justification>
  </clause>

  <clause id="14010">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,13738,a,b,13998,a)].">
      <j1 rule="hyper" parents="35 13738 13998"/>
    </justification>
  </clause>

  <clause id="14012">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,13660,a,b,14010,a),flip(a)].">
      <j1 rule="hyper" parents="316 13660 14010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14018">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,14010,a,b,2295,a),flip(a)].">
      <j1 rule="hyper" parents="139 14010 2295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14019">
    <literal><![CDATA[
      x * a(a(y,z,u),w,v5) = x * a(v5,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,14010,a,b,9,a)].">
      <j1 rule="hyper" parents="139 14010 9"/>
    </justification>
  </clause>

  <clause id="14021">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * v5 = a(w,u,a(x,y,z)) * v5
    ]]></literal>
    <justification jstring="[hyper(138,a,14010,a,b,11,a)].">
      <j1 rule="hyper" parents="138 14010 11"/>
    </justification>
  </clause>

  <clause id="14022">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) \ x = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(14010(a,1),7297(a,1,1))].">
      <j1 rule="para" parents="14010 7297"/>
    </justification>
  </clause>

  <clause id="14024">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(a(w,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(14010(a,2),13689(a,2,2))].">
      <j1 rule="para" parents="14010 13689"/>
    </justification>
  </clause>

  <clause id="14026">
    <literal><![CDATA[
      x * (y * a(a(z,u,w),y,x)) = L(x,y,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(14010(a,2),13764(a,1,2,2))].">
      <j1 rule="para" parents="14010 13764"/>
    </justification>
  </clause>

  <clause id="14027">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,w),a(u,z,y),w) = L(x,w,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(14010(a,2),13694(a,1,1,2))].">
      <j1 rule="para" parents="14010 13694"/>
    </justification>
  </clause>

  <clause id="14028">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)),v5,v6) \ 1 = L(a(x,y,a(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(14010(a,1),13742(a,1,1,1))].">
      <j1 rule="para" parents="14010 13742"/>
    </justification>
  </clause>

  <clause id="14029">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,14010,a,b,14012,a)].">
      <j1 rule="hyper" parents="316 14010 14012"/>
    </justification>
  </clause>

  <clause id="14031">
    <literal><![CDATA[
      a(a(x,y * (z * (u \ 1)),w),v5,v6) = a(v6,v5,a(w,y * (z * u),x))
    ]]></literal>
    <justification jstring="[hyper(316,a,12021,a(flip),b,14012,a),flip(a)].">
      <j1 rule="hyper" parents="316 12021 14012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14032">
    <literal><![CDATA[
      a(a(x,L(y \ 1,z,u),w),v5,v6) = a(v6,v5,a(w,L(y,z,u),x))
    ]]></literal>
    <justification jstring="[hyper(316,a,12019,a(flip),b,14012,a),flip(a)].">
      <j1 rule="hyper" parents="316 12019 14012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14034">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * v5 = a(w,u,a(z,y,x)) * v5
    ]]></literal>
    <justification jstring="[hyper(138,a,14012,a,b,11,a)].">
      <j1 rule="hyper" parents="138 14012 11"/>
    </justification>
  </clause>

  <clause id="14035">
    <literal><![CDATA[
      a(x,y,z) \ (u \ a(x,y,z)) = u \ a(a(z,y,x),u,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,14012,a,b,7413,a),flip(a)].">
      <j1 rule="hyper" parents="133 14012 7413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14036">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ v5 = a(w,u,a(z,y,x)) \ v5
    ]]></literal>
    <justification jstring="[hyper(61,a,14012,a)].">
      <j1 rule="hyper" parents="61 14012"/>
    </justification>
  </clause>

  <clause id="14038">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),y,a(w,u,z)) = L(x,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[para(14012(a,1),9456(a,1,1,2))].">
      <j1 rule="para" parents="14012 9456"/>
    </justification>
  </clause>

  <clause id="14043">
    <literal><![CDATA[
      a(a(a(x,y,z),u,w),v5,v6) = a(a(w,u,a(z,y,x)),v5,v6)
    ]]></literal>
    <justification jstring="[para(13660(a,1),14029(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13660 14029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14045">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ u = u * (z \ L(L(z,y,x),y,x))
    ]]></literal>
    <justification jstring="[para(13997(a,1),10045(a,1,1))].">
      <j1 rule="para" parents="13997 10045"/>
    </justification>
  </clause>

  <clause id="14046">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * u = z * (L(L(z,y,x),y,x) \ u)
    ]]></literal>
    <justification jstring="[para(13997(a,1),10068(a,1,1))].">
      <j1 rule="para" parents="13997 10068"/>
    </justification>
  </clause>

  <clause id="14047">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 \ (v5 * v6)) = v6 * a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,161,a,b,14018,a)].">
      <j1 rule="hyper" parents="63 161 14018"/>
    </justification>
  </clause>

  <clause id="14048">
    <literal><![CDATA[
      (x * y) * a(a(z,u,w),x,y) = x * L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,13821,a(flip),b,14018,a),flip(a)].">
      <j1 rule="hyper" parents="63 13821 14018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14049">
    <literal><![CDATA[
      x * a(a(y,a(z,u,y),w),v5,v6) = x * a(v6,v5,a(w,y,a(z,u,y)))
    ]]></literal>
    <justification jstring="[para(13089(a,2),14019(a,1,2))].">
      <j1 rule="para" parents="13089 14019"/>
    </justification>
  </clause>

  <clause id="14050">
    <literal><![CDATA[
      (a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1 = a(y,y,a(z,y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,8766,a(flip),b,14036,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 8766 14036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14051">
    <literal><![CDATA[
      (x \ a(y,z,u)) * (u \ L(L(u,z,y),z,y)) = x \ (a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(13994(a,1),10061(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13994 10061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14052">
    <literal><![CDATA[
      a(x,y,z) * (u * (z \ L(L(z,y,x),y,x))) = (a(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[para(13994(a,1),12323(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13994 12323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14053">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(w,a(x,y,z) \ u,a(x,y,z)) = a(x,y,z) \ (u * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8437,a(flip),b,14048,a),flip(a)].">
      <j1 rule="hyper" parents="63 8437 14048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14054">
    <literal><![CDATA[
      a(x,y,z) * (u * L(w,u,a(x,y,z))) = (a(x,y,z) * u) * w
    ]]></literal>
    <justification jstring="[hyper(139,a,14048,a(flip),b,8422,a)].">
      <j1 rule="hyper" parents="139 14048 8422"/>
    </justification>
  </clause>

  <clause id="14055">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(34,a,8441,a(flip),b,14048,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 8441 14048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14056">
    <literal><![CDATA[
      L(a(x,L(y,x,a(z,u,w)),a(z,u,w)) * L(y,x,a(z,u,w)),a(z,u,w),x) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,8920,a,b,14055,a)].">
      <j1 rule="hyper" parents="63 8920 14055"/>
    </justification>
  </clause>

  <clause id="14057">
    <literal><![CDATA[
      L(1 / x,y,a(z,u,w)) = 1 / L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9882,a(flip),b,14055,a)].">
      <j1 rule="hyper" parents="63 9882 14055"/>
    </justification>
  </clause>

  <clause id="14058">
    <literal><![CDATA[
      L((a(x,y,z) * u) \ w,u,a(x,y,z)) = u \ (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,536,a(flip),b,14055,a)].">
      <j1 rule="hyper" parents="63 536 14055"/>
    </justification>
  </clause>

  <clause id="14059">
    <literal><![CDATA[
      L((x * a(y,z,u)) \ w,x,a(y,z,u)) = x \ (a(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(41,a,2354,a,b,14055,a),flip(a)].">
      <j1 rule="hyper" parents="41 2354 14055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14060">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ x = x \ L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(133,a,9867,a(flip),b,14055,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 9867 14055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14061">
    <literal><![CDATA[
      a(x,y,z) * (L(u,w,a(x,y,z)) * w) = u * (w * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14055(a,1),5382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14055 5382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14062">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (x \ v5) = x * (L(x,y,a(z,u,w)) \ v5)
    ]]></literal>
    <justification jstring="[para(14055(a,1),13617(a,1,2,1))].">
      <j1 rule="para" parents="14055 13617"/>
    </justification>
  </clause>

  <clause id="14063">
    <literal><![CDATA[
      L(1 / x,y,a(z,u,w)) \ 1 = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(137,a,14057,a,b,163,a)].">
      <j1 rule="hyper" parents="137 14057 163"/>
    </justification>
  </clause>

  <clause id="14064">
    <literal><![CDATA[
      a(x,y,z * (L(L(u,w,v5),w,v5) \ v6)) = a(x,y,z * (u \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,14000,a)].">
      <j1 rule="hyper" parents="63 5469 14000"/>
    </justification>
  </clause>

  <clause id="14065">
    <literal><![CDATA[
      L(a(a(x,y,z),u,w),v5,v6) = L(a(w,u,a(x,y,z)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(39,a,13742,a,b,14028,a)].">
      <j1 rule="hyper" parents="39 13742 14028"/>
    </justification>
  </clause>

  <clause id="14066">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),w,a(y,z,u)) = x * a(w,x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(41,a,14055,a,b,14038,a)].">
      <j1 rule="hyper" parents="41 14055 14038"/>
    </justification>
  </clause>

  <clause id="14069">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ L(L(w,v5,v6),v5,v6)))) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(14045(a,1),5835(a,1,3,2))].">
      <j1 rule="para" parents="14045 5835"/>
    </justification>
  </clause>

  <clause id="14072">
    <literal><![CDATA[
      a(x * (y * (z \ L(L(z,u,w),u,w))),v5,v6) = a(x * y,v5,v6)
    ]]></literal>
    <justification jstring="[para(14045(a,1),13081(a,1,1,2))].">
      <j1 rule="para" parents="14045 13081"/>
    </justification>
  </clause>

  <clause id="14074">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ u) = u * (a(z,y,x) * a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,5349,a(flip),b,14046,a),flip(a)].">
      <j1 rule="hyper" parents="63 5349 14046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14075">
    <literal><![CDATA[
      x \ (y * (L(L(y,z,u),z,u) \ w)) = (x \ w) * (a(u,z,y) * a(u,z,y))
    ]]></literal>
    <justification jstring="[para(14046(a,1),5363(a,1,2))].">
      <j1 rule="para" parents="14046 5363"/>
    </justification>
  </clause>

  <clause id="14076">
    <literal><![CDATA[
      a(x,y,z) * (u * L(u \ w,u,a(x,y,z))) = (w / u) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5348,a,b,14054,a),flip(a)].">
      <j1 rule="hyper" parents="316 5348 14054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14077">
    <literal><![CDATA[
      (x * a(y,z,u)) * (x \ (a(y,z,u) \ w)) = a(y,z,u) * (x * ((a(y,z,u) * x) \ w))
    ]]></literal>
    <justification jstring="[hyper(139,a,14058,a(flip),b,2353,a)].">
      <j1 rule="hyper" parents="139 14058 2353"/>
    </justification>
  </clause>

  <clause id="14078">
    <literal><![CDATA[
      x * L(((x * x) * a(y,z,u)) \ w,x * x,a(y,z,u)) = x \ L(a(y,z,u) \ w,x,x)
    ]]></literal>
    <justification jstring="[para(14059(a,2),1118(a,1,2))].">
      <j1 rule="para" parents="14059 1118"/>
    </justification>
  </clause>

  <clause id="14080">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),a(z,u,w),y) = x * a(y,x,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,30,a,b,14066,a)].">
      <j1 rule="hyper" parents="63 30 14066"/>
    </justification>
  </clause>

  <clause id="14081">
    <literal><![CDATA[
      (x * a(y,x,a(z,u,w))) * (L(x * a(y,x,a(z,u,w)),y,a(w,u,z)) \ (x * a(y,x,a(z,u,w)))) = L(x,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(41,a,9863,a,b,14066,a)].">
      <j1 rule="hyper" parents="41 9863 14066"/>
    </justification>
  </clause>

  <clause id="14082">
    <literal><![CDATA[
      L(x,a(y,z,u),w) \ (x * a(w,x,a(u,z,y))) = L(x \ L(x,w,a(y,z,u)),a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(133,a,14066,a(flip),b,2137,a)].">
      <j1 rule="hyper" parents="133 14066 2137"/>
    </justification>
  </clause>

  <clause id="14083">
    <literal><![CDATA[
      a(x,y,z * (u \ L(L(w,v5,v6),v5,v6))) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[para(10050(a,1),14069(a,1,3,2))].">
      <j1 rule="para" parents="10050 14069"/>
    </justification>
  </clause>

  <clause id="14084">
    <literal><![CDATA[
      a(x * L(L(y,z,u),z,u),w,v5) = a(x * y,w,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),14072(a,1,1,2))].">
      <j1 rule="para" parents="10 14072"/>
    </justification>
  </clause>

  <clause id="14085">
    <literal><![CDATA[
      a(x * (y * a(z,y,y)),u,w) = a(x * L(y,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(8470(a,1),14084(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8470 14084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14086">
    <literal><![CDATA[
      a(x * (y * (L(y,z,u) \ y)),w,v5) = a(x * L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(9863(a,1),14084(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9863 14084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14087">
    <literal><![CDATA[
      (x \ y) * (a(z,u,x) * a(z,u,x)) = L(L(x,u,z),u,z) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,1846,a(flip),b,14074,a),flip(a)].">
      <j1 rule="hyper" parents="63 1846 14074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14088">
    <literal><![CDATA[
      x * (L(L(y,z,u),z,u) \ y) = y * (L(L(y,z,u),z,u) \ x)
    ]]></literal>
    <justification jstring="[para(13997(a,2),14074(a,2,2)),flip(a)].">
      <j1 rule="para" parents="13997 14074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14092">
    <literal><![CDATA[
      (x * (y * (L(L(z,u,w),u,w) \ z))) \ (x * (y * ((L(L(z,u,w),u,w) \ z) * v5))) = L(L(v5,L(L(z,u,w),u,w) \ z,y),z * (L(L(z,u,w),u,w) \ y),x)
    ]]></literal>
    <justification jstring="[para(14088(a,1),460(a,2,2))].">
      <j1 rule="para" parents="14088 460"/>
    </justification>
  </clause>

  <clause id="14093">
    <literal><![CDATA[
      (x \ a(y,z,L(u,w,v5))) * (u \ L(L(u,z,y),z,y)) = x \ (a(y,z,L(u,w,v5)) \ 1)
    ]]></literal>
    <justification jstring="[para(10080(a,1),14051(a,1,2))].">
      <j1 rule="para" parents="10080 14051"/>
    </justification>
  </clause>

  <clause id="14094">
    <literal><![CDATA[
      (x \ (a(y,z,u) * w)) * (u \ L(L(u,z,y),z,y)) = x \ ((a(y,z,u) \ 1) * w)
    ]]></literal>
    <justification jstring="[para(14052(a,1),10084(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14052 10084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14096">
    <literal><![CDATA[
      L(x,x,a(y,x,z)) = (a(z,x,y) / ((z \ ((z * x) * y)) / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,7339,a(flip),b,14050,a)].">
      <j1 rule="hyper" parents="316 7339 14050"/>
    </justification>
  </clause>

  <clause id="14097">
    <literal><![CDATA[
      ((a(x,y,z) \ u) / w) * (w * a(x,y,z)) = a(x,y,z) * (w * ((a(x,y,z) * w) \ u))
    ]]></literal>
    <justification jstring="[para(298(a,1),14076(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="298 14076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14099">
    <literal><![CDATA[
      a(x * y,x * y,L(a(z,u,w),x,y)) = a(x \ y,y * x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,13734,a(flip),b,13869,a),flip(a)].">
      <j1 rule="hyper" parents="316 13734 13869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14100">
    <literal><![CDATA[
      a(x * y,x * y,a(z,z,L(u,x,y))) = a(x \ y,y * x,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5178,a,b,14099,a)].">
      <j1 rule="hyper" parents="63 5178 14099"/>
    </justification>
  </clause>

  <clause id="14106">
    <literal><![CDATA[
      a(x,y,z) \ ((u / z) * (z * a(x,y,z))) = a(x,y,z) * (L(a(x,y,z),z,u) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9126,a,b,13858,a)].">
      <j1 rule="hyper" parents="63 9126 13858"/>
    </justification>
  </clause>

  <clause id="14108">
    <literal><![CDATA[
      R(x \ (y * (L(y,z,u) \ x)),w,v5) = L(x \ (y * (L(y,z,u) \ x)),w,v5)
    ]]></literal>
    <justification jstring="[para(13790(a,1),13861(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13790 13861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14109">
    <literal><![CDATA[
      ((x * y) * (z \ (u * (L(u,w,v5) \ z)))) \ ((x * y) * L(z \ (u * (L(u,w,v5) \ z)),y,x)) = a(z \ (u * (L(u,w,v5) \ z)),y,x)
    ]]></literal>
    <justification jstring="[para(14108(a,1),3428(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14108 3428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14113">
    <literal><![CDATA[
      L(x,y,z) * (R(x,u,w) \ a(x,u,w)) = L(x,a(w,u,x),u) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,9474,a(flip),b,13947,a),flip(a)].">
      <j1 rule="hyper" parents="316 9474 13947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14115">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)) * a(a(z,u,w),L(x,y,a(z,u,w)),y),a(z,u,w),y) = x
    ]]></literal>
    <justification jstring="[para(14018(a,1),14056(a,1,1))].">
      <j1 rule="para" parents="14018 14056"/>
    </justification>
  </clause>

  <clause id="14118">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),a(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[para(9460(a,1),14115(a,1,1))].">
      <j1 rule="para" parents="9460 14115"/>
    </justification>
  </clause>

  <clause id="14119">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * a(x,a(y,z,u),w) = 1
    ]]></literal>
    <justification jstring="[hyper(132,a,14118,a,b,13995,a),flip(a)].">
      <j1 rule="hyper" parents="132 14118 13995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14121">
    <literal><![CDATA[
      (x / y) * L(y,a(z,u,w),v5) = y * (L(y,a(z,u,w),v5) \ x)
    ]]></literal>
    <justification jstring="[para(14118(a,1),13829(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14118 13829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14122">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ 1 = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(144,a,14119,a)].">
      <j1 rule="hyper" parents="144 14119"/>
    </justification>
  </clause>

  <clause id="14123">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(35,a,13743,a,b,14119,a)].">
      <j1 rule="hyper" parents="35 13743 14119"/>
    </justification>
  </clause>

  <clause id="14124">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(35,a,13737,a,b,14119,a)].">
      <j1 rule="hyper" parents="35 13737 14119"/>
    </justification>
  </clause>

  <clause id="14125">
    <literal><![CDATA[
      x \ (y \ ((y * a(z,u,w)) * (a(z,u,w) \ x))) = a(a(z,u,w) \ x,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(316,a,8451,a,b,14123,a)].">
      <j1 rule="hyper" parents="316 8451 14123"/>
    </justification>
  </clause>

  <clause id="14126">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * v5 = v5 * a(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(139,a,14123,a,b,2295,a),flip(a)].">
      <j1 rule="hyper" parents="139 14123 2295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14127">
    <literal><![CDATA[
      x * a(y,a(z,u,w),v5) = x * a(v5,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(139,a,14123,a,b,9,a)].">
      <j1 rule="hyper" parents="139 14123 9"/>
    </justification>
  </clause>

  <clause id="14128">
    <literal><![CDATA[
      x * (L(x,a(y,z,x),u) \ (w * a(u,x,a(y,z,x)))) = L(w,a(u,x,a(y,z,x)),L(x,a(y,z,x),u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9480,a(flip),b,14121,a),flip(a)].">
      <j1 rule="hyper" parents="63 9480 14121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14129">
    <literal><![CDATA[
      a(x,y,((z * (u \ 1)) \ w) \ (u \ (z \ w))) = a(x,y,a(z,u,w \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5814,a(flip),b,13905,a)].">
      <j1 rule="hyper" parents="63 5814 13905"/>
    </justification>
  </clause>

  <clause id="14130">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) \ (z \ (u \ w))) = a(x,y,a(u,z,w \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7590,a(flip),b,14129,a)].">
      <j1 rule="hyper" parents="63 7590 14129"/>
    </justification>
  </clause>

  <clause id="14131">
    <literal><![CDATA[
      x * L(y \ (L(y \ R(y,z,u),w,v5) \ R(y,z,u)),R(y,z,u) \ y,x) = (R(y,z,u) \ y) * (L(R(y,z,u) \ y,w,v5) \ x)
    ]]></literal>
    <justification jstring="[para(1774(a,1),13916(a,1,2,1,2,1,1))].">
      <j1 rule="para" parents="1774 13916"/>
    </justification>
  </clause>

  <clause id="14132">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),z * v5,z * v5)) = a(x,y,v5 * (z * (L(z,u,w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13986,a(flip),b,13964,a)].">
      <j1 rule="hyper" parents="63 13986 13964"/>
    </justification>
  </clause>

  <clause id="14133">
    <literal><![CDATA[
      a(x,y,z) \ ((u / z) * (z * a(x,y,z))) = u * a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,9967,a(flip),b,14106,a),flip(a)].">
      <j1 rule="hyper" parents="316 9967 14106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14134">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),v5 * z,v5 * z)) = a(x,y,v5 * (z * (L(z,u,w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10847,a,b,14132,a)].">
      <j1 rule="hyper" parents="63 10847 14132"/>
    </justification>
  </clause>

  <clause id="14135">
    <literal><![CDATA[
      a(x,y,(z * u) * (u * (z * (u \ L(u,w,v5))))) = a(x,y,z * (u * (L(u,w,v5) \ z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7975,a,b,14134,a)].">
      <j1 rule="hyper" parents="63 7975 14134"/>
    </justification>
  </clause>

  <clause id="14136">
    <literal><![CDATA[
      L(x,y,z) \ L(u,x,x \ L(x,y,z)) = x \ ((x \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11649,a(flip),b,13828,a),flip(a)].">
      <j1 rule="hyper" parents="63 11649 13828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14137">
    <literal><![CDATA[
      L(L(x,y,z) \ u,x,x \ L(x,y,z)) = x \ ((x \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6847,a,b,14136,a)].">
      <j1 rule="hyper" parents="63 6847 14136"/>
    </justification>
  </clause>

  <clause id="14138">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((L(1 / x,u,w) \ 1) \ v5)) = x \ (L(x,y,z) \ (L(x,u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,4416,a(flip),b,13833,a),flip(a)].">
      <j1 rule="hyper" parents="316 4416 13833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14139">
    <literal><![CDATA[
      L(x,y,z) \ ((L(x,a(z,y,x),y) \ L(x,y,z)) * u) = a(x,y,z) * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,8657,a(flip),b,13934,a),flip(a)].">
      <j1 rule="hyper" parents="316 8657 13934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14140">
    <literal><![CDATA[
      a(x,L(y,y \ L(y,x,z),u),a(z,x,y)) \ u = (y \ R(y,x,z)) * (a(y,x,z) \ u)
    ]]></literal>
    <justification jstring="[para(13747(a,2),13948(a,1,1))].">
      <j1 rule="para" parents="13747 13948"/>
    </justification>
  </clause>

  <clause id="14141">
    <literal><![CDATA[
      a(x,y,z) * ((u * w) * L(L(w \ 1,w,u),u * w,a(x,y,z))) = ((u * w) * a(x,y,z)) * ((u * w) \ (a(x,y,z) \ (a(x,y,z) * u)))
    ]]></literal>
    <justification jstring="[para(381(a,2),14077(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="381 14077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14142">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) \ x) \ (u \ a(z,y,L(x,w,v5))) = u \ (a(z,y,L(x,w,v5)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,10045,a,b,14093,a)].">
      <j1 rule="hyper" parents="63 10045 14093"/>
    </justification>
  </clause>

  <clause id="14143">
    <literal><![CDATA[
      L(x,y,z) \ ((a(z,y,x) \ 1) * u) = a(x,y,z) * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(11632(a,1),14139(a,1,2,1))].">
      <j1 rule="para" parents="11632 14139"/>
    </justification>
  </clause>

  <clause id="14144">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * a(x,y,L(z,u,w)) = L(L(z,y,x),y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(39,a,5453,a,b,14142,a)].">
      <j1 rule="hyper" parents="39 5453 14142"/>
    </justification>
  </clause>

  <clause id="14145">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * a(x,y,L(z,u,w)) = a(x,y,z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,13997,a(flip),b,14144,a),flip(a)].">
      <j1 rule="hyper" parents="316 13997 14144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14146">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(v5,v6,L(v7,v8,v9)) \ (a(v5,v6,v7) * a(v5,v6,v7))) = a(v5,v6,L(v7,v8,v9)) * a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(14145(a,1),14047(a,1,2,2))].">
      <j1 rule="para" parents="14145 14047"/>
    </justification>
  </clause>

  <clause id="14147">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ (a(z,y,x) \ v5) = a(z,y,x) \ (L(L(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(13635(a,1),13650(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13635 13650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14148">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,L(y,z,u) \ y) = R(x,a(u,z,y),a(u,z,y))
    ]]></literal>
    <justification jstring="[para(13640(a,2),13722(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13640 13722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14149">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,L(y,z,u) \ y) = L(x,a(u,z,y),a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,10628,a(flip),b,14148,a),flip(a)].">
      <j1 rule="hyper" parents="316 10628 14148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14150">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),L(y,z,u) \ y) = L(x,a(u,z,y),a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,12402,a(flip),b,14149,a)].">
      <j1 rule="hyper" parents="63 12402 14149"/>
    </justification>
  </clause>

  <clause id="14151">
    <literal><![CDATA[
      T(a(x,y \ z,y \ z) \ x,y \ z) = ((z \ y) \ 1) \ (x / (((z \ y) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,3664,a(flip),b,13872,a)].">
      <j1 rule="hyper" parents="63 3664 13872"/>
    </justification>
  </clause>

  <clause id="14152">
    <literal><![CDATA[
      ((x \ y) \ 1) \ (z / (((x \ y) \ 1) \ 1)) = (y \ x) \ (z / ((y \ x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,11657,a(flip),b,14151,a),flip(a)].">
      <j1 rule="hyper" parents="63 11657 14151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14153">
    <literal><![CDATA[
      (1 / (x \ y)) \ (z / (x \ y)) = (y \ x) \ (z / ((y \ x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,4910,a(flip),b,14152,a)].">
      <j1 rule="hyper" parents="63 4910 14152"/>
    </justification>
  </clause>

  <clause id="14154">
    <literal><![CDATA[
      x * L(a(y,z,u) \ ((x * x) \ w),x * x,a(y,z,u)) = x \ L(a(y,z,u) \ w,x,x)
    ]]></literal>
    <justification jstring="[para(10630(a,1),14078(a,1,2,1))].">
      <j1 rule="para" parents="10630 14078"/>
    </justification>
  </clause>

  <clause id="14155">
    <literal><![CDATA[
      x * (a(y,z,u) \ ((x * x) \ w)) = x \ L(a(y,z,u) \ w,x,x)
    ]]></literal>
    <justification jstring="[para(5379(a,1),14154(a,1,2))].">
      <j1 rule="para" parents="5379 14154"/>
    </justification>
  </clause>

  <clause id="14156">
    <literal><![CDATA[
      L(a(x,y,z) \ u,z,z) = a(x,y,z) \ L(u,z,z)
    ]]></literal>
    <justification jstring="[hyper(38,a,7007,a(flip),b,14155,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 7007 14155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14158">
    <literal><![CDATA[
      L(a(x,y,z) \ a(z,u,w),z,z) = a(x,y,z) \ a(z,u,w)
    ]]></literal>
    <justification jstring="[para(8510(a,1),14156(a,2,2))].">
      <j1 rule="para" parents="8510 14156"/>
    </justification>
  </clause>

  <clause id="14159">
    <literal><![CDATA[
      x * (x * (L(x,x,x \ y) \ ((y \ (y / x)) * z))) = L(L(z,y \ (x \ y),x),x,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,8660,a(flip),b,13771,a),flip(a)].">
      <j1 rule="hyper" parents="316 8660 13771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14160">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(L(w,v5,v6) \ v7,w,w))) = a(x,y,z \ (u \ (v7 * L(w \ 1,v5,v6))))
    ]]></literal>
    <justification jstring="[hyper(63,a,6387,a(flip),b,13807,a)].">
      <j1 rule="hyper" parents="63 6387 13807"/>
    </justification>
  </clause>

  <clause id="14161">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,v5) * (v6 / u))) = a(x,y,z \ (u * (L(u,w,v5) \ v6)))
    ]]></literal>
    <justification jstring="[para(5081(a,1),13812(a,1,3,2,1))].">
      <j1 rule="para" parents="5081 13812"/>
    </justification>
  </clause>

  <clause id="14162">
    <literal><![CDATA[
      a(x,y,z \ ((u / w) * L(w,v5,v6))) = a(x,y,z \ (w * (L(w,v5,v6) \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,14161,a)].">
      <j1 rule="hyper" parents="63 5490 14161"/>
    </justification>
  </clause>

  <clause id="14163">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,v5) * (u \ v6))) = a(x,y,z \ (u * (L(u,w,v5) \ v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5599,a(flip),b,14161,a)].">
      <j1 rule="hyper" parents="63 5599 14161"/>
    </justification>
  </clause>

  <clause id="14164">
    <literal><![CDATA[
      a(x,y,z \ ((u \ w) * L(u,v5,v6))) = a(x,y,z \ (u * (L(u,v5,v6) \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5627,a(flip),b,14162,a)].">
      <j1 rule="hyper" parents="63 5627 14162"/>
    </justification>
  </clause>

  <clause id="14165">
    <literal><![CDATA[
      a(x,y,z \ (u * (L(u,w \ 1,w) \ v5))) = a(x,y,z \ ((u \ v5) * L(u,w,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11753,a(flip),b,14163,a),flip(a)].">
      <j1 rule="hyper" parents="63 11753 14163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14166">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * L((z * u) \ z,w,v5)) = a(x,y,z \ (u * (L(u,w,v5) \ z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8962,a,b,14164,a)].">
      <j1 rule="hyper" parents="63 8962 14164"/>
    </justification>
  </clause>

  <clause id="14167">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * (L(u * w,w \ 1,w) \ v5))) = a(x,y,z \ (((u * w) \ v5) * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12147,a(flip),b,14164,a),flip(a)].">
      <j1 rule="hyper" parents="63 12147 14164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14168">
    <literal><![CDATA[
      a(x,y,z \ (((u * w) \ v5) * (1 / (w \ (u \ 1))))) = a(x,y,z \ ((u * w) * (L(u * w,w,u) \ v5)))
    ]]></literal>
    <justification jstring="[para(9895(a,1),14164(a,1,3,2,2))].">
      <j1 rule="para" parents="9895 14164"/>
    </justification>
  </clause>

  <clause id="14169">
    <literal><![CDATA[
      a(x,y,z \ ((u * T(w,v5)) * (L(u * T(w,v5),v6,v7) \ ((w * u) * v8)))) = a(x,y,z \ ((K(v5,w) * (K(w,u) * v8)) * L(u * T(w,v5),v6,v7)))
    ]]></literal>
    <justification jstring="[para(10275(a,1),14164(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="10275 14164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14170">
    <literal><![CDATA[
      a(x,y,z \ ((u / (w \ 1)) * (L(u / (w \ 1),w \ 1,w) \ v5))) = a(x,y,z \ (((u / (w \ 1)) \ v5) * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,12088,a(flip),b,14165,a),flip(a)].">
      <j1 rule="hyper" parents="316 12088 14165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14171">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) \ (x \ R(x,y,z)) = x \ (L(x \ R(x,y,z),u,w) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1774(a,1),13912(a,2,2,1,1))].">
      <j1 rule="para" parents="1774 13912"/>
    </justification>
  </clause>

  <clause id="14173">
    <literal><![CDATA[
      (x * a(x \ y,x,x)) * ((y \ (y / x)) * z) = L(L(z,y \ (x \ y),x),x,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13804,a(flip),b,14159,a)].">
      <j1 rule="hyper" parents="63 13804 14159"/>
    </justification>
  </clause>

  <clause id="14174">
    <literal><![CDATA[
      L(x,y \ (z \ y),(y \ (z \ y)) \ 1) = x * (L(L(x,y \ (z \ y),z),z,a(z,z,y)) / x)
    ]]></literal>
    <justification jstring="[para(14173(a,1),12315(a,2,2,1))].">
      <j1 rule="para" parents="14173 12315"/>
    </justification>
  </clause>

  <clause id="14175">
    <literal><![CDATA[
      R(x,y,z) \ (L(x / R(x,y,z),u,w) \ x) = x \ (L(x \ R(x,y,z),u,w) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13906,a(flip),b,14171,a)].">
      <j1 rule="hyper" parents="63 13906 14171"/>
    </justification>
  </clause>

  <clause id="14176">
    <literal><![CDATA[
      L(x,y \ (z \ y),(y \ (z \ y)) \ 1) = x * (x \ L(L(x,y \ (z \ y),z),z,a(z,z,y)))
    ]]></literal>
    <justification jstring="[para(4440(a,1),14174(a,2,2))].">
      <j1 rule="para" parents="4440 14174"/>
    </justification>
  </clause>

  <clause id="14177">
    <literal><![CDATA[
      (x \ (L(x \ R(x,y,z),u,w) \ R(x,y,z))) \ x = R(x,y,z) * L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(14175(a,1),9192(a,1,1))].">
      <j1 rule="para" parents="14175 9192"/>
    </justification>
  </clause>

  <clause id="14178">
    <literal><![CDATA[
      L(L(x,y \ (z \ y),z),z,a(z,z,y)) = L(x,y \ (z \ y),(y \ (z \ y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,10,a(flip),b,14176,a)].">
      <j1 rule="hyper" parents="316 10 14176"/>
    </justification>
  </clause>

  <clause id="14179">
    <literal><![CDATA[
      L(L(x,y \ (z \ y),z),z,a(z,z,y)) = L(x,z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,13898,a(flip),b,14178,a),flip(a)].">
      <j1 rule="hyper" parents="316 13898 14178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14182">
    <literal><![CDATA[
      L(x,y,z) * (L(L(x,y,z),u,w) \ (z * (y * x))) = (z * y) * L(L(1 / x,u,w) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(9945(a,2),13792(a,2,2))].">
      <j1 rule="para" parents="9945 13792"/>
    </justification>
  </clause>

  <clause id="14183">
    <literal><![CDATA[
      R(x,y * (L(y,z,u) \ y),L(y,z,u)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,11451,a(flip),b,13808,a),flip(a)].">
      <j1 rule="hyper" parents="63 11451 13808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14185">
    <literal><![CDATA[
      a(x,L(y \ 1,z,u) \ 1,L(y,z,u)) = x \ R(x,y,y)
    ]]></literal>
    <justification jstring="[para(14183(a,1),11343(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14183 11343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14186">
    <literal><![CDATA[
      a(x,L(y \ 1,z,u) \ 1,L(y,z,u)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2380,a(flip),b,14185,a),flip(a)].">
      <j1 rule="hyper" parents="316 2380 14185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14188">
    <literal><![CDATA[
      a(x \ y,(x \ y) \ L(x \ y,x,x \ 1),z) = a(z,x \ y,(x \ y) * ((x \ 1) * y)) \ 1
    ]]></literal>
    <justification jstring="[para(5642(a,1),13844(a,2,1))].">
      <j1 rule="para" parents="5642 13844"/>
    </justification>
  </clause>

  <clause id="14189">
    <literal><![CDATA[
      L(a(x,y,z * L(z,u,w)),z \ L(z,u,w),y) = L(z,u,w) \ (L(L(z,u,w) \ z,y,x) \ z)
    ]]></literal>
    <justification jstring="[para(1378(a,1),13909(a,2,2,1,1))].">
      <j1 rule="para" parents="1378 13909"/>
    </justification>
  </clause>

  <clause id="14190">
    <literal><![CDATA[
      L(x,y,z) * (L(L(x,y,z),u,w) \ (z * (y * x))) = z * (y * (L(1 / x,u,w) \ 1))
    ]]></literal>
    <justification jstring="[hyper(316,a,100,a(flip),b,14182,a),flip(a)].">
      <j1 rule="hyper" parents="316 100 14182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14191">
    <literal><![CDATA[
      a(x \ y,(x \ y) \ L(x \ y,x,x \ 1),z) = a(z,x \ y,(x \ y) * (y * x)) \ 1
    ]]></literal>
    <justification jstring="[para(5902(a,1),14188(a,2,1))].">
      <j1 rule="para" parents="5902 14188"/>
    </justification>
  </clause>

  <clause id="14192">
    <literal><![CDATA[
      a(x \ y,(x \ y) \ L(x \ y,x,x \ 1),z) = a(z,x \ y,a(x,x \ 1,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8473(a,1),14191(a,2,1))].">
      <j1 rule="para" parents="8473 14191"/>
    </justification>
  </clause>

  <clause id="14193">
    <literal><![CDATA[
      a(x \ y,(x \ y) \ L(x \ y,x,x \ 1),z) = a(z,x \ y,a(y,x,x)) \ 1
    ]]></literal>
    <justification jstring="[para(8829(a,1),14192(a,2,1))].">
      <j1 rule="para" parents="8829 14192"/>
    </justification>
  </clause>

  <clause id="14194">
    <literal><![CDATA[
      a(x \ y,(x \ y) \ ((1 / x) * y),z) = a(z,x \ y,a(y,x,x)) \ 1
    ]]></literal>
    <justification jstring="[para(887(a,1),14193(a,1,2,2))].">
      <j1 rule="para" parents="887 14193"/>
    </justification>
  </clause>

  <clause id="14195">
    <literal><![CDATA[
      L(a(x,y,z * L(z,u,w)),z \ L(z,u,w),y) = L(z,u,w) \ (z * L(z \ L(z,u,w),y,x))
    ]]></literal>
    <justification jstring="[para(13392(a,1),14189(a,2,2))].">
      <j1 rule="para" parents="13392 14189"/>
    </justification>
  </clause>

  <clause id="14196">
    <literal><![CDATA[
      L(a(x,y,z * L(z,u,w)),z \ L(z,u,w),y) = z * (L(z,u,w) \ L(z \ L(z,u,w),y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,1129,a(flip),b,14195,a),flip(a)].">
      <j1 rule="hyper" parents="316 1129 14195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14197">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) \ (x \ R(x,y,z)) = x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,13551,a(flip),b,14196,a)].">
      <j1 rule="hyper" parents="63 13551 14196"/>
    </justification>
  </clause>

  <clause id="14198">
    <literal><![CDATA[
      x \ (L(x \ R(x,y,z),u,w) \ R(x,y,z)) = x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14171,a(flip),b,14197,a)].">
      <j1 rule="hyper" parents="63 14171 14197"/>
    </justification>
  </clause>

  <clause id="14199">
    <literal><![CDATA[
      (x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))) \ x = R(x,y,z) * L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(14198(a,1),14177(a,1,1))].">
      <j1 rule="para" parents="14198 14177"/>
    </justification>
  </clause>

  <clause id="14202">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ L(v5,a(x,a(u,z,y),w),a(x,a(u,z,y),w)) = v5 * a(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(13733(a,1),13679(a,2,2))].">
      <j1 rule="para" parents="13733 13679"/>
    </justification>
  </clause>

  <clause id="14203">
    <literal><![CDATA[
      (a(x,y,L(a(z,x,y),u,w)) \ y) * L(a(z,x,y) \ 1,u,w) = y * L(y \ L(y,x,z),u,w)
    ]]></literal>
    <justification jstring="[para(2655(a,1),13768(a,1,1,1))].">
      <j1 rule="para" parents="2655 13768"/>
    </justification>
  </clause>

  <clause id="14204">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y,z,u)) \ x = a(y,L(L(y,z,u),z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10117,a(flip),b,13866,a),flip(a)].">
      <j1 rule="hyper" parents="63 10117 13866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14205">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y,z,u)) \ x = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,14001,a(flip),b,14204,a),flip(a)].">
      <j1 rule="hyper" parents="316 14001 14204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14207">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4952,a(flip),b,14205,a)].">
      <j1 rule="hyper" parents="63 4952 14205"/>
    </justification>
  </clause>

  <clause id="14208">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y,z,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,4952,a,b,14205,a),flip(a)].">
      <j1 rule="hyper" parents="39 4952 14205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14209">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y,z,u)) = a(y,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,14205,a),flip(a)].">
      <j1 rule="hyper" parents="39 2301 14205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14211">
    <literal><![CDATA[
      a(R(x,y,z),L(x,y,z),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4643,a,b,14207,a)].">
      <j1 rule="hyper" parents="63 4643 14207"/>
    </justification>
  </clause>

  <clause id="14212">
    <literal><![CDATA[
      a(x \ (y \ z),L((y * x) \ z,x,y),u) = a((y * x) \ z,(y * x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14007,a(flip),b,14207,a)].">
      <j1 rule="hyper" parents="63 14007 14207"/>
    </justification>
  </clause>

  <clause id="14213">
    <literal><![CDATA[
      a(x \ (y \ x),L(y \ 1,y,x),z) = a(y \ 1,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8065,a(flip),b,14207,a)].">
      <j1 rule="hyper" parents="63 8065 14207"/>
    </justification>
  </clause>

  <clause id="14214">
    <literal><![CDATA[
      L((x * L(L(x,y,z),y,z)) * u,x,x) = L(x,y,z) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9960,a(flip),b,14208,a),flip(a)].">
      <j1 rule="hyper" parents="63 9960 14208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14215">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ L(v5,z,z)) = L(x,y,v5 * (L(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(14208(a,1),3335(a,1,3,2))].">
      <j1 rule="para" parents="14208 3335"/>
    </justification>
  </clause>

  <clause id="14216">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(L(w,v5,v6) \ v7,w,w))) = a(x,y,z \ (u \ (v7 * L(w,v5,v6))))
    ]]></literal>
    <justification jstring="[para(14208(a,1),6392(a,1,3,2,2))].">
      <j1 rule="para" parents="14208 6392"/>
    </justification>
  </clause>

  <clause id="14217">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11325,a,b,14211,a)].">
      <j1 rule="hyper" parents="63 11325 14211"/>
    </justification>
  </clause>

  <clause id="14218">
    <literal><![CDATA[
      L(x,y \ (z \ y),y \ (z \ y)) = a(z \ 1,z \ 1,x) \ x
    ]]></literal>
    <justification jstring="[para(14213(a,1),11377(a,2,1))].">
      <j1 rule="para" parents="14213 11377"/>
    </justification>
  </clause>

  <clause id="14219">
    <literal><![CDATA[
      L(x,y \ (z \ y),y \ (z \ y)) = L(x,z \ 1,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,4950,a(flip),b,14218,a),flip(a)].">
      <j1 rule="hyper" parents="316 4950 14218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14221">
    <literal><![CDATA[
      L(x,y \ T((y / z) * u,u \ z),y \ (L(u \ z,u,z \ y) \ y)) = L(x,L(u \ z,u,z \ y) \ 1,L(u \ z,u,z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(3740(a,1),14219(a,1,2,2))].">
      <j1 rule="para" parents="3740 14219"/>
    </justification>
  </clause>

  <clause id="14222">
    <literal><![CDATA[
      L(x,(y * z) \ T(a(u,y,z) * y,z),(y * z) \ (L(z,y,u) \ (y * z))) = L(x,L(z,y,u) \ 1,L(z,y,u) \ 1)
    ]]></literal>
    <justification jstring="[para(13637(a,2),14219(a,1,2,2))].">
      <j1 rule="para" parents="13637 14219"/>
    </justification>
  </clause>

  <clause id="14224">
    <literal><![CDATA[
      a((x * y) \ z,(x * y) \ z,u) = a(y \ (x \ z),y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14004,a(flip),b,14212,a),flip(a)].">
      <j1 rule="hyper" parents="63 14004 14212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14225">
    <literal><![CDATA[
      L(x,L((y * z) \ u,w,v5),L((y * z) \ u,w,v5)) = a(z \ (y \ u),z \ (y \ u),x) \ x
    ]]></literal>
    <justification jstring="[para(14224(a,1),14209(a,2,1))].">
      <j1 rule="para" parents="14224 14209"/>
    </justification>
  </clause>

  <clause id="14226">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * L(v5 \ 1,v6,v7)))) = a(x,y,z \ (u \ (w * L(v5,v6,v7))))
    ]]></literal>
    <justification jstring="[hyper(63,a,14160,a(flip),b,14216,a)].">
      <j1 rule="hyper" parents="63 14160 14216"/>
    </justification>
  </clause>

  <clause id="14227">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * L(1 / v5,v6,v7)))) = a(x,y,z \ (u \ (w * L(v5,v6,v7))))
    ]]></literal>
    <justification jstring="[hyper(63,a,6044,a,b,14226,a)].">
      <j1 rule="hyper" parents="63 6044 14226"/>
    </justification>
  </clause>

  <clause id="14228">
    <literal><![CDATA[
      L(x,L((y * z) \ u,w,v5),L((y * z) \ u,w,v5)) = L(x,z \ (y \ u),z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(316,a,4950,a(flip),b,14225,a),flip(a)].">
      <j1 rule="hyper" parents="316 4950 14225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14229">
    <literal><![CDATA[
      L(x,(y * z) \ u,(y * z) \ u) = L(x,z \ (y \ u),z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14208,a(flip),b,14228,a)].">
      <j1 rule="hyper" parents="63 14208 14228"/>
    </justification>
  </clause>

  <clause id="14230">
    <literal><![CDATA[
      L(x,L(y \ z,y,u),(u * y) \ (u * z)) = L(x,y \ (u \ (u * z)),y \ (u \ (u * z)))
    ]]></literal>
    <justification jstring="[para(102(a,2),14229(a,1,2))].">
      <j1 rule="para" parents="102 14229"/>
    </justification>
  </clause>

  <clause id="14231">
    <literal><![CDATA[
      L(x,y \ (z \ ((z * u) * T(y,u))),y \ (z \ ((z * u) * T(y,u)))) = L(x,L(u * a(z,u,y),y,z),(z * y) \ ((z * u) * T(y,u)))
    ]]></literal>
    <justification jstring="[para(8578(a,1),14229(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8578 14229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14232">
    <literal><![CDATA[
      L(x,L(y \ z,y,u),L(y \ z,y,u)) = L(x,y \ (u \ (u * z)),y \ (u \ (u * z)))
    ]]></literal>
    <justification jstring="[para(102(a,2),14230(a,1,3))].">
      <j1 rule="para" parents="102 14230"/>
    </justification>
  </clause>

  <clause id="14233">
    <literal><![CDATA[
      L(x,y \ (y \ (y * z)),y \ (y \ (y * z))) = L(x,L(y \ z,y,y),z * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,3442,a(flip),b,14232,a),flip(a)].">
      <j1 rule="hyper" parents="63 3442 14232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14234">
    <literal><![CDATA[
      L(x,y \ (y \ (y * z)),y \ (y \ (y * z))) = L(x,(y \ 1) * z,z * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(316,a,10993,a(flip),b,14233,a),flip(a)].">
      <j1 rule="hyper" parents="316 10993 14233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14235">
    <literal><![CDATA[
      L(x,y \ z,y \ (y \ (y * z))) = L(x,(y \ 1) * z,z * (y \ 1))
    ]]></literal>
    <justification jstring="[para(9(a,1),14234(a,1,2,2))].">
      <j1 rule="para" parents="9 14234"/>
    </justification>
  </clause>

  <clause id="14236">
    <literal><![CDATA[
      L(x,(y \ 1) * z,z * (y \ 1)) = L(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),14235(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 14235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14237">
    <literal><![CDATA[
      L(x,(y \ 1) * z,(y \ 1) * z) = L(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1668,a,b,14236,a)].">
      <j1 rule="hyper" parents="63 1668 14236"/>
    </justification>
  </clause>

  <clause id="14238">
    <literal><![CDATA[
      L(x,((y \ 1) \ 1) * z,z * y) = L(x,(y \ 1) \ z,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1683,a(flip),b,14236,a)].">
      <j1 rule="hyper" parents="63 1683 14236"/>
    </justification>
  </clause>

  <clause id="14239">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,(y \ 1) \ z) = L(x,y * z,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10807,a(flip),b,14238,a),flip(a)].">
      <j1 rule="hyper" parents="63 10807 14238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14241">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,(y \ 1) \ z) = L(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1668,a,b,14239,a),flip(a)].">
      <j1 rule="hyper" parents="316 1668 14239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14245">
    <literal><![CDATA[
      x * ((L(x,a(y,z,x),u) \ w) * a(u,x,a(y,z,x))) = L(w,a(u,x,a(y,z,x)),L(x,a(y,z,x),u))
    ]]></literal>
    <justification jstring="[para(7017(a,1),14128(a,1,2))].">
      <j1 rule="para" parents="7017 14128"/>
    </justification>
  </clause>

  <clause id="14246">
    <literal><![CDATA[
      a(x,y,z \ (((u * w) \ v5) * ((w \ (u \ 1)) \ 1))) = a(x,y,z \ ((u * w) * (L(u * w,w,u) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5599,a(flip),b,14168,a)].">
      <j1 rule="hyper" parents="63 5599 14168"/>
    </justification>
  </clause>

  <clause id="14247">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,z)),L(z,a(u,w,z),y)) = z * L(z \ x,z,a(y,z,a(u,w,z)))
    ]]></literal>
    <justification jstring="[para(13528(a,1),14245(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13528 14245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14248">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,z)),L(z,a(u,w,z),y)) = L(x,z,a(z,a(u,w,z),y))
    ]]></literal>
    <justification jstring="[hyper(316,a,13284,a(flip),b,14247,a),flip(a)].">
      <j1 rule="hyper" parents="316 13284 14247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14249">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * (L(u * w,w,u) \ v5))) = a(x,y,z \ ((w \ (u \ 1)) * ((u * w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6680,a(flip),b,14246,a),flip(a)].">
      <j1 rule="hyper" parents="63 6680 14246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14250">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * (L(u * w,w,u) \ v5))) = a(x,y,z \ (((u * w) \ v5) * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,6355,a(flip),b,14249,a),flip(a)].">
      <j1 rule="hyper" parents="316 6355 14249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14261">
    <literal><![CDATA[
      a(x,1 / (1 / y),L(y,z,u)) \ (1 / (1 / y)) = L(L(y,z,u),y,x) * ((L(y,z,u) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(10804(a,1),13765(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10804 13765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14262">
    <literal><![CDATA[
      a(x,1 / (1 / y),L(y,z,u)) \ (1 / (1 / y)) = y * ((L(y,z,u) \ 1) * L(L(y,z,u),y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,9708,a(flip),b,14261,a),flip(a)].">
      <j1 rule="hyper" parents="316 9708 14261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14264">
    <literal><![CDATA[
      a(x,1 / (1 / y),L(y,z,u)) \ (1 / (1 / y)) = y * L((y \ 1) * L(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(13128(a,1),14262(a,2,2))].">
      <j1 rule="para" parents="13128 14262"/>
    </justification>
  </clause>

  <clause id="14265">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) \ (1 / (1 / y)) = y * L((y \ 1) * L(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(11197(a,1),14264(a,1,1))].">
      <j1 rule="para" parents="11197 14264"/>
    </justification>
  </clause>

  <clause id="14267">
    <literal><![CDATA[
      (x / (y * z)) * ((y * z) * (y * (z / (y * z)))) = (y * z) * (L(y * z,(y * z) \ z,y) \ x)
    ]]></literal>
    <justification jstring="[para(2218(a,1),13813(a,1,2,2))].">
      <j1 rule="para" parents="2218 13813"/>
    </justification>
  </clause>

  <clause id="14269">
    <literal><![CDATA[
      (x * y) * (L(x * y,(x * y) \ y,x) \ z) = (z / (x * y)) * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(9199(a,1),14267(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9199 14267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14270">
    <literal><![CDATA[
      (x * y) * (L(x * y,y \ (x \ y),x) \ z) = (z / (x * y)) * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(10957(a,1),14269(a,1,2,1))].">
      <j1 rule="para" parents="10957 14269"/>
    </justification>
  </clause>

  <clause id="14271">
    <literal><![CDATA[
      L(x,y,z) \ R(L(x,y,z),L(x,u,w),v5) = a(L(x,y,z),L(x,u,w),v5)
    ]]></literal>
    <justification jstring="[para(5321(a,1),13933(a,1,1,1))].">
      <j1 rule="para" parents="5321 13933"/>
    </justification>
  </clause>

  <clause id="14272">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,L(x,u,w),v5),y,z) = a(L(x,y,z),L(x,u,w),v5)
    ]]></literal>
    <justification jstring="[para(29(a,1),14271(a,1,2))].">
      <j1 rule="para" parents="29 14271"/>
    </justification>
  </clause>

  <clause id="14273">
    <literal><![CDATA[
      a(L(R(T(x,y),z,x),u,w),L(R(T(x,y),z,x),z,x),v5) = L(R(T(x,y),z,x),u,w) \ L(R(R(T(x,y),z,x),T(x,y),v5),u,w)
    ]]></literal>
    <justification jstring="[para(1639(a,1),14272(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1639 14272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14275">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (((z * y) \ ((z * (y * x)) / x)) \ 1) = x * (L(x,y,z) \ L(x \ L(x,y,z),x,z * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1129,a(flip),b,13498,a),flip(a)].">
      <j1 rule="hyper" parents="63 1129 13498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14277">
    <literal><![CDATA[
      a((x \ 1) * y,((x \ 1) * y) \ L((x \ 1) * y,z,u),w) = a(y * x,(y * x) \ L(y * x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,13818,a(flip),b,13845,a),flip(a)].">
      <j1 rule="hyper" parents="316 13818 13845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14284">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (((z * y) \ ((z * (y * x)) / x)) \ 1) = x * (x \ a(z * y,x,x * L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(13842(a,1),14275(a,2,2))].">
      <j1 rule="para" parents="13842 14275"/>
    </justification>
  </clause>

  <clause id="14285">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (((z * y) \ ((z * (y * x)) / x)) \ 1) = x * (x \ a(z * y,x,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(11826(a,1),14284(a,2,2,2))].">
      <j1 rule="para" parents="11826 14284"/>
    </justification>
  </clause>

  <clause id="14286">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (((z * y) \ ((z * (y * x)) / x)) \ 1) = a(z * y,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,10,a(flip),b,14285,a),flip(a)].">
      <j1 rule="hyper" parents="316 10 14285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14288">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((y \ (z \ ((z * (y * x)) / x))) \ 1) = a(z * y,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(9350(a,1),14286(a,1,2,1))].">
      <j1 rule="para" parents="9350 14286"/>
    </justification>
  </clause>

  <clause id="14289">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ a(z,y,L(x,y,z)) = a(z * y,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(13503(a,1),14288(a,1,2))].">
      <j1 rule="para" parents="13503 14288"/>
    </justification>
  </clause>

  <clause id="14290">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ L(a(z,y,L(x,y,z)),u,w) = L(a(z * y,x,a(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(14289(a,1),12679(a,2,1))].">
      <j1 rule="para" parents="14289 12679"/>
    </justification>
  </clause>

  <clause id="14291">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ L(a(z,y,L(x,y,z)),u,w) = L(a(y,x,a(z,y,x)),u,w)
    ]]></literal>
    <justification jstring="[para(13936(a,1),14290(a,2,1))].">
      <j1 rule="para" parents="13936 14290"/>
    </justification>
  </clause>

  <clause id="14292">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ L(a(z,y,L(x,y,z)),u,w) = a(y,L(x,u,w),a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,13747,a,b,14291,a),flip(a)].">
      <j1 rule="hyper" parents="316 13747 14291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14293">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ L(a(z,y,x),u,w) = a(y,L(x,u,w),a(z,y,x))
    ]]></literal>
    <justification jstring="[para(13635(a,1),14292(a,1,2,1))].">
      <j1 rule="para" parents="13635 14292"/>
    </justification>
  </clause>

  <clause id="14294">
    <literal><![CDATA[
      L(((x * a(y,z,u)) \ (a(y,z,u) * (w * x))) \ T(w,x),v5,v6) = L(L(a(a(y,z,u),x,w),v5,v6),T(w,x),x)
    ]]></literal>
    <justification jstring="[para(5476(a,1),13419(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5476 13419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14296">
    <literal><![CDATA[
      a(L(x,y,z) * (L(L(x,y,z),u,w) \ (z * (y * x))),v5,v6) = a((z * y) * L(L(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(13811(a,1),14086(a,1,1))].">
      <j1 rule="para" parents="13811 14086"/>
    </justification>
  </clause>

  <clause id="14297">
    <literal><![CDATA[
      a(L(x,y,z) * (L(L(x,y,z),u,w) \ (z * (y * x))),v5,v6) = a(z * (y * L(x,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(403(a,1),14296(a,2,1))].">
      <j1 rule="para" parents="403 14296"/>
    </justification>
  </clause>

  <clause id="14298">
    <literal><![CDATA[
      a(x * (y * (L(1 / z,u,w) \ 1)),v5,v6) = a(x * (y * L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(14190(a,1),14297(a,1,1))].">
      <j1 rule="para" parents="14190 14297"/>
    </justification>
  </clause>

  <clause id="14299">
    <literal><![CDATA[
      a(x * (y * (z * (L(z,u,w) \ z))),v5,v6) = a(x * (y * L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,7924,a(flip),b,14298,a)].">
      <j1 rule="hyper" parents="63 7924 14298"/>
    </justification>
  </clause>

  <clause id="14300">
    <literal><![CDATA[
      a(a(x,x \ y,z * (L(z,u,w) \ z)) * ((x \ y) * L(z,u,w)),v5,v6) = a(x \ (y * (z * (L(z,u,w) \ z))),v5,v6)
    ]]></literal>
    <justification jstring="[para(8458(a,1),14299(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8458 14299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14301">
    <literal><![CDATA[
      a(x,y,z \ ((u / (w \ 1)) * (L(u / (w \ 1),w \ 1,w) \ v5))) = a(x,y,z \ ((((w \ 1) \ u) \ v5) * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5633,a(flip),b,14170,a),flip(a)].">
      <j1 rule="hyper" parents="316 5633 14170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14302">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),L(z,u,w),y) = L((u * w) \ ((u * z) * w),y,x) \ ((u * w) \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(5737(a,1),13406(a,1,1))].">
      <j1 rule="para" parents="5737 13406"/>
    </justification>
  </clause>

  <clause id="14303">
    <literal><![CDATA[
      L((x * y) \ ((x * z) * y),u,w) \ ((x * y) \ ((x * z) * y)) = L(L(z,x,y),u,w) \ L(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13403,a(flip),b,14302,a),flip(a)].">
      <j1 rule="hyper" parents="63 13403 14302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14304">
    <literal><![CDATA[
      L((x * y) \ ((x * z) * y),u,w) \ ((x * y) \ ((x * z) * y)) = L(L(z,u,w) \ z,x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,13383,a(flip),b,14303,a),flip(a)].">
      <j1 rule="hyper" parents="316 13383 14303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14305">
    <literal><![CDATA[
      ((x * y) * z) \ (L((x * z) / ((x * y) * z),u,w) \ (x * z)) = L(L(y,u,w) \ y,x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13906,a(flip),b,14304,a)].">
      <j1 rule="hyper" parents="63 13906 14304"/>
    </justification>
  </clause>

  <clause id="14306">
    <literal><![CDATA[
      (((x * y) * L((x * y) \ x,z,u)) * w) \ (x * w) = L(L(y,z,u) \ y,x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9189,a(flip),b,14305,a)].">
      <j1 rule="hyper" parents="63 9189 14305"/>
    </justification>
  </clause>

  <clause id="14307">
    <literal><![CDATA[
      ((x * (y * L(y \ 1,z,u))) * w) \ (x * w) = L(L(y,z,u) \ y,x,w)
    ]]></literal>
    <justification jstring="[para(777(a,1),14306(a,1,1,1))].">
      <j1 rule="para" parents="777 14306"/>
    </justification>
  </clause>

  <clause id="14308">
    <literal><![CDATA[
      ((x * (y \ L(y,z,u))) * w) \ (x * w) = L(L(y,z,u) \ y,x,w)
    ]]></literal>
    <justification jstring="[para(1064(a,1),14307(a,1,1,1,2))].">
      <j1 rule="para" parents="1064 14307"/>
    </justification>
  </clause>

  <clause id="14309">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * (v5 * L(x \ L(x,y,z),u,w)) = (v5 * ((L(x,y,z) \ x) \ 1)) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(13390(a,1),13606(a,1,2,2))].">
      <j1 rule="para" parents="13390 13606"/>
    </justification>
  </clause>

  <clause id="14310">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * (v5 * L(x \ L(x,y,z),u,w)) = (v5 * (x \ L(x,y,z))) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(5076(a,1),14309(a,2,1,2))].">
      <j1 rule="para" parents="5076 14309"/>
    </justification>
  </clause>

  <clause id="14312">
    <literal><![CDATA[
      L(x,(y * z) \ (a(u,z,y) * z),(z * y) \ (L(y,z,u) \ (z * y))) = L(x,L(y,z,u) \ 1,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(13011(a,1),14222(a,1,2))].">
      <j1 rule="para" parents="13011 14222"/>
    </justification>
  </clause>

  <clause id="14313">
    <literal><![CDATA[
      L(x,(y * z) \ (a(u,z,y) * z),(z * y) \ T(a(u,z,y) * z,y)) = L(x,L(y,z,u) \ 1,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(13637(a,2),14312(a,1,3,2))].">
      <j1 rule="para" parents="13637 14312"/>
    </justification>
  </clause>

  <clause id="14314">
    <literal><![CDATA[
      L(x,(y * z) \ (a(u,z,y) * z),(y * z) \ (a(u,z,y) * z)) = L(x,L(y,z,u) \ 1,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(13011(a,1),14313(a,1,3))].">
      <j1 rule="para" parents="13011 14313"/>
    </justification>
  </clause>

  <clause id="14316">
    <literal><![CDATA[
      a(a(x,x \ y,z * (z * L(z,u,w))) * ((x \ y) * L(z,u,w)),v5,v6) = a(x \ (y * (z * (L(z,u,w) \ z))),v5,v6)
    ]]></literal>
    <justification jstring="[para(5903(a,1),14300(a,1,1,1))].">
      <j1 rule="para" parents="5903 14300"/>
    </justification>
  </clause>

  <clause id="14320">
    <literal><![CDATA[
      a(a(x,x \ y,L(z * (z * z),u,w)) * ((x \ y) * L(z,u,w)),v5,v6) = a(x \ (y * (z * (L(z,u,w) \ z))),v5,v6)
    ]]></literal>
    <justification jstring="[para(1367(a,2),14316(a,1,1,1,3))].">
      <j1 rule="para" parents="1367 14316"/>
    </justification>
  </clause>

  <clause id="14321">
    <literal><![CDATA[
      a(x \ (y * (z * (L(z,u,w) \ z))),v5,v6) = a(a(x,x \ y,L(z,u,w)) * ((x \ y) * L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(5817(a,1),14320(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5817 14320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14323">
    <literal><![CDATA[
      a(x \ (y * (z * (L(z,u,w) \ z))),v5,v6) = a(x \ (y * L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(8458(a,1),14321(a,2,1))].">
      <j1 rule="para" parents="8458 14321"/>
    </justification>
  </clause>

  <clause id="14324">
    <literal><![CDATA[
      a(x \ (y * (L(z \ 1,u,w) \ 1)),v5,v6) = a(x \ (y * L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,4572,a,b,14323,a)].">
      <j1 rule="hyper" parents="63 4572 14323"/>
    </justification>
  </clause>

  <clause id="14325">
    <literal><![CDATA[
      a(x \ ((y \ z) * L(y,u,w)),v5,v6) = a(x \ (y * (L(y,u,w) \ z)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,13629,a(flip),b,14324,a),flip(a)].">
      <j1 rule="hyper" parents="63 13629 14324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14326">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ L(L(z,y,x) \ z,u,w) = a(y,z,L(a(x,y,z),u,w)) \ 1
    ]]></literal>
    <justification jstring="[para(6904(a,1),13420(a,1,1))].">
      <j1 rule="para" parents="6904 13420"/>
    </justification>
  </clause>

  <clause id="14328">
    <literal><![CDATA[
      ((R(x,y,z) \ 1) \ (x \ (u / (x \ 1)))) * (R(x,y,z) \ 1) = R(x,y,z) \ ((R(x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(116(a,1),13836(a,1,2)),flip(a)].">
      <j1 rule="para" parents="116 13836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14329">
    <literal><![CDATA[
      R(x,y,z) \ ((R(x,y,z) \ 1) \ u) = ((x \ 1) \ (x \ (u / (x \ 1)))) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,7795,a(flip),b,14328,a),flip(a)].">
      <j1 rule="hyper" parents="63 7795 14328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14331">
    <literal><![CDATA[
      R(x,y,z) \ ((R(x,y,z) \ 1) \ u) = x \ T(u / (x \ 1),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,851,a(flip),b,14329,a),flip(a)].">
      <j1 rule="hyper" parents="316 851 14329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14332">
    <literal><![CDATA[
      R(x,y,z) \ ((R(x,y,z) \ 1) \ u) = x \ ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(116(a,1),14331(a,2,2))].">
      <j1 rule="para" parents="116 14331"/>
    </justification>
  </clause>

  <clause id="14333">
    <literal><![CDATA[
      ((x * y) \ (z * y)) \ ((R(T(z / x,x * y),x,y) \ 1) \ u) = T(z / x,x * y) \ ((T(z / x,x * y) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(789(a,1),14332(a,1,1))].">
      <j1 rule="para" parents="789 14332"/>
    </justification>
  </clause>

  <clause id="14334">
    <literal><![CDATA[
      T((x * y) \ (z * y),x) \ ((R(T(x \ z,x * y),x,y) \ 1) \ u) = T(x \ z,x * y) \ ((T(x \ z,x * y) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(845(a,1),14332(a,1,1))].">
      <j1 rule="para" parents="845 14332"/>
    </justification>
  </clause>

  <clause id="14335">
    <literal><![CDATA[
      ((x * y) / z) \ ((R(x / (z / y),y \ z,y) \ 1) \ u) = (x / (z / y)) \ (((x / (z / y)) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(4481(a,1),14332(a,1,1))].">
      <j1 rule="para" parents="4481 14332"/>
    </justification>
  </clause>

  <clause id="14336">
    <literal><![CDATA[
      ((x * y) / z) \ ((((x * y) / z) \ 1) \ u) = (x / (z / y)) \ (((x / (z / y)) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(4481(a,1),14335(a,1,2,1,1))].">
      <j1 rule="para" parents="4481 14335"/>
    </justification>
  </clause>

  <clause id="14337">
    <literal><![CDATA[
      T(x / y,y * z) \ ((T(x / y,y * z) \ 1) \ u) = ((y * z) \ (x * z)) \ ((((y * z) \ (x * z)) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(789(a,1),14333(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="789 14333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14338">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * L((a(z,y,x) \ 1) \ (x \ L(x,y,z)),u,w) = L(1 / R(x \ L(x,y,z),u,w),x,y) \ 1
    ]]></literal>
    <justification jstring="[para(8380(a,1),13510(a,1,1))].">
      <j1 rule="para" parents="8380 13510"/>
    </justification>
  </clause>

  <clause id="14339">
    <literal><![CDATA[
      (L(x,x,a(y,z,u)) \ ((x \ ((x * x) * a(y,z,u))) * w)) / w = a(y,z,u) * (a(w,a(y,z,u),L(x,x,a(y,z,u))) \ 1)
    ]]></literal>
    <justification jstring="[para(5264(a,1),13744(a,1,1,1))].">
      <j1 rule="para" parents="5264 13744"/>
    </justification>
  </clause>

  <clause id="14340">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,L(x,w,z),L(x,w,z) \ L(L(x,w,z),y,z)) = (u / L(x,w,z)) * L(L(x,w,z),y,z)
    ]]></literal>
    <justification jstring="[para(9935(a,1),13887(a,1,1))].">
      <j1 rule="para" parents="9935 13887"/>
    </justification>
  </clause>

  <clause id="14341">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,L(x,w,z),L(x \ L(x,y,z),w,z)) = (u / L(x,w,z)) * L(L(x,w,z),y,z)
    ]]></literal>
    <justification jstring="[para(2136(a,1),14340(a,1,2,3))].">
      <j1 rule="para" parents="2136 14340"/>
    </justification>
  </clause>

  <clause id="14342">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,L(x,w,z),x \ L(x,y,z)) = (u / L(x,w,z)) * L(L(x,w,z),y,z)
    ]]></literal>
    <justification jstring="[para(9935(a,1),14341(a,1,2,3))].">
      <j1 rule="para" parents="9935 14341"/>
    </justification>
  </clause>

  <clause id="14343">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,L(x,y,z),x \ L(x,y,z)) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,13252,a(flip),b,14342,a),flip(a)].">
      <j1 rule="hyper" parents="316 13252 14342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14345">
    <literal><![CDATA[
      L(x,L(y,z,u),y \ L(y,z,u)) = L(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(34,a,13886,a,b,14343,a),flip(a)].">
      <j1 rule="hyper" parents="34 13886 14343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14346">
    <literal><![CDATA[
      L(L(x,y,z) \ u,x,x \ L(x,y,z)) = (x \ u) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9240,a(flip),b,14345,a),flip(a)].">
      <j1 rule="hyper" parents="63 9240 14345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14348">
    <literal><![CDATA[
      L(x,y,y \ L(y,z,u)) * y = (x * L(y,z,u)) * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(14345(a,1),9214(a,1,1))].">
      <j1 rule="para" parents="14345 9214"/>
    </justification>
  </clause>

  <clause id="14349">
    <literal><![CDATA[
      x \ ((x \ L(x,y,z)) \ u) = (x \ u) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,14137,a(flip),b,14346,a)].">
      <j1 rule="hyper" parents="63 14137 14346"/>
    </justification>
  </clause>

  <clause id="14350">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(38,a,6551,a,b,14349,a),flip(a)].">
      <j1 rule="hyper" parents="38 6551 14349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14351">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ u = u * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(38,a,5152,a,b,14349,a),flip(a)].">
      <j1 rule="hyper" parents="38 5152 14349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14352">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ u = (x \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(320,a,14350,a),flip(a)].">
      <j1 rule="hyper" parents="320 14350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14355">
    <literal><![CDATA[
      x \ ((y \ L(y,z,u)) \ x) = L(y,z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(133,a,14350,a,b,6496,a(flip))].">
      <j1 rule="hyper" parents="133 14350 6496"/>
    </justification>
  </clause>

  <clause id="14356">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (u * (x \ L(x,y,z))) = u
    ]]></literal>
    <justification jstring="[hyper(63,a,5014,a(flip),b,14350,a),flip(a)].">
      <j1 rule="hyper" parents="63 5014 14350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14357">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * (x \ L(x,y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(38,a,5014,a,b,14350,a)].">
      <j1 rule="hyper" parents="38 5014 14350"/>
    </justification>
  </clause>

  <clause id="14358">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ u = u * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,5014,a(flip),b,14350,a(flip))].">
      <j1 rule="hyper" parents="133 5014 14350"/>
    </justification>
  </clause>

  <clause id="14361">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) * (L(x,y,z) \ x) = u
    ]]></literal>
    <justification jstring="[hyper(322,a,14351,a),flip(a)].">
      <j1 rule="hyper" parents="322 14351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14362">
    <literal><![CDATA[
      x / (y \ L(y,z,u)) = x * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5015,a,b,14351,a)].">
      <j1 rule="hyper" parents="63 5015 14351"/>
    </justification>
  </clause>

  <clause id="14363">
    <literal><![CDATA[
      (a(x \ 1,x,y) \ L(y,z,u)) * (L(y,z,u) \ y) = L(y,x,x \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12191,a(flip),b,14351,a),flip(a)].">
      <j1 rule="hyper" parents="63 12191 14351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14364">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * (L(y,z,u) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,5014,a(flip),b,14351,a),flip(a)].">
      <j1 rule="hyper" parents="63 5014 14351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14366">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),y * L(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,12415,a,b,14351,a)].">
      <j1 rule="hyper" parents="38 12415 14351"/>
    </justification>
  </clause>

  <clause id="14367">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),L(y,z,u) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,12412,a,b,14351,a)].">
      <j1 rule="hyper" parents="38 12412 14351"/>
    </justification>
  </clause>

  <clause id="14369">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (y \ L(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,5014,a,b,14351,a)].">
      <j1 rule="hyper" parents="38 5014 14351"/>
    </justification>
  </clause>

  <clause id="14377">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (L(y,z,u) \ y) = x * (L(L(y,z,u),z,u) \ y)
    ]]></literal>
    <justification jstring="[para(14351(a,1),10047(a,1,1))].">
      <j1 rule="para" parents="14351 10047"/>
    </justification>
  </clause>

  <clause id="14378">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (u * (x \ R(x,y,z))) = u
    ]]></literal>
    <justification jstring="[hyper(63,a,12838,a,b,14366,a)].">
      <j1 rule="hyper" parents="63 12838 14366"/>
    </justification>
  </clause>

  <clause id="14379">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,L(y,z,u) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,12409,a,b,14366,a)].">
      <j1 rule="hyper" parents="63 12409 14366"/>
    </justification>
  </clause>

  <clause id="14380">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),y * L(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(132,a,14366,a(flip),b,12420,a),flip(a)].">
      <j1 rule="hyper" parents="132 14366 12420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14381">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,14150,a(flip),b,14367,a)].">
      <j1 rule="hyper" parents="63 14150 14367"/>
    </justification>
  </clause>

  <clause id="14385">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,14381,a,b,4951,a),flip(a)].">
      <j1 rule="hyper" parents="134 14381 4951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14387">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ 1) * v5 = L(a(x,y,z),u,w) \ v5
    ]]></literal>
    <justification jstring="[hyper(63,a,13799,a(flip),b,14381,a)].">
      <j1 rule="hyper" parents="63 13799 14381"/>
    </justification>
  </clause>

  <clause id="14388">
    <literal><![CDATA[
      (a(x,y,z) * u) \ L(a(x,y,z) * u,w,v5) = a(x,y,z) \ (u * L(u \ a(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,12508,a(flip),b,14381,a),flip(a)].">
      <j1 rule="hyper" parents="63 12508 14381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14389">
    <literal><![CDATA[
      (x \ ((y \ 1) * (y * x))) * z = (y * (x / (y * x))) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,12301,a(flip),b,14381,a)].">
      <j1 rule="hyper" parents="63 12301 14381"/>
    </justification>
  </clause>

  <clause id="14391">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * u = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,6124,a(flip),b,14381,a)].">
      <j1 rule="hyper" parents="63 6124 14381"/>
    </justification>
  </clause>

  <clause id="14392">
    <literal><![CDATA[
      (1 / a(x,y,z)) * u = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,6123,a(flip),b,14381,a)].">
      <j1 rule="hyper" parents="63 6123 14381"/>
    </justification>
  </clause>

  <clause id="14393">
    <literal><![CDATA[
      x * (a(y,z,u) \ 1) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,5380,a(flip),b,14381,a)].">
      <j1 rule="hyper" parents="63 5380 14381"/>
    </justification>
  </clause>

  <clause id="14394">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5376,a(flip),b,14381,a),flip(a)].">
      <j1 rule="hyper" parents="63 5376 14381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14395">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * u = a(x,y,z) * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1114,a(flip),b,14381,a),flip(a)].">
      <j1 rule="hyper" parents="63 1114 14381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14396">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * u = a(x,y,z) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,14381,a(flip),b,2496,a)].">
      <j1 rule="hyper" parents="139 14381 2496"/>
    </justification>
  </clause>

  <clause id="14397">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * (a(x,y,z) \ u) = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(139,a,14381,a(flip),b,820,a)].">
      <j1 rule="hyper" parents="139 14381 820"/>
    </justification>
  </clause>

  <clause id="14398">
    <literal><![CDATA[
      (a(x,y,z) \ u) / u = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(136,a,14381,a(flip),b,6124,a(flip))].">
      <j1 rule="hyper" parents="136 14381 6124"/>
    </justification>
  </clause>

  <clause id="14399">
    <literal><![CDATA[
      x \ (a(y,z,u) \ x) = a(y,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,14381,a(flip),b,5380,a(flip))].">
      <j1 rule="hyper" parents="133 14381 5380"/>
    </justification>
  </clause>

  <clause id="14400">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ u = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(39,a,8846,a(flip),b,14381,a(flip))].">
      <j1 rule="hyper" parents="39 8846 14381"/>
    </justification>
  </clause>

  <clause id="14401">
    <literal><![CDATA[
      L(x \ R(x,y * a(z,u,w),a(z,u,w)),x,y) = a(x,y * a(z,u,w),a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14381(a,1),3476(a,1,3))].">
      <j1 rule="para" parents="14381 3476"/>
    </justification>
  </clause>

  <clause id="14402">
    <literal><![CDATA[
      R(x,y,a(z,u,w) \ v5) = R(x,y,v5 * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14381(a,1),4801(a,1,3,2))].">
      <j1 rule="para" parents="14381 4801"/>
    </justification>
  </clause>

  <clause id="14403">
    <literal><![CDATA[
      a(x,y,a(z,u,w) \ v5) = a(x,y,a(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(14381(a,1),5811(a,1,3))].">
      <j1 rule="para" parents="14381 5811"/>
    </justification>
  </clause>

  <clause id="14404">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,v5) \ v6)) = a(x,y,z \ (a(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(14381(a,1),6348(a,1,3,2,2))].">
      <j1 rule="para" parents="14381 6348"/>
    </justification>
  </clause>

  <clause id="14405">
    <literal><![CDATA[
      a(x,y,z \ (u \ (a(w,v5,v6) \ v7))) = a(x,y,z \ (u \ (v7 * a(w,v5,v6))))
    ]]></literal>
    <justification jstring="[para(14381(a,1),6392(a,1,3,2,2))].">
      <j1 rule="para" parents="14381 6392"/>
    </justification>
  </clause>

  <clause id="14406">
    <literal><![CDATA[
      a(x,y,L(L(a(z,u,w) \ v5,v6,v7),v8,v9)) = a(x,y,L(L(a(z,u,w) * v5,v6,v7),v8,v9))
    ]]></literal>
    <justification jstring="[para(14381(a,1),6042(a,1,3))].">
      <j1 rule="para" parents="14381 6042"/>
    </justification>
  </clause>

  <clause id="14407">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) \ v5) * v6) = a(x,y,(v5 * a(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[para(14381(a,1),7456(a,1,3,1,2))].">
      <j1 rule="para" parents="14381 7456"/>
    </justification>
  </clause>

  <clause id="14408">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ v5,v6,v7)) = a(x,y,L(a(z,u,w) * v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(14381(a,1),8604(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14381 8604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14409">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) \ v5) * v6) = a(x,y,v6 * (v5 * a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(14381(a,1),8686(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="14381 8686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14410">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) \ w = w * a(y,a(z,u,y),x)
    ]]></literal>
    <justification jstring="[para(14381(a,1),9479(a,1,2))].">
      <j1 rule="para" parents="14381 9479"/>
    </justification>
  </clause>

  <clause id="14411">
    <literal><![CDATA[
      a(x,y,z \ (u * (a(w,v5,v6) \ v7))) = a(x,y,z \ (u * (a(w,v5,v6) * v7)))
    ]]></literal>
    <justification jstring="[para(14381(a,1),11754(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="14381 11754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14413">
    <literal><![CDATA[
      a(a(x,y,z) \ u,w,v5) = a(a(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(14381(a,1),13084(a,1,1))].">
      <j1 rule="para" parents="14381 13084"/>
    </justification>
  </clause>

  <clause id="14414">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ v5 = v5 * a(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(14381(a,1),14202(a,1,2))].">
      <j1 rule="para" parents="14381 14202"/>
    </justification>
  </clause>

  <clause id="14416">
    <literal><![CDATA[
      a(x,a(y,z,u),a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,14385,a,b,13737,a),flip(a)].">
      <j1 rule="hyper" parents="134 14385 13737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14418">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(52,a,14416,a)].">
      <j1 rule="hyper" parents="52 14416"/>
    </justification>
  </clause>

  <clause id="14420">
    <literal><![CDATA[
      a(x,y,z) * (u * (z \ L(L(z,y,x),y,x))) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,14052,a,b,14391,a)].">
      <j1 rule="hyper" parents="63 14052 14391"/>
    </justification>
  </clause>

  <clause id="14422">
    <literal><![CDATA[
      a(x,y,z) * (u * (w * (a(x,y,z) \ 1))) = a(x,y,z) \ (u * (w * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9843,a(flip),b,14391,a)].">
      <j1 rule="hyper" parents="63 9843 14391"/>
    </justification>
  </clause>

  <clause id="14423">
    <literal><![CDATA[
      a(x,y,z) \ (a(x,y,z) \ (u \ a(x,y,z))) = u \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,14391,a(flip),b,5054,a(flip))].">
      <j1 rule="hyper" parents="133 14391 5054"/>
    </justification>
  </clause>

  <clause id="14424">
    <literal><![CDATA[
      (a(x,y,z) \ K(u,w)) * v5 = K(u,w) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(14391(a,1),2468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14391 2468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14425">
    <literal><![CDATA[
      x * ((a(y,z,u) \ 1) * L(x,w,v5)) = L(x,w,v5) * (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(14391(a,1),4398(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14391 4398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14426">
    <literal><![CDATA[
      (x \ L(x,y,y)) * z = a(y,y,x) \ z
    ]]></literal>
    <justification jstring="[para(5088(a,1),14391(a,1,1))].">
      <j1 rule="para" parents="5088 14391"/>
    </justification>
  </clause>

  <clause id="14427">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) * w = a(x,x,L(y,z,u)) \ w
    ]]></literal>
    <justification jstring="[para(5124(a,2),14391(a,1,1))].">
      <j1 rule="para" parents="5124 14391"/>
    </justification>
  </clause>

  <clause id="14428">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,v5) \ v6)) = a(x,y,z * (v6 * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(14391(a,1),5902(a,1,3,2))].">
      <j1 rule="para" parents="14391 5902"/>
    </justification>
  </clause>

  <clause id="14429">
    <literal><![CDATA[
      x * (L(x,y,z) \ (a(u,w,v5) \ 1)) = L(x,y,z) \ (a(u,w,v5) \ x)
    ]]></literal>
    <justification jstring="[para(14391(a,1),5055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14391 5055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14430">
    <literal><![CDATA[
      x \ (y * (a(z,u,w) \ (v5 * v5))) = (x \ (a(z,u,w) \ y)) * (v5 * v5)
    ]]></literal>
    <justification jstring="[para(14391(a,1),5057(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14391 5057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14433">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,u,w) \ y) = (x * y) * (a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(14391(a,1),8254(a,1,2))].">
      <j1 rule="para" parents="14391 8254"/>
    </justification>
  </clause>

  <clause id="14435">
    <literal><![CDATA[
      a(x,a(y,z,u) \ w,v5) = a(x,w * a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[para(14391(a,1),13064(a,1,2))].">
      <j1 rule="para" parents="14391 13064"/>
    </justification>
  </clause>

  <clause id="14436">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ (((a(y,z,u) \ 1) * x) * w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(14391(a,1),13062(a,1,1,2))].">
      <j1 rule="para" parents="14391 13062"/>
    </justification>
  </clause>

  <clause id="14437">
    <literal><![CDATA[
      (x \ y) * L(a(z,u,w) \ 1,x \ y,x) = x \ (a(z,u,w) \ y)
    ]]></literal>
    <justification jstring="[para(14391(a,1),13496(a,2,2))].">
      <j1 rule="para" parents="14391 13496"/>
    </justification>
  </clause>

  <clause id="14438">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,w) \ v5 = a(x \ L(x,y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(13555(a,1),14391(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13555 14391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14440">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ v5 = a(w,u,a(x,y,z)) * v5
    ]]></literal>
    <justification jstring="[para(13734(a,1),14391(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13734 14391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14443">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ v5 = a(x,y,a(z,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(14009(a,1),14391(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14009 14391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14444">
    <literal><![CDATA[
      (x \ (a(y,z,u) * w)) * (u \ L(L(u,z,y),z,y)) = x \ (a(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(14391(a,1),14094(a,2,2))].">
      <j1 rule="para" parents="14391 14094"/>
    </justification>
  </clause>

  <clause id="14445">
    <literal><![CDATA[
      L(x,y,z) \ (a(z,y,x) \ u) = a(x,y,z) * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(14391(a,1),14143(a,1,2))].">
      <j1 rule="para" parents="14391 14143"/>
    </justification>
  </clause>

  <clause id="14450">
    <literal><![CDATA[
      (a(x,y,z) * u) \ u = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,9,a(flip),b,14393,a)].">
      <j1 rule="hyper" parents="133 9 14393"/>
    </justification>
  </clause>

  <clause id="14451">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ (a(u,z,y) \ 1) = a(u,z,y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,13991,a,b,14393,a)].">
      <j1 rule="hyper" parents="63 13991 14393"/>
    </justification>
  </clause>

  <clause id="14452">
    <literal><![CDATA[
      x / (a(y,z,u) \ K(w,v5)) = a(y,z,u) * (x * K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,3858,a(flip),b,14393,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 3858 14393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14453">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * (w * u) = w * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(14393(a,1),5010(a,2,2))].">
      <j1 rule="para" parents="14393 5010"/>
    </justification>
  </clause>

  <clause id="14455">
    <literal><![CDATA[
      x * (y \ L(y,y,z)) = a(z,y,y) \ x
    ]]></literal>
    <justification jstring="[para(7304(a,1),14393(a,1,2))].">
      <j1 rule="para" parents="7304 14393"/>
    </justification>
  </clause>

  <clause id="14460">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * (w * a(u,w,L(a(x,y,z),u,w))) = u \ ((a(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(14393(a,1),9637(a,2,2,1))].">
      <j1 rule="para" parents="14393 9637"/>
    </justification>
  </clause>

  <clause id="14461">
    <literal><![CDATA[
      L(L(1 / (a(x,y,z) \ 1),u,w) \ 1,w,u) = u \ (w \ (u * (a(x,y,z) \ T(w,u))))
    ]]></literal>
    <justification jstring="[para(14393(a,1),9991(a,2,2,2,2))].">
      <j1 rule="para" parents="14393 9991"/>
    </justification>
  </clause>

  <clause id="14462">
    <literal><![CDATA[
      (a(x \ 1,x,y) \ z) * (z \ y) = a(x \ 1,x,L(y,z,z)) \ y
    ]]></literal>
    <justification jstring="[para(14393(a,1),12529(a,1,1))].">
      <j1 rule="para" parents="14393 12529"/>
    </justification>
  </clause>

  <clause id="14464">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u \ ((a(x,y,z) \ w) * v5)) = a(x,y,z) \ (u \ ((w * a(x,y,z)) * v5))
    ]]></literal>
    <justification jstring="[para(14393(a,1),13221(a,1,2,2,1))].">
      <j1 rule="para" parents="14393 13221"/>
    </justification>
  </clause>

  <clause id="14465">
    <literal><![CDATA[
      x \ ((a(y,z,u) \ w) * (w \ x)) = L(a(y,z,u) \ 1,w,w \ x)
    ]]></literal>
    <justification jstring="[para(14393(a,1),13295(a,1,2,1))].">
      <j1 rule="para" parents="14393 13295"/>
    </justification>
  </clause>

  <clause id="14467">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ v5 = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(13734(a,1),14393(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13734 14393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14468">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) \ w = w * a(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(13740(a,1),14393(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13740 14393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14470">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ v5 = v5 * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14009(a,1),14393(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14009 14393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14474">
    <literal><![CDATA[
      (a(x,y,z * u) \ 1) \ w = w * a(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(5469(a,1),14394(a,1,1,1))].">
      <j1 rule="para" parents="5469 14394"/>
    </justification>
  </clause>

  <clause id="14475">
    <literal><![CDATA[
      a(x,y,z \ ((a(u,w,v5) \ v6) \ v7)) = a(x,y,z \ ((v6 * a(u,w,v5)) \ v7))
    ]]></literal>
    <justification jstring="[para(14394(a,1),7743(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="14394 7743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14476">
    <literal><![CDATA[
      (x * a(y,z,u)) \ R(x,w,v5) = a(y,z,u) \ (x \ R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(14394(a,1),9774(a,1,1))].">
      <j1 rule="para" parents="14394 9774"/>
    </justification>
  </clause>

  <clause id="14477">
    <literal><![CDATA[
      a(a(x,y,z) \ u,w,v5) = a(u * a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(14394(a,1),13085(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14394 13085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14482">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u * a(x,y,z),w) = (w * (u * a(x,y,z))) \ (w * u)
    ]]></literal>
    <justification jstring="[para(14399(a,1),4788(a,1,1))].">
      <j1 rule="para" parents="14399 4788"/>
    </justification>
  </clause>

  <clause id="14486">
    <literal><![CDATA[
      a(x \ y,x,x) \ (z * (1 / (y \ (y / x)))) = a(x \ y,x,x) * (z * L(x,x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,9528,a,b,14400,a)].">
      <j1 rule="hyper" parents="63 9528 14400"/>
    </justification>
  </clause>

  <clause id="14487">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ L(u,w,v5) = a(x,y,z) * (u \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,9765,a(flip),b,14400,a)].">
      <j1 rule="hyper" parents="63 9765 14400"/>
    </justification>
  </clause>

  <clause id="14488">
    <literal><![CDATA[
      L(a(x,y,z),u,w \ (a(v5,v6,v7) \ v8)) = L(a(x,y,z),u,w \ (a(v5,v6,v7) * v8))
    ]]></literal>
    <justification jstring="[para(14400(a,1),11643(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="14400 11643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14489">
    <literal><![CDATA[
      a(x,y * (a(z,u,w) \ v5),v6) = a(x,y * (a(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(14400(a,1),13060(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14400 13060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14492">
    <literal><![CDATA[
      L(a(x \ 1,y,z),a(x,y,z),u) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11380,a(flip),b,14418,a)].">
      <j1 rule="hyper" parents="63 11380 14418"/>
    </justification>
  </clause>

  <clause id="14500">
    <literal><![CDATA[
      a(x,y,L(a(z,x,y),u,w)) * L(L(y,x,z) \ y,u,w) = L(a(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(39,a,14326,a,b,14450,a),flip(a)].">
      <j1 rule="hyper" parents="39 14326 14450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14504">
    <literal><![CDATA[
      a(L(x,y,z) \ x,L(x,y,z) \ x,u) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,14379,a,b,4951,a),flip(a)].">
      <j1 rule="hyper" parents="134 14379 4951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14505">
    <literal><![CDATA[
      a(x,L(y,z,u) \ y,L(y,z,u) \ y) = 1
    ]]></literal>
    <justification jstring="[hyper(132,a,14379,a(flip),b,11943,a),flip(a)].">
      <j1 rule="hyper" parents="132 14379 11943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14506">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,y,z) \ x,u) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(52,a,14505,a)].">
      <j1 rule="hyper" parents="52 14505"/>
    </justification>
  </clause>

  <clause id="14507">
    <literal><![CDATA[
      a(x,L(y,z,u) \ y,a(u,z,y)) = L(1,y,z)
    ]]></literal>
    <justification jstring="[para(14505(a,1),13569(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14505 13569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14509">
    <literal><![CDATA[
      a(x,y,y \ (z \ y)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(39,a,13758,a,b,14352,a)].">
      <j1 rule="hyper" parents="39 13758 14352"/>
    </justification>
  </clause>

  <clause id="14510">
    <literal><![CDATA[
      a(x,y,L(z,z,y)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,6745,a,b,14509,a)].">
      <j1 rule="hyper" parents="63 6745 14509"/>
    </justification>
  </clause>

  <clause id="14511">
    <literal><![CDATA[
      L(x,y,z) = a(z,y,y \ (x \ y)) \ x
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,14509,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 2301 14509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14514">
    <literal><![CDATA[
      a(x,y,L((z \ u) * u,L(z,u * z,u * z),y)) = L(L(z,u * z,u * z),y,x) \ L(z,u * z,u * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13989,a(flip),b,14510,a)].">
      <j1 rule="hyper" parents="63 13989 14510"/>
    </justification>
  </clause>

  <clause id="14515">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u),L(z,z,u \ z),y)) = L(L(z,z,u \ z),y,x) \ L(z,z,u \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9379,a(flip),b,14510,a)].">
      <j1 rule="hyper" parents="63 9379 14510"/>
    </justification>
  </clause>

  <clause id="14516">
    <literal><![CDATA[
      a(x,L(y,z,z),L(z,z,y)) = L(z,L(y,z,z),x) \ z
    ]]></literal>
    <justification jstring="[para(7159(a,1),14510(a,1,3))].">
      <j1 rule="para" parents="7159 14510"/>
    </justification>
  </clause>

  <clause id="14517">
    <literal><![CDATA[
      a(x,L(y,z,u),L(L(y,L(y,w,v5),y),w,v5)) = L(L(y,w,v5),L(y,z,u),x) \ L(y,w,v5)
    ]]></literal>
    <justification jstring="[para(7997(a,1),14510(a,1,3))].">
      <j1 rule="para" parents="7997 14510"/>
    </justification>
  </clause>

  <clause id="14519">
    <literal><![CDATA[
      a(x,a(L(y,y,z),z,u),w) = a(x,L(y,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[para(14510(a,1),13658(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14510 13658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14522">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ a(x,y,z) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14418(a,1),14510(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14418 14510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14525">
    <literal><![CDATA[
      L((1 / x) \ (y * (x \ L(x,z,u))),x,x \ L(x,z,u)) = (1 / L(x,z,u)) \ y
    ]]></literal>
    <justification jstring="[para(14356(a,1),9249(a,2,2))].">
      <j1 rule="para" parents="14356 9249"/>
    </justification>
  </clause>

  <clause id="14527">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * (L(y,z,u) \ (y * L(y \ L(y,z,u),w,v5))) = x * L(x \ ((L(y,z,u) \ y) \ x),w,v5)
    ]]></literal>
    <justification jstring="[para(14358(a,1),5134(a,1,1))].">
      <j1 rule="para" parents="14358 5134"/>
    </justification>
  </clause>

  <clause id="14528">
    <literal><![CDATA[
      ((x * (y \ L(y,z,u))) \ 1) \ 1 = (L(y,z,u) \ y) \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(14358(a,1),12842(a,1,1,1))].">
      <j1 rule="para" parents="14358 12842"/>
    </justification>
  </clause>

  <clause id="14529">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((u * (L(x,y,z) \ x)) * L(x \ L(x,y,z),w,v5)) = L(L(x,y,z) / x,w,v5) * u
    ]]></literal>
    <justification jstring="[para(14362(a,1),10725(a,1,2,1))].">
      <j1 rule="para" parents="14362 10725"/>
    </justification>
  </clause>

  <clause id="14530">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * (v5 * L(x \ L(x,y,z),u,w)) = v5
    ]]></literal>
    <justification jstring="[hyper(63,a,14310,a,b,14364,a)].">
      <j1 rule="hyper" parents="63 14310 14364"/>
    </justification>
  </clause>

  <clause id="14531">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ v5 = v5 * L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,14364,a(flip),b,14310,a)].">
      <j1 rule="hyper" parents="133 14364 14310"/>
    </justification>
  </clause>

  <clause id="14532">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u * (x \ L(x,y,z)),w) = (w * (u * (x \ L(x,y,z)))) \ (w * u)
    ]]></literal>
    <justification jstring="[para(14364(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="14364 18"/>
    </justification>
  </clause>

  <clause id="14533">
    <literal><![CDATA[
      L(x * (y \ L(y,z,u)),y,y \ L(y,z,u)) = y * ((L(1 / y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(14364(a,1),13256(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14364 13256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14536">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[para(2193(a,1),14378(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2193 14378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14537">
    <literal><![CDATA[
      a(x,L(y,z,u) \ y,a(u,z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(316,a,470,a(flip),b,14507,a),flip(a)].">
      <j1 rule="hyper" parents="316 470 14507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14540">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),a(u,z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,12828,a(flip),b,14537,a)].">
      <j1 rule="hyper" parents="63 12828 14537"/>
    </justification>
  </clause>

  <clause id="14541">
    <literal><![CDATA[
      L(a(x,y,z),z \ L(z,y,x),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(52,a,14540,a)].">
      <j1 rule="hyper" parents="52 14540"/>
    </justification>
  </clause>

  <clause id="14542">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(320,a,14536,a),flip(a)].">
      <j1 rule="hyper" parents="320 14536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14546">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (u * R(u \ ((R(x,y,z) \ x) \ u),w,v5)) = u * ((R(x,y,z) \ x) * R((R(x,y,z) \ x) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,2464,a(flip),b,14536,a),flip(a)].">
      <j1 rule="hyper" parents="316 2464 14536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14550">
    <literal><![CDATA[
      (L(x,y,z) \ L(R(x,u,w),y,z)) \ v5 = (R(R(x,y,z),u,w) \ R(x,y,z)) * v5
    ]]></literal>
    <justification jstring="[para(12497(a,1),14536(a,1,1))].">
      <j1 rule="para" parents="12497 14536"/>
    </justification>
  </clause>

  <clause id="14551">
    <literal><![CDATA[
      (L(x \ 1,y,z) * y) \ R(x \ 1,a(z,y,x) \ y,y * a(z,y,x)) = (a(z,y,x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(14402(a,1),13780(a,1,2))].">
      <j1 rule="para" parents="14402 13780"/>
    </justification>
  </clause>

  <clause id="14553">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) \ a(z,x,y) = L(y,x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(316,a,13404,a(flip),b,14410,a),flip(a)].">
      <j1 rule="hyper" parents="316 13404 14410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14554">
    <literal><![CDATA[
      a(a(x,y,z) \ ((u * (w * a(x,y,z))) / a(x,y,z)),v5,v6) = a(L(a(x,y,z),w,u) * (u * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(4415(a,2),14413(a,2,1))].">
      <j1 rule="para" parents="4415 14413"/>
    </justification>
  </clause>

  <clause id="14556">
    <literal><![CDATA[
      R(1 * a(x,a(y,z,u),w),x,(u * (y * z)) \ (y * (u * z))) = x \ L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(14414(a,1),10010(a,1,1))].">
      <j1 rule="para" parents="14414 10010"/>
    </justification>
  </clause>

  <clause id="14560">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ v5 = v5 * a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,13689,a(flip),b,14440,a),flip(a)].">
      <j1 rule="hyper" parents="316 13689 14440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14564">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(x,y,a(w,u,z)) * v5) = v5
    ]]></literal>
    <justification jstring="[hyper(139,a,14440,a(flip),b,14036,a(flip))].">
      <j1 rule="hyper" parents="139 14440 14036"/>
    </justification>
  </clause>

  <clause id="14565">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * a(x,y,a(z,u,w))) = v5
    ]]></literal>
    <justification jstring="[hyper(139,a,2290,a(flip),b,14443,a)].">
      <j1 rule="hyper" parents="139 2290 14443"/>
    </justification>
  </clause>

  <clause id="14566">
    <literal><![CDATA[
      ((x / y) * (y * a(z,u,w))) / a(z,u,w) = a(y \ x,y,a(z,u,w)) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,6918,a(flip),b,14443,a)].">
      <j1 rule="hyper" parents="63 6918 14443"/>
    </justification>
  </clause>

  <clause id="14567">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * y) * a(z,u,w) = y * L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(14443(a,1),13759(a,1,1))].">
      <j1 rule="para" parents="14443 13759"/>
    </justification>
  </clause>

  <clause id="14568">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,x,L(y,z,u))) * L(L(y,x,w) \ y,z,u) = a(w,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,13383,a(flip),b,14553,a)].">
      <j1 rule="hyper" parents="139 13383 14553"/>
    </justification>
  </clause>

  <clause id="14570">
    <literal><![CDATA[
      L(1 * a(x,y * x,a(z,u,y * x)),x,y) = a(x,y * x,a(y * x,u,z))
    ]]></literal>
    <justification jstring="[para(14560(a,1),11772(a,1,1))].">
      <j1 rule="para" parents="14560 11772"/>
    </justification>
  </clause>

  <clause id="14572">
    <literal><![CDATA[
      ((x * (y * z)) / L(z,z,y)) \ (x * R(y,z,z)) = L(z,L(y,z,z),x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,11326,a,b,14516,a)].">
      <j1 rule="hyper" parents="63 11326 14516"/>
    </justification>
  </clause>

  <clause id="14573">
    <literal><![CDATA[
      a(x,a(L(y,y,z),z,u),w) = a(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,12828,a(flip),b,14519,a),flip(a)].">
      <j1 rule="hyper" parents="316 12828 14519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14577">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u,w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13453,a(flip),b,14522,a)].">
      <j1 rule="hyper" parents="63 13453 14522"/>
    </justification>
  </clause>

  <clause id="14578">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(y,z,u)) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7553,a(flip),b,14522,a)].">
      <j1 rule="hyper" parents="63 7553 14522"/>
    </justification>
  </clause>

  <clause id="14579">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ a(z,u,w) = L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,14522,a)].">
      <j1 rule="hyper" parents="39 2301 14522"/>
    </justification>
  </clause>

  <clause id="14582">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(x,y,z)) = L(a(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,14522,a(flip),b,13453,a(flip))].">
      <j1 rule="hyper" parents="139 14522 13453"/>
    </justification>
  </clause>

  <clause id="14586">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) \ a(x,y,y) = a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(13562(a,2),14522(a,1,1))].">
      <j1 rule="para" parents="13562 14522"/>
    </justification>
  </clause>

  <clause id="14587">
    <literal><![CDATA[
      a(a(x,y,z) \ L(a(x,y,z),u,w),v5,v6) = a(v6,v5,a(w,u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(14522(a,1),13772(a,2,3))].">
      <j1 rule="para" parents="14522 13772"/>
    </justification>
  </clause>

  <clause id="14589">
    <literal><![CDATA[
      x * L(L(a(y,z,a(u,w,v5)),v6,v7),L(a(u,w,v5),v6,v7),x) = L(a(u,w,v5),v6,v7) * (L(L(a(u,w,v5),v6,v7),z,y) \ x)
    ]]></literal>
    <justification jstring="[para(14522(a,1),13789(a,1,2,1,1))].">
      <j1 rule="para" parents="14522 13789"/>
    </justification>
  </clause>

  <clause id="14590">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u,w) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,14010,a,b,14577,a),flip(a)].">
      <j1 rule="hyper" parents="316 14010 14577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14591">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u * R(w,v5,v6),v7) = a(v7,u * L(w,v5,v6),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,12037,a(flip),b,14577,a),flip(a)].">
      <j1 rule="hyper" parents="316 12037 14577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14592">
    <literal><![CDATA[
      a(x,y,z) * a(a(x,y,z),u,w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,14010,a,b,14577,a)].">
      <j1 rule="hyper" parents="139 14010 14577"/>
    </justification>
  </clause>

  <clause id="14593">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(z,y,x)) = L(a(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,13660,a,b,14577,a)].">
      <j1 rule="hyper" parents="139 13660 14577"/>
    </justification>
  </clause>

  <clause id="14595">
    <literal><![CDATA[
      a(x,y,z) * a(u,x,a(z,y,x)) = L(a(x,y,z),x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,13688,a(flip),b,14577,a)].">
      <j1 rule="hyper" parents="139 13688 14577"/>
    </justification>
  </clause>

  <clause id="14596">
    <literal><![CDATA[
      a(x,y,z) * a(u,a(z,y,x),L(z,w,v5)) = L(a(x,y,z),L(z,w,v5),u)
    ]]></literal>
    <justification jstring="[hyper(139,a,13672,a(flip),b,14577,a)].">
      <j1 rule="hyper" parents="139 13672 14577"/>
    </justification>
  </clause>

  <clause id="14597">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,u,w) = L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,14577,a)].">
      <j1 rule="hyper" parents="38 2295 14577"/>
    </justification>
  </clause>

  <clause id="14598">
    <literal><![CDATA[
      a(x,y,z) \ a(u,w,a(x,y,z)) = L(a(x,y,z) \ 1,w,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,14577,a(flip),b,1064,a)].">
      <j1 rule="hyper" parents="133 14577 1064"/>
    </justification>
  </clause>

  <clause id="14599">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(z,u,w) \ v5) = v5 * L(v5 \ (a(z,u,w) \ v5),y,x)
    ]]></literal>
    <justification jstring="[para(14577(a,1),1415(a,1,1))].">
      <j1 rule="para" parents="14577 1415"/>
    </justification>
  </clause>

  <clause id="14600">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ L(a(v5,v6,a(x,y,z)),u,w) = L(L(a(x,y,z),u,w) \ 1,v6,v5)
    ]]></literal>
    <justification jstring="[para(14577(a,1),2140(a,1,2,1))].">
      <j1 rule="para" parents="14577 2140"/>
    </justification>
  </clause>

  <clause id="14601">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) * L(a(v6,v7,a(x,y,z)),u,w) = v5 * L(v5 \ (L(a(x,y,z),u,w) \ v5),v7,v6)
    ]]></literal>
    <justification jstring="[para(14577(a,1),5135(a,1,2,1))].">
      <j1 rule="para" parents="14577 5135"/>
    </justification>
  </clause>

  <clause id="14604">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * a(a(y,a(z,u,y),x),w,v5) = L(a(x,y,a(z,u,y)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,14049,a,b,14582,a)].">
      <j1 rule="hyper" parents="63 14049 14582"/>
    </justification>
  </clause>

  <clause id="14605">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,u,z) = L(a(w,u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13689,a,b,14582,a)].">
      <j1 rule="hyper" parents="63 13689 14582"/>
    </justification>
  </clause>

  <clause id="14606">
    <literal><![CDATA[
      L(a(x,y,z),x,y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13949,a(flip),b,14582,a),flip(a)].">
      <j1 rule="hyper" parents="63 13949 14582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14608">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,13488,a,b,14606,a),flip(a)].">
      <j1 rule="hyper" parents="41 13488 14606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14611">
    <literal><![CDATA[
      a(L(x,y,z),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,6959,a(flip),b,14608,a)].">
      <j1 rule="hyper" parents="316 6959 14608"/>
    </justification>
  </clause>

  <clause id="14612">
    <literal><![CDATA[
      x \ (y * R(y \ x,y,z)) = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,475,a(flip),b,14608,a)].">
      <j1 rule="hyper" parents="316 475 14608"/>
    </justification>
  </clause>

  <clause id="14613">
    <literal><![CDATA[
      (x * y) * a(y,x,z) = x * R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,14608,a,b,102,a(flip))].">
      <j1 rule="hyper" parents="139 14608 102"/>
    </justification>
  </clause>

  <clause id="14614">
    <literal><![CDATA[
      L(a(x,y,z),u,x) = L(x \ R(x,y,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8510,a,b,14608,a)].">
      <j1 rule="hyper" parents="63 8510 14608"/>
    </justification>
  </clause>

  <clause id="14616">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * (T(y,z) * (y \ R(y,z,u))))) = L(a(y,z,u),y * z,x)
    ]]></literal>
    <justification jstring="[para(14608(a,2),3295(a,2,1))].">
      <j1 rule="para" parents="14608 3295"/>
    </justification>
  </clause>

  <clause id="14617">
    <literal><![CDATA[
      L(R(x,y,z) \ x,x,y) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(14608(a,2),13511(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14608 13511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14620">
    <literal><![CDATA[
      (a(x,y,z) * y) \ (y * z) = L(z,y,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(14611(a,1),13636(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14611 13636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14621">
    <literal><![CDATA[
      L(x,y \ (a(z,u,w) \ u),v5) = L(x,y \ (a(w,u,z) * u),v5)
    ]]></literal>
    <justification jstring="[para(14611(a,1),13638(a,1,2,2,1))].">
      <j1 rule="para" parents="14611 13638"/>
    </justification>
  </clause>

  <clause id="14622">
    <literal><![CDATA[
      a(x,y,z) * (y * x) = y * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a,b,14613,a)].">
      <j1 rule="hyper" parents="63 2290 14613"/>
    </justification>
  </clause>

  <clause id="14625">
    <literal><![CDATA[
      T(a(x,y,z) * y,x) = x \ (y * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(390,a,14622,a(flip),b,8402,a)].">
      <j1 rule="hyper" parents="390 14622 8402"/>
    </justification>
  </clause>

  <clause id="14626">
    <literal><![CDATA[
      L(a(x,y,z),y * x,y * x) = (1 / (y * x)) * (y * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(14622(a,1),11590(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14622 11590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14627">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,y) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(41,a,13449,a,b,14617,a)].">
      <j1 rule="hyper" parents="41 13449 14617"/>
    </justification>
  </clause>

  <clause id="14628">
    <literal><![CDATA[
      ((R(x,y,z) \ x) \ (u * (a(x,y,z) \ 1))) * (R(x,y,z) \ x) = T(u,R(x,y,z) \ x) * L(R(x,y,z) \ x,x,y)
    ]]></literal>
    <justification jstring="[para(14617(a,1),4439(a,1,1,2,2))].">
      <j1 rule="para" parents="14617 4439"/>
    </justification>
  </clause>

  <clause id="14629">
    <literal><![CDATA[
      (L(R(x,y,z) \ x,x,y) \ (R(x,y,z) \ x)) * (u * (R(x,y,z) \ x)) = (((a(x,y,z) \ 1) \ (R(x,y,z) \ x)) * u) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(14617(a,1),11574(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14617 11574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14630">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),x,y) = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(14627(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14627 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14631">
    <literal><![CDATA[
      a(x * (y \ z),y,a(x,y \ z,y)) = z \ (y * R(y \ z,y,a(x,y \ z,y)))
    ]]></literal>
    <justification jstring="[hyper(316,a,13937,a,b,14612,a)].">
      <j1 rule="hyper" parents="316 13937 14612"/>
    </justification>
  </clause>

  <clause id="14632">
    <literal><![CDATA[
      (x / y) \ ((x / y) * (y * R(y \ 1,x,z))) = a(x \ (x / y),x,z)
    ]]></literal>
    <justification jstring="[para(1017(a,2),14612(a,1,2))].">
      <j1 rule="para" parents="1017 14612"/>
    </justification>
  </clause>

  <clause id="14633">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ R(L(L(x,y,z),u,w),x,v5) = a(L(L(x,y,z),u,w),x,v5)
    ]]></literal>
    <justification jstring="[hyper(41,a,9000,a(flip),b,14614,a)].">
      <j1 rule="hyper" parents="41 9000 14614"/>
    </justification>
  </clause>

  <clause id="14634">
    <literal><![CDATA[
      (x / y) * R(y,x,z) = a(y,x,z) * x
    ]]></literal>
    <justification jstring="[hyper(40,a,1552,a,b,14625,a)].">
      <j1 rule="hyper" parents="40 1552 14625"/>
    </justification>
  </clause>

  <clause id="14635">
    <literal><![CDATA[
      L(x,y,z \ ((u \ w) * R(u,w,v5))) = L(x,y,z \ (a(u,w,v5) * w))
    ]]></literal>
    <justification jstring="[para(14634(a,1),4174(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="14634 4174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14636">
    <literal><![CDATA[
      L(x,y,L(z,y,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13636,a,b,14620,a),flip(a)].">
      <j1 rule="hyper" parents="63 13636 14620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14637">
    <literal><![CDATA[
      L(x,y,(x * y) \ z) = L(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(298(a,1),14636(a,1,3))].">
      <j1 rule="para" parents="298 14636"/>
    </justification>
  </clause>

  <clause id="14638">
    <literal><![CDATA[
      L(x,x \ 1,(x \ 1) \ y) = L(x,x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(474(a,1),14636(a,1,3)),flip(a)].">
      <j1 rule="para" parents="474 14636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14640">
    <literal><![CDATA[
      x * (L(x,y,z) \ (z * y)) = R(z,y,x) * y
    ]]></literal>
    <justification jstring="[para(14636(a,1),4635(a,1,2,1))].">
      <j1 rule="para" parents="14636 4635"/>
    </justification>
  </clause>

  <clause id="14642">
    <literal><![CDATA[
      L(x,y,y \ R(y,x,z)) = L(x,y,a(y,x,z))
    ]]></literal>
    <justification jstring="[para(14606(a,1),14636(a,1,3))].">
      <j1 rule="para" parents="14606 14636"/>
    </justification>
  </clause>

  <clause id="14643">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = L(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4173,a,b,14637,a)].">
      <j1 rule="hyper" parents="63 4173 14637"/>
    </justification>
  </clause>

  <clause id="14644">
    <literal><![CDATA[
      x / L(y,z,z \ (y \ x)) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(14637(a,1),4191(a,1,2))].">
      <j1 rule="para" parents="14637 4191"/>
    </justification>
  </clause>

  <clause id="14645">
    <literal><![CDATA[
      a(x,y,L(L(z,u,u \ (z \ w)),L(z,u,(z * u) \ w),w)) = a(x,y,w \ (u * ((z * u) \ w)))
    ]]></literal>
    <justification jstring="[para(14637(a,1),12027(a,1,3,1))].">
      <j1 rule="para" parents="14637 12027"/>
    </justification>
  </clause>

  <clause id="14647">
    <literal><![CDATA[
      L(x,y,z) * (R(z,y,x) * y) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,14640,a(flip),b,1129,a)].">
      <j1 rule="hyper" parents="139 14640 1129"/>
    </justification>
  </clause>

  <clause id="14648">
    <literal><![CDATA[
      L(x,y,y \ L(y,x,z)) = L(x,y,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7482,a(flip),b,14642,a)].">
      <j1 rule="hyper" parents="63 7482 14642"/>
    </justification>
  </clause>

  <clause id="14649">
    <literal><![CDATA[
      L(x,y,y \ (x \ z)) \ z = T((z / (y * x)) * y,x)
    ]]></literal>
    <justification jstring="[para(14643(a,1),4362(a,1,1))].">
      <j1 rule="para" parents="14643 4362"/>
    </justification>
  </clause>

  <clause id="14650">
    <literal><![CDATA[
      ((x * (y * z)) / z) \ (L(x,z,y) * R(y,z,x)) = a(L(x,z,y),R(y,z,x),z)
    ]]></literal>
    <justification jstring="[para(14647(a,1),6925(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14647 6925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14651">
    <literal><![CDATA[
      L(x,x \ 1,x * y) = y \ (y / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,10493,a(flip),b,14638,a),flip(a)].">
      <j1 rule="hyper" parents="63 10493 14638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14652">
    <literal><![CDATA[
      L(x \ 1,(x \ 1) \ 1,x \ R(x * y,z,u)) = R((x \ 1) \ y,z,u) \ (R((x \ 1) \ y,z,u) / (1 / (x \ 1)))
    ]]></literal>
    <justification jstring="[para(901(a,1),14651(a,1,3))].">
      <j1 rule="para" parents="901 14651"/>
    </justification>
  </clause>

  <clause id="14653">
    <literal><![CDATA[
      L(a(x,y,z),u,L(w * v5,v5 * w,L(v5,v5,w))) = a(x,y,z) * a(a(x,y,z),u,L(v5 \ w,w,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,11180,a(flip),b,14590,a),flip(a)].">
      <j1 rule="hyper" parents="139 11180 14590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14655">
    <literal><![CDATA[
      ((x / y) * (y * a(z,u,w))) / x = a(z,u,w) * a(a(z,u,w),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,2437,a,b,14592,a)].">
      <j1 rule="hyper" parents="316 2437 14592"/>
    </justification>
  </clause>

  <clause id="14657">
    <literal><![CDATA[
      a(x \ L(x,y,z),L(x,y,z),a(u,w,v5)) * a(u,w,v5) = L(a(u,w,v5),x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,14345,a(flip),b,14597,a),flip(a)].">
      <j1 rule="hyper" parents="316 14345 14597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14659">
    <literal><![CDATA[
      T((x / (y * z)) * y,z) * R((L(z,y,y \ (z \ x)) \ x) \ x,u,w) = R(L(z,y,y \ (z \ x)),u,w) * (L(z,y,y \ (z \ x)) \ x)
    ]]></literal>
    <justification jstring="[para(14649(a,1),611(a,1,1))].">
      <j1 rule="para" parents="14649 611"/>
    </justification>
  </clause>

  <clause id="14661">
    <literal><![CDATA[
      x \ (L(a(y,z,u),w,v5) \ x) = L(a(y,z,u),w,v5) \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,5012,a,b,14387,a)].">
      <j1 rule="hyper" parents="35 5012 14387"/>
    </justification>
  </clause>

  <clause id="14662">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * v5 = L(a(x,y,z),u,w) \ v5
    ]]></literal>
    <justification jstring="[para(13442(a,2),14387(a,1,1))].">
      <j1 rule="para" parents="13442 14387"/>
    </justification>
  </clause>

  <clause id="14663">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)),v5,v6) \ v7 = L(a(x,y,a(z,u,w)),v5,v6) * v7
    ]]></literal>
    <justification jstring="[para(14028(a,1),14387(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14028 14387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14665">
    <literal><![CDATA[
      (x \ ((y \ 1) * (y * x))) \ z = (y * (x / (y * x))) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,9,a(flip),b,14389,a)].">
      <j1 rule="hyper" parents="133 9 14389"/>
    </justification>
  </clause>

  <clause id="14672">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L((L(x,y,z) \ x) \ a(u,L(x,y,z) \ x,L(x,y,z) \ x),w,v5) = L((L(x,y,z) \ x) \ L(L(x,y,z) \ x,w,v5),L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(14506(a,1),7437(a,1,1))].">
      <j1 rule="para" parents="14506 7437"/>
    </justification>
  </clause>

  <clause id="14674">
    <literal><![CDATA[
      x \ (L(a(y,z,u),w,v5) \ x) = L(a(y,z,u) \ 1,w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,13442,a,b,14661,a),flip(a)].">
      <j1 rule="hyper" parents="316 13442 14661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14675">
    <literal><![CDATA[
      x * L(a(y,z,u) \ 1,w,v5) = L(a(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,13442,a,b,14661,a)].">
      <j1 rule="hyper" parents="139 13442 14661"/>
    </justification>
  </clause>

  <clause id="14676">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ (x * y) = L(a(z,u,w),y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,9681,a(flip),b,14661,a)].">
      <j1 rule="hyper" parents="63 9681 14661"/>
    </justification>
  </clause>

  <clause id="14678">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) \ (L(a(x,y,z) \ 1,u,w) * (v5 * v6)) = L(v6,v5,L(a(x,y,z) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(14662(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14662 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14679">
    <literal><![CDATA[
      T((L(a(x,y,z),u,w) \ (v5 * v6)) / (L(a(x,y,z) \ 1,u,w) * v5),v5) = (L(a(x,y,z) \ 1,u,w) * (v6 * v5)) / (L(a(x,y,z) \ 1,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(14662(a,1),1566(a,1,1,1))].">
      <j1 rule="para" parents="14662 1566"/>
    </justification>
  </clause>

  <clause id="14680">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w) * R(L(a(x,y,z),u,w),v5,v6),L(a(x,y,z),u,w),v5 * v6) = a(L(a(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(14662(a,2),3422(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14662 3422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14681">
    <literal><![CDATA[
      R(x * K(y,L(a(z,u,w) \ 1,v5,v6)),y,L(a(z,u,w) \ 1,v5,v6)) = ((x * y) * L(a(z,u,w) \ 1,v5,v6)) / (L(a(z,u,w),v5,v6) \ y)
    ]]></literal>
    <justification jstring="[para(14662(a,1),4488(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14662 4488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14682">
    <literal><![CDATA[
      L(x \ L(x,x \ 1,y),z,u) * w = L(a(y,x \ 1,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(7383(a,1),14662(a,1,1,1))].">
      <j1 rule="para" parents="7383 14662"/>
    </justification>
  </clause>

  <clause id="14683">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),L(a(x,y,z),u,w),v5) * L(L(a(x,y,z) \ 1,u,w) * a(v5,L(a(x,y,z),u,w),L(a(x,y,z),u,w)),v6,v7) = L(L(a(x,y,z),u,w) \ L(L(a(x,y,z),u,w),v6,v7),L(a(x,y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(14662(a,2),7437(a,1,2,1))].">
      <j1 rule="para" parents="14662 7437"/>
    </justification>
  </clause>

  <clause id="14684">
    <literal><![CDATA[
      x \ (L(a(y,z,x \ u),x \ u,u) \ u) = a(y,z,x \ u) \ (x \ u)
    ]]></literal>
    <justification jstring="[para(14662(a,1),9343(a,1,2))].">
      <j1 rule="para" parents="14662 9343"/>
    </justification>
  </clause>

  <clause id="14685">
    <literal><![CDATA[
      a(x,y,L(((z \ ((u \ 1) * (u * z))) * w) \ v5,z \ ((u \ 1) * (u * z)),w)) = a(x,y,(u * (z / (u * z))) * (w \ v5))
    ]]></literal>
    <justification jstring="[para(14665(a,1),11881(a,2,3))].">
      <j1 rule="para" parents="14665 11881"/>
    </justification>
  </clause>

  <clause id="14687">
    <literal><![CDATA[
      x * L(y \ (a(z,u,w) \ y),v5,v6) = L(a(z,u,w),v5,v6) \ x
    ]]></literal>
    <justification jstring="[para(14399(a,2),14675(a,1,2,1))].">
      <j1 rule="para" parents="14399 14675"/>
    </justification>
  </clause>

  <clause id="14689">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ (w * u) = w * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14662,a(flip),b,14453,a)].">
      <j1 rule="hyper" parents="63 14662 14453"/>
    </justification>
  </clause>

  <clause id="14690">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ (x * w) = L(a(y,z,u),w,x)
    ]]></literal>
    <justification jstring="[para(14689(a,1),2309(a,1,1))].">
      <j1 rule="para" parents="14689 2309"/>
    </justification>
  </clause>

  <clause id="14691">
    <literal><![CDATA[
      a(x,y,z) \ (a(u,w,v5) * a(u,w,v5)) = a(u,w,v5) * (a(x,y,z) \ a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(14381(a,1),14689(a,1,1))].">
      <j1 rule="para" parents="14381 14689"/>
    </justification>
  </clause>

  <clause id="14692">
    <literal><![CDATA[
      (x * (a(y,z,z) \ u)) \ (x * u) = a(y,z,L(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,13562,a,b,14690,a),flip(a)].">
      <j1 rule="hyper" parents="316 13562 14690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14693">
    <literal><![CDATA[
      (x * ((y * z) * a(a(u,w,v5),y,z))) \ (x * ((a(u,w,v5) * y) * z)) = L(a(u,w,v5),(a(u,w,v5) * y) * z,x)
    ]]></literal>
    <justification jstring="[para(8422(a,1),14690(a,1,1,2))].">
      <j1 rule="para" parents="8422 14690"/>
    </justification>
  </clause>

  <clause id="14694">
    <literal><![CDATA[
      a(x \ y,z,u) * a(y,x \ y,a(u,z,x \ y)) = L(a(x \ y,z,u),x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,1588,a(flip),b,14595,a),flip(a)].">
      <j1 rule="hyper" parents="316 1588 14595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14695">
    <literal><![CDATA[
      L(a(x,y,z),x,x \ u) = L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14593,a(flip),b,14595,a),flip(a)].">
      <j1 rule="hyper" parents="63 14593 14595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14696">
    <literal><![CDATA[
      L(x \ ((x / y) * R(y,z,u)),y,z * u) = L(a(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3446,a,b,14695,a)].">
      <j1 rule="hyper" parents="63 3446 14695"/>
    </justification>
  </clause>

  <clause id="14697">
    <literal><![CDATA[
      a(x,y,z) \ a(u,w,a(z,y,x)) = L(a(x,y,z) \ 1,w,u)
    ]]></literal>
    <justification jstring="[para(13660(a,1),14598(a,1,2))].">
      <j1 rule="para" parents="13660 14598"/>
    </justification>
  </clause>

  <clause id="14699">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,z) * u) = z * (L(L(z,y,x),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14046,a(flip),b,14395,a),flip(a)].">
      <j1 rule="hyper" parents="63 14046 14395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14700">
    <literal><![CDATA[
      a(x,y,z) * (u * a(x,y,z)) = z * (L(L(z,y,x),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14046,a(flip),b,14396,a),flip(a)].">
      <j1 rule="hyper" parents="63 14046 14396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14702">
    <literal><![CDATA[
      a(x,y,z \ ((u * (w \ (u \ w))) \ v5)) = a(x,y,z \ (a(u,u \ 1,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,11712,a,b,14404,a)].">
      <j1 rule="hyper" parents="63 11712 14404"/>
    </justification>
  </clause>

  <clause id="14703">
    <literal><![CDATA[
      a(x,y,((z * (u \ (z \ u))) \ w) * v5) = a(x,y,(w * a(u,z,z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10583,a,b,14407,a)].">
      <j1 rule="hyper" parents="63 10583 14407"/>
    </justification>
  </clause>

  <clause id="14704">
    <literal><![CDATA[
      L(L(x,y,z),y,z) * a(z,y,x) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,2297,a(flip),b,14420,a)].">
      <j1 rule="hyper" parents="63 2297 14420"/>
    </justification>
  </clause>

  <clause id="14705">
    <literal><![CDATA[
      L(L(x,y,z),a(z,y,x),y) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,13901,a(flip),b,14704,a)].">
      <j1 rule="hyper" parents="63 13901 14704"/>
    </justification>
  </clause>

  <clause id="14706">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,a(z,y,x),y) * L(x,y,z) = (L(x,y,z) \ 1) * (a(z,y,x) \ x)
    ]]></literal>
    <justification jstring="[para(14705(a,1),4442(a,2,2))].">
      <j1 rule="para" parents="14705 4442"/>
    </justification>
  </clause>

  <clause id="14707">
    <literal><![CDATA[
      L(L((x \ y) \ y,z,u),a(u,z,x),z) = a(u,z,(x \ y) \ y) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(5479(a,1),14705(a,1,2))].">
      <j1 rule="para" parents="5479 14705"/>
    </justification>
  </clause>

  <clause id="14708">
    <literal><![CDATA[
      L((L(x,y,z) \ 1) \ 1,a(z,y,x),y) \ L(x,y,z) = ((a(z,y,x) \ x) \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(14705(a,1),8209(a,2,1,1))].">
      <j1 rule="para" parents="14705 8209"/>
    </justification>
  </clause>

  <clause id="14709">
    <literal><![CDATA[
      a(x,y,z) \ (L(L(z,y,x),a(x,y,z),y) \ u) = (a(x,y,z) \ z) \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(14705(a,1),14147(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14705 14147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14710">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,y,x) \ u) = a(z,y,x) * (R(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6996,a(flip),b,14445,a)].">
      <j1 rule="hyper" parents="63 6996 14445"/>
    </justification>
  </clause>

  <clause id="14712">
    <literal><![CDATA[
      (x * L(y \ L(y,z,u),w,v5)) * L(L(y,z,u) \ y,w,v5) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,6493,a(flip),b,14530,a)].">
      <j1 rule="hyper" parents="63 6493 14530"/>
    </justification>
  </clause>

  <clause id="14713">
    <literal><![CDATA[
      (x * L(y \ L(y,z,u),w,v5)) \ x = L(L(y,z,u) \ y,w,v5)
    ]]></literal>
    <justification jstring="[hyper(133,a,14530,a(flip),b,6493,a(flip))].">
      <j1 rule="hyper" parents="133 14530 6493"/>
    </justification>
  </clause>

  <clause id="14714">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ v5 = L(x \ L(x,y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[hyper(316,a,5022,a,b,14531,a),flip(a)].">
      <j1 rule="hyper" parents="316 5022 14531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14717">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),L(x \ L(x,y,z),u,w),v5) = v5 \ (v5 * L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(14531(a,1),13545(a,2,2))].">
      <j1 rule="para" parents="14531 13545"/>
    </justification>
  </clause>

  <clause id="14719">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,u)) = x \ ((x / y) * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,3427,a,b,14696,a)].">
      <j1 rule="hyper" parents="41 3427 14696"/>
    </justification>
  </clause>

  <clause id="14720">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,u) = u \ ((u / x) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(41,a,3423,a,b,14696,a)].">
      <j1 rule="hyper" parents="41 3423 14696"/>
    </justification>
  </clause>

  <clause id="14721">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,u) = u \ (R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(316,a,3212,a,b,14720,a),flip(a)].">
      <j1 rule="hyper" parents="316 3212 14720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14722">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,x \ u) = L(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,1602,a,b,14720,a)].">
      <j1 rule="hyper" parents="316 1602 14720"/>
    </justification>
  </clause>

  <clause id="14723">
    <literal><![CDATA[
      L(L(x,y,z) \ L(R(x,u,w),y,z),L(x,y,z),v5) = v5 \ (R(L(x,y,z),u,w) * (L(x,y,z) \ v5))
    ]]></literal>
    <justification jstring="[para(29(a,1),14721(a,1,1,2))].">
      <j1 rule="para" parents="29 14721"/>
    </justification>
  </clause>

  <clause id="14724">
    <literal><![CDATA[
      ((x * (y * z)) \ (x * (y * R(z,u,w)))) \ (y \ ((y / z) * R(z,u,w))) = a(x,y * z,(y * R(z,u,w)) \ (y * z))
    ]]></literal>
    <justification jstring="[para(14719(a,1),13372(a,1,2))].">
      <j1 rule="para" parents="14719 13372"/>
    </justification>
  </clause>

  <clause id="14725">
    <literal><![CDATA[
      T((R(x,y,z) * (x \ u)) / u,x) = L(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4512,a,b,14722,a)].">
      <j1 rule="hyper" parents="63 4512 14722"/>
    </justification>
  </clause>

  <clause id="14726">
    <literal><![CDATA[
      (x * a(y,z,u)) * a(y,z,u) = u * (L(L(u,z,y),z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2340,a(flip),b,14699,a)].">
      <j1 rule="hyper" parents="63 2340 14699"/>
    </justification>
  </clause>

  <clause id="14727">
    <literal><![CDATA[
      a(x,y,z) * ((z \ u) * a(x,y,z)) = L(L(z,y,x),y,x) \ u
    ]]></literal>
    <justification jstring="[hyper(316,a,1846,a(flip),b,14700,a),flip(a)].">
      <j1 rule="hyper" parents="316 1846 14700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14728">
    <literal><![CDATA[
      a(x,y,z) \ (L(L(z,y,x),y,x) \ u) = (z \ u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,1846,a(flip),b,14700,a)].">
      <j1 rule="hyper" parents="133 1846 14700"/>
    </justification>
  </clause>

  <clause id="14729">
    <literal><![CDATA[
      a(x,y,z) * (R(x,y,z) \ L(u,L(x,y,z) \ 1,L(x,y,z))) = a(z,y,x) \ ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(387(a,1),14710(a,1,2)),flip(a)].">
      <j1 rule="para" parents="387 14710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14730">
    <literal><![CDATA[
      a(L(x,y,z),y,z) * (R(L(x,y,z),y,z) \ u) = a(z,y,x) \ (L(L(x,y,z),y,z) \ u)
    ]]></literal>
    <justification jstring="[para(13635(a,1),14710(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13635 14710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14731">
    <literal><![CDATA[
      x / L(y \ L(y,z,u),w,v5) = x * L(L(y,z,u) \ y,w,v5)
    ]]></literal>
    <justification jstring="[hyper(630,a,14712,a),flip(a)].">
      <j1 rule="hyper" parents="630 14712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14733">
    <literal><![CDATA[
      (x * (y * (z \ L(z,u,w)))) \ (x * y) = L(L(z,u,w) \ z,y,x)
    ]]></literal>
    <justification jstring="[para(100(a,1),14713(a,1,1))].">
      <j1 rule="para" parents="100 14713"/>
    </justification>
  </clause>

  <clause id="14734">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ a(y,L(x,u,w),a(z,y,x)) = L(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,14293,a(flip),b,14714,a(flip))].">
      <j1 rule="hyper" parents="133 14293 14714"/>
    </justification>
  </clause>

  <clause id="14735">
    <literal><![CDATA[
      a(x,y,z) \ ((L(L(z,y,x),y,x) \ 1) * L(z,y,x)) = (z \ (1 / (1 / L(z,y,x)))) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,6721,a(flip),b,14727,a)].">
      <j1 rule="hyper" parents="133 6721 14727"/>
    </justification>
  </clause>

  <clause id="14736">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ v5 = v5 * L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5019,a(flip),b,14731,a)].">
      <j1 rule="hyper" parents="63 5019 14731"/>
    </justification>
  </clause>

  <clause id="14739">
    <literal><![CDATA[
      L(a(x,y,z),u \ w,u) \ (u \ w) = u \ (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14675,a(flip),b,14437,a)].">
      <j1 rule="hyper" parents="63 14675 14437"/>
    </justification>
  </clause>

  <clause id="14740">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ w)) \ (x \ w) = L(a(y,z,u),x \ w,x)
    ]]></literal>
    <justification jstring="[para(14739(a,1),2309(a,1,1))].">
      <j1 rule="para" parents="14739 2309"/>
    </justification>
  </clause>

  <clause id="14741">
    <literal><![CDATA[
      L(a(x,y,z),u \ (a(x,y,z) \ w),u) = L(a(x,y,z),u \ w,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13468,a,b,14740,a)].">
      <j1 rule="hyper" parents="63 13468 14740"/>
    </justification>
  </clause>

  <clause id="14742">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ w) \ w = (a(x,y,z) \ u) * (u \ w)
    ]]></literal>
    <justification jstring="[hyper(38,a,14674,a,b,14465,a)].">
      <j1 rule="hyper" parents="38 14674 14465"/>
    </justification>
  </clause>

  <clause id="14743">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ a(x,y,z)) = u * ((a(x,y,z) \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(39,a,7690,a,b,14742,a),flip(a)].">
      <j1 rule="hyper" parents="39 7690 14742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14746">
    <literal><![CDATA[
      L(x,a(y,z,x),u) * a(x,z,y) = x * L(a(x,z,y),x,u)
    ]]></literal>
    <justification jstring="[para(13699(a,1),14567(a,1,1))].">
      <j1 rule="para" parents="13699 14567"/>
    </justification>
  </clause>

  <clause id="14747">
    <literal><![CDATA[
      L(a(x,y,z),u \ (a(x,y,z) \ w),u) = a(x,y,z) * a(u,u \ w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,14582,a,b,14741,a),flip(a)].">
      <j1 rule="hyper" parents="316 14582 14741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14748">
    <literal><![CDATA[
      L(x * y,y,y \ L(y,z,u)) = (x * L(y,z,u)) * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1559,a,b,14348,a)].">
      <j1 rule="hyper" parents="63 1559 14348"/>
    </justification>
  </clause>

  <clause id="14749">
    <literal><![CDATA[
      a(x,y,z) * L(u \ (a(x,y,z) \ 1),w,v5) = a(x,y,z) \ L(u \ a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(14423(a,1),1363(a,1,2,1))].">
      <j1 rule="para" parents="14423 1363"/>
    </justification>
  </clause>

  <clause id="14750">
    <literal><![CDATA[
      L(x,y,z) * (a(u,w,v5) \ x) = x * (a(u,w,v5) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(14391(a,1),14425(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14391 14425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14751">
    <literal><![CDATA[
      L(x,y,z) * (((x * (L(x,y,z) \ (a(u,w,v5) \ 1))) \ 1) \ 1) = (((L(x,y,z) / (a(u,w,v5) \ x)) \ 1) \ 1) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(14429(a,2),2449(a,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14429 2449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14752">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (w * w) = u * (a(x,y,z) \ (w * w))
    ]]></literal>
    <justification jstring="[hyper(139,a,182,a(flip),b,14430,a)].">
      <j1 rule="hyper" parents="139 182 14430"/>
    </justification>
  </clause>

  <clause id="14753">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,u,w) \ y) = a(z,u,w) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,14393,a(flip),b,14433,a),flip(a)].">
      <j1 rule="hyper" parents="316 14393 14433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14754">
    <literal><![CDATA[
      ((x * (y \ L(y,z,u))) \ 1) \ 1 = ((x \ 1) \ 1) * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,14358,a(flip),b,14528,a),flip(a)].">
      <j1 rule="hyper" parents="316 14358 14528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14756">
    <literal><![CDATA[
      a(x \ (x / y),x,z) = y * R(y \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(322,a,14632,a),flip(a)].">
      <j1 rule="hyper" parents="322 14632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14758">
    <literal><![CDATA[
      a(x \ (x / (y \ 1)),x,z) = y \ R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,977,a(flip),b,14756,a),flip(a)].">
      <j1 rule="hyper" parents="316 977 14756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14759">
    <literal><![CDATA[
      a(L(x,x,y),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1824,a,b,14758,a)].">
      <j1 rule="hyper" parents="63 1824 14758"/>
    </justification>
  </clause>

  <clause id="14760">
    <literal><![CDATA[
      a(R(x,y,z) * L(x \ L(x,R(x,y,z),u),y,z),u,w) = R(x,y,z) \ R(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(8387(a,2),14759(a,1,1))].">
      <j1 rule="para" parents="8387 14759"/>
    </justification>
  </clause>

  <clause id="14763">
    <literal><![CDATA[
      (x * L(y \ R(y,z,x),x,z)) \ u = ((x \ u) / x) * L(x,z,L(y,y,z))
    ]]></literal>
    <justification jstring="[para(14759(a,1),13853(a,1,1,2,1))].">
      <j1 rule="para" parents="14759 13853"/>
    </justification>
  </clause>

  <clause id="14765">
    <literal><![CDATA[
      L(x,y,z \ ((u \ w) * L(u,w,v5))) = L(x,y,z \ (a(u,w,v5) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,11964,a(flip),b,14635,a)].">
      <j1 rule="hyper" parents="63 11964 14635"/>
    </justification>
  </clause>

  <clause id="14767">
    <literal><![CDATA[
      L(x \ L(x,x \ 1,y),z,u) * w = a(y,x \ 1,L(x,z,u)) \ w
    ]]></literal>
    <justification jstring="[para(13878(a,2),14682(a,2,1))].">
      <j1 rule="para" parents="13878 14682"/>
    </justification>
  </clause>

  <clause id="14769">
    <literal><![CDATA[
      x * L(y \ L(y,y \ 1,z),u,w) = a(z,y \ 1,L(y,u,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,5022,a(flip),b,14767,a)].">
      <j1 rule="hyper" parents="63 5022 14767"/>
    </justification>
  </clause>

  <clause id="14771">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w \ (u \ w))) \ v5)) = a(x,y,(v5 * a(w,u,u)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12485,a(flip),b,14703,a)].">
      <j1 rule="hyper" parents="63 12485 14703"/>
    </justification>
  </clause>

  <clause id="14772">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (L(y,z,u) \ y) = x * (a(u,z,y) * a(u,z,y))
    ]]></literal>
    <justification jstring="[para(13997(a,1),14377(a,2,2))].">
      <j1 rule="para" parents="13997 14377"/>
    </justification>
  </clause>

  <clause id="14773">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ ((a(y,z,u) \ x) * w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(14391(a,1),14436(a,1,2,1))].">
      <j1 rule="para" parents="14391 14436"/>
    </justification>
  </clause>

  <clause id="14774">
    <literal><![CDATA[
      x \ ((a(y,z,u) \ w) \ (w * (a(y,z,u) \ x))) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,12865,a(flip),b,14773,a)].">
      <j1 rule="hyper" parents="63 12865 14773"/>
    </justification>
  </clause>

  <clause id="14775">
    <literal><![CDATA[
      a(x,y,z) \ (u \ (a(x,y,z) * w)) = a(x,y,z) * (u \ (a(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[para(14444(a,1),14420(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14444 14420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14776">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (a(w,v5,u) \ v6)) \ v7)) = a(x,y,z \ (((u \ v6) * a(w,v5,u)) \ v7))
    ]]></literal>
    <justification jstring="[para(6920(a,1),14475(a,1,3,2,1))].">
      <j1 rule="para" parents="6920 14475"/>
    </justification>
  </clause>

  <clause id="14777">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u * a(x,y,z),w) = L(a(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,14676,a(flip),b,14482,a),flip(a)].">
      <j1 rule="hyper" parents="316 14676 14482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14779">
    <literal><![CDATA[
      L(a(x,y,z),u * a(x,y,z),w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(39,a,13442,a(flip),b,14777,a(flip))].">
      <j1 rule="hyper" parents="39 13442 14777"/>
    </justification>
  </clause>

  <clause id="14780">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u * a(x,y,z),w) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(133,a,14779,a,b,14593,a)].">
      <j1 rule="hyper" parents="133 14779 14593"/>
    </justification>
  </clause>

  <clause id="14781">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z) * u,w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10797,a,b,14779,a)].">
      <j1 rule="hyper" parents="63 10797 14779"/>
    </justification>
  </clause>

  <clause id="14782">
    <literal><![CDATA[
      a(x,y,y) \ L(a(x,y,y),R(x,y,y),z) = a(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(2381(a,1),14780(a,1,2,2))].">
      <j1 rule="para" parents="2381 14780"/>
    </justification>
  </clause>

  <clause id="14783">
    <literal><![CDATA[
      a(x,y,y) \ L(a(x,y,y),L(x,y,y),z) = a(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(10977(a,1),14782(a,1,2))].">
      <j1 rule="para" parents="10977 14782"/>
    </justification>
  </clause>

  <clause id="14784">
    <literal><![CDATA[
      a(x,y,y) \ a(x,y,L(y,L(x,y,y),z)) = a(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(13562(a,2),14783(a,1,2))].">
      <j1 rule="para" parents="13562 14783"/>
    </justification>
  </clause>

  <clause id="14785">
    <literal><![CDATA[
      a(x,y,z) \ ((u / w) * (w * a(x,y,z))) = a(w \ u,w,a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,2276,a(flip),b,14566,a)].">
      <j1 rule="hyper" parents="63 2276 14566"/>
    </justification>
  </clause>

  <clause id="14786">
    <literal><![CDATA[
      a(x,y,L(((z \ u) / z) * L(z,w,L(v5,v5,w)),L(v5 \ R(v5,w,z),z,w),z)) = a(x,y,L(v5 \ R(v5,w,z),z,w) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(14763(a,1),11865(a,1,3,1))].">
      <j1 rule="para" parents="14763 11865"/>
    </justification>
  </clause>

  <clause id="14787">
    <literal><![CDATA[
      a(x,y,z) \ (u \ (w * a(x,y,z))) = a(x,y,z) * (u \ (a(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,2393,a(flip),b,14775,a)].">
      <j1 rule="hyper" parents="63 2393 14775"/>
    </justification>
  </clause>

  <clause id="14788">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ L(a(z,y,x),u,w) = a(y,x,L(a(z,y,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(133,a,14500,a(flip),b,6493,a)].">
      <j1 rule="hyper" parents="133 14500 6493"/>
    </justification>
  </clause>

  <clause id="14789">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(z,u,w) \ v5) = L(a(z,u,w),y,x) \ v5
    ]]></literal>
    <justification jstring="[hyper(316,a,14687,a(flip),b,14599,a),flip(a)].">
      <j1 rule="hyper" parents="316 14687 14599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14791">
    <literal><![CDATA[
      a(x \ (a(y,z,u) \ w),x,a(y,z,u)) * (a(y,z,u) \ w) = T((w / (x * a(y,z,u))) * x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,14649,a(flip),b,14789,a),flip(a)].">
      <j1 rule="hyper" parents="316 14649 14789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14792">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z),u,w) \ v5) = a(w,u,a(x,y,z)) * v5
    ]]></literal>
    <justification jstring="[para(14789(a,1),6892(a,1,2))].">
      <j1 rule="para" parents="14789 6892"/>
    </justification>
  </clause>

  <clause id="14793">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z),u,w) \ v5) = a(a(x,y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[hyper(316,a,14021,a,b,14792,a),flip(a)].">
      <j1 rule="hyper" parents="316 14021 14792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14794">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z),u,w) \ v5) = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,2290,a(flip),b,14792,a),flip(a)].">
      <j1 rule="hyper" parents="316 2290 14792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14796">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ a(x,y,z)) * v5 = a(x,y,z) * (L(a(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(14522(a,2),14792(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14522 14792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14797">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (a(x,y,z) \ v5) = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13858,a,b,14794,a)].">
      <j1 rule="hyper" parents="63 13858 14794"/>
    </justification>
  </clause>

  <clause id="14806">
    <literal><![CDATA[
      ((x * (y * z)) / z) \ (L(x,z,y) * R(y,z,x)) = a(L(x,z,y),L(y,z,x),z)
    ]]></literal>
    <justification jstring="[hyper(316,a,11325,a(flip),b,14650,a),flip(a)].">
      <j1 rule="hyper" parents="316 11325 14650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14807">
    <literal><![CDATA[
      a(x,y,z \ ((u * (w \ (u \ w))) \ v5)) = a(x,y,z \ (v5 * a(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,12222,a(flip),b,14702,a),flip(a)].">
      <j1 rule="hyper" parents="316 12222 14702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14808">
    <literal><![CDATA[
      a(x,y,L(((z * (u \ (z \ u))) * w) \ v5,w,a(z,z,u))) = a(x,y,w \ (v5 * a(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11883,a,b,14807,a)].">
      <j1 rule="hyper" parents="63 11883 14807"/>
    </justification>
  </clause>

  <clause id="14809">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,x,y)) = a(x,y,L(a(w,x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14293,a(flip),b,14788,a)].">
      <j1 rule="hyper" parents="63 14293 14788"/>
    </justification>
  </clause>

  <clause id="14812">
    <literal><![CDATA[
      a(x,a(y,x,z),L(y,u,w)) = a(x,y,L(a(z,x,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,13672,a(flip),b,14809,a)].">
      <j1 rule="hyper" parents="63 13672 14809"/>
    </justification>
  </clause>

  <clause id="14813">
    <literal><![CDATA[
      a(x,L(y,y \ L(y,x,z),u),a(z,x,y)) = a(x,y,a(z,x,y))
    ]]></literal>
    <justification jstring="[para(14541(a,1),14809(a,2,3))].">
      <j1 rule="para" parents="14541 14809"/>
    </justification>
  </clause>

  <clause id="14814">
    <literal><![CDATA[
      1 * a(x,a(y,x,z),L(y,u,w)) = a(x,y,L(a(z,x,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(225,a,14812,a)].">
      <j1 rule="hyper" parents="225 14812"/>
    </justification>
  </clause>

  <clause id="14815">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (a(x,y,z) \ u) = a(y,x,a(z,y,x)) \ u
    ]]></literal>
    <justification jstring="[para(14813(a,1),14140(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14813 14140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14816">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (a(x,y,z) \ u) = a(y,x,a(z,y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(316,a,14443,a(flip),b,14815,a),flip(a)].">
      <j1 rule="hyper" parents="316 14443 14815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14817">
    <literal><![CDATA[
      a(x,y,z) * ((x \ R(x,y,z)) \ u) = a(y,x,a(z,y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(139,a,75,a(flip),b,14815,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 75 14815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14820">
    <literal><![CDATA[
      a(x,y,z) * ((R(x,y,z) \ x) * u) = a(y,x,a(z,y,x)) * u
    ]]></literal>
    <justification jstring="[para(14536(a,1),14817(a,1,2))].">
      <j1 rule="para" parents="14536 14817"/>
    </justification>
  </clause>

  <clause id="14822">
    <literal><![CDATA[
      a(x,L(y,y \ L(y,x,z),u),a(z,x,y)) * w = a(y,x,z) * ((y \ R(y,x,z)) \ w)
    ]]></literal>
    <justification jstring="[para(14813(a,2),14817(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14813 14817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14825">
    <literal><![CDATA[
      a(x,y,z) \ (u * (w * a(x,y,z))) = a(x,y,z) * (u * (a(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[para(14393(a,1),14422(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14393 14422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14826">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,z) * (u * (a(x,y,z) \ w))) = u * (w * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(152,a,14825,a)].">
      <j1 rule="hyper" parents="152 14825"/>
    </justification>
  </clause>

  <clause id="14827">
    <literal><![CDATA[
      a(x \ y,x,a(z,u,w)) * y = a(z,u,w) * ((y / x) * (a(z,u,w) \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,14785,a(flip),b,14825,a)].">
      <j1 rule="hyper" parents="63 14785 14825"/>
    </justification>
  </clause>

  <clause id="14828">
    <literal><![CDATA[
      a(x,y,z) * ((u / z) * (a(x,y,z) \ z)) = u * a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14133,a(flip),b,14825,a),flip(a)].">
      <j1 rule="hyper" parents="63 14133 14825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14829">
    <literal><![CDATA[
      (a(x,y,z) * ((u / w) * (a(x,y,z) \ w))) \ u = a(w \ u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14825(a,1),6956(a,1,1))].">
      <j1 rule="para" parents="14825 6956"/>
    </justification>
  </clause>

  <clause id="14830">
    <literal><![CDATA[
      (x * y) \ (a(z,u,w) * (x * (a(z,u,w) \ y))) = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(14825(a,1),8576(a,1,2))].">
      <j1 rule="para" parents="14825 8576"/>
    </justification>
  </clause>

  <clause id="14831">
    <literal><![CDATA[
      a(x,y,z) * ((u / z) * (a(x,y,z) \ z)) = L(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,11690,a(flip),b,14828,a),flip(a)].">
      <j1 rule="hyper" parents="316 11690 14828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14832">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ z)) = L(u * z,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),14831(a,1,2,1))].">
      <j1 rule="para" parents="11 14831"/>
    </justification>
  </clause>

  <clause id="14833">
    <literal><![CDATA[
      a(x,a(y,z,u) \ w,a(y,z,u)) = a(a(y,z,u),w,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2543,a(flip),b,14830,a)].">
      <j1 rule="hyper" parents="63 2543 14830"/>
    </justification>
  </clause>

  <clause id="14834">
    <literal><![CDATA[
      a(x,y * a(z,u,w),a(z,u,w)) = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,14435,a(flip),b,14833,a)].">
      <j1 rule="hyper" parents="63 14435 14833"/>
    </justification>
  </clause>

  <clause id="14835">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z) * u,w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8048,a(flip),b,14833,a),flip(a)].">
      <j1 rule="hyper" parents="63 8048 14833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14836">
    <literal><![CDATA[
      a(a(x,y,z),u * a(x,y,z),w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(2275(a,1),14833(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2275 14833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14837">
    <literal><![CDATA[
      a(x,a(y,z,u) * w,a(y,z,u)) = a(a(y,z,u),w,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11190,a,b,14834,a)].">
      <j1 rule="hyper" parents="63 11190 14834"/>
    </justification>
  </clause>

  <clause id="14838">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * y = a(z,u,w) * (x * (a(z,u,w) \ y))
    ]]></literal>
    <justification jstring="[hyper(34,a,14061,a,b,14826,a)].">
      <j1 rule="hyper" parents="34 14061 14826"/>
    </justification>
  </clause>

  <clause id="14839">
    <literal><![CDATA[
      L(x * y,y,a(z,u,y)) = L(x,y,a(z,u,y)) * y
    ]]></literal>
    <justification jstring="[hyper(316,a,14832,a(flip),b,14838,a)].">
      <j1 rule="hyper" parents="316 14832 14838"/>
    </justification>
  </clause>

  <clause id="14840">
    <literal><![CDATA[
      (a(x,y,z) * ((u / (w * z)) * ((a(x,y,z) \ w) * z))) \ u = a((w * z) \ u,w * z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(6869(a,1),14829(a,1,1,2,2))].">
      <j1 rule="para" parents="6869 14829"/>
    </justification>
  </clause>

  <clause id="14841">
    <literal><![CDATA[
      (a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w)))) \ u = a((z \ w) \ u,z \ w,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(6920(a,1),14829(a,1,1,2,2))].">
      <j1 rule="para" parents="6920 14829"/>
    </justification>
  </clause>

  <clause id="14842">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ (a(w,v5,v6) * v7)) * (a(w,v5,v6) \ v7) = ((v7 / a(w,v5,v6)) / u) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14488(a,1),7538(a,1,1))].">
      <j1 rule="para" parents="14488 7538"/>
    </justification>
  </clause>

  <clause id="14843">
    <literal><![CDATA[
      L(((1 / x) \ y) * (x \ L(x,z,u)),x,x \ L(x,z,u)) = (1 / L(x,z,u)) \ y
    ]]></literal>
    <justification jstring="[para(7552(a,1),14525(a,1,1))].">
      <j1 rule="para" parents="7552 14525"/>
    </justification>
  </clause>

  <clause id="14844">
    <literal><![CDATA[
      L(x * (y \ L(y,z,u)),y,y \ L(y,z,u)) = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,13795,a(flip),b,14533,a),flip(a)].">
      <j1 rule="hyper" parents="316 13795 14533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14845">
    <literal><![CDATA[
      (L(x,y,z) \ L(R(x,u,w),y,z)) \ v5 = (L(R(x,u,w),y,z) \ L(x,y,z)) * v5
    ]]></literal>
    <justification jstring="[para(12236(a,1),14550(a,2,1))].">
      <j1 rule="para" parents="12236 14550"/>
    </justification>
  </clause>

  <clause id="14846">
    <literal><![CDATA[
      a(x * (y \ z),y,a(x,y \ z,y)) = z \ (y * L(y \ z,y,a(x,y \ z,y)))
    ]]></literal>
    <justification jstring="[para(5371(a,1),14631(a,2,2,2))].">
      <j1 rule="para" parents="5371 14631"/>
    </justification>
  </clause>

  <clause id="14847">
    <literal><![CDATA[
      a(x,y,z) \ (a(u,w,v5) * a(u,w,v5)) = (a(x,y,z) \ a(u,w,v5)) * a(u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,2290,a(flip),b,14691,a),flip(a)].">
      <j1 rule="hyper" parents="316 2290 14691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14848">
    <literal><![CDATA[
      L(L((x \ y) \ y,z,u),a(u,z,x),z) = a(u,z,x) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(5479(a,1),14707(a,2,1))].">
      <j1 rule="para" parents="5479 14707"/>
    </justification>
  </clause>

  <clause id="14850">
    <literal><![CDATA[
      a(x,x \ (a(y,z,u) \ w),a(y,z,u)) = a(x,x \ w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(34,a,14582,a,b,14747,a(flip))].">
      <j1 rule="hyper" parents="34 14582 14747"/>
    </justification>
  </clause>

  <clause id="14851">
    <literal><![CDATA[
      x / (y * (a(z,u,w) * (y \ (a(z,u,w) \ x)))) = a(y,y \ x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9790,a,b,14850,a)].">
      <j1 rule="hyper" parents="63 9790 14850"/>
    </justification>
  </clause>

  <clause id="14852">
    <literal><![CDATA[
      (a(x,y,z) * (u \ (a(x,y,z) \ w))) \ (u \ w) = a(u,u \ w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7146,a,b,14850,a)].">
      <j1 rule="hyper" parents="63 7146 14850"/>
    </justification>
  </clause>

  <clause id="14853">
    <literal><![CDATA[
      (((1 / x) \ y) / x) * L(x,z,u) = (1 / L(x,z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,14844,a(flip),b,14843,a)].">
      <j1 rule="hyper" parents="63 14844 14843"/>
    </justification>
  </clause>

  <clause id="14854">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) \ u) = x * ((1 / L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,14853,a(flip),b,4382,a),flip(a)].">
      <j1 rule="hyper" parents="139 14853 4382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14855">
    <literal><![CDATA[
      ((L(R(x,y,z),u,w) \ L(x,u,w)) * v5) \ v5 = L(x,u,w) \ L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14845(a,1),2621(a,1,1))].">
      <j1 rule="para" parents="14845 2621"/>
    </justification>
  </clause>

  <clause id="14856">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * ((a(v5,v6,L(v7,v8,v9)) \ a(v5,v6,v7)) * a(v5,v6,v7)) = a(v5,v6,L(v7,v8,v9)) * a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(14847(a,1),14146(a,1,2))].">
      <j1 rule="para" parents="14847 14146"/>
    </justification>
  </clause>

  <clause id="14857">
    <literal><![CDATA[
      a(x \ 1,x,L(y,L(y,z,u),L(y,z,u))) \ y = L(y,x,x \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14462,a(flip),b,14363,a)].">
      <j1 rule="hyper" parents="63 14462 14363"/>
    </justification>
  </clause>

  <clause id="14858">
    <literal><![CDATA[
      a(x \ 1,x,L(y,L(y,z,u),y)) \ y = L(y,x,x \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(7995(a,1),14857(a,1,1,3))].">
      <j1 rule="para" parents="7995 14857"/>
    </justification>
  </clause>

  <clause id="14859">
    <literal><![CDATA[
      L(x,y,y \ (x \ L(x,z,u))) = a(y \ 1,y,x) \ x
    ]]></literal>
    <justification jstring="[para(5574(a,1),14858(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5574 14858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14861">
    <literal><![CDATA[
      L(x,y,y \ (x \ L(x,z,u))) = L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,2406,a(flip),b,14859,a),flip(a)].">
      <j1 rule="hyper" parents="316 2406 14859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14863">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ (a(x,y,z) \ L(a(x,y,z),w,v5))) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,11604,a(flip),b,14861,a),flip(a)].">
      <j1 rule="hyper" parents="316 11604 14861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14864">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ a(w,v5,a(x,y,z))) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[para(14577(a,1),14863(a,1,3,2))].">
      <j1 rule="para" parents="14577 14863"/>
    </justification>
  </clause>

  <clause id="14865">
    <literal><![CDATA[
      L(x \ L(x,y * a(z,u,w),a(z,u,w)),x,y) = a(x,y * a(z,u,w),a(z,u,w))
    ]]></literal>
    <justification jstring="[para(5371(a,1),14401(a,1,1,2))].">
      <j1 rule="para" parents="5371 14401"/>
    </justification>
  </clause>

  <clause id="14872">
    <literal><![CDATA[
      L(a(x,y,z),u * R(w,v5,v6),v7) = L(a(x,y,z),u * L(w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(38,a,14577,a,b,14591,a),flip(a)].">
      <j1 rule="hyper" parents="38 14577 14591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14873">
    <literal><![CDATA[
      L(a(x,y,z * L(u,w,v5)),z * L(u,w,v5),y) = L(z * R(u,w,v5),y,x) \ (z * R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,13411,a(flip),b,14872,a),flip(a)].">
      <j1 rule="hyper" parents="63 13411 14872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14874">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * (K(y,z) * R(y,z,u)))) = L(a(y,z,u),y * z,x)
    ]]></literal>
    <justification jstring="[para(2799(a,1),14616(a,1,2,2,2))].">
      <j1 rule="para" parents="2799 14616"/>
    </justification>
  </clause>

  <clause id="14875">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * R(T(y,z),z,u))) = L(a(y,z,u),y * z,x)
    ]]></literal>
    <justification jstring="[para(2812(a,1),14874(a,1,2,2,2))].">
      <j1 rule="para" parents="2812 14874"/>
    </justification>
  </clause>

  <clause id="14876">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (R(y,z,u) * z)) = L(a(y,z,u),y * z,x)
    ]]></literal>
    <justification jstring="[para(252(a,1),14875(a,1,2,2))].">
      <j1 rule="para" parents="252 14875"/>
    </justification>
  </clause>

  <clause id="14877">
    <literal><![CDATA[
      a(x,y,L(L(a(z,u,w) * u,z,w),v5,v6)) = a(x,y,L((w * z) \ (z * (u * w)),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,12908,a(flip),b,14406,a),flip(a)].">
      <j1 rule="hyper" parents="63 12908 14406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14878">
    <literal><![CDATA[
      x \ (y \ (x * (a(z,u,w) \ T(y,x)))) = L(L(a(z,u,w),x,y) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(80(a,1),14461(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 14461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14880">
    <literal><![CDATA[
      x \ (y \ (x * (a(z,u,w) \ T(y,x)))) = L(L(a(z,u,w) \ 1,x,y),y,x)
    ]]></literal>
    <justification jstring="[para(13442(a,2),14878(a,2,1))].">
      <j1 rule="para" parents="13442 14878"/>
    </justification>
  </clause>

  <clause id="14881">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),w,u) = u \ (w \ ((a(x,y,z) \ w) * u))
    ]]></literal>
    <justification jstring="[para(5329(a,1),14880(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5329 14880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14882">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u * (x \ L(x,y,z)),w) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,14733,a(flip),b,14532,a),flip(a)].">
      <j1 rule="hyper" parents="316 14733 14532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14883">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u * (L(x,y,z) \ x),w) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(14369(a,1),14882(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14369 14882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14884">
    <literal><![CDATA[
      L(L(L(x,y,z),u,w) \ L(x,y,z),L(L(x,y,z),u,w) * (L(L(x,y,z),u,w) \ L(x,y,z)),z * y) = ((z * y) * L(L(x,y,z),u,w)) \ (z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(316,a,489,a(flip),b,14883,a),flip(a)].">
      <j1 rule="hyper" parents="316 489 14883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14885">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ L(a(v5,v6,a(x,y,z)),u,w) = L(L(a(x,y,z) \ 1,u,w),v6,v5)
    ]]></literal>
    <justification jstring="[para(13442(a,2),14600(a,2,1))].">
      <j1 rule="para" parents="13442 14600"/>
    </justification>
  </clause>

  <clause id="14887">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * (a(z,y,x) \ x) = (x \ a(z,y,x)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(13904(a,1),14706(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13904 14706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14888">
    <literal><![CDATA[
      L(a(x,y,a(z,x,y)),y \ L(y,x,z),u) * w = a(y,x,z) * ((y \ R(y,x,z)) \ w)
    ]]></literal>
    <justification jstring="[para(13747(a,1),14822(a,1,1))].">
      <j1 rule="para" parents="13747 14822"/>
    </justification>
  </clause>

  <clause id="14889">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * L(L(a(x,y,z) \ 1,u,w),v5,v6) = L(a(v6,v5,a(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(152,a,14885,a)].">
      <j1 rule="hyper" parents="152 14885"/>
    </justification>
  </clause>

  <clause id="14892">
    <literal><![CDATA[
      L(a(x * y,z,a(z,y,x)),z \ L(z,y,x),u) * w = a(z,y,x) * ((z \ R(z,y,x)) \ w)
    ]]></literal>
    <justification jstring="[para(13936(a,2),14888(a,1,1,1))].">
      <j1 rule="para" parents="13936 14888"/>
    </justification>
  </clause>

  <clause id="14893">
    <literal><![CDATA[
      a(x \ y,x,x) \ (z * (1 / (y \ (y / x)))) = L(z,x,a(x,x,x \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,13875,a(flip),b,14486,a),flip(a)].">
      <j1 rule="hyper" parents="316 13875 14486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14894">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u),L(z,z,u \ z),y)) = L(L(z,y,x) \ z,z,u \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,13383,a(flip),b,14515,a),flip(a)].">
      <j1 rule="hyper" parents="316 13383 14515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14895">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u),L(z,z,u \ z),y)) = L(L(z,y,x) \ z,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,11641,a(flip),b,14894,a),flip(a)].">
      <j1 rule="hyper" parents="316 11641 14894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14896">
    <literal><![CDATA[
      L(L(x,y,z),L(x,u,w),v5) \ L(x,y,z) = a(v5,L(x,u,w),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8003,a(flip),b,14517,a),flip(a)].">
      <j1 rule="hyper" parents="63 8003 14517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14898">
    <literal><![CDATA[
      L(L(x,L(x,y,z),u) \ x,w,v5) = a(u,L(x,y,z),L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,13383,a(flip),b,14896,a)].">
      <j1 rule="hyper" parents="63 13383 14896"/>
    </justification>
  </clause>

  <clause id="14899">
    <literal><![CDATA[
      a(x,L(y,z,u),L(y,w,v5)) = L(a(x,y,L(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(10016(a,1),14898(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10016 14898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14900">
    <literal><![CDATA[
      a(x,L(y,z,u),L(y,w,v5)) = a(x,y,L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,13557,a,b,14899,a),flip(a)].">
      <j1 rule="hyper" parents="316 13557 14899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14901">
    <literal><![CDATA[
      a(x,L(a(y,z,u) \ w,v5,v6),L(a(y,z,u) * w,v7,v8)) = a(x,a(y,z,u) \ w,L(L(a(y,z,u) \ w,v5,v6),v7,v8))
    ]]></literal>
    <justification jstring="[hyper(63,a,14408,a(flip),b,14900,a)].">
      <j1 rule="hyper" parents="63 14408 14900"/>
    </justification>
  </clause>

  <clause id="14902">
    <literal><![CDATA[
      R(a(x,a(y,z,u),w),x,(u * (y * z)) \ (y * (u * z))) = x \ L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(7(a,1),14556(a,1,1))].">
      <j1 rule="para" parents="7 14556"/>
    </justification>
  </clause>

  <clause id="14903">
    <literal><![CDATA[
      L(a(x,a(y,z,u),w),x,a(u,z,y)) = x \ L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5443,a(flip),b,14902,a)].">
      <j1 rule="hyper" parents="63 5443 14902"/>
    </justification>
  </clause>

  <clause id="14904">
    <literal><![CDATA[
      a(L(x,y,z),y,z) * (R(L(x,y,z),y,z) \ u) = (x \ u) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,14728,a(flip),b,14730,a),flip(a)].">
      <j1 rule="hyper" parents="316 14728 14730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14905">
    <literal><![CDATA[
      a(x,y,z) * (R(L(x,y,z),y,z) \ u) = (x \ u) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(14611(a,1),14904(a,1,1))].">
      <j1 rule="para" parents="14611 14904"/>
    </justification>
  </clause>

  <clause id="14906">
    <literal><![CDATA[
      a(x,y,z) * (L(R(x,y,z),y,z) \ u) = (x \ u) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(29(a,1),14905(a,1,2,1))].">
      <j1 rule="para" parents="29 14905"/>
    </justification>
  </clause>

  <clause id="14907">
    <literal><![CDATA[
      a(a(x,y,z) * L(R(x,y,z),y,z),a(u,w,v5),v6) = a((x \ 1) * a(z,y,x),a(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(14906(a,1),11932(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14906 11932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14909">
    <literal><![CDATA[
      (a(x,y,z) \ (u * L(u \ a(x,y,z),w,v5))) \ 1 = L(a(x,y,z) * u,w,v5) \ (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(14388(a,1),1894(a,1,1))].">
      <j1 rule="para" parents="14388 1894"/>
    </justification>
  </clause>

  <clause id="14911">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ (w * a(u,w,L(a(x,y,z),u,w))) = u \ ((a(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14662,a(flip),b,14460,a)].">
      <j1 rule="hyper" parents="63 14662 14460"/>
    </justification>
  </clause>

  <clause id="14912">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),w,u) \ w = u \ ((a(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,13632,a(flip),b,14911,a)].">
      <j1 rule="hyper" parents="63 13632 14911"/>
    </justification>
  </clause>

  <clause id="14913">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ w) * a(u,w,L(a(x,y,z),u,w)) = u \ ((a(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6862,a(flip),b,14911,a)].">
      <j1 rule="hyper" parents="63 6862 14911"/>
    </justification>
  </clause>

  <clause id="14914">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),w,u) \ u = w \ ((a(x,y,z) \ w) * u)
    ]]></literal>
    <justification jstring="[para(30(a,1),14912(a,1,1))].">
      <j1 rule="para" parents="30 14912"/>
    </justification>
  </clause>

  <clause id="14915">
    <literal><![CDATA[
      x \ (L(L(a(y,z,u),x,w),w,x) \ T(x,L(L(a(y,z,u),x,w),w,x) \ 1)) = (w \ ((a(y,z,u) \ w) * x)) / x
    ]]></literal>
    <justification jstring="[para(14914(a,1),3138(a,2,1))].">
      <j1 rule="para" parents="14914 3138"/>
    </justification>
  </clause>

  <clause id="14916">
    <literal><![CDATA[
      a(x,y,z) \ (u \ ((w * a(x,y,z)) * v5)) = a(x,y,z) * (u \ ((a(x,y,z) \ w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,14400,a(flip),b,14464,a),flip(a)].">
      <j1 rule="hyper" parents="63 14400 14464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14917">
    <literal><![CDATA[
      a(x,y,z) \ (u * (a(w,a(x,y,z),u) * a(x,y,z))) = a(x,y,z) * (w \ ((a(x,y,z) \ w) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8738,a(flip),b,14916,a)].">
      <j1 rule="hyper" parents="63 8738 14916"/>
    </justification>
  </clause>

  <clause id="14918">
    <literal><![CDATA[
      L(L((x \ 1) \ 1,y,z),a(z,y,x),y) \ L(x,y,z) = ((a(z,y,x) \ x) \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(6570(a,2),14708(a,1,1,1))].">
      <j1 rule="para" parents="6570 14708"/>
    </justification>
  </clause>

  <clause id="14919">
    <literal><![CDATA[
      a(R(x,y,z) * L(x \ L(x,L(x,y,z),u),y,z),u,w) = R(x,y,z) \ R(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(10977(a,1),14760(a,1,1,2,1,2))].">
      <j1 rule="para" parents="10977 14760"/>
    </justification>
  </clause>

  <clause id="14920">
    <literal><![CDATA[
      a(a(x,y,z) * L(R(x,y,z),y,z),a(u,w,v5),v6) = a(x \ a(z,y,x),a(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(6861(a,1),14907(a,2,1))].">
      <j1 rule="para" parents="6861 14907"/>
    </justification>
  </clause>

  <clause id="14921">
    <literal><![CDATA[
      a(a(x,y,z) * L(R(x,y,z),y,z),a(u,w,v5),v6) = a(x * a(z,y,x),a(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,11469,a(flip),b,14920,a),flip(a)].">
      <j1 rule="hyper" parents="316 11469 14920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14922">
    <literal><![CDATA[
      a(a(x,y,z) * L(L(x,y,z),y,z),a(u,w,v5),v6) = a(x * a(z,y,x),a(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,12991,a(flip),b,14921,a)].">
      <j1 rule="hyper" parents="63 12991 14921"/>
    </justification>
  </clause>

  <clause id="14923">
    <literal><![CDATA[
      a(a(x,y,z) * x,a(u,w,v5),v6) = a(x * a(z,y,x),a(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,14084,a(flip),b,14922,a)].">
      <j1 rule="hyper" parents="63 14084 14922"/>
    </justification>
  </clause>

  <clause id="14925">
    <literal><![CDATA[
      (a(x,y,z) \ ((z \ 1) \ 1)) \ L(z,y,x) = ((a(x,y,z) \ z) \ 1) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(14848(a,1),14918(a,1,1))].">
      <j1 rule="para" parents="14848 14918"/>
    </justification>
  </clause>

  <clause id="14926">
    <literal><![CDATA[
      ((x \ 1) \ (a(y,z,x) \ 1)) \ L(x,z,y) = ((a(y,z,x) \ x) \ 1) * L(x,z,y)
    ]]></literal>
    <justification jstring="[para(6964(a,1),14925(a,1,1))].">
      <j1 rule="para" parents="6964 14925"/>
    </justification>
  </clause>

  <clause id="14927">
    <literal><![CDATA[
      a(x,y,L(L(z,u,u \ (z \ w)),L(z,u,u \ (z \ w)),w)) = a(x,y,w \ (u * ((z * u) \ w)))
    ]]></literal>
    <justification jstring="[para(14637(a,1),14645(a,1,3,2))].">
      <j1 rule="para" parents="14637 14645"/>
    </justification>
  </clause>

  <clause id="14929">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),L(x \ L(x,y,z),u,w),v5) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,9,a(flip),b,14717,a),flip(a)].">
      <j1 rule="hyper" parents="316 9 14717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14932">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),v5,v6) \ L(x \ L(x,y,z),u,w) = a(v6,v5,L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(14929(a,1),14510(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14929 14510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14933">
    <literal><![CDATA[
      L(x * R(y,z,u),w,v5) \ (x * R(y,z,u)) = L(x * L(y,z,u),w,v5) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13403,a(flip),b,14873,a),flip(a)].">
      <j1 rule="hyper" parents="63 13403 14873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14935">
    <literal><![CDATA[
      L(a(x,y,z),u,L(w * v5,v5 * w,L(v5,v5,w))) = L(a(x,y,z),u,L(v5 \ w,w,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,14592,a(flip),b,14653,a),flip(a)].">
      <j1 rule="hyper" parents="316 14592 14653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14936">
    <literal><![CDATA[
      (x * y) \ (R(L(z,y,x),u,w) * (L(z,y,x) \ (x * y))) = (x * (y * z)) \ ((x * y) * L(R(z,u,w),y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,488,a(flip),b,14723,a),flip(a)].">
      <j1 rule="hyper" parents="63 488 14723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14937">
    <literal><![CDATA[
      L(L(x,y,z) \ L(R(x,u,w),y,z),L(x,y,z),v5) = v5 \ (L(R(x,u,w),y,z) * (L(x,y,z) \ v5))
    ]]></literal>
    <justification jstring="[para(29(a,1),14723(a,2,2,1))].">
      <j1 rule="para" parents="29 14723"/>
    </justification>
  </clause>

  <clause id="14938">
    <literal><![CDATA[
      (x \ (1 / (1 / L(x,y,z)))) * a(z,y,x) = a(z,y,x) \ ((L(x,y,z) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(9979(a,1),14735(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9979 14735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14939">
    <literal><![CDATA[
      (x \ (1 / (1 / L(x,y,z)))) * a(z,y,x) = (a(z,y,x) \ (L(x,y,z) \ 1)) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,6869,a(flip),b,14938,a),flip(a)].">
      <j1 rule="hyper" parents="316 6869 14938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14941">
    <literal><![CDATA[
      (x \ (1 / (1 / L(x,y,z)))) * a(z,y,x) = (a(x,y,z) * (R(x,y,z) \ 1)) * x
    ]]></literal>
    <justification jstring="[para(14710(a,1),14939(a,2,1))].">
      <j1 rule="para" parents="14710 14939"/>
    </justification>
  </clause>

  <clause id="14942">
    <literal><![CDATA[
      (x \ (1 / (1 / L(x,y,z)))) * a(z,y,x) = (R(x,y,z) \ a(x,y,z)) * x
    ]]></literal>
    <justification jstring="[para(8658(a,1),14941(a,2,1))].">
      <j1 rule="para" parents="8658 14941"/>
    </justification>
  </clause>

  <clause id="14943">
    <literal><![CDATA[
      (x \ L(1 / (1 / x),y,z)) * a(z,y,x) = (R(x,y,z) \ a(x,y,z)) * x
    ]]></literal>
    <justification jstring="[para(6582(a,2),14942(a,1,1,2))].">
      <j1 rule="para" parents="6582 14942"/>
    </justification>
  </clause>

  <clause id="14944">
    <literal><![CDATA[
      ((x \ 1) * L(x,y,z)) * a(z,y,x) = (R(x,y,z) \ a(x,y,z)) * x
    ]]></literal>
    <justification jstring="[para(1295(a,1),14943(a,1,1))].">
      <j1 rule="para" parents="1295 14943"/>
    </justification>
  </clause>

  <clause id="14945">
    <literal><![CDATA[
      a(x,y,z) * ((z \ 1) * L(z,y,x)) = (R(z,y,x) \ a(z,y,x)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a,b,14944,a)].">
      <j1 rule="hyper" parents="63 2290 14944"/>
    </justification>
  </clause>

  <clause id="14946">
    <literal><![CDATA[
      (x \ 1) * (a(y,z,x) * L(x,z,y)) = (R(x,z,y) \ a(x,z,y)) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,6878,a(flip),b,14945,a)].">
      <j1 rule="hyper" parents="63 6878 14945"/>
    </justification>
  </clause>

  <clause id="14947">
    <literal><![CDATA[
      L(a(x,y,z) * u,w,v5) \ (a(x,y,z) * u) = u \ (L(a(x,y,z) / u,w,v5) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13911,a(flip),b,14909,a),flip(a)].">
      <j1 rule="hyper" parents="63 13911 14909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14948">
    <literal><![CDATA[
      L(x * a(y,z,u),w,v5) \ (x * a(y,z,u)) = x \ (L(a(y,z,u) / x,w,v5) \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6408,a,b,14947,a)].">
      <j1 rule="hyper" parents="63 6408 14947"/>
    </justification>
  </clause>

  <clause id="14949">
    <literal><![CDATA[
      x \ (L(a(y,z,z) / x,z,y) \ a(y,z,z)) = L(x,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,13529,a(flip),b,14948,a),flip(a)].">
      <j1 rule="hyper" parents="63 13529 14948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14950">
    <literal><![CDATA[
      a(x,y,z) * (u \ ((a(x,y,z) \ u) * w)) = a(x,y,z) * (w * (a(x,y,z) \ a(u,a(x,y,z),w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14825,a(flip),b,14917,a),flip(a)].">
      <j1 rule="hyper" parents="63 14825 14917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14951">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),v5,v6) \ L(x \ L(x,y,z),u,w) = a(v6,v5,L(x * L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5893,a(flip),b,14932,a),flip(a)].">
      <j1 rule="hyper" parents="316 5893 14932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14953">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),v5,v6) \ (a(x,y,z) * ((a(x,y,z) \ L(L(a(x,y,z),u,w),v5,v6)) * v7)) = a(x,y,z) * (v7 * (a(x,y,z) \ a(L(L(a(x,y,z),u,w),v5,v6),a(x,y,z),v7)))
    ]]></literal>
    <justification jstring="[hyper(63,a,1845,a,b,14950,a)].">
      <j1 rule="hyper" parents="63 1845 14950"/>
    </justification>
  </clause>

  <clause id="14954">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z)),v5,v6) = a(w,u,L(x * L(x,y,z),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,13383,a(flip),b,14951,a)].">
      <j1 rule="hyper" parents="63 13383 14951"/>
    </justification>
  </clause>

  <clause id="14955">
    <literal><![CDATA[
      L(L(x,y,z) \ (L(x / L(x,y,z),u,w) \ x),v5,v6) = a(w,u,L(x * L(x,y,z),v5,v6))
    ]]></literal>
    <justification jstring="[para(13906(a,1),14954(a,1,1))].">
      <j1 rule="para" parents="13906 14954"/>
    </justification>
  </clause>

  <clause id="14956">
    <literal><![CDATA[
      L(L(x,y,z) \ (L(L(x,y,z) \ x,u,w) \ x),v5,v6) = a(w,u,L(x * L(x,y,z),v5,v6))
    ]]></literal>
    <justification jstring="[para(1378(a,1),14955(a,1,1,2,1,1))].">
      <j1 rule="para" parents="1378 14955"/>
    </justification>
  </clause>

  <clause id="14957">
    <literal><![CDATA[
      L(L(x,y,z) \ (x * L(x \ L(x,y,z),u,w)),v5,v6) = a(w,u,L(x * L(x,y,z),v5,v6))
    ]]></literal>
    <justification jstring="[para(13392(a,1),14956(a,1,1,2))].">
      <j1 rule="para" parents="13392 14956"/>
    </justification>
  </clause>

  <clause id="14959">
    <literal><![CDATA[
      a(a(x,y,z) \ (a(x,y,z) \ (u * (w * a(x,y,z)))),v5,v6) = a(L(a(x,y,z),w,u) * (u * w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,3323,a(flip),b,14554,a)].">
      <j1 rule="hyper" parents="63 3323 14554"/>
    </justification>
  </clause>

  <clause id="14960">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) \ (L(a(x,y,z),u,w) \ (v5 * v6)) = L(v6,v5,L(a(x,y,z) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(14662(a,1),14678(a,1,2))].">
      <j1 rule="para" parents="14662 14678"/>
    </justification>
  </clause>

  <clause id="14961">
    <literal><![CDATA[
      a(a(x,y,z) \ (a(x,y,z) * (u * (a(x,y,z) \ w))),v5,v6) = a(L(a(x,y,z),w,u) * (u * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(14825(a,1),14959(a,1,1,2))].">
      <j1 rule="para" parents="14825 14959"/>
    </justification>
  </clause>

  <clause id="14962">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w) * (w * u),v5,v6) = a(w * (a(x,y,z) \ u),v5,v6)
    ]]></literal>
    <justification jstring="[para(9(a,1),14961(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 14961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14963">
    <literal><![CDATA[
      a(x * (a(y,z,u) \ w),v5,v6) = a(x * (w * a(y,z,u)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,2790,a(flip),b,14962,a),flip(a)].">
      <j1 rule="hyper" parents="63 2790 14962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14965">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) * L(a(v6,v7,a(x,y,z)),u,w) = v5 * L(L(a(x,y,z) \ 1,u,w),v7,v6)
    ]]></literal>
    <justification jstring="[para(14674(a,1),14601(a,2,2,1))].">
      <j1 rule="para" parents="14674 14601"/>
    </justification>
  </clause>

  <clause id="14967">
    <literal><![CDATA[
      x * a(y \ (a(z,u,w) * x),y,a(z,u,w)) = ((x / a(z,u,w)) / y) * (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14797,a(flip),b,14842,a)].">
      <j1 rule="hyper" parents="63 14797 14842"/>
    </justification>
  </clause>

  <clause id="14968">
    <literal><![CDATA[
      x * a(a(y,z,u),w,w \ (a(y,z,u) * x)) = ((x / a(y,z,u)) / w) * (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14019,a,b,14967,a)].">
      <j1 rule="hyper" parents="63 14019 14967"/>
    </justification>
  </clause>

  <clause id="14969">
    <literal><![CDATA[
      (x * y) \ (R(L(z,y,x),u,w) * (L(z,y,x) \ (x * y))) = (x * (y * z)) \ (x * (y * R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(100(a,1),14936(a,2,2))].">
      <j1 rule="para" parents="100 14936"/>
    </justification>
  </clause>

  <clause id="14970">
    <literal><![CDATA[
      (x * y) \ (L(R(z,u,w),y,x) * (L(z,y,x) \ (x * y))) = (x * (y * z)) \ (x * (y * R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(29(a,1),14969(a,1,2,1))].">
      <j1 rule="para" parents="29 14969"/>
    </justification>
  </clause>

  <clause id="14971">
    <literal><![CDATA[
      a(x,y,L((z \ u) * u,L(z,u * z,u * z),y)) = L(L(z,y,x) \ z,u * z,u * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,13383,a(flip),b,14514,a),flip(a)].">
      <j1 rule="hyper" parents="316 13383 14514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14972">
    <literal><![CDATA[
      L(T(a(x,y,z),u * w),w * (u * a(a(x,y,z),u,w)),v5) = L(a(x,y,z),(a(x,y,z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11009,a(flip),b,14693,a)].">
      <j1 rule="hyper" parents="63 11009 14693"/>
    </justification>
  </clause>

  <clause id="14973">
    <literal><![CDATA[
      L(a(x,y,z),u * (w * a(a(x,y,z),w,u)),v5) = L(a(x,y,z),(a(x,y,z) * w) * u,v5)
    ]]></literal>
    <justification jstring="[para(2286(a,1),14972(a,1,1))].">
      <j1 rule="para" parents="2286 14972"/>
    </justification>
  </clause>

  <clause id="14975">
    <literal><![CDATA[
      L(a(x,y,z),L(u,w,a(x,y,z)) * w,v5) = L(a(x,y,z),(a(x,y,z) * w) * u,v5)
    ]]></literal>
    <justification jstring="[para(14026(a,1),14973(a,1,2))].">
      <j1 rule="para" parents="14026 14973"/>
    </justification>
  </clause>

  <clause id="14978">
    <literal><![CDATA[
      x \ (L(L(a(y,z,u),x,w),w,x) \ T(x,a(y,z,u) \ 1)) = (w \ ((a(y,z,u) \ w) * x)) / x
    ]]></literal>
    <justification jstring="[para(6476(a,1),14915(a,1,2,2))].">
      <j1 rule="para" parents="6476 14915"/>
    </justification>
  </clause>

  <clause id="14979">
    <literal><![CDATA[
      x \ (L(L(a(y,z,u),x,w),w,x) \ x) = (w \ ((a(y,z,u) \ w) * x)) / x
    ]]></literal>
    <justification jstring="[para(4989(a,1),14978(a,1,2,2))].">
      <j1 rule="para" parents="4989 14978"/>
    </justification>
  </clause>

  <clause id="14981">
    <literal><![CDATA[
      (x \ ((a(y,z,u) \ x) * w)) / w = w \ (x \ ((a(y,z,u) \ x) * w))
    ]]></literal>
    <justification jstring="[para(14914(a,1),14979(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14914 14979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14982">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),w,u) = (w \ ((a(x,y,z) \ w) * u)) / u
    ]]></literal>
    <justification jstring="[hyper(316,a,14881,a,b,14981,a)].">
      <j1 rule="hyper" parents="316 14881 14981"/>
    </justification>
  </clause>

  <clause id="14983">
    <literal><![CDATA[
      L(L(a(x,y,L(z,z,y)) \ 1,u,w),w,u) = (w \ (((L(z,y,x) \ z) \ w) * u)) / u
    ]]></literal>
    <justification jstring="[para(14510(a,1),14982(a,2,1,2,1,1))].">
      <j1 rule="para" parents="14510 14982"/>
    </justification>
  </clause>

  <clause id="14984">
    <literal><![CDATA[
      L(L(a(x,y,L(z,z,y)) \ 1,u,w),w,u) = (w \ ((w * (z \ L(z,y,x))) * u)) / u
    ]]></literal>
    <justification jstring="[para(14358(a,1),14983(a,2,1,2,1))].">
      <j1 rule="para" parents="14358 14983"/>
    </justification>
  </clause>

  <clause id="14985">
    <literal><![CDATA[
      L(L((L(x,y,z) \ x) \ 1,u,w),w,u) = (w \ ((w * (x \ L(x,y,z))) * u)) / u
    ]]></literal>
    <justification jstring="[para(14510(a,1),14984(a,1,1,1,1))].">
      <j1 rule="para" parents="14510 14984"/>
    </justification>
  </clause>

  <clause id="14986">
    <literal><![CDATA[
      (x \ ((x * (y \ L(y,z,u))) * w)) / w = L(L(y \ L(y,z,u),w,x),x,w)
    ]]></literal>
    <justification jstring="[para(5076(a,1),14985(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5076 14985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14987">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * (y * (L(y,z,u) \ L(y \ L(y,z,u),w,v5))) = x * L(x \ ((L(y,z,u) \ y) \ x),w,v5)
    ]]></literal>
    <justification jstring="[para(1129(a,1),14527(a,1,2))].">
      <j1 rule="para" parents="1129 14527"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      ((R(x,y,z) \ x) \ (a(x,y,z) \ u)) * (R(x,y,z) \ x) = T(u,R(x,y,z) \ x) * L(R(x,y,z) \ x,x,y)
    ]]></literal>
    <justification jstring="[para(14393(a,1),14628(a,1,1,2))].">
      <j1 rule="para" parents="14393 14628"/>
    </justification>
  </clause>

  <clause id="14989">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * (a(x,y,z) \ u)) * (R(x,y,z) \ x) = T(u,R(x,y,z) \ x) * L(R(x,y,z) \ x,x,y)
    ]]></literal>
    <justification jstring="[para(14542(a,1),14988(a,1,1))].">
      <j1 rule="para" parents="14542 14988"/>
    </justification>
  </clause>

  <clause id="14990">
    <literal><![CDATA[
      T(x,R(y,z,u) \ y) * L(R(y,z,u) \ y,y,z) = (a(z,y,a(u,z,y)) * x) * (R(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(14816(a,1),14989(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14816 14989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14991">
    <literal><![CDATA[
      (a(x,y,a(z,x,y)) * u) * (R(y,x,z) \ y) = u * L(R(y,x,z) \ y,y,x)
    ]]></literal>
    <justification jstring="[para(3509(a,1),14990(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3509 14990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14992">
    <literal><![CDATA[
      (a(x,y,a(z,x,y)) * u) * (R(y,x,z) \ y) = u * (a(y,x,z) \ 1)
    ]]></literal>
    <justification jstring="[para(14617(a,1),14991(a,2,2))].">
      <j1 rule="para" parents="14617 14991"/>
    </justification>
  </clause>

  <clause id="14993">
    <literal><![CDATA[
      (a(x,y,a(z,x,y)) * u) * (R(y,x,z) \ y) = a(y,x,z) \ u
    ]]></literal>
    <justification jstring="[hyper(316,a,14393,a(flip),b,14992,a),flip(a)].">
      <j1 rule="hyper" parents="316 14393 14992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14994">
    <literal><![CDATA[
      L(x \ 1,(x \ 1) \ 1,x \ L(x * y,z,u)) = R((x \ 1) \ y,z,u) \ (R((x \ 1) \ y,z,u) / (1 / (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7482,a(flip),b,14652,a)].">
      <j1 rule="hyper" parents="63 7482 14652"/>
    </justification>
  </clause>

  <clause id="14996">
    <literal><![CDATA[
      ((x * (y * z)) \ (x * (y * R(z,u,w)))) \ (y \ ((y / z) * R(z,u,w))) = a(x,y * z,(y * L(z,u,w)) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,9539,a(flip),b,14724,a),flip(a)].">
      <j1 rule="hyper" parents="316 9539 14724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14997">
    <literal><![CDATA[
      a(x,a(y,z,u) \ z,L(L(a(y,z,u) \ z,y,u),w,v5)) = a(x,L(z,u,y),L(a(y,z,u) * z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,11355,a(flip),b,14901,a),flip(a)].">
      <j1 rule="hyper" parents="63 11355 14901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14998">
    <literal><![CDATA[
      a(x,a(y,z,u) \ z,L(L(a(y,z,u) * z,y,u),w,v5)) = a(x,L(z,u,y),L(a(y,z,u) * z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,14406,a(flip),b,14997,a)].">
      <j1 rule="hyper" parents="63 14406 14997"/>
    </justification>
  </clause>

  <clause id="15000">
    <literal><![CDATA[
      L(x \ 1,(x \ 1) \ 1,x * L(x \ y,z,u)) = R((x \ 1) \ y,z,u) \ (R((x \ 1) \ y,z,u) / (1 / (x \ 1)))
    ]]></literal>
    <justification jstring="[para(1355(a,1),14994(a,1,3))].">
      <j1 rule="para" parents="1355 14994"/>
    </justification>
  </clause>

  <clause id="15001">
    <literal><![CDATA[
      ((x * (y * z)) \ (x * (y * R(z,u,w)))) \ (y \ ((y / z) * R(z,u,w))) = a(x,y * z,y \ (z * (L(z,u,w) \ y)))
    ]]></literal>
    <justification jstring="[para(9170(a,1),14996(a,2,3))].">
      <j1 rule="para" parents="9170 14996"/>
    </justification>
  </clause>

  <clause id="15002">
    <literal><![CDATA[
      L(x \ 1,x,x * L(x \ y,z,u)) = R((x \ 1) \ y,z,u) \ (R((x \ 1) \ y,z,u) / (1 / (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10800,a(flip),b,15000,a)].">
      <j1 rule="hyper" parents="63 10800 15000"/>
    </justification>
  </clause>

  <clause id="15006">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w) * L(R(a(x,y,z),v5,v6),u,w),L(a(x,y,z),u,w),v5 * v6) = a(L(a(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(29(a,1),14680(a,1,1,2))].">
      <j1 rule="para" parents="29 14680"/>
    </justification>
  </clause>

  <clause id="15007">
    <literal><![CDATA[
      a(x,y,L(((z * (u / (z * u))) \ w) \ v5,u \ ((z \ 1) * (z * u)),w)) = a(x,y,(z * (u / (z * u))) * (w \ v5))
    ]]></literal>
    <justification jstring="[para(14389(a,1),14685(a,1,3,1,1))].">
      <j1 rule="para" parents="14389 14685"/>
    </justification>
  </clause>

  <clause id="15008">
    <literal><![CDATA[
      a(x,y,L(((z * (u / (z * u))) \ w) \ v5,u \ L(u,z,z),w)) = a(x,y,(z * (u / (z * u))) * (w \ v5))
    ]]></literal>
    <justification jstring="[para(11020(a,1),15007(a,1,3))].">
      <j1 rule="para" parents="11020 15007"/>
    </justification>
  </clause>

  <clause id="15009">
    <literal><![CDATA[
      a(x,y,L(((z * (u / (z * u))) \ w) \ v5,a(u,z,z),w)) = a(x,y,(z * (u / (z * u))) * (w \ v5))
    ]]></literal>
    <justification jstring="[para(9852(a,1),15008(a,1,3))].">
      <j1 rule="para" parents="9852 15008"/>
    </justification>
  </clause>

  <clause id="15010">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w) * L(L(a(x,y,z),v5,v6),u,w),L(a(x,y,z),u,w),v5 * v6) = a(L(a(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(11586(a,1),15006(a,1,1,2,1))].">
      <j1 rule="para" parents="11586 15006"/>
    </justification>
  </clause>

  <clause id="15011">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w) \ L(L(a(x,y,z),v5,v6),u,w),L(a(x,y,z),u,w),v5 * v6) = a(L(a(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(14662(a,1),15010(a,1,1))].">
      <j1 rule="para" parents="14662 15010"/>
    </justification>
  </clause>

  <clause id="15012">
    <literal><![CDATA[
      L(L(a(x,y,z) \ L(a(x,y,z),u,w),v5,v6),L(a(x,y,z),v5,v6),u * w) = a(L(a(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(2138(a,1),15011(a,1,1))].">
      <j1 rule="para" parents="2138 15011"/>
    </justification>
  </clause>

  <clause id="15014">
    <literal><![CDATA[
      (x * a(y,x,a(z,u,w))) * (L(x,a(w,u,z),y) \ (x * a(y,x,a(z,u,w)))) = L(x,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[para(14038(a,1),14081(a,1,2,1))].">
      <j1 rule="para" parents="14038 14081"/>
    </justification>
  </clause>

  <clause id="15015">
    <literal><![CDATA[
      (x * a(y,x,a(z,u,w))) * L(x \ L(x,y,a(w,u,z)),a(w,u,z),y) = L(x,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[para(14082(a,1),15014(a,1,2))].">
      <j1 rule="para" parents="14082 15014"/>
    </justification>
  </clause>

  <clause id="15021">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * L(a(z,y,x) * (x \ L(x,y,z)),u,w) = L(1 / R(x \ L(x,y,z),u,w),x,y) \ 1
    ]]></literal>
    <justification jstring="[para(14400(a,1),14338(a,1,2,1))].">
      <j1 rule="para" parents="14400 14338"/>
    </justification>
  </clause>

  <clause id="15022">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * L(a(x,a(z,y,x),y),u,w) = L(1 / R(x \ L(x,y,z),u,w),x,y) \ 1
    ]]></literal>
    <justification jstring="[para(11625(a,1),15021(a,1,2,1))].">
      <j1 rule="para" parents="11625 15021"/>
    </justification>
  </clause>

  <clause id="15023">
    <literal><![CDATA[
      (L(x,x,a(y,z,u)) \ (((x \ a(y,z,u)) * (x * x)) * w)) / w = a(y,z,u) * (a(w,a(y,z,u),L(x,x,a(y,z,u))) \ 1)
    ]]></literal>
    <justification jstring="[para(2300(a,1),14339(a,1,1,2,1))].">
      <j1 rule="para" parents="2300 14339"/>
    </justification>
  </clause>

  <clause id="15024">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (u * R(u \ ((x \ R(x,y,z)) * u),w,v5)) = u * ((R(x,y,z) \ x) * R((R(x,y,z) \ x) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(14542(a,1),14546(a,1,2,2,1,2))].">
      <j1 rule="para" parents="14542 14546"/>
    </justification>
  </clause>

  <clause id="15025">
    <literal><![CDATA[
      L(x,y,z) * (((x * (L(x,y,z) \ (a(u,w,v5) \ 1))) \ 1) \ 1) = ((((x / a(u,w,v5)) \ L(x,y,z)) \ 1) \ 1) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(6833(a,1),14751(a,2,1,1,1))].">
      <j1 rule="para" parents="6833 14751"/>
    </justification>
  </clause>

  <clause id="15027">
    <literal><![CDATA[
      (L(x,x,a(y,z,u)) \ (((1 / x) \ a(y,z,u)) * w)) / w = a(y,z,u) * (a(w,a(y,z,u),L(x,x,a(y,z,u))) \ 1)
    ]]></literal>
    <justification jstring="[para(5359(a,1),15023(a,1,1,2,1))].">
      <j1 rule="para" parents="5359 15023"/>
    </justification>
  </clause>

  <clause id="15028">
    <literal><![CDATA[
      (L(x,x,a(y,z,u)) \ (((1 / x) \ a(y,z,u)) * w)) / w = a(y,z,u) * ((L(x,a(y,z,u),w) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(14510(a,1),15027(a,2,2,1))].">
      <j1 rule="para" parents="14510 15027"/>
    </justification>
  </clause>

  <clause id="15029">
    <literal><![CDATA[
      (L(x,x,a(y,z,u)) \ (((1 / x) \ a(y,z,u)) * w)) / w = a(y,z,u) * (x \ L(x,a(y,z,u),w))
    ]]></literal>
    <justification jstring="[para(5076(a,1),15028(a,2,2))].">
      <j1 rule="para" parents="5076 15028"/>
    </justification>
  </clause>

  <clause id="15030">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (u * R(T(x \ R(x,y,z),u),w,v5)) = u * ((R(x,y,z) \ x) * R((R(x,y,z) \ x) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(22(a,2),15024(a,1,2,2,1))].">
      <j1 rule="para" parents="22 15024"/>
    </justification>
  </clause>

  <clause id="15031">
    <literal><![CDATA[
      x * ((R(y,z,u) \ y) * R((R(y,z,u) \ y) \ 1,w,v5)) = (y \ R(y,z,u)) \ (x * R(y \ R(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(2196(a,1),15030(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2196 15030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15033">
    <literal><![CDATA[
      L(x,y,z) * (((x * (L(x,y,z) \ (a(u,w,v5) \ 1))) \ 1) \ 1) = ((((a(u,w,v5) \ x) \ L(x,y,z)) \ 1) \ 1) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2276(a,1),15025(a,2,1,1,1,1))].">
      <j1 rule="para" parents="2276 15025"/>
    </justification>
  </clause>

  <clause id="15036">
    <literal><![CDATA[
      L(x,y,z) * (((x * (L(x,y,z) \ (a(u,w,v5) \ 1))) \ 1) \ 1) = (((a(u,w,v5) * (x \ L(x,y,z))) \ 1) \ 1) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(14487(a,1),15033(a,2,1,1,1))].">
      <j1 rule="para" parents="14487 15033"/>
    </justification>
  </clause>

  <clause id="15037">
    <literal><![CDATA[
      L(x,y,z) * (((x * (L(x,y,z) \ (a(u,w,v5) \ 1))) \ 1) \ 1) = (((a(u,w,v5) \ 1) \ 1) * (x \ L(x,y,z))) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(14754(a,1),15036(a,2,1))].">
      <j1 rule="para" parents="14754 15036"/>
    </justification>
  </clause>

  <clause id="15038">
    <literal><![CDATA[
      L(x,y,z) * (((x * (L(x,y,z) \ (a(u,w,v5) \ 1))) \ 1) \ 1) = (a(u,w,v5) * (x \ L(x,y,z))) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2301(a,1),15037(a,2,1,1))].">
      <j1 rule="para" parents="2301 15037"/>
    </justification>
  </clause>

  <clause id="15040">
    <literal><![CDATA[
      L(x,y,z) * (((L(x,y,z) \ (a(u,w,v5) \ x)) \ 1) \ 1) = (a(u,w,v5) * (x \ L(x,y,z))) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(14429(a,1),15038(a,1,2,1,1))].">
      <j1 rule="para" parents="14429 15038"/>
    </justification>
  </clause>

  <clause id="15041">
    <literal><![CDATA[
      (a(x,y,z) * (u \ L(u,w,v5))) \ L(u,w,v5) = L(u,w,v5) * (L(u,w,v5) \ (a(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(7066(a,1),15040(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7066 15040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15042">
    <literal><![CDATA[
      (a(x,y,z) * (u \ L(u,w,v5))) \ L(u,w,v5) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(316,a,10,a(flip),b,15041,a),flip(a)].">
      <j1 rule="hyper" parents="316 10 15041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15045">
    <literal><![CDATA[
      (x \ a(x,y,z)) \ L(x,u,w) = L(x,u,w) * (a(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(15042(a,1),12852(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15042 12852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15046">
    <literal><![CDATA[
      (x \ a(x,y,z)) \ L(x,u,w) = x * (a(x,y,z) \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,14750,a(flip),b,15045,a),flip(a)].">
      <j1 rule="hyper" parents="316 14750 15045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15049">
    <literal><![CDATA[
      a(x / y,L(1 / y,z,u) \ 1,L(1 / y,z,u) \ 1) = ((x / y) / L(y \ 1,z,u)) \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(6573(a,1),13793(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6573 13793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15050">
    <literal><![CDATA[
      T((x * y) \ (z * y),x) \ ((T((x * y) \ (z * y),x) \ 1) \ u) = T(x \ z,x * y) \ ((T(x \ z,x * y) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(845(a,1),14334(a,1,2,1,1))].">
      <j1 rule="para" parents="845 14334"/>
    </justification>
  </clause>

  <clause id="15051">
    <literal><![CDATA[
      T(x \ y,x * z) \ ((T(x \ y,x * z) \ 1) \ u) = ((x * z) \ (y * z)) \ ((((x * z) \ (y * z)) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10257,a(flip),b,15050,a),flip(a)].">
      <j1 rule="hyper" parents="63 10257 15050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15053">
    <literal><![CDATA[
      ((x * y) \ (z * y)) \ ((((x * y) \ (z * y)) \ 1) \ u) = (x \ z) \ (((x \ z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10257,a(flip),b,15051,a),flip(a)].">
      <j1 rule="hyper" parents="63 10257 15051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15055">
    <literal><![CDATA[
      T(x / y,y * z) \ ((T(x / y,y * z) \ 1) \ u) = (y \ x) \ (((y \ x) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14337,a,b,15053,a)].">
      <j1 rule="hyper" parents="63 14337 15053"/>
    </justification>
  </clause>

  <clause id="15057">
    <literal><![CDATA[
      (x / y) \ (((x / y) \ 1) \ z) = (y \ x) \ (((y \ x) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10257,a(flip),b,15055,a)].">
      <j1 rule="hyper" parents="63 10257 15055"/>
    </justification>
  </clause>

  <clause id="15059">
    <literal><![CDATA[
      (x / (y / z)) \ (((x / (y / z)) \ 1) \ u) = (y \ (x * z)) \ (((y \ (x * z)) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14336,a(flip),b,15057,a)].">
      <j1 rule="hyper" parents="63 14336 15057"/>
    </justification>
  </clause>

  <clause id="15060">
    <literal><![CDATA[
      a(x,(y \ (z * u)) \ (((y \ (z * u)) \ 1) \ w),v5) = a(x,L(w,z / (y / u),z / (y / u)),v5)
    ]]></literal>
    <justification jstring="[para(15059(a,1),13067(a,1,2))].">
      <j1 rule="para" parents="15059 13067"/>
    </justification>
  </clause>

  <clause id="15061">
    <literal><![CDATA[
      a(x,(K(y,z) * (u * w)) \ (((K(z,y) \ (u * w)) \ 1) \ v5),v6) = a(x,L(v5,u / (K(z,y) / w),u / (K(z,y) / w)),v6)
    ]]></literal>
    <justification jstring="[para(2981(a,1),15060(a,1,2,1))].">
      <j1 rule="para" parents="2981 15060"/>
    </justification>
  </clause>

  <clause id="15062">
    <literal><![CDATA[
      a(x,(K(y,z) * (u * w)) \ (((u * w) \ K(z,y)) \ v5),v6) = a(x,L(v5,u / (K(z,y) / w),u / (K(z,y) / w)),v6)
    ]]></literal>
    <justification jstring="[para(425(a,1),15061(a,1,2,2,1))].">
      <j1 rule="para" parents="425 15061"/>
    </justification>
  </clause>

  <clause id="15063">
    <literal><![CDATA[
      a(x,(y * z) \ (K(u,w) * (((y * z) \ K(u,w)) \ v5)),v6) = a(x,L(v5,y / (K(u,w) / z),y / (K(u,w) / z)),v6)
    ]]></literal>
    <justification jstring="[para(3009(a,1),15062(a,1,2))].">
      <j1 rule="para" parents="3009 15062"/>
    </justification>
  </clause>

  <clause id="15064">
    <literal><![CDATA[
      a(x,L(y,z / (K(u,w) / v5),z / (K(u,w) / v5)),v6) = a(x,(z * v5) \ (((z * v5) \ 1) \ y),v6)
    ]]></literal>
    <justification jstring="[para(10218(a,1),15063(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10218 15063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15065">
    <literal><![CDATA[
      a(x,L(y,z / (K(u,w) / v5),z / (K(u,w) / v5)),v6) = a(x,L(y,z * v5,z * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,13067,a(flip),b,15064,a),flip(a)].">
      <j1 rule="hyper" parents="316 13067 15064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15067">
    <literal><![CDATA[
      a(x,L(y,z / (K(u,w) / v5),(v5 \ K(u,w)) \ z),v6) = a(x,L(y,z * v5,z * v5),v6)
    ]]></literal>
    <justification jstring="[para(3239(a,1),15065(a,1,2))].">
      <j1 rule="para" parents="3239 15065"/>
    </justification>
  </clause>

  <clause id="15068">
    <literal><![CDATA[
      a(x,L(y,z / (K(u,w) / v5),(v5 \ 1) \ z),v6) = a(x,L(y,z * v5,z * v5),v6)
    ]]></literal>
    <justification jstring="[para(4196(a,1),15067(a,1,2))].">
      <j1 rule="para" parents="4196 15067"/>
    </justification>
  </clause>

  <clause id="15070">
    <literal><![CDATA[
      a(x,L(y,(K(z,u) / w) \ v5,(w \ 1) \ v5),v6) = a(x,L(y,v5 * w,v5 * w),v6)
    ]]></literal>
    <justification jstring="[para(10798(a,1),15068(a,1,2))].">
      <j1 rule="para" parents="10798 15068"/>
    </justification>
  </clause>

  <clause id="15071">
    <literal><![CDATA[
      a(x,L(y,(z \ 1) \ u,(z \ 1) \ u),w) = a(x,L(y,u * z,u * z),w)
    ]]></literal>
    <justification jstring="[para(338(a,1),15070(a,1,2,2,1))].">
      <j1 rule="para" parents="338 15070"/>
    </justification>
  </clause>

  <clause id="15072">
    <literal><![CDATA[
      a(x,L(y,(z \ 1) \ u,z \ u),w) = a(x,L(y,u * z,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11333,a(flip),b,15071,a)].">
      <j1 rule="hyper" parents="63 11333 15071"/>
    </justification>
  </clause>

  <clause id="15073">
    <literal><![CDATA[
      a(x,L(y,z \ u,z \ u),w) = a(x,L(y,u * z,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,12365,a(flip),b,15072,a)].">
      <j1 rule="hyper" parents="63 12365 15072"/>
    </justification>
  </clause>

  <clause id="15074">
    <literal><![CDATA[
      a(L(R(T(x,y),z,x),u,w),L(R(T(x,y),z,x),z,x),v5) = L(R(T(x,y),z,x),u,w) \ L(R(R(T(x,y),z,x),x,v5),u,w)
    ]]></literal>
    <justification jstring="[para(10738(a,1),14273(a,2,2,1))].">
      <j1 rule="para" parents="10738 14273"/>
    </justification>
  </clause>

  <clause id="15075">
    <literal><![CDATA[
      L(R(T(x,y),z,x),u,w) \ L(R(R(T(x,y),z,x),x,v5),u,w) = a(L(R(T(x,y),z,x),u,w),T(x,y),v5)
    ]]></literal>
    <justification jstring="[para(1639(a,1),15074(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1639 15074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15077">
    <literal><![CDATA[
      L(R(T(x,y),z,x),u,w) \ L(R(R(T(x,y),z,x),x,v5),u,w) = a(L(R(T(x,y),z,x),u,w),x,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,11194,a(flip),b,15075,a),flip(a)].">
      <j1 rule="hyper" parents="316 11194 15075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15080">
    <literal><![CDATA[
      L(R(T(x,y),z,x),u,w) \ L(R(R(T(x,y),z,x),x,v5),u,w) = a(L(L(T(x,y),z,x),u,w),x,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,4653,a(flip),b,15077,a),flip(a)].">
      <j1 rule="hyper" parents="316 4653 15077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15081">
    <literal><![CDATA[
      L(R(T(x,y),z,x),u,w) \ L(R(R(T(x,y),z,x),x,v5),u,w) = a(L(L(x,z,x),u,w),x,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,1823,a(flip),b,15080,a),flip(a)].">
      <j1 rule="hyper" parents="316 1823 15080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15083">
    <literal><![CDATA[
      L(R(T(x,y),z,x),u,w) \ L(R(R(T(x,y),z,x),x,v5),u,w) = a(L(x,u,w),x,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,4863,a(flip),b,15081,a),flip(a)].">
      <j1 rule="hyper" parents="316 4863 15081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15085">
    <literal><![CDATA[
      L(R(T(x,y),z,x),u,w) \ L(R(R(T(x,y),z,x),x,v5),u,w) = a(x,L(x,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,1529,a(flip),b,15083,a),flip(a)].">
      <j1 rule="hyper" parents="316 1529 15083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15087">
    <literal><![CDATA[
      L(x,y \ (1 / z),(y \ (1 / z)) \ L(y \ (1 / z),y,z)) = x * a(y \ (1 / z),a(z,y,z * y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(11842(a,1),13826(a,2,2,2))].">
      <j1 rule="para" parents="11842 13826"/>
    </justification>
  </clause>

  <clause id="15088">
    <literal><![CDATA[
      L(x,y \ (1 / z),(y \ (1 / z)) \ L(y \ (1 / z),y,z)) = x * a(y \ (1 / z),a(z,y,z * y),x)
    ]]></literal>
    <justification jstring="[para(13061(a,1),15087(a,2,2))].">
      <j1 rule="para" parents="13061 15087"/>
    </justification>
  </clause>

  <clause id="15089">
    <literal><![CDATA[
      L(x,y \ (1 / z),(y \ (1 / z)) \ L(y \ (1 / z),y,z)) = x * a(y \ (z \ 1),a(z,y,z * y),x)
    ]]></literal>
    <justification jstring="[para(3323(a,1),15088(a,2,2))].">
      <j1 rule="para" parents="3323 15088"/>
    </justification>
  </clause>

  <clause id="15090">
    <literal><![CDATA[
      L(x,y \ (1 / z),(y \ (1 / z)) \ L(y \ (1 / z),y,z)) = x * a(y \ z,a(z,y,z * y),x)
    ]]></literal>
    <justification jstring="[para(11466(a,1),15089(a,2,2))].">
      <j1 rule="para" parents="11466 15089"/>
    </justification>
  </clause>

  <clause id="15091">
    <literal><![CDATA[
      ((x * y) * (z \ (u * (L(u,w,v5) \ z)))) \ (x * (y * (z \ (u * (L(u,w,v5) \ z))))) = a(z \ (u * (L(u,w,v5) \ z)),y,x)
    ]]></literal>
    <justification jstring="[para(100(a,1),14109(a,1,2))].">
      <j1 rule="para" parents="100 14109"/>
    </justification>
  </clause>

  <clause id="15092">
    <literal><![CDATA[
      a(x,y,z \ (u * (L(u,w,v5) \ z))) \ 1 = a(z \ (u * (L(u,w,v5) \ z)),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13736,a(flip),b,15091,a)].">
      <j1 rule="hyper" parents="63 13736 15091"/>
    </justification>
  </clause>

  <clause id="15117">
    <literal><![CDATA[
      L(L(x \ 1,x,x \ (y \ z)) \ (y * (L(y,u,w) \ y)),(z / y) \ (x \ (z / y)),z / y) = ((z / y) / x) \ (y * (L(y,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(3243(a,1),13814(a,1,1,1))].">
      <j1 rule="para" parents="3243 13814"/>
    </justification>
  </clause>

  <clause id="15119">
    <literal><![CDATA[
      L(x,y \ (z \ ((z * u) * T(y,u))),y \ (z \ ((z * u) * T(y,u)))) = L(x,L(u * a(z,u,y),y,z),L(u * a(z,u,y),y,z))
    ]]></literal>
    <justification jstring="[para(8578(a,1),14231(a,2,3))].">
      <j1 rule="para" parents="8578 14231"/>
    </justification>
  </clause>

  <clause id="15120">
    <literal><![CDATA[
      L(x,y \ (z \ ((z * u) * T(y,u))),y \ (z \ ((z * u) * T(y,u)))) = L(x,L(u * a(z,u,y),y,z),L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,8754,a(flip),b,15119,a),flip(a)].">
      <j1 rule="hyper" parents="316 8754 15119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15121">
    <literal><![CDATA[
      L(x,y \ (z \ ((z * u) * T(y,u))),y \ (z \ ((z * u) * T(y,u)))) = L(x,L(u,z,y),L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,11025,a(flip),b,15120,a),flip(a)].">
      <j1 rule="hyper" parents="316 11025 15120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15122">
    <literal><![CDATA[
      L(x,y \ (z \ ((z * u) * T(y,u))),y \ (z \ ((z * u) * T(y,u)))) = L(x,u,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,14208,a(flip),b,15121,a),flip(a)].">
      <j1 rule="hyper" parents="316 14208 15121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15124">
    <literal><![CDATA[
      L(x,y * a(z,y,u),u \ (z \ ((z * y) * T(u,y)))) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(8573(a,1),15122(a,1,2))].">
      <j1 rule="para" parents="8573 15122"/>
    </justification>
  </clause>

  <clause id="15125">
    <literal><![CDATA[
      L(x,y * a(z,y,u),y * a(z,y,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(8573(a,1),15124(a,1,3))].">
      <j1 rule="para" parents="8573 15124"/>
    </justification>
  </clause>

  <clause id="15126">
    <literal><![CDATA[
      a(x,y,(L(z * a(u,z,w),z,z) \ v5) * v6) = a(x,y,((z * a(u,z,w)) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(15125(a,1),8080(a,1,3,1,1))].">
      <j1 rule="para" parents="15125 8080"/>
    </justification>
  </clause>

  <clause id="15128">
    <literal><![CDATA[
      L(L(x \ 1,x,x \ (y \ z)) \ (y * (L(y,u,w) \ y)),(z / y) \ (x \ (z / y)),y \ z) = ((z / y) / x) \ (y * (L(y,u,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1586,a(flip),b,15117,a)].">
      <j1 rule="hyper" parents="63 1586 15117"/>
    </justification>
  </clause>

  <clause id="15133">
    <literal><![CDATA[
      L(L(x \ 1,x,x \ (y \ z)) \ (y * (L(y,u,w) \ y)),(z / y) \ (x \ (y \ z)),y \ z) = ((z / y) / x) \ (y * (L(y,u,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10915,a(flip),b,15128,a)].">
      <j1 rule="hyper" parents="63 10915 15128"/>
    </justification>
  </clause>

  <clause id="15134">
    <literal><![CDATA[
      L(L(x \ 1,x,x \ (y \ z)) \ (y * (L(y,u,w) \ y)),(y \ z) \ (x \ (y \ z)),y \ z) = ((z / y) / x) \ (y * (L(y,u,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10809,a(flip),b,15133,a)].">
      <j1 rule="hyper" parents="63 10809 15133"/>
    </justification>
  </clause>

  <clause id="15135">
    <literal><![CDATA[
      ((x \ y) / z) \ ((x \ y) * (x * (L(x,u,w) \ x))) = ((y / x) / z) \ (x * (L(x,u,w) \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10893,a(flip),b,15134,a)].">
      <j1 rule="hyper" parents="63 10893 15134"/>
    </justification>
  </clause>

  <clause id="15136">
    <literal><![CDATA[
      ((x / y) / z) \ (y * (L(y,u,w) \ x)) = ((y \ x) / z) \ ((L(y,u,w) \ x) * y)
    ]]></literal>
    <justification jstring="[para(13849(a,1),15135(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13849 15135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15137">
    <literal><![CDATA[
      a(x / y,L(1 / y,z,u) \ 1,L(1 / y,z,u) \ 1) = ((y \ x) / L(y \ 1,z,u)) \ ((L(y,z,u) \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15049,a,b,15136,a)].">
      <j1 rule="hyper" parents="63 15049 15136"/>
    </justification>
  </clause>

  <clause id="15138">
    <literal><![CDATA[
      a(x / y,L(1 / y,z,u) \ 1,L(1 / y,z,u) \ 1) = a(L(y,z,u) \ x,y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,7089,a(flip),b,15137,a),flip(a)].">
      <j1 rule="hyper" parents="316 7089 15137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15139">
    <literal><![CDATA[
      a(x / y,L(1 / y,z,u) \ 1,L(1 / y,z,u)) = a(L(y,z,u) \ x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2534,a(flip),b,15138,a)].">
      <j1 rule="hyper" parents="63 2534 15138"/>
    </justification>
  </clause>

  <clause id="15140">
    <literal><![CDATA[
      a(x / y,L(1 / y,z,u) \ 1,L(y,z,u)) = a(L(y,z,u) \ x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2650,a(flip),b,15139,a)].">
      <j1 rule="hyper" parents="63 2650 15139"/>
    </justification>
  </clause>

  <clause id="15141">
    <literal><![CDATA[
      a(x / y,L(y \ 1,z,u) \ 1,L(y,z,u)) = a(L(y,z,u) \ x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,11248,a(flip),b,15140,a)].">
      <j1 rule="hyper" parents="63 11248 15140"/>
    </justification>
  </clause>

  <clause id="15142">
    <literal><![CDATA[
      a(L(x,y,z) \ u,x,x) = a(u / x,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,14186,a(flip),b,15141,a),flip(a)].">
      <j1 rule="hyper" parents="63 14186 15141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15144">
    <literal><![CDATA[
      a(L(x,y,z) \ u,x,x) = a(x \ u,x,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,1813,a(flip),b,15142,a),flip(a)].">
      <j1 rule="hyper" parents="316 1813 15142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15145">
    <literal><![CDATA[
      a(x \ y,x,x) \ x = (y / L(x,z,u)) * ((y * (L(x,z,u) \ 1)) \ x)
    ]]></literal>
    <justification jstring="[para(15144(a,1),13984(a,1,1))].">
      <j1 rule="para" parents="15144 13984"/>
    </justification>
  </clause>

  <clause id="15146">
    <literal><![CDATA[
      (x / L(y,z,u)) * ((x * (L(y,z,u) \ 1)) \ y) = L(y,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(7317,a,15145,a),flip(a)].">
      <j1 rule="hyper" parents="7317 15145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15148">
    <literal><![CDATA[
      L(x,x,L(x,y,z) \ u) = L(x,x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13955,a(flip),b,15146,a)].">
      <j1 rule="hyper" parents="63 13955 15146"/>
    </justification>
  </clause>

  <clause id="15150">
    <literal><![CDATA[
      a(x,y,z) * ((u * w) * L(L(w \ 1,w,u),u * w,a(x,y,z))) = ((u * w) * a(x,y,z)) * ((u * w) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),14141(a,2,2,2))].">
      <j1 rule="para" parents="9 14141"/>
    </justification>
  </clause>

  <clause id="15151">
    <literal><![CDATA[
      a(x,y,z) * (u * (w * L(w \ 1,u * w,a(x,y,z)))) = ((u * w) * a(x,y,z)) * ((u * w) \ u)
    ]]></literal>
    <justification jstring="[para(403(a,1),15150(a,1,2))].">
      <j1 rule="para" parents="403 15150"/>
    </justification>
  </clause>

  <clause id="15152">
    <literal><![CDATA[
      a(x,y,z) * (u * (w \ L(w,u * w,a(x,y,z)))) = ((u * w) * a(x,y,z)) * ((u * w) \ u)
    ]]></literal>
    <justification jstring="[para(1064(a,1),15151(a,1,2,2))].">
      <j1 rule="para" parents="1064 15151"/>
    </justification>
  </clause>

  <clause id="15153">
    <literal><![CDATA[
      L(x,y \ T((y / z) * u,u \ z),y \ T((y / z) * u,u \ z)) = L(x,L(u \ z,u,z \ y) \ 1,L(u \ z,u,z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(3740(a,1),14221(a,1,3,2))].">
      <j1 rule="para" parents="3740 14221"/>
    </justification>
  </clause>

  <clause id="15154">
    <literal><![CDATA[
      L(x,L(y \ z,y,z \ u) \ 1,L(y \ z,y,z \ u) \ 1) = L(x,u \ T((u / z) * y,y \ z),u \ ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,3319,a(flip),b,15153,a),flip(a)].">
      <j1 rule="hyper" parents="63 3319 15153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15156">
    <literal><![CDATA[
      L(x,L(y \ z,y,z \ u) \ 1,L(y \ z,y,z \ u) \ 1) = L(x,u \ T((u / z) * y,y \ z),u \ ((z \ u) * y))
    ]]></literal>
    <justification jstring="[hyper(316,a,4174,a(flip),b,15154,a),flip(a)].">
      <j1 rule="hyper" parents="316 4174 15154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15157">
    <literal><![CDATA[
      L(x,L(y \ z,y,z \ u) \ 1,L(y \ z,y,z \ u) \ 1) = L(x,u \ ((u / z) * y),u \ ((z \ u) * y))
    ]]></literal>
    <justification jstring="[hyper(316,a,10811,a(flip),b,15156,a),flip(a)].">
      <j1 rule="hyper" parents="316 10811 15156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15159">
    <literal><![CDATA[
      L(x,L(y \ z,y,z \ u) \ 1,L(y \ z,y,z \ u) \ 1) = L(x,u \ ((z \ u) * y),u \ ((z \ u) * y))
    ]]></literal>
    <justification jstring="[hyper(316,a,10898,a(flip),b,15157,a),flip(a)].">
      <j1 rule="hyper" parents="316 10898 15157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15160">
    <literal><![CDATA[
      (L(R(x,y,z) \ x,x,y) \ (R(x,y,z) \ x)) * (u * (R(x,y,z) \ x)) = ((a(x,y,z) * (R(x,y,z) \ x)) * u) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(14400(a,1),14629(a,2,1,1))].">
      <j1 rule="para" parents="14400 14629"/>
    </justification>
  </clause>

  <clause id="15161">
    <literal><![CDATA[
      (L(R(x,y,z) \ x,x,y) \ (R(x,y,z) \ x)) * (u * (R(x,y,z) \ x)) = ((x * (R(x,y,z) \ a(x,y,z))) * u) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(8671(a,1),15160(a,2,1,1))].">
      <j1 rule="para" parents="8671 15160"/>
    </justification>
  </clause>

  <clause id="15162">
    <literal><![CDATA[
      (L(R(x,y,z) \ x,x,y) \ (R(x,y,z) \ x)) * (u * (R(x,y,z) \ x)) = (a(y,x,a(z,y,x)) * u) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(13945(a,1),15161(a,2,1,1))].">
      <j1 rule="para" parents="13945 15161"/>
    </justification>
  </clause>

  <clause id="15163">
    <literal><![CDATA[
      (L(R(x,y,z) \ x,x,y) \ (R(x,y,z) \ x)) * (u * (R(x,y,z) \ x)) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(316,a,14993,a(flip),b,15162,a),flip(a)].">
      <j1 rule="hyper" parents="316 14993 15162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15164">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ (R(x,y,z) \ x)) * (u * (R(x,y,z) \ x)) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(14617(a,1),15163(a,1,1,1))].">
      <j1 rule="para" parents="14617 15163"/>
    </justification>
  </clause>

  <clause id="15165">
    <literal><![CDATA[
      (a(x,y,z) * (R(x,y,z) \ x)) * (u * (R(x,y,z) \ x)) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(14400(a,1),15164(a,1,1))].">
      <j1 rule="para" parents="14400 15164"/>
    </justification>
  </clause>

  <clause id="15166">
    <literal><![CDATA[
      (x * (R(x,y,z) \ a(x,y,z))) * (u * (R(x,y,z) \ x)) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(8671(a,1),15165(a,1,1))].">
      <j1 rule="para" parents="8671 15165"/>
    </justification>
  </clause>

  <clause id="15167">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * (u * (R(y,x,z) \ y)) = a(y,x,z) \ u
    ]]></literal>
    <justification jstring="[para(13945(a,1),15166(a,1,1))].">
      <j1 rule="para" parents="13945 15166"/>
    </justification>
  </clause>

  <clause id="15168">
    <literal><![CDATA[
      T((x / (y * z)) * y,z) * R(T((x / (y * z)) * y,z) \ x,u,w) = R(L(z,y,y \ (z \ x)),u,w) * (L(z,y,y \ (z \ x)) \ x)
    ]]></literal>
    <justification jstring="[para(14649(a,1),14659(a,1,2,1,1))].">
      <j1 rule="para" parents="14649 14659"/>
    </justification>
  </clause>

  <clause id="15169">
    <literal><![CDATA[
      R(L(x,y,y \ (x \ z)),u,w) * (L(x,y,y \ (x \ z)) \ z) = ((z / (y * x)) * y) * R(((z / (y * x)) * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3316,a(flip),b,15168,a),flip(a)].">
      <j1 rule="hyper" parents="63 3316 15168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15171">
    <literal><![CDATA[
      R(L(x,y,y \ (x \ z)),u,w) * (L(x,y,y \ (x \ z)) \ z) = (z / (y * x)) * (y * R(y \ (y * x),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,885,a(flip),b,15169,a),flip(a)].">
      <j1 rule="hyper" parents="316 885 15169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15172">
    <literal><![CDATA[
      R(L(x,y,y \ (x \ z)),u,w) * (L(x,y,y \ (x \ z)) \ z) = (z / (y * x)) * (y * R(x,u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),15171(a,2,2,2,1))].">
      <j1 rule="para" parents="9 15171"/>
    </justification>
  </clause>

  <clause id="15173">
    <literal><![CDATA[
      L(x,y,y \ (x \ 1)) \ R(L(x,y,y \ (x \ 1)),z,u) = (1 / (y * x)) * (y * R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,978,a(flip),b,15172,a)].">
      <j1 rule="hyper" parents="63 978 15172"/>
    </justification>
  </clause>

  <clause id="15174">
    <literal><![CDATA[
      L(x,y,y \ (x \ 1)) \ L(R(x,z,u),y,y \ (x \ 1)) = (1 / (y * x)) * (y * R(x,z,u))
    ]]></literal>
    <justification jstring="[para(29(a,1),15173(a,1,2))].">
      <j1 rule="para" parents="29 15173"/>
    </justification>
  </clause>

  <clause id="15175">
    <literal><![CDATA[
      R(x * K(y,L(a(z,u,w) \ 1,v5,v6)),y,L(a(z,u,w) \ 1,v5,v6)) = (L(a(z,u,w),v5,v6) \ (x * y)) / (L(a(z,u,w),v5,v6) \ y)
    ]]></literal>
    <justification jstring="[para(14675(a,1),14681(a,2,1))].">
      <j1 rule="para" parents="14675 14681"/>
    </justification>
  </clause>

  <clause id="15176">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * (u * w)) / ((w * (K(v5,v6) * (a(x,y,z) \ (v7 * v7)))) * (v7 \ (v7 \ K(v6,v5)))) = R(u,w * (K(v5,v6) * (v7 * v7)),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11782,a(flip),b,11783,a)].">
      <j1 rule="hyper" parents="63 11782 11783"/>
    </justification>
  </clause>

  <clause id="15177">
    <literal><![CDATA[
      L(a(x * y,z,a(z,y,x)),L(z,y,x) \ z,u) * u = (u / (L(z,y,x) \ z)) * (L(1 / (L(z,y,x) \ z),z,x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(13541(a,1),11890(a,1,1,1))].">
      <j1 rule="para" parents="13541 11890"/>
    </justification>
  </clause>

  <clause id="15178">
    <literal><![CDATA[
      L(a(x * y,z,a(z,y,x)),z \ L(z,y,x),u) * u = (u / (L(z,y,x) \ z)) * (L(1 / (L(z,y,x) \ z),z,x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(12400(a,1),15177(a,1,1))].">
      <j1 rule="para" parents="12400 15177"/>
    </justification>
  </clause>

  <clause id="15179">
    <literal><![CDATA[
      L(a(x * y,z,a(z,y,x)),z \ L(z,y,x),u) * u = ((L(z,y,x) \ z) \ u) * (L(1 / (L(z,y,x) \ z),z,x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(6483(a,1),15178(a,2,1))].">
      <j1 rule="para" parents="6483 15178"/>
    </justification>
  </clause>

  <clause id="15180">
    <literal><![CDATA[
      L(a(x * y,z,a(z,y,x)),z \ L(z,y,x),u) * u = ((L(z,y,x) \ z) \ u) * (L(z \ L(z,y,x),z,x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(1895(a,1),15179(a,2,2,1,1))].">
      <j1 rule="para" parents="1895 15179"/>
    </justification>
  </clause>

  <clause id="15181">
    <literal><![CDATA[
      L(a(x * y,z,a(z,y,x)),z \ L(z,y,x),u) * u = ((L(z,y,x) \ z) \ u) * ((a(x,y,L(z,y,x)) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(13425(a,1),15180(a,2,2,1))].">
      <j1 rule="para" parents="13425 15180"/>
    </justification>
  </clause>

  <clause id="15182">
    <literal><![CDATA[
      L(a(x * y,z,a(z,y,x)),z \ L(z,y,x),u) * u = ((L(z,y,x) \ z) \ u) * a(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(2301(a,1),15181(a,2,2))].">
      <j1 rule="para" parents="2301 15181"/>
    </justification>
  </clause>

  <clause id="15183">
    <literal><![CDATA[
      ((L(x,y,z) \ x) \ u) * a(z,y,L(x,y,z)) = a(x,y,z) * ((x \ R(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14892,a(flip),b,15182,a),flip(a)].">
      <j1 rule="hyper" parents="63 14892 15182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15186">
    <literal><![CDATA[
      x \ ((L(y,z,u) \ y) * (L(L(y,z,u) \ y,y,u * z) \ x)) = (a(y,z,u) * ((y \ R(y,z,u)) \ x)) \ x
    ]]></literal>
    <justification jstring="[para(15183(a,1),12946(a,2,1))].">
      <j1 rule="para" parents="15183 12946"/>
    </justification>
  </clause>

  <clause id="15187">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,z * y) * ((L(x,y,z) \ x) \ u) = a(x,y,z) * ((x \ R(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(39,a,12926,a,b,15186,a(flip))].">
      <j1 rule="hyper" parents="39 12926 15186"/>
    </justification>
  </clause>

  <clause id="15188">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ u) * L(x \ L(x,y,z),x,z * y) = a(x,y,z) * ((x \ R(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9607,a(flip),b,15187,a)].">
      <j1 rule="hyper" parents="63 9607 15187"/>
    </justification>
  </clause>

  <clause id="15189">
    <literal><![CDATA[
      a(x,y,z) * ((L(z,y,x) \ z) \ u) = a(z,y,x) * ((z \ R(z,y,x)) \ u)
    ]]></literal>
    <justification jstring="[para(13625(a,2),15187(a,1,1))].">
      <j1 rule="para" parents="13625 15187"/>
    </justification>
  </clause>

  <clause id="15190">
    <literal><![CDATA[
      a(x,y,z) * ((x \ R(x,y,z)) \ u) = a(z,y,x) * (u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(14358(a,1),15189(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14358 15189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15191">
    <literal><![CDATA[
      a(x,y,z) * ((R(x,y,z) \ x) * u) = a(z,y,x) * (u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(14536(a,1),15190(a,1,2))].">
      <j1 rule="para" parents="14536 15190"/>
    </justification>
  </clause>

  <clause id="15192">
    <literal><![CDATA[
      a(x,y,z) * ((R(x,y,z) \ x) * (u * (L(x,y,z) \ x))) = a(z,y,x) * u
    ]]></literal>
    <justification jstring="[para(14369(a,1),15191(a,2,2))].">
      <j1 rule="para" parents="14369 15191"/>
    </justification>
  </clause>

  <clause id="15193">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * (u * (L(y,x,z) \ y)) = a(z,x,y) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,14820,a(flip),b,15192,a)].">
      <j1 rule="hyper" parents="63 14820 15192"/>
    </justification>
  </clause>

  <clause id="15194">
    <literal><![CDATA[
      (x / (y \ L(y,z,u))) * L(y \ L(y,z,u),y,u * z) = a(y,z,u) * ((y \ R(y,z,u)) \ x)
    ]]></literal>
    <justification jstring="[para(5015(a,2),15188(a,1,1))].">
      <j1 rule="para" parents="5015 15188"/>
    </justification>
  </clause>

  <clause id="15196">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (a(x,y,z) * ((x \ R(x,y,z)) \ u)) = L(x \ L(x,y,z),x,z * y) * u
    ]]></literal>
    <justification jstring="[hyper(139,a,15194,a(flip),b,4382,a)].">
      <j1 rule="hyper" parents="139 15194 4382"/>
    </justification>
  </clause>

  <clause id="15199">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (a(x,y,z) * ((x \ R(x,y,z)) \ u)) = (a(z,y,x) \ 1) * u
    ]]></literal>
    <justification jstring="[para(13659(a,1),15196(a,2,1))].">
      <j1 rule="para" parents="13659 15196"/>
    </justification>
  </clause>

  <clause id="15200">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (a(y,x,a(z,y,x)) * u) = (a(z,y,x) \ 1) * u
    ]]></literal>
    <justification jstring="[para(14817(a,1),15199(a,1,2))].">
      <j1 rule="para" parents="14817 15199"/>
    </justification>
  </clause>

  <clause id="15201">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (a(y,x,a(z,y,x)) * u) = a(z,y,x) \ u
    ]]></literal>
    <justification jstring="[hyper(316,a,14391,a(flip),b,15200,a),flip(a)].">
      <j1 rule="hyper" parents="316 14391 15200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15202">
    <literal><![CDATA[
      (a(x,y,a(z,x,y)) * u) * (y \ L(y,x,z)) = a(z,x,y) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,5023,a(flip),b,15201,a)].">
      <j1 rule="hyper" parents="63 5023 15201"/>
    </justification>
  </clause>

  <clause id="15210">
    <literal><![CDATA[
      L(x,y,z) \ (u / (T(x \ L(x,w,v5),u) \ 1)) = (x \ L(x,w,v5)) \ (L(x,y,z) \ (((x \ L(x,w,v5)) * (x \ L(x,w,v5))) * u))
    ]]></literal>
    <justification jstring="[para(10313(a,2),13309(a,1,2))].">
      <j1 rule="para" parents="10313 13309"/>
    </justification>
  </clause>

  <clause id="15211">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (L(x,u,w) \ (((x \ L(x,y,z)) * (x \ L(x,y,z))) * v5)) = L(x,u,w) \ (v5 / (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(5043(a,1),15210(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5043 15210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15213">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (L(x,u,w) \ (((x \ L(x,y,z)) * (x \ L(x,y,z))) * v5)) = L(x,u,w) \ ((L(x,y,z) \ x) \ v5)
    ]]></literal>
    <justification jstring="[para(6483(a,1),15211(a,2,2))].">
      <j1 rule="para" parents="6483 15211"/>
    </justification>
  </clause>

  <clause id="15214">
    <literal><![CDATA[
      L(x \ L(x,y,z),x \ L(x,y,z),u) * u = (L(x,y,z) \ x) \ u
    ]]></literal>
    <justification jstring="[hyper(38,a,13309,a,b,15213,a(flip))].">
      <j1 rule="hyper" parents="38 13309 15213"/>
    </justification>
  </clause>

  <clause id="15215">
    <literal><![CDATA[
      L(x \ L(x,y,z),x \ L(x,y,z),u) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,14352,a(flip),b,15214,a),flip(a)].">
      <j1 rule="hyper" parents="35 14352 15214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15216">
    <literal><![CDATA[
      L(x,x \ L(x,y,z),u) * (x \ L(x,y,z)) = L(L(x,x \ L(x,y,z),u),y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,15215,a(flip),b,2136,a)].">
      <j1 rule="hyper" parents="139 15215 2136"/>
    </justification>
  </clause>

  <clause id="15219">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z)) = a(w,u,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(15215(a,1),14510(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15215 14510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15220">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z)) = a(w,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5566,a(flip),b,15219,a),flip(a)].">
      <j1 rule="hyper" parents="316 5566 15219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15226">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ u) * (L(x \ L(x,y,z),w,v5) \ (x \ L(x,y,z))) = (x \ L(x,y,z)) \ (a(v5,w,x * L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(15220(a,1),6551(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15220 6551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15230">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(u,w,x * L(x,y,z)) = L(x \ L(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[para(15220(a,1),13355(a,1,2))].">
      <j1 rule="para" parents="15220 13355"/>
    </justification>
  </clause>

  <clause id="15231">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),v5,v6)) = L(a(x,y,z * L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(15220(a,1),14954(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15220 14954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15232">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,w) * (x \ L(x,y,z)) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,13775,a,b,15230,a)].">
      <j1 rule="hyper" parents="63 13775 15230"/>
    </justification>
  </clause>

  <clause id="15234">
    <literal><![CDATA[
      a(a(x,y,z) \ L(a(x,y,z),u,w),v5,x) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,8899,a(flip),b,15232,a),flip(a)].">
      <j1 rule="hyper" parents="134 8899 15232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15235">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x \ L(x,y,z),u,w) = a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(35,a,14357,a,b,15232,a)].">
      <j1 rule="hyper" parents="35 14357 15232"/>
    </justification>
  </clause>

  <clause id="15237">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,(w * (v5 * v6)) * v7) * (x \ L(x,y,z)) = L(x \ L(x,y,z),u,(((v6 \ 1) * v5) * w) * v7)
    ]]></literal>
    <justification jstring="[para(6092(a,1),15232(a,1,1))].">
      <j1 rule="para" parents="6092 15232"/>
    </justification>
  </clause>

  <clause id="15239">
    <literal><![CDATA[
      a(x,y,a(z,u,a(x,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,14587,a(flip),b,15234,a)].">
      <j1 rule="hyper" parents="63 14587 15234"/>
    </justification>
  </clause>

  <clause id="15241">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,x))) = 1
    ]]></literal>
    <justification jstring="[para(13433(a,1),15239(a,1,3))].">
      <j1 rule="para" parents="13433 15239"/>
    </justification>
  </clause>

  <clause id="15242">
    <literal><![CDATA[
      a(a(a(x,y,z),u,w),v5,z) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,14012,a,b,15241,a)].">
      <j1 rule="hyper" parents="63 14012 15241"/>
    </justification>
  </clause>

  <clause id="15243">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)),v5,w) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(52,a,15241,a)].">
      <j1 rule="hyper" parents="52 15241"/>
    </justification>
  </clause>

  <clause id="15244">
    <literal><![CDATA[
      L(x,y,a(a(z,u,x),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,15242,a)].">
      <j1 rule="hyper" parents="52 15242"/>
    </justification>
  </clause>

  <clause id="15245">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,x))) = x
    ]]></literal>
    <justification jstring="[para(14010(a,1),15244(a,1,3))].">
      <j1 rule="para" parents="14010 15244"/>
    </justification>
  </clause>

  <clause id="15246">
    <literal><![CDATA[
      L(x,y,a(z,u,a(x,w,v5))) = x
    ]]></literal>
    <justification jstring="[para(14012(a,1),15244(a,1,3))].">
      <j1 rule="para" parents="14012 15244"/>
    </justification>
  </clause>

  <clause id="15248">
    <literal><![CDATA[
      (x * y) * a(z,u,a(w,v5,x)) = x * (y * a(z,u,a(w,v5,x)))
    ]]></literal>
    <justification jstring="[para(15245(a,1),5383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15245 5383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15251">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (a(u,w,a(x,v5,v6)) * x) = a(u,w,a(x,v5,v6)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(15246(a,1),12820(a,1,2,2))].">
      <j1 rule="para" parents="15246 12820"/>
    </justification>
  </clause>

  <clause id="15261">
    <literal><![CDATA[
      x * (L(x,y,z) \ L(x \ L(x,y,z),u,w)) = a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6845,a(flip),b,15235,a)].">
      <j1 rule="hyper" parents="63 6845 15235"/>
    </justification>
  </clause>

  <clause id="15265">
    <literal><![CDATA[
      x \ (L(x \ R(x,y,z),u,w) \ R(x,y,z)) = a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14198,a,b,15261,a)].">
      <j1 rule="hyper" parents="63 14198 15261"/>
    </justification>
  </clause>

  <clause id="15266">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,w) = x * a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,15261,a(flip),b,8260,a),flip(a)].">
      <j1 rule="hyper" parents="139 15261 8260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15268">
    <literal><![CDATA[
      R(x,y,z) * L(R(x,y,z) \ x,u,w) = a(x \ L(x,y,z),u,w) \ x
    ]]></literal>
    <justification jstring="[para(15261(a,1),14199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15261 14199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15269">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * a(y \ L(y,z,u),w,v5) = x * L(x \ ((L(y,z,u) \ y) \ x),w,v5)
    ]]></literal>
    <justification jstring="[para(15261(a,1),14987(a,1,2))].">
      <j1 rule="para" parents="15261 14987"/>
    </justification>
  </clause>

  <clause id="15270">
    <literal><![CDATA[
      x * L(a(y \ L(y,z,u),w,v5),R(y,z,u) \ y,x) = (R(y,z,u) \ y) * (L(R(y,z,u) \ y,w,v5) \ x)
    ]]></literal>
    <justification jstring="[para(15265(a,1),14131(a,1,2,1))].">
      <j1 rule="para" parents="15265 14131"/>
    </justification>
  </clause>

  <clause id="15272">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,w) = x * a(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13530,a,b,15266,a)].">
      <j1 rule="hyper" parents="63 13530 15266"/>
    </justification>
  </clause>

  <clause id="15274">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) * L(L(x,a(z,u,y),y) \ x,w,v5) = x * a(x \ L(x,a(z,u,y),y),w,v5)
    ]]></literal>
    <justification jstring="[para(6997(a,1),15266(a,1,1))].">
      <j1 rule="para" parents="6997 15266"/>
    </justification>
  </clause>

  <clause id="15277">
    <literal><![CDATA[
      R(x,y,z) * L(R(x,y,z) \ x,u,w) = a(x \ L(x,y,z),u,w) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,14438,a(flip),b,15268,a),flip(a)].">
      <j1 rule="hyper" parents="316 14438 15268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15278">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,w) = x * a(z,y,x * L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,13774,a(flip),b,15272,a),flip(a)].">
      <j1 rule="hyper" parents="316 13774 15272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15279">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,u) = x * a(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[para(7260(a,1),15272(a,2,2))].">
      <j1 rule="para" parents="7260 15272"/>
    </justification>
  </clause>

  <clause id="15280">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,u) = a(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,15266,a(flip),b,15279,a(flip))].">
      <j1 rule="hyper" parents="34 15266 15279"/>
    </justification>
  </clause>

  <clause id="15281">
    <literal><![CDATA[
      a(x,x,L(y,z,u) \ y) = a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13772,a(flip),b,15280,a)].">
      <j1 rule="hyper" parents="63 13772 15280"/>
    </justification>
  </clause>

  <clause id="15282">
    <literal><![CDATA[
      a(x,x,y * L(y,z,u)) = a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13642,a(flip),b,15280,a)].">
      <j1 rule="hyper" parents="63 13642 15280"/>
    </justification>
  </clause>

  <clause id="15283">
    <literal><![CDATA[
      a(a(x,y,y),z,z) = a(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7276,a(flip),b,15282,a),flip(a)].">
      <j1 rule="hyper" parents="63 7276 15282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15285">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) = a(z,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14012,a(flip),b,15283,a),flip(a)].">
      <j1 rule="hyper" parents="63 14012 15283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15286">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) = a(z,z,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,14010,a(flip),b,15283,a)].">
      <j1 rule="hyper" parents="63 14010 15283"/>
    </justification>
  </clause>

  <clause id="15289">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x \ (a(x \ L(x,y,z),u,w) * x)) = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(15277(a,1),9618(a,1,2,2))].">
      <j1 rule="para" parents="15277 9618"/>
    </justification>
  </clause>

  <clause id="15293">
    <literal><![CDATA[
      x * a(x \ L(x,y,z),u,w) = x * a(z,y,x * L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15266,a(flip),b,15278,a)].">
      <j1 rule="hyper" parents="63 15266 15278"/>
    </justification>
  </clause>

  <clause id="15295">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,w) = a(z,y,x * L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(34,a,15266,a(flip),b,15278,a(flip))].">
      <j1 rule="hyper" parents="34 15266 15278"/>
    </justification>
  </clause>

  <clause id="15296">
    <literal><![CDATA[
      a(x \ L(x,a(y,z,u),w),v5,v6) = a(x * L(x,v5,v6),a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,14123,a,b,15295,a),flip(a)].">
      <j1 rule="hyper" parents="316 14123 15295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15297">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (((y * x) \ y) * a(z,u,w * L(w,v5,v6))) = a(w \ L(w,u,z),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,396,a,b,15295,a)].">
      <j1 rule="hyper" parents="316 396 15295"/>
    </justification>
  </clause>

  <clause id="15299">
    <literal><![CDATA[
      a(L(x,y,z) \ x,u,w) = a(z,y,x * L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12270,a,b,15295,a)].">
      <j1 rule="hyper" parents="63 12270 15295"/>
    </justification>
  </clause>

  <clause id="15300">
    <literal><![CDATA[
      a(x,y \ L(y,z,x),u) = a(x,z,y * L(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12475,a(flip),b,15295,a)].">
      <j1 rule="hyper" parents="63 12475 15295"/>
    </justification>
  </clause>

  <clause id="15303">
    <literal><![CDATA[
      x * a(y,z,u * L(u,w,v5)) = x * a(v5,w,u * L(u,z,y))
    ]]></literal>
    <justification jstring="[para(15295(a,1),13774(a,1,2))].">
      <j1 rule="para" parents="15295 13774"/>
    </justification>
  </clause>

  <clause id="15304">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) * v5 = a(w,u,z * L(z,y,x)) * v5
    ]]></literal>
    <justification jstring="[para(15295(a,1),13776(a,1,1))].">
      <j1 rule="para" parents="15295 13776"/>
    </justification>
  </clause>

  <clause id="15308">
    <literal><![CDATA[
      a(L(x,y,z) \ x,u,u) = a(z,y,a(x,u,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,7276,a(flip),b,15299,a),flip(a)].">
      <j1 rule="hyper" parents="316 7276 15299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15309">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[para(7290(a,1),15299(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7290 15299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15311">
    <literal><![CDATA[
      x \ L(x,x \ L(x,y,z),u) = a(a(u,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13840,a,b,15309,a)].">
      <j1 rule="hyper" parents="63 13840 15309"/>
    </justification>
  </clause>

  <clause id="15313">
    <literal><![CDATA[
      a(x \ L(x,y,z),x,u) = a(a(u,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13642,a,b,15309,a)].">
      <j1 rule="hyper" parents="63 13642 15309"/>
    </justification>
  </clause>

  <clause id="15314">
    <literal><![CDATA[
      x \ L(x,y,y \ L(y,z,u)) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8241,a,b,15309,a)].">
      <j1 rule="hyper" parents="63 8241 15309"/>
    </justification>
  </clause>

  <clause id="15315">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),y) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8234,a,b,15309,a)].">
      <j1 rule="hyper" parents="63 8234 15309"/>
    </justification>
  </clause>

  <clause id="15317">
    <literal><![CDATA[
      a(a(x,y,y),x,z) = a(x,y,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13646,a(flip),b,15309,a),flip(a)].">
      <j1 rule="hyper" parents="63 13646 15309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15318">
    <literal><![CDATA[
      a(a(x,y,y),z,z) = a(x,y,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4962,a(flip),b,15309,a),flip(a)].">
      <j1 rule="hyper" parents="63 4962 15309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15321">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = a(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14010,a(flip),b,15317,a),flip(a)].">
      <j1 rule="hyper" parents="63 14010 15317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15323">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * u = u * a(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(15317(a,1),13708(a,1,1))].">
      <j1 rule="para" parents="15317 13708"/>
    </justification>
  </clause>

  <clause id="15325">
    <literal><![CDATA[
      a(a(x,y,y),z,z) = a(y,a(z,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,13469,a,b,15318,a),flip(a)].">
      <j1 rule="hyper" parents="316 13469 15318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15327">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) = a(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15283,a(flip),b,15318,a),flip(a)].">
      <j1 rule="hyper" parents="63 15283 15318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15328">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) = a(z,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14010,a(flip),b,15318,a),flip(a)].">
      <j1 rule="hyper" parents="63 14010 15318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15330">
    <literal><![CDATA[
      a(x,a(y,y,x),z) = a(x,y,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,13681,a,b,15321,a)].">
      <j1 rule="hyper" parents="316 13681 15321"/>
    </justification>
  </clause>

  <clause id="15331">
    <literal><![CDATA[
      x * a(x,y,a(z,x,y)) = L(x,a(y,y,x),z)
    ]]></literal>
    <justification jstring="[para(15321(a,2),13698(a,1,2))].">
      <j1 rule="para" parents="15321 13698"/>
    </justification>
  </clause>

  <clause id="15333">
    <literal><![CDATA[
      a(x,a(y,y,x),z) = a(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15283,a(flip),b,15325,a),flip(a)].">
      <j1 rule="hyper" parents="63 15283 15325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15334">
    <literal><![CDATA[
      a(x,a(y,y,x),z) = a(y,y,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14012,a(flip),b,15325,a),flip(a)].">
      <j1 rule="hyper" parents="63 14012 15325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15337">
    <literal><![CDATA[
      a(x,a(x,y,y),z) = a(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13675,a,b,15327,a)].">
      <j1 rule="hyper" parents="63 13675 15327"/>
    </justification>
  </clause>

  <clause id="15338">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) = a(z,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13660,a,b,15328,a)].">
      <j1 rule="hyper" parents="63 13660 15328"/>
    </justification>
  </clause>

  <clause id="15339">
    <literal><![CDATA[
      x * a(y,y,a(x,z,z)) = L(x,z,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,15328,a(flip),b,11689,a)].">
      <j1 rule="hyper" parents="139 15328 11689"/>
    </justification>
  </clause>

  <clause id="15340">
    <literal><![CDATA[
      (((x / y) * (y * a(z,y \ x,y))) / a(z,y \ x,y)) \ x = a(y \ x,a(y,y,y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(316,a,6948,a,b,15330,a)].">
      <j1 rule="hyper" parents="316 6948 15330"/>
    </justification>
  </clause>

  <clause id="15342">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = a(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15330,a(flip),b,15333,a)].">
      <j1 rule="hyper" parents="63 15330 15333"/>
    </justification>
  </clause>

  <clause id="15343">
    <literal><![CDATA[
      x * a(y,y,a(x,z,z)) = L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(15333(a,1),13480(a,1,2))].">
      <j1 rule="para" parents="15333 13480"/>
    </justification>
  </clause>

  <clause id="15345">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = a(y,y,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15330,a(flip),b,15334,a)].">
      <j1 rule="hyper" parents="63 15330 15334"/>
    </justification>
  </clause>

  <clause id="15346">
    <literal><![CDATA[
      a(x,x,a(x \ y,x \ y,z)) = a(x \ y,a(x,x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12258,a(flip),b,15334,a),flip(a)].">
      <j1 rule="hyper" parents="63 12258 15334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15347">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) = a(y,y,a(z,z,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,15285,a(flip),b,15338,a),flip(a)].">
      <j1 rule="hyper" parents="316 15285 15338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15348">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = a(y,y,a(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,15321,a,b,15338,a)].">
      <j1 rule="hyper" parents="63 15321 15338"/>
    </justification>
  </clause>

  <clause id="15349">
    <literal><![CDATA[
      a(x * y,x * y,a(z,y,y)) = a(z,y,a(x,y * x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13376,a(flip),b,15338,a),flip(a)].">
      <j1 rule="hyper" parents="63 13376 15338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15350">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) = a(z,y,a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,15328,a,b,15342,a)].">
      <j1 rule="hyper" parents="316 15328 15342"/>
    </justification>
  </clause>

  <clause id="15351">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * u = u * a(y,y,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(138,a,15345,a,b,2287,a)].">
      <j1 rule="hyper" parents="138 15345 2287"/>
    </justification>
  </clause>

  <clause id="15352">
    <literal><![CDATA[
      a(x,y,z) * a(z,z,a(y,y,x)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,15345,a(flip),b,9953,a)].">
      <j1 rule="hyper" parents="139 15345 9953"/>
    </justification>
  </clause>

  <clause id="15355">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) * (L(a(x,x,a(y,y,z)),u,w) \ v5) = v5 * a(w,u,a(y,x,a(z,y,x)))
    ]]></literal>
    <justification jstring="[para(15345(a,2),14794(a,2,2,3))].">
      <j1 rule="para" parents="15345 14794"/>
    </justification>
  </clause>

  <clause id="15357">
    <literal><![CDATA[
      a(x,y,y) * (z * (a(x,x,a(y,y,z)) \ x)) = L(a(x,y,y),x,z) * (z * x)
    ]]></literal>
    <justification jstring="[para(15347(a,1),8534(a,1,2,2,1))].">
      <j1 rule="para" parents="15347 8534"/>
    </justification>
  </clause>

  <clause id="15358">
    <literal><![CDATA[
      (a(x,x,a(y,y,z)) \ x) * a(x,y,y) = x * L(a(x,y,y),x,z)
    ]]></literal>
    <justification jstring="[para(15347(a,1),13759(a,1,1,1))].">
      <j1 rule="para" parents="15347 13759"/>
    </justification>
  </clause>

  <clause id="15359">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,x,L(y,z,u))) = a(y,y,a(w,x,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,14207,a(flip),b,15348,a),flip(a)].">
      <j1 rule="hyper" parents="316 14207 15348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15360">
    <literal><![CDATA[
      a(x,y,a(L(z,u,x),x,y)) = a(y,y,a(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,12057,a(flip),b,15348,a),flip(a)].">
      <j1 rule="hyper" parents="316 12057 15348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15361">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * u = a(y,y,a(z,x,x)) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,15348,a,b,11,a)].">
      <j1 rule="hyper" parents="138 15348 11"/>
    </justification>
  </clause>

  <clause id="15362">
    <literal><![CDATA[
      a(x,a(y,z,x),z) = a(x,x,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13469,a,b,15348,a)].">
      <j1 rule="hyper" parents="63 13469 15348"/>
    </justification>
  </clause>

  <clause id="15363">
    <literal><![CDATA[
      L(x,y,z) * a(x,x,a(z,y,y)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,15348,a(flip),b,9958,a)].">
      <j1 rule="hyper" parents="139 15348 9958"/>
    </justification>
  </clause>

  <clause id="15364">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * x = L(x,a(y,z,x),z)
    ]]></literal>
    <justification jstring="[para(15348(a,1),13478(a,1,1))].">
      <j1 rule="para" parents="15348 13478"/>
    </justification>
  </clause>

  <clause id="15365">
    <literal><![CDATA[
      (x * (a(y,z,a(x,y,z)) \ z)) * a(y,y,z) = x * (z * a(y,y,z))
    ]]></literal>
    <justification jstring="[para(15350(a,1),8531(a,1,1,2,1))].">
      <j1 rule="para" parents="15350 8531"/>
    </justification>
  </clause>

  <clause id="15366">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * (a(x,y,a(z,x,y)) \ y) = L(a(x,x,y) \ 1,y,z) * y
    ]]></literal>
    <justification jstring="[para(15350(a,1),13766(a,1,2,1))].">
      <j1 rule="para" parents="15350 13766"/>
    </justification>
  </clause>

  <clause id="15367">
    <literal><![CDATA[
      L(x,y,z) \ a(x,x,a(z,y,y)) = x \ a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,15362,a(flip),b,11626,a)].">
      <j1 rule="hyper" parents="133 15362 11626"/>
    </justification>
  </clause>

  <clause id="15370">
    <literal><![CDATA[
      x * a(y \ L(y,z,u),y,w) = a(u,z,a(w,y,y)) * x
    ]]></literal>
    <justification jstring="[para(15313(a,2),13715(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15313 13715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15373">
    <literal><![CDATA[
      L(x,a(y,y,x),z) = L(x,y,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,11690,a(flip),b,15331,a),flip(a)].">
      <j1 rule="hyper" parents="63 11690 15331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15376">
    <literal><![CDATA[
      L(x,y,a(z,z,y)) = L(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15339,a(flip),b,15343,a)].">
      <j1 rule="hyper" parents="63 15339 15343"/>
    </justification>
  </clause>

  <clause id="15377">
    <literal><![CDATA[
      L(x,a(y,z,x),z) = L(x,x,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7339,a(flip),b,15364,a),flip(a)].">
      <j1 rule="hyper" parents="63 7339 15364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15378">
    <literal><![CDATA[
      L(x,a(y,z,x),z) = L(x,x,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,9220,a(flip),b,15377,a),flip(a)].">
      <j1 rule="hyper" parents="316 9220 15377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15379">
    <literal><![CDATA[
      R(x,y,z) = a(x,y,z) * L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,15377,a(flip),b,13927,a),flip(a)].">
      <j1 rule="hyper" parents="139 15377 13927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15380">
    <literal><![CDATA[
      a(x,y,z) \ L(z,z,a(x,y,y)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,15377,a(flip),b,11630,a)].">
      <j1 rule="hyper" parents="133 15377 11630"/>
    </justification>
  </clause>

  <clause id="15381">
    <literal><![CDATA[
      L(x,y,z) \ L(x,x,a(z,y,y)) = a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,15377,a(flip),b,11629,a)].">
      <j1 rule="hyper" parents="133 15377 11629"/>
    </justification>
  </clause>

  <clause id="15382">
    <literal><![CDATA[
      R(x,y,z) = L(x,x,a(z,y,y)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(15377(a,1),13931(a,2,1))].">
      <j1 rule="para" parents="15377 13931"/>
    </justification>
  </clause>

  <clause id="15383">
    <literal><![CDATA[
      L(x,x,a(y,z,z)) \ R(x,z,y) = a(x,z,y)
    ]]></literal>
    <justification jstring="[para(15377(a,1),13932(a,1,1))].">
      <j1 rule="para" parents="15377 13932"/>
    </justification>
  </clause>

  <clause id="15384">
    <literal><![CDATA[
      a(x,y,z) * L(z,y,x) = L(z,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,11630,a,b,15378,a)].">
      <j1 rule="hyper" parents="63 11630 15378"/>
    </justification>
  </clause>

  <clause id="15386">
    <literal><![CDATA[
      R(x,y,z) = a(x,y,z) * L(x,x,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,15378,a(flip),b,13927,a),flip(a)].">
      <j1 rule="hyper" parents="139 15378 13927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15387">
    <literal><![CDATA[
      L(x,y,z) \ L(x,x,a(y,y,z)) = a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,15378,a(flip),b,11629,a)].">
      <j1 rule="hyper" parents="133 15378 11629"/>
    </justification>
  </clause>

  <clause id="15388">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) \ L(x,y,z) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(15378(a,1),11632(a,1,1))].">
      <j1 rule="para" parents="15378 11632"/>
    </justification>
  </clause>

  <clause id="15389">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) \ R(x,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(15378(a,1),13932(a,1,1))].">
      <j1 rule="para" parents="15378 13932"/>
    </justification>
  </clause>

  <clause id="15390">
    <literal><![CDATA[
      a(x,y,L(z,u,y)) * L(x,x,a(y,y,z)) = R(x,y,L(z,u,y))
    ]]></literal>
    <justification jstring="[para(9224(a,1),15379(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9224 15379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15392">
    <literal><![CDATA[
      a(x * ((y * z) \ u),w,v5) \ L(v5,v5,a(x * ((y * z) \ u),w,w)) = L(v5,w,x * ((z * y) \ u))
    ]]></literal>
    <justification jstring="[hyper(316,a,6251,a,b,15380,a),flip(a)].">
      <j1 rule="hyper" parents="316 6251 15380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15395">
    <literal><![CDATA[
      a(x * ((y * y) \ z),u,w) \ L(w,w,a(((y * y) \ x) * z,u,u)) = L(w,u,((y * y) \ x) * z)
    ]]></literal>
    <justification jstring="[para(12108(a,1),15380(a,1,1))].">
      <j1 rule="para" parents="12108 15380"/>
    </justification>
  </clause>

  <clause id="15396">
    <literal><![CDATA[
      a(x,y * (z \ R(u,w,v5)),v6) \ L(v6,v6,a(x,y * (z \ R(u,w,v5)),y * (z \ L(u,w,v5)))) = L(v6,y * (z \ R(u,w,v5)),x)
    ]]></literal>
    <justification jstring="[para(12120(a,1),15380(a,1,2,3))].">
      <j1 rule="para" parents="12120 15380"/>
    </justification>
  </clause>

  <clause id="15397">
    <literal><![CDATA[
      L(x,y,z * (y \ 1)) \ L(x,x,a(z * (y \ 1),y,y)) = (y * x) \ ((z * (1 / y)) \ (R(z,y \ 1,y) * x))
    ]]></literal>
    <justification jstring="[hyper(316,a,8787,a,b,15381,a),flip(a)].">
      <j1 rule="hyper" parents="316 8787 15381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15398">
    <literal><![CDATA[
      L(x,L(y,z,u),a(u,z,y)) * L(y,y,a(z,z,u)) = a(u,z,y) * (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(15384(a,1),5275(a,1,2))].">
      <j1 rule="para" parents="15384 5275"/>
    </justification>
  </clause>

  <clause id="15399">
    <literal><![CDATA[
      (R(x,y,z) \ a(x,y,z)) * x = (x \ 1) * L(x,x,a(y,y,z))
    ]]></literal>
    <justification jstring="[para(15384(a,1),14946(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15384 14946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15401">
    <literal><![CDATA[
      a(x,y * z,u) * L(x,x,a(z * y,y * z,u)) = R(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(2771(a,1),15386(a,2,2,3)),flip(a)].">
      <j1 rule="para" parents="2771 15386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15402">
    <literal><![CDATA[
      a(x,y,z * (((u * (w \ v5)) * v6) * v7)) * L(x,x,a(y,y,z * (((u * (v5 / w)) * v6) * v7))) = R(x,y,z * (((u * (v5 / w)) * v6) * v7))
    ]]></literal>
    <justification jstring="[para(9550(a,1),15386(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9550 15386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15403">
    <literal><![CDATA[
      a(x,a(y,z,u) \ w,v5) * L(x,x,a(a(y,z,u) * w,a(y,z,u) \ w,v5)) = R(x,a(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(14413(a,1),15386(a,2,2,3)),flip(a)].">
      <j1 rule="para" parents="14413 15386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15404">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ u) \ L(x,x,a(y,y,z \ u)) = a((z \ 1) \ u,y,x)
    ]]></literal>
    <justification jstring="[para(5814(a,1),15387(a,1,2,3))].">
      <j1 rule="para" parents="5814 15387"/>
    </justification>
  </clause>

  <clause id="15405">
    <literal><![CDATA[
      L(x,y,L(z * u,u,z)) \ L(x,x,a(y,y,u \ z)) = a(L(z * u,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(9926(a,1),15387(a,1,2,3))].">
      <j1 rule="para" parents="9926 15387"/>
    </justification>
  </clause>

  <clause id="15406">
    <literal><![CDATA[
      L(x,L(y,z,u),w) \ L(x,x,a(y,y,w)) = a(w,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(14207(a,1),15387(a,1,2,3))].">
      <j1 rule="para" parents="14207 15387"/>
    </justification>
  </clause>

  <clause id="15407">
    <literal><![CDATA[
      (R(x,y,z) * L(x \ L(x,R(x,y,z),a(u,u,w)),y,z)) \ R(R(x,y,z),u,w) = a(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(8387(a,2),15389(a,1,1))].">
      <j1 rule="para" parents="8387 15389"/>
    </justification>
  </clause>

  <clause id="15408">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * (u * (R(x,z,L(y,w,z)) \ x)) = a(x,z,L(y,w,z)) \ u
    ]]></literal>
    <justification jstring="[para(15360(a,1),15167(a,1,1))].">
      <j1 rule="para" parents="15360 15167"/>
    </justification>
  </clause>

  <clause id="15409">
    <literal><![CDATA[
      L(x,x \ L(x,y,z),u) = a(a(u,x,x),y,z) * x
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,15311,a),flip(a)].">
      <j1 rule="hyper" parents="38 2295 15311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15410">
    <literal><![CDATA[
      L(x,y,y \ L(y,z,u)) = a(a(x,y,y),z,u) * x
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,15314,a),flip(a)].">
      <j1 rule="hyper" parents="38 2295 15314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15415">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * a(z,y,a(x,x,y))) = a(z,y,x) \ u
    ]]></literal>
    <justification jstring="[para(15323(a,1),15201(a,1,2))].">
      <j1 rule="para" parents="15323 15201"/>
    </justification>
  </clause>

  <clause id="15417">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * a(x,x,a(y,y,z))) = a(z,y,x) \ u
    ]]></literal>
    <justification jstring="[para(15351(a,1),15201(a,1,2))].">
      <j1 rule="para" parents="15351 15201"/>
    </justification>
  </clause>

  <clause id="15418">
    <literal><![CDATA[
      a(a(x,y,y),z,u) * a(u,u,a(x,z,a(y,y,z))) = L(u,z,a(x,y,y)) \ u
    ]]></literal>
    <justification jstring="[para(15327(a,2),15352(a,1,2,3))].">
      <j1 rule="para" parents="15327 15352"/>
    </justification>
  </clause>

  <clause id="15420">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y,w,v5)) * a(x,x,a(y,L(y,z,u),y)) = a(L(y,w,v5),L(y,z,u),x) \ x
    ]]></literal>
    <justification jstring="[para(9201(a,1),15363(a,1,2,3))].">
      <j1 rule="para" parents="9201 15363"/>
    </justification>
  </clause>

  <clause id="15421">
    <literal><![CDATA[
      L(x,x,1) \ L(x,y \ z,a(z,y,y)) = a(a(z,y,y),y \ z,x) \ 1
    ]]></literal>
    <justification jstring="[para(8223(a,1),15388(a,1,1,3))].">
      <j1 rule="para" parents="8223 15388"/>
    </justification>
  </clause>

  <clause id="15422">
    <literal><![CDATA[
      L(x,y,z * (L(u,u,a(w,w,v5)) \ R(u,w,v5))) = L(x,y,z * (a(v5,w,u) \ 1))
    ]]></literal>
    <justification jstring="[para(15388(a,1),10708(a,2,3,2))].">
      <j1 rule="para" parents="15388 10708"/>
    </justification>
  </clause>

  <clause id="15423">
    <literal><![CDATA[
      L(x,y,y \ L(y,x,z)) = a(x,a(x,y,y),z) * x
    ]]></literal>
    <justification jstring="[para(8744(a,1),15410(a,2,1))].">
      <j1 rule="para" parents="8744 15410"/>
    </justification>
  </clause>

  <clause id="15425">
    <literal><![CDATA[
      L(x,y,y \ L(y,x,z)) = a(x,x,a(z,y,y)) * x
    ]]></literal>
    <justification jstring="[para(15337(a,1),15423(a,2,1))].">
      <j1 rule="para" parents="15337 15423"/>
    </justification>
  </clause>

  <clause id="15426">
    <literal><![CDATA[
      L(x,y,y \ L(y,x,z)) = L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,7339,a(flip),b,15425,a),flip(a)].">
      <j1 rule="hyper" parents="316 7339 15425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15427">
    <literal><![CDATA[
      L(x,y,a(y,x,z)) = L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14648,a(flip),b,15426,a)].">
      <j1 rule="hyper" parents="63 14648 15426"/>
    </justification>
  </clause>

  <clause id="15428">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ L(L(z,y,x) \ z,u,w) = a(z,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13437,a,b,15359,a)].">
      <j1 rule="hyper" parents="63 13437 15359"/>
    </justification>
  </clause>

  <clause id="15429">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L(L(x,z,y) \ x,u,w) = a(y,z,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(15359(a,1),14568(a,1,1))].">
      <j1 rule="para" parents="15359 14568"/>
    </justification>
  </clause>

  <clause id="15430">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * (u * (R(L(x,w,v5),z,y) \ L(x,w,v5))) = a(L(x,w,v5),z,y) \ u
    ]]></literal>
    <justification jstring="[para(15359(a,1),15167(a,1,1))].">
      <j1 rule="para" parents="15359 15167"/>
    </justification>
  </clause>

  <clause id="15434">
    <literal><![CDATA[
      a(x,a(y,z,u),w * L(w,v5,v6)) = a(v6,v5,w * L(w,a(u,z,y),x))
    ]]></literal>
    <justification jstring="[hyper(34,a,13677,a,b,15303,a)].">
      <j1 rule="hyper" parents="34 13677 15303"/>
    </justification>
  </clause>

  <clause id="15437">
    <literal><![CDATA[
      (R(x,y,z) \ a(x,y,z)) * x = a(x \ a(y,y,z),x,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,13517,a(flip),b,15399,a),flip(a)].">
      <j1 rule="hyper" parents="316 13517 15399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15438">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * (v5 * a(z,y,a(R(x,u,w),R(x,u,w),y))) = a(z,y,R(x,u,w)) \ v5
    ]]></literal>
    <justification jstring="[para(8381(a,1),15415(a,1,1))].">
      <j1 rule="para" parents="8381 15415"/>
    </justification>
  </clause>

  <clause id="15439">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((u * a(x,x,a(y,y,z))) * a(w,v5,x \ L(x,y,z))) = (a(z,y,x) \ u) * a(w,v5,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(15417(a,1),6858(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15417 6858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15440">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * (v5 * a(R(x,u,w),R(x,u,w),a(y,y,z))) = a(z,y,R(x,u,w)) \ v5
    ]]></literal>
    <justification jstring="[para(8381(a,1),15417(a,1,1))].">
      <j1 rule="para" parents="8381 15417"/>
    </justification>
  </clause>

  <clause id="15444">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) * a(x,y,y) = x * L(a(x,y,y),x,z)
    ]]></literal>
    <justification jstring="[para(14022(a,1),15358(a,1,1))].">
      <j1 rule="para" parents="14022 15358"/>
    </justification>
  </clause>

  <clause id="15445">
    <literal><![CDATA[
      L(x,a(y,y,x),z) = L(x,x,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,14746,a,b,15444,a)].">
      <j1 rule="hyper" parents="35 14746 15444"/>
    </justification>
  </clause>

  <clause id="15446">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) * (a(y,y,x) * z) = (x * a(y,y,x)) * z
    ]]></literal>
    <justification jstring="[para(15445(a,1),10590(a,1,1))].">
      <j1 rule="para" parents="15445 10590"/>
    </justification>
  </clause>

  <clause id="15450">
    <literal><![CDATA[
      (x * (y * a(z,y,a(x,z,y)))) * a(z,z,y) = x * (y * a(z,z,y))
    ]]></literal>
    <justification jstring="[para(14470(a,1),15365(a,1,1,2))].">
      <j1 rule="para" parents="14470 15365"/>
    </justification>
  </clause>

  <clause id="15452">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ a(x,x,a(z,y,y)) = a(z,y,L(x,u,w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,15428,a(flip),b,14393,a)].">
      <j1 rule="hyper" parents="133 15428 14393"/>
    </justification>
  </clause>

  <clause id="15453">
    <literal><![CDATA[
      a(L(x \ a(y,z,y),u,w),L(x \ a(y,z,y),u,w),a(v5,v6,v6)) * L(L(L(x \ a(y,z,y),u,w),v6,v5) \ L(x \ a(y,z,y),u,w),v7,v8) = a(v5,v6,L(L(x,u,w),v7,v8))
    ]]></literal>
    <justification jstring="[hyper(316,a,8091,a(flip),b,15429,a),flip(a)].">
      <j1 rule="hyper" parents="316 8091 15429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15454">
    <literal><![CDATA[
      a(x,x,a(L(y,z,u),y,y)) * L(L(x,y,L(y,z,u)) \ x,w,v5) = a(y,L(y,z,u),L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,1529,a(flip),b,15429,a),flip(a)].">
      <j1 rule="hyper" parents="316 1529 15429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15455">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * L(L(y,x,z) \ y,u,w) = a(z,x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15361,a,b,15429,a)].">
      <j1 rule="hyper" parents="63 15361 15429"/>
    </justification>
  </clause>

  <clause id="15456">
    <literal><![CDATA[
      a(L(x,y,z),(y * z) \ (z * (x * y)),a(u,w,w)) * L(L((y * z) \ (z * (x * y)),w,u) \ ((y * z) \ (z * (x * y))),v5,v6) = a(u,w,L((y * z) \ (z * (x * y)),v5,v6))
    ]]></literal>
    <justification jstring="[para(4640(a,1),15429(a,1,1))].">
      <j1 rule="para" parents="4640 15429"/>
    </justification>
  </clause>

  <clause id="15457">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) * L(L(x,y,z) \ x,u,w) = a(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(7280(a,1),15429(a,1,1))].">
      <j1 rule="para" parents="7280 15429"/>
    </justification>
  </clause>

  <clause id="15458">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) \ ((L(x,z,y) \ x) * (L(L(x,z,y) \ x,u,w) \ a(x,x,a(y,z,z)))) = a(y,z,L(x,u,w)) \ (a(x,x,a(y,z,z)) * (L(x,z,y) \ x))
    ]]></literal>
    <justification jstring="[para(15429(a,1),9170(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15429 9170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15459">
    <literal><![CDATA[
      a(x,y,L(z,u,x)) = a(z,z,a(x,y,y)) * (L(z,y,x) \ z)
    ]]></literal>
    <justification jstring="[para(9861(a,1),15429(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9861 15429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15460">
    <literal><![CDATA[
      a(x * R(y,z,u),x * L(y,z,u),a(w,v5,v5)) * L(L(x * R(y,z,u),v5,w) \ (x * R(y,z,u)),v6,v7) = a(w,v5,L(x * R(y,z,u),v6,v7))
    ]]></literal>
    <justification jstring="[para(12037(a,1),15429(a,1,1))].">
      <j1 rule="para" parents="12037 15429"/>
    </justification>
  </clause>

  <clause id="15461">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * L(L(z,y,x) \ z,u,w) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(15338(a,2),15429(a,1,1))].">
      <j1 rule="para" parents="15338 15429"/>
    </justification>
  </clause>

  <clause id="15463">
    <literal><![CDATA[
      a(x,y,L(z,u,x)) = z * (L(z,y,x) \ a(z,z,a(x,y,y)))
    ]]></literal>
    <justification jstring="[hyper(316,a,8670,a(flip),b,15459,a),flip(a)].">
      <j1 rule="hyper" parents="316 8670 15459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15464">
    <literal><![CDATA[
      a(x,y,L(z,u,x)) = z * (z \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(15367(a,1),15463(a,2,2))].">
      <j1 rule="para" parents="15367 15463"/>
    </justification>
  </clause>

  <clause id="15465">
    <literal><![CDATA[
      a(x,y,L(z,u,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,10,a(flip),b,15464,a),flip(a)].">
      <j1 rule="hyper" parents="316 10 15464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15480">
    <literal><![CDATA[
      a(x,y,(z * x) \ u) = a(x,y,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11881,a(flip),b,15465,a),flip(a)].">
      <j1 rule="hyper" parents="63 11881 15465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15485">
    <literal><![CDATA[
      a(x,y,x \ z) = a(x,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8605,a(flip),b,15465,a)].">
      <j1 rule="hyper" parents="63 8605 15465"/>
    </justification>
  </clause>

  <clause id="15491">
    <literal><![CDATA[
      a(x,y,L(L(z,x,u) \ z,w,v5)) = a(x,y,L(a(u,x,z),w,v5))
    ]]></literal>
    <justification jstring="[para(10006(a,1),15465(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10006 15465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15514">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,w),a(u,z,y),L(w,v5,a(y,z,u))) = L(x,L(w,v5,a(y,z,u)),a(u,z,y))
    ]]></literal>
    <justification jstring="[para(15465(a,1),14027(a,1,1,2))].">
      <j1 rule="para" parents="15465 14027"/>
    </justification>
  </clause>

  <clause id="15521">
    <literal><![CDATA[
      a(x,y,a(z \ u,w,z)) = a(x,y,a(z,w,z * u))
    ]]></literal>
    <justification jstring="[para(15485(a,1),13660(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15485 13660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15522">
    <literal><![CDATA[
      a(x,y,L(z * a(u,z,u * w),u,u \ w)) = a(x,y,L(z,u \ w,u))
    ]]></literal>
    <justification jstring="[para(15485(a,1),13880(a,1,3,1,2))].">
      <j1 rule="para" parents="15485 13880"/>
    </justification>
  </clause>

  <clause id="15523">
    <literal><![CDATA[
      a(x,y,L(z * L(z,x,u),w,v5)) = a(x,y,L(a(u,x,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,6000,a(flip),b,15491,a)].">
      <j1 rule="hyper" parents="63 6000 15491"/>
    </justification>
  </clause>

  <clause id="15524">
    <literal><![CDATA[
      (x * L(y,a(x,z,y),z)) * a(z,z,y) = x * (y * a(z,z,y))
    ]]></literal>
    <justification jstring="[para(13417(a,1),15450(a,1,1,2))].">
      <j1 rule="para" parents="13417 15450"/>
    </justification>
  </clause>

  <clause id="15525">
    <literal><![CDATA[
      (x * L(y,y,a(z,z,x))) * a(z,z,y) = x * (y * a(z,z,y))
    ]]></literal>
    <justification jstring="[para(15378(a,1),15524(a,1,1,2))].">
      <j1 rule="para" parents="15378 15524"/>
    </justification>
  </clause>

  <clause id="15526">
    <literal><![CDATA[
      a(x,y,a(y,R(z,u,w) \ v5,L(z,u,w) \ v5)) * L(L(R(z,u,w) \ v5,y,x) \ (R(z,u,w) \ v5),v6,v7) = a(x,y,L(R(z,u,w) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(9541(a,1),15461(a,1,1,3))].">
      <j1 rule="para" parents="9541 15461"/>
    </justification>
  </clause>

  <clause id="15527">
    <literal><![CDATA[
      a(x,y,a(y,z \ u,z \ u)) * L(L(z \ T(u,w),y,x) \ (z \ T(u,w)),v5,v6) = a(x,y,L(z \ u,v5,v6))
    ]]></literal>
    <justification jstring="[para(10617(a,2),15461(a,1,2,1))].">
      <j1 rule="para" parents="10617 15461"/>
    </justification>
  </clause>

  <clause id="15530">
    <literal><![CDATA[
      a(a(x,y,y),y \ x,z) \ 1 = z \ L(z,y \ x,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(227(a,1),15421(a,1,1)),flip(a)].">
      <j1 rule="para" parents="227 15421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15532">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L(x \ L(x,z,y),u,w) = a(y,z,L(x,u,w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,14531,a(flip),b,15452,a)].">
      <j1 rule="hyper" parents="63 14531 15452"/>
    </justification>
  </clause>

  <clause id="15535">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * a(a(z,y,y),x,x) = a(z,y,L(x,u,w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,14018,a(flip),b,15532,a)].">
      <j1 rule="hyper" parents="63 14018 15532"/>
    </justification>
  </clause>

  <clause id="15539">
    <literal><![CDATA[
      a(x,y,y) * (z * L(x,x,a(y,y,z))) = L(a(x,y,y),x,z) * (z * x)
    ]]></literal>
    <justification jstring="[para(14022(a,1),15357(a,1,2,2))].">
      <j1 rule="para" parents="14022 15357"/>
    </justification>
  </clause>

  <clause id="15540">
    <literal><![CDATA[
      a(x,y,y) * (z * L(x,x,a(y,y,z))) = z * (x * a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,2307,a(flip),b,15539,a),flip(a)].">
      <j1 rule="hyper" parents="316 2307 15539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15541">
    <literal><![CDATA[
      a(x,y,y) * (z * L(x,x,a(y,y,z))) = z * R(x,y,y)
    ]]></literal>
    <justification jstring="[para(2381(a,1),15540(a,2,2))].">
      <j1 rule="para" parents="2381 15540"/>
    </justification>
  </clause>

  <clause id="15542">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * (y * a(x,y,a(z,x,y))) = L(a(x,x,y) \ 1,y,z) * y
    ]]></literal>
    <justification jstring="[para(14470(a,1),15366(a,1,2))].">
      <j1 rule="para" parents="14470 15366"/>
    </justification>
  </clause>

  <clause id="15544">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * L(y,a(z,x,y),x) = L(a(x,x,y) \ 1,y,z) * y
    ]]></literal>
    <justification jstring="[para(13417(a,1),15542(a,1,2))].">
      <j1 rule="para" parents="13417 15542"/>
    </justification>
  </clause>

  <clause id="15545">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * L(y,y,a(x,x,z)) = L(a(x,x,y) \ 1,y,z) * y
    ]]></literal>
    <justification jstring="[para(15378(a,1),15544(a,1,2))].">
      <j1 rule="para" parents="15378 15544"/>
    </justification>
  </clause>

  <clause id="15546">
    <literal><![CDATA[
      a(x,x,y) \ L(y,y,a(x,x,z)) = L(a(x,x,y) \ 1,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,14391,a(flip),b,15545,a)].">
      <j1 rule="hyper" parents="63 14391 15545"/>
    </justification>
  </clause>

  <clause id="15548">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),y) \ L(y,z,u) = L(L(y,y \ L(y,z,u),x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13652,a(flip),b,15216,a)].">
      <j1 rule="hyper" parents="63 13652 15216"/>
    </justification>
  </clause>

  <clause id="15549">
    <literal><![CDATA[
      L(L(x,x \ L(x,y,z),u),y,z) = a(a(u,x,x),y,z) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(15315(a,1),15548(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15315 15548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15550">
    <literal><![CDATA[
      L(L(x,x \ L(x,y,z),u),y,z) = a(z,y,a(u,x,x)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,14440,a(flip),b,15549,a),flip(a)].">
      <j1 rule="hyper" parents="316 14440 15549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15551">
    <literal><![CDATA[
      L(x,y,z) * a(x \ L(x,y,z),x,u) = L(L(x,x \ L(x,y,z),u),y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,15370,a,b,15550,a)].">
      <j1 rule="hyper" parents="316 15370 15550"/>
    </justification>
  </clause>

  <clause id="15552">
    <literal><![CDATA[
      x * (a(y,z,a(x,u,w)) * (x \ L(x,v5,v6))) = a(y,z,a(x,u,w)) * L(x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,5131,a(flip),b,15251,a)].">
      <j1 rule="hyper" parents="63 5131 15251"/>
    </justification>
  </clause>

  <clause id="15553">
    <literal><![CDATA[
      L(x,y,z * (a(u,w,v5) \ 1)) = L(x,y,z * a(v5,w,u))
    ]]></literal>
    <justification jstring="[para(15389(a,1),15422(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="15389 15422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15554">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ v5) = L(x,y,v5 * a(w,u,z))
    ]]></literal>
    <justification jstring="[para(14393(a,1),15553(a,1,3))].">
      <j1 rule="para" parents="14393 15553"/>
    </justification>
  </clause>

  <clause id="15555">
    <literal><![CDATA[
      (R(x,y,z) \ x) * a(x \ L(x,y,z),u,w) = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(2295(a,1),15289(a,1,2))].">
      <j1 rule="para" parents="2295 15289"/>
    </justification>
  </clause>

  <clause id="15556">
    <literal><![CDATA[
      x * (R(x,y,z) \ L(x \ R(x,y,z),u,w)) = a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(34,a,1255,a,b,15555,a)].">
      <j1 rule="hyper" parents="34 1255 15555"/>
    </justification>
  </clause>

  <clause id="15558">
    <literal><![CDATA[
      (R(x,y,z) \ x) * L(x \ R(x,y,z),u,w) = a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9619,a,b,15556,a)].">
      <j1 rule="hyper" parents="63 9619 15556"/>
    </justification>
  </clause>

  <clause id="15560">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,w) * (x \ R(x,y,z)) = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(34,a,14378,a,b,15558,a)].">
      <j1 rule="hyper" parents="34 14378 15558"/>
    </justification>
  </clause>

  <clause id="15562">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * L(y \ R(y,x,z),u,w) = a(y,x,z) * a(y \ L(y,x,z),u,w)
    ]]></literal>
    <justification jstring="[para(15558(a,1),14820(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15558 14820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15563">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(u,w,x * L(x,y,z)) = L(x \ R(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13775,a(flip),b,15560,a)].">
      <j1 rule="hyper" parents="63 13775 15560"/>
    </justification>
  </clause>

  <clause id="15566">
    <literal><![CDATA[
      x \ ((y / x) \ R(y,z,u)) = L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9771,a(flip),b,15563,a)].">
      <j1 rule="hyper" parents="63 9771 15563"/>
    </justification>
  </clause>

  <clause id="15567">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ L(x \ R(x,y,z),u,w) = a(z,y,x * L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(133,a,15563,a(flip),b,15303,a)].">
      <j1 rule="hyper" parents="133 15563 15303"/>
    </justification>
  </clause>

  <clause id="15568">
    <literal><![CDATA[
      L((x * y) \ R(x * y,z,u),y,y) = y \ (x \ R(x * y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),15566(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 15566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15572">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (((y * x) \ y) * a(z,u,(w \ (v5 \ w)) * L((w * v5) \ w,v6,v7))) = a(((w * v5) \ w) \ L((w * v5) \ w,u,z),v6,v7)
    ]]></literal>
    <justification jstring="[para(7777(a,1),15297(a,1,2,2))].">
      <j1 rule="para" parents="7777 15297"/>
    </justification>
  </clause>

  <clause id="15573">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * (u * (L(R(x,z,y),w,v5) \ L(x,w,v5))) = a(L(x,w,v5),z,y) \ u
    ]]></literal>
    <justification jstring="[para(29(a,1),15430(a,1,2,2,1))].">
      <j1 rule="para" parents="29 15430"/>
    </justification>
  </clause>

  <clause id="15575">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) * L(x \ R(x,y,z),u,w) = a(x,y,z) * a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(15345(a,1),15562(a,1,1))].">
      <j1 rule="para" parents="15345 15562"/>
    </justification>
  </clause>

  <clause id="15576">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) * L(x \ R(x,y,z),u,w) = a(x,y,z) * a(z,y,x * L(x,u,w))
    ]]></literal>
    <justification jstring="[para(15295(a,1),15575(a,2,2))].">
      <j1 rule="para" parents="15295 15575"/>
    </justification>
  </clause>

  <clause id="15577">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) * a(x,x,a(y,y,z)) = a(x,y,z) * a(z,y,x * L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,2298,a,b,15576,a)].">
      <j1 rule="hyper" parents="63 2298 15576"/>
    </justification>
  </clause>

  <clause id="15578">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) * a(x,x,a(y,y,z)) = a(z,y,x * L(x,u,w)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2290,a,b,15577,a),flip(a)].">
      <j1 rule="hyper" parents="316 2290 15577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15579">
    <literal><![CDATA[
      (((x / y) * (y * a(z,y \ x,y))) / a(z,y \ x,y)) \ x = a(y \ x,a(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(316,a,12258,a(flip),b,15340,a),flip(a)].">
      <j1 rule="hyper" parents="316 12258 15340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15580">
    <literal><![CDATA[
      a(x,y,a(z,z,a(u,u,w))) * v5 = v5 * a(x,y,a(u,z,a(w,u,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14792,a(flip),b,15355,a)].">
      <j1 rule="hyper" parents="63 14792 15355"/>
    </justification>
  </clause>

  <clause id="15582">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * a(y \ L(y,z,u),w,v5) = x * L(x \ (x * (y \ L(y,z,u))),w,v5)
    ]]></literal>
    <justification jstring="[para(14358(a,1),15269(a,2,2,1,2))].">
      <j1 rule="para" parents="14358 15269"/>
    </justification>
  </clause>

  <clause id="15583">
    <literal><![CDATA[
      a(L(x,y,z),L(x,u,w),v5) \ v5 = L(v5,L(x,u,w),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5411,a(flip),b,15420,a),flip(a)].">
      <j1 rule="hyper" parents="63 5411 15420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15585">
    <literal><![CDATA[
      a(x,x,a(y,L(y,z,u),y)) * L(L(x,y,L(y,z,u)) \ x,w,v5) = a(y,L(y,z,u),L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(1529(a,1),15454(a,1,1,3))].">
      <j1 rule="para" parents="1529 15454"/>
    </justification>
  </clause>

  <clause id="15586">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * a(y \ L(y,z,u),w,v5) = x * L(y \ L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),15582(a,2,2,1))].">
      <j1 rule="para" parents="9 15582"/>
    </justification>
  </clause>

  <clause id="15588">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * L(y \ L(y,z,u),w,v5) = x * a(y \ L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(14369(a,1),15586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14369 15586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15589">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * a(x \ L(x,y,z),w,v5)) = L(L(x,y,z) / x,w,v5) * u
    ]]></literal>
    <justification jstring="[para(15588(a,1),14529(a,1,2))].">
      <j1 rule="para" parents="15588 14529"/>
    </justification>
  </clause>

  <clause id="15590">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * a(x \ L(x,y,z),w,v5)) = L(x \ L(x,y,z),w,v5) * u
    ]]></literal>
    <justification jstring="[para(1272(a,1),15589(a,2,1,1))].">
      <j1 rule="para" parents="1272 15589"/>
    </justification>
  </clause>

  <clause id="15591">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * a(w,v5,x * L(x,y,z))) = L(x \ L(x,y,z),v5,w) * u
    ]]></literal>
    <justification jstring="[para(13642(a,1),15590(a,1,2,2))].">
      <j1 rule="para" parents="13642 15590"/>
    </justification>
  </clause>

  <clause id="15592">
    <literal><![CDATA[
      1 * L(L(x,y,L(y,z,u)) \ x,w,v5) = a(y,L(y,z,u),L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(5410(a,1),15585(a,1,1))].">
      <j1 rule="para" parents="5410 15585"/>
    </justification>
  </clause>

  <clause id="15594">
    <literal><![CDATA[
      1 * L(a(x,L(x,y,z),u),w,v5) = a(x,L(x,y,z),L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(13815(a,1),15592(a,1,2,1))].">
      <j1 rule="para" parents="13815 15592"/>
    </justification>
  </clause>

  <clause id="15595">
    <literal><![CDATA[
      a(x,L(x,y,z),L(u,w,v5)) = L(a(x,L(x,y,z),u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(141,a,15594,a),flip(a)].">
      <j1 rule="hyper" parents="141 15594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15596">
    <literal><![CDATA[
      a(x * ((y * y) \ z),u,w) \ L(w,w,a(x * ((y * y) \ z),u,u)) = L(w,u,((y * y) \ x) * z)
    ]]></literal>
    <justification jstring="[para(12108(a,1),15395(a,1,2,3))].">
      <j1 rule="para" parents="12108 15395"/>
    </justification>
  </clause>

  <clause id="15597">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * (v5 * a(z,y,a(x,x,y))) = a(z,y,R(x,u,w)) \ v5
    ]]></literal>
    <justification jstring="[para(14217(a,1),15438(a,1,2,2,3))].">
      <j1 rule="para" parents="14217 15438"/>
    </justification>
  </clause>

  <clause id="15598">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * (v5 * a(z,y,a(x,x,y))) = a(z,y,L(x,u,w)) \ v5
    ]]></literal>
    <justification jstring="[para(5746(a,1),15597(a,2,1))].">
      <j1 rule="para" parents="5746 15597"/>
    </justification>
  </clause>

  <clause id="15600">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * (v5 * a(x,x,a(y,y,z))) = a(z,y,R(x,u,w)) \ v5
    ]]></literal>
    <justification jstring="[para(14217(a,1),15440(a,1,2,2))].">
      <j1 rule="para" parents="14217 15440"/>
    </justification>
  </clause>

  <clause id="15601">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * (v5 * a(x,x,a(y,y,z))) = a(z,y,L(x,u,w)) \ v5
    ]]></literal>
    <justification jstring="[para(5746(a,1),15600(a,2,1))].">
      <j1 rule="para" parents="5746 15600"/>
    </justification>
  </clause>

  <clause id="15604">
    <literal><![CDATA[
      L(x,y,((z * z) \ u) * w) = L(x,y,u * ((z * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15392,a(flip),b,15596,a),flip(a)].">
      <j1 rule="hyper" parents="63 15392 15596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15607">
    <literal><![CDATA[
      (R(x,y,z) * L(x \ L(x,L(x,y,z),a(u,u,w)),y,z)) \ R(R(x,y,z),u,w) = a(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(10977(a,1),15407(a,1,1,2,1,2))].">
      <j1 rule="para" parents="10977 15407"/>
    </justification>
  </clause>

  <clause id="15608">
    <literal><![CDATA[
      (R(x,y,z) * L(x \ L(x,x,L(a(u,u,w),y,z)),y,z)) \ R(R(x,y,z),u,w) = a(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(11920(a,1),15607(a,1,1,2,1,2))].">
      <j1 rule="para" parents="11920 15607"/>
    </justification>
  </clause>

  <clause id="15609">
    <literal><![CDATA[
      (R(x,y,z) * L(x \ L(x,x,a(u,u,L(w,y,z))),y,z)) \ R(R(x,y,z),u,w) = a(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(11868(a,2),15608(a,1,1,2,1,2,3))].">
      <j1 rule="para" parents="11868 15608"/>
    </justification>
  </clause>

  <clause id="15610">
    <literal><![CDATA[
      (R(x,y,z) * L(a(x,x,a(u,u,L(w,y,z))),y,z)) \ R(R(x,y,z),u,w) = a(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(7328(a,1),15609(a,1,1,2,1))].">
      <j1 rule="para" parents="7328 15609"/>
    </justification>
  </clause>

  <clause id="15611">
    <literal><![CDATA[
      (R(x,y,z) * a(x,x,L(a(u,u,L(w,y,z)),y,z))) \ R(R(x,y,z),u,w) = a(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(11868(a,2),15610(a,1,1,2))].">
      <j1 rule="para" parents="11868 15610"/>
    </justification>
  </clause>

  <clause id="15612">
    <literal><![CDATA[
      (R(x,y,z) * a(x,x,a(u,u,w))) \ R(R(x,y,z),u,w) = a(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(9943(a,1),15611(a,1,1,2,3))].">
      <j1 rule="para" parents="9943 15611"/>
    </justification>
  </clause>

  <clause id="15613">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) \ (R(x,u,w) \ R(R(x,u,w),y,z)) = a(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14476,a(flip),b,15612,a)].">
      <j1 rule="hyper" parents="63 14476 15612"/>
    </justification>
  </clause>

  <clause id="15615">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) \ (L(x,u,w) \ L(R(x,y,z),u,w)) = a(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(12497(a,1),15613(a,1,2))].">
      <j1 rule="para" parents="12497 15613"/>
    </justification>
  </clause>

  <clause id="15616">
    <literal><![CDATA[
      (L(x,y,z) \ L(R(x,u,w),y,z)) * a(x,x,a(u,u,w)) = a(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14470,a(flip),b,15615,a)].">
      <j1 rule="hyper" parents="63 14470 15615"/>
    </justification>
  </clause>

  <clause id="15617">
    <literal><![CDATA[
      (L(x,y,z) \ L(R(x,u,w),y,z)) * a(x,x,a(u,u,w)) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,4643,a(flip),b,15616,a),flip(a)].">
      <j1 rule="hyper" parents="316 4643 15616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15618">
    <literal><![CDATA[
      a(x,y * a(z,u,w),v5) * L(x,x,a(a(z,u,w) * y,a(z,u,w) \ y,v5)) = R(x,a(z,u,w) \ y,v5)
    ]]></literal>
    <justification jstring="[para(14435(a,1),15403(a,1,1))].">
      <j1 rule="para" parents="14435 15403"/>
    </justification>
  </clause>

  <clause id="15621">
    <literal><![CDATA[
      a(x,y * a(z,u,w),v5) * L(x,x,a(a(z,u,w) * y,y * a(z,u,w),v5)) = R(x,a(z,u,w) \ y,v5)
    ]]></literal>
    <justification jstring="[para(14435(a,1),15618(a,1,2,3))].">
      <j1 rule="para" parents="14435 15618"/>
    </justification>
  </clause>

  <clause id="15622">
    <literal><![CDATA[
      R(x,a(y,z,u) \ w,v5) = R(x,w * a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,15401,a(flip),b,15621,a),flip(a)].">
      <j1 rule="hyper" parents="63 15401 15621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15624">
    <literal><![CDATA[
      x * L(a(y \ L(y,z,u),w,v5),L(y,z,u) \ y,x) = (R(y,z,u) \ y) * (L(R(y,z,u) \ y,w,v5) \ x)
    ]]></literal>
    <justification jstring="[para(12609(a,1),15270(a,1,2))].">
      <j1 rule="para" parents="12609 15270"/>
    </justification>
  </clause>

  <clause id="15627">
    <literal><![CDATA[
      L(x,y,z * (y \ 1)) \ L(x,x,a(y \ z,y,y)) = (y * x) \ ((z * (1 / y)) \ (R(z,y \ 1,y) * x))
    ]]></literal>
    <justification jstring="[para(6952(a,1),15397(a,1,2,3))].">
      <j1 rule="para" parents="6952 15397"/>
    </justification>
  </clause>

  <clause id="15628">
    <literal><![CDATA[
      L(x,y,z * (y \ 1)) \ L(x,x,a(z,y,y)) = (y * x) \ ((z * (1 / y)) \ (R(z,y \ 1,y) * x))
    ]]></literal>
    <justification jstring="[para(8214(a,1),15627(a,1,2))].">
      <j1 rule="para" parents="8214 15627"/>
    </justification>
  </clause>

  <clause id="15629">
    <literal><![CDATA[
      L(x,y,z * (y \ 1)) \ L(x,x,a(z,y,y)) = a(z * (y \ 1),y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,8787,a(flip),b,15628,a),flip(a)].">
      <j1 rule="hyper" parents="316 8787 15628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15630">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,(((w \ 1) * v5) * v6) * v7) = L(x \ L(x,y,z),u,(v6 * (v5 * w)) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,15232,a(flip),b,15237,a),flip(a)].">
      <j1 rule="hyper" parents="63 15232 15237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15631">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((u * a(x,x,a(y,y,z))) * a(w,v5,x \ L(x,y,z))) = (a(z,y,x) \ u) * a(w,v5,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5566(a,1),15439(a,2,2))].">
      <j1 rule="para" parents="5566 15439"/>
    </justification>
  </clause>

  <clause id="15632">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((u * a(x,x,a(y,y,z))) * a(w,v5,x * L(x,y,z))) = (a(z,y,x) \ u) * a(w,v5,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5566(a,1),15631(a,1,2,2))].">
      <j1 rule="para" parents="5566 15631"/>
    </justification>
  </clause>

  <clause id="15633">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * (v5 * a(x,x,a(y,y,z))) = (a(z,y,x) \ v5) * a(w,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15591,a(flip),b,15632,a)].">
      <j1 rule="hyper" parents="63 15591 15632"/>
    </justification>
  </clause>

  <clause id="15634">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(w,v5,z * L(z,y,x)) = a(x,y,L(z,v5,w)) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,15601,a(flip),b,15633,a),flip(a)].">
      <j1 rule="hyper" parents="63 15601 15633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15635">
    <literal><![CDATA[
      a(x,y,z) \ a(u,w,z * L(z,y,x)) = a(x,y,L(z,w,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,14391,a(flip),b,15634,a)].">
      <j1 rule="hyper" parents="63 14391 15634"/>
    </justification>
  </clause>

  <clause id="15636">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ (a(x,y,z) * v5) = v5 * a(w,u,z * L(z,y,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),15634(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 15634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15638">
    <literal><![CDATA[
      (a(x,y,L(z,u,w)) \ v5) * a(v6,v7,L(z * L(z,y,x),u,w)) = a(x,y,L(L(z,u,w),v7,v6)) \ v5
    ]]></literal>
    <justification jstring="[para(7442(a,1),15634(a,1,2))].">
      <j1 rule="para" parents="7442 15634"/>
    </justification>
  </clause>

  <clause id="15641">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ ((a(x,y,z) * a(x,y,z)) * v5) = (a(x,y,z) * v5) * a(w,u,z * L(z,y,x))
    ]]></literal>
    <justification jstring="[para(14395(a,2),15636(a,1,2))].">
      <j1 rule="para" parents="14395 15636"/>
    </justification>
  </clause>

  <clause id="15643">
    <literal><![CDATA[
      (a(x,y,L(z,u,w)) \ v5) * a(u,w,L(z * L(z,y,x),u,w)) = a(x,y,u \ (w \ ((w * z) * u))) \ v5
    ]]></literal>
    <justification jstring="[para(11904(a,2),15638(a,2,1))].">
      <j1 rule="para" parents="11904 15638"/>
    </justification>
  </clause>

  <clause id="15645">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ u) * (L(x \ L(x,y,z),w,v5) \ (x \ L(x,y,z))) = (a(v5,w,x * L(x,y,z)) * u) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,14351,a(flip),b,15226,a),flip(a)].">
      <j1 rule="hyper" parents="316 14351 15226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15659">
    <literal><![CDATA[
      a(x,y,z * (((u * (w \ v5)) * v6) * v7)) * L(x,x,a(y,y,z * (((u * (w \ v5)) * v6) * v7))) = R(x,y,z * (((u * (v5 / w)) * v6) * v7))
    ]]></literal>
    <justification jstring="[para(9550(a,1),15402(a,1,2,3))].">
      <j1 rule="para" parents="9550 15402"/>
    </justification>
  </clause>

  <clause id="15660">
    <literal><![CDATA[
      R(x,y,z * (((u * (w / v5)) * v6) * v7)) = R(x,y,z * (((u * (v5 \ w)) * v6) * v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,15386,a,b,15659,a),flip(a)].">
      <j1 rule="hyper" parents="63 15386 15659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15661">
    <literal><![CDATA[
      a(((x * y) \ x) \ L((x * y) \ x,z,u),w,v5) = L(v6 \ 1,v6,v7) \ (((v7 * v6) \ v7) * a(u,z,x \ (y * (L(y,w,v5) \ x))))
    ]]></literal>
    <attribute><![CDATA[
      label(flip_matches_hint)
    ]]></attribute>
    <justification jstring="[para(14166(a,1),15572(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14166 15572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15662">
    <literal><![CDATA[
      a(((x * y) \ x) \ L((x * y) \ x,z,u),w,v5) = a(u,z,x \ (y * (L(y,w,v5) \ x)))
    ]]></literal>
    <justification jstring="[hyper(316,a,396,a(flip),b,15661,a),flip(a)].">
      <j1 rule="hyper" parents="316 396 15661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15663">
    <literal><![CDATA[
      a(x \ ((x / y) * L(y,z,u)),w,v5) = a(u,z,x \ (y * (L(y,w,v5) \ x)))
    ]]></literal>
    <justification jstring="[para(7148(a,1),15662(a,1,1))].">
      <j1 rule="para" parents="7148 15662"/>
    </justification>
  </clause>

  <clause id="15664">
    <literal><![CDATA[
      a(x \ ((y \ x) * L(y,z,u)),w,v5) = a(u,z,x \ (y * (L(y,w,v5) \ x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,4177,a(flip),b,15663,a)].">
      <j1 rule="hyper" parents="63 4177 15663"/>
    </justification>
  </clause>

  <clause id="15665">
    <literal><![CDATA[
      a(x \ (y * (L(y,z,u) \ x)),w,v5) = a(u,z,x \ (y * (L(y,w,v5) \ x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14325,a(flip),b,15664,a)].">
      <j1 rule="hyper" parents="63 14325 15664"/>
    </justification>
  </clause>

  <clause id="15670">
    <literal><![CDATA[
      a(x,y,z \ ((u * T(w,v5)) * (L(u * T(w,v5),v6,v7) \ ((w * u) * v8)))) = a(x,y,z \ (K(v5,w) * ((K(w,u) * v8) * L(u * T(w,v5),v6,v7))))
    ]]></literal>
    <justification jstring="[para(406(a,1),14169(a,2,3,2))].">
      <j1 rule="para" parents="406 14169"/>
    </justification>
  </clause>

  <clause id="15671">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * (u * w)) / (w * ((K(v5,v6) * (a(x,y,z) \ (v7 * v7))) * (v7 \ (v7 \ K(v6,v5))))) = R(u,w * (K(v5,v6) * (v7 * v7)),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(7072(a,1),15176(a,1,2))].">
      <j1 rule="para" parents="7072 15176"/>
    </justification>
  </clause>

  <clause id="15672">
    <literal><![CDATA[
      a(x,y,z \ ((u * T(w,v5)) * (L(u * T(w,v5),v6,v7) \ ((w * u) * v8)))) = a(x,y,z \ (K(v5,w) * (K(w,u) * (v8 * L(u * T(w,v5),v6,v7)))))
    ]]></literal>
    <justification jstring="[para(406(a,1),15670(a,2,3,2,2))].">
      <j1 rule="para" parents="406 15670"/>
    </justification>
  </clause>

  <clause id="15673">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * (u * w)) / (w * (K(v5,v6) * ((a(x,y,z) \ (v7 * v7)) * (v7 \ (v7 \ K(v6,v5)))))) = R(u,w * (K(v5,v6) * (v7 * v7)),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(406(a,1),15671(a,1,2,2))].">
      <j1 rule="para" parents="406 15671"/>
    </justification>
  </clause>

  <clause id="15674">
    <literal><![CDATA[
      a(x,y,z \ ((u * T(w,v5)) * (L(u * T(w,v5),v6,v7) \ ((w * u) * v8)))) = a(x,y,z \ (K(v5,w) * (v8 * L(u * T(w,v5),v6,v7))))
    ]]></literal>
    <justification jstring="[hyper(316,a,5509,a(flip),b,15672,a),flip(a)].">
      <j1 rule="hyper" parents="316 5509 15672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15676">
    <literal><![CDATA[
      a(x,y,z \ ((u * T(w,v5)) * (L(u * T(w,v5),v6,v7) \ ((w * u) * v8)))) = a(x,y,z \ (v8 * L(u * T(w,v5),v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5496,a(flip),b,15674,a),flip(a)].">
      <j1 rule="hyper" parents="316 5496 15674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15678">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * (L(u * w,v5,v6) \ ((w * u) * v7)))) = a(x,y,z \ (v7 * L(u * T(w,v8),v5,v6)))
    ]]></literal>
    <justification jstring="[para(10578(a,1),15676(a,1,3,2))].">
      <j1 rule="para" parents="10578 15676"/>
    </justification>
  </clause>

  <clause id="15680">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * ((w * u) * (L(u * w,v5,v6) \ v7)))) = a(x,y,z \ (v7 * L(u * T(w,v8),v5,v6)))
    ]]></literal>
    <justification jstring="[para(12945(a,1),15678(a,1,3,2,2))].">
      <j1 rule="para" parents="12945 15678"/>
    </justification>
  </clause>

  <clause id="15681">
    <literal><![CDATA[
      a(x,y,z \ ((L(1 / (u * w),v5,v6) \ 1) * v7)) = a(x,y,z \ (v7 * L(w * T(u,v8),v5,v6)))
    ]]></literal>
    <justification jstring="[para(13837(a,1),15680(a,1,3,2))].">
      <j1 rule="para" parents="13837 15680"/>
    </justification>
  </clause>

  <clause id="15682">
    <literal><![CDATA[
      a(x,y,z \ (L(1 / (u * w),v5,v6) * v7)) = a(x,y,z \ (v7 * L(w * T(u,v8),v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6682,a(flip),b,15681,a)].">
      <j1 rule="hyper" parents="63 6682 15681"/>
    </justification>
  </clause>

  <clause id="15683">
    <literal><![CDATA[
      a(x,y,z \ (L((u * w) \ 1,v5,v6) * v7)) = a(x,y,z \ (v7 * L(w * T(u,v8),v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5729,a(flip),b,15682,a)].">
      <j1 rule="hyper" parents="63 5729 15682"/>
    </justification>
  </clause>

  <clause id="15684">
    <literal><![CDATA[
      a(x,y,z \ (u * L(w * T(v5,v6),v7,v8))) = a(x,y,z \ (L(v5 * w,v7,v8) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7620,a(flip),b,15683,a),flip(a)].">
      <j1 rule="hyper" parents="63 7620 15683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15685">
    <literal><![CDATA[
      R(x,y * (K(z,u) * (w * w)),a(v5,v6,v7)) = ((a(v5,v6,v7) \ 1) * (x * y)) / (y * (K(z,u) * (a(v5,v6,v7) \ K(u,z))))
    ]]></literal>
    <justification jstring="[para(4258(a,1),15673(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4258 15673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15686">
    <literal><![CDATA[
      R(x,y * (K(z,u) * (w * w)),a(v5,v6,v7)) = ((a(v5,v6,v7) \ 1) * (x * y)) / (y * (a(v5,v6,v7) \ 1))
    ]]></literal>
    <justification jstring="[para(2980(a,1),15685(a,2,2,2))].">
      <j1 rule="para" parents="2980 15685"/>
    </justification>
  </clause>

  <clause id="15688">
    <literal><![CDATA[
      R(x,y * (K(z,u) * (w * w)),a(v5,v6,v7)) = R(x,y,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(316,a,7549,a(flip),b,15686,a),flip(a)].">
      <j1 rule="hyper" parents="316 7549 15686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15690">
    <literal><![CDATA[
      R(x,y * (z * z),a(u,w,v5)) = R(x,y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,10742,a(flip),b,15688,a)].">
      <j1 rule="hyper" parents="63 10742 15688"/>
    </justification>
  </clause>

  <clause id="15691">
    <literal><![CDATA[
      L(x,y * (z * z),a(u,w,v5)) = R(x,y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5371,a(flip),b,15690,a)].">
      <j1 rule="hyper" parents="63 5371 15690"/>
    </justification>
  </clause>

  <clause id="15693">
    <literal><![CDATA[
      L(x,y * (z * z),a(u,w,v5)) = L(x,y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,5371,a(flip),b,15691,a),flip(a)].">
      <j1 rule="hyper" parents="316 5371 15691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15694">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,a(u,w,v5)) = L(x,y \ z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,10965,a(flip),b,15693,a)].">
      <j1 rule="hyper" parents="63 10965 15693"/>
    </justification>
  </clause>

  <clause id="15695">
    <literal><![CDATA[
      L(x,(y \ 1) * z,a(u,w,v5)) = L(x,z * y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,10937,a(flip),b,15693,a),flip(a)].">
      <j1 rule="hyper" parents="63 10937 15693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15697">
    <literal><![CDATA[
      L(x,y * (y * z),a(u,w,v5)) = L(x,L(z,y,y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,10920,a(flip),b,15693,a)].">
      <j1 rule="hyper" parents="63 10920 15693"/>
    </justification>
  </clause>

  <clause id="15698">
    <literal><![CDATA[
      L(x,(y * y) \ z,a(u,w,v5)) = L(x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,10799,a(flip),b,15693,a),flip(a)].">
      <j1 rule="hyper" parents="63 10799 15693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15699">
    <literal><![CDATA[
      L(x,y \ 1,a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(229(a,1),15693(a,1,2)),flip(a)].">
      <j1 rule="para" parents="229 15693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15700">
    <literal><![CDATA[
      L(x,y \ (z \ 1),a(u,w,v5)) = L(x,y \ z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(584(a,1),15693(a,1,2)),flip(a)].">
      <j1 rule="para" parents="584 15693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15701">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,(y * (v5 * v5)) * a(z,u,w)) = a(x,y * (v5 * v5),a(z,u,w))
    ]]></literal>
    <justification jstring="[para(15693(a,1),5385(a,1,1,2))].">
      <j1 rule="para" parents="15693 5385"/>
    </justification>
  </clause>

  <clause id="15702">
    <literal><![CDATA[
      L(x,L(L(y,z,z),z,z),a(u,w,v5)) = L(x,y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(8599(a,1),15693(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8599 15693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15709">
    <literal><![CDATA[
      L(T(x,x \ 1),x,a(y,z,u)) = L(x,x,x \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7173,a(flip),b,15699,a),flip(a)].">
      <j1 rule="hyper" parents="63 7173 15699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15711">
    <literal><![CDATA[
      L(x,L((y \ 1) \ z,u,w),a(v5,v6,v7)) = L(x,L(y \ z,u,w),a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,11494,a(flip),b,15698,a),flip(a)].">
      <j1 rule="hyper" parents="63 11494 15698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15716">
    <literal><![CDATA[
      L(x,a(y,z,u) \ u,a(w,v5,v6)) = L(x,u * a(y,z,u),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(6890(a,1),15694(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6890 15694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15718">
    <literal><![CDATA[
      L(x,y * (z \ 1),a(u,w,v5)) = L(x,z * y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,10807,a(flip),b,15695,a),flip(a)].">
      <j1 rule="hyper" parents="63 10807 15695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15719">
    <literal><![CDATA[
      L(x \ L(x,y * z,a(u,w,v5)),x,((z \ 1) * y) * a(u,w,v5)) = a(x,(z \ 1) * y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(15695(a,1),5385(a,1,1,2))].">
      <j1 rule="para" parents="15695 5385"/>
    </justification>
  </clause>

  <clause id="15720">
    <literal><![CDATA[
      x \ L(x,x,x \ a(y,z,u)) = x * L(1 / x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(15709(a,1),4468(a,1,2))].">
      <j1 rule="para" parents="15709 4468"/>
    </justification>
  </clause>

  <clause id="15721">
    <literal><![CDATA[
      L(x,L(y,z,u) * (u * z),a(w,v5,v6)) = L(x,((u * (z * y)) / y) * (y \ 1),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(4415(a,2),15718(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4415 15718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15722">
    <literal><![CDATA[
      L(x,L(L(y \ z,u,w),y,y),a(v5,v6,v7)) = L(x,L(y * z,u,w),a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(1356(a,1),15697(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1356 15697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15724">
    <literal><![CDATA[
      a(x,x \ 1,a(y,z,u) * x) = x \ L(x,x,x \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,8529,a,b,15720,a)].">
      <j1 rule="hyper" parents="316 8529 15720"/>
    </justification>
  </clause>

  <clause id="15725">
    <literal><![CDATA[
      x \ L(x,x,x \ a(y,x,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,11903,a(flip),b,15724,a),flip(a)].">
      <j1 rule="hyper" parents="63 11903 15724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15727">
    <literal><![CDATA[
      L(x,y * a(z,y,y),a(u,w,v5)) = L(x,L(y,y,z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(7297(a,1),15716(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7297 15716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15728">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u),a(w,v5,v6)) = L(x,L(y,z,u),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,10837,a(flip),b,15711,a),flip(a)].">
      <j1 rule="hyper" parents="63 10837 15711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15729">
    <literal><![CDATA[
      L(x,L(y * z,y,y),a(u,w,v5)) = L(x,y \ z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,15702,a(flip),b,15722,a),flip(a)].">
      <j1 rule="hyper" parents="63 15702 15722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15730">
    <literal><![CDATA[
      L(x * y,x,x) \ L(L(x * y,x,x),x \ y,a(z,u,w)) = a(x * y,x * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(15729(a,1),11925(a,1,2))].">
      <j1 rule="para" parents="15729 11925"/>
    </justification>
  </clause>

  <clause id="15731">
    <literal><![CDATA[
      L(x,(y * (z * u)) / (u * u),a(w,v5,v6)) = L(x,L(u,z,y) * (y * z),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(566(a,1),15721(a,2,2)),flip(a)].">
      <j1 rule="para" parents="566 15721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15732">
    <literal><![CDATA[
      L(x,L(y,z,u) * (u * z),a(w,v5,v6)) = L(x,u * ((z * y) / (y * y)),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(683(a,1),15731(a,1,2)),flip(a)].">
      <j1 rule="para" parents="683 15731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15733">
    <literal><![CDATA[
      L(x,L(y,z,u) * (u * z),a(w,v5,v6)) = L(x,u * (z * (y \ 1)),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(562(a,1),15732(a,2,2,2))].">
      <j1 rule="para" parents="562 15732"/>
    </justification>
  </clause>

  <clause id="15734">
    <literal><![CDATA[
      L(x,y * (z * (u \ 1)),a(w,v5,v6)) = L(x,y * (z * u),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,10814,a(flip),b,15733,a),flip(a)].">
      <j1 rule="hyper" parents="63 10814 15733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15735">
    <literal><![CDATA[
      L(x,((y \ 1) * z) * u,a(w,v5,v6)) = L(x,u * (z * y),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,10883,a,b,15734,a)].">
      <j1 rule="hyper" parents="63 10883 15734"/>
    </justification>
  </clause>

  <clause id="15736">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,y * ((v5 * v5) * a(z,u,w))) = a(x,y * (v5 * v5),a(z,u,w))
    ]]></literal>
    <justification jstring="[para(2620(a,1),15701(a,1,3))].">
      <j1 rule="para" parents="2620 15701"/>
    </justification>
  </clause>

  <clause id="15737">
    <literal><![CDATA[
      L((x * y) \ L(x * y,x \ y,a(z,u,w)),x,x) = a(x * y,x * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,2136,a(flip),b,15730,a)].">
      <j1 rule="hyper" parents="63 2136 15730"/>
    </justification>
  </clause>

  <clause id="15738">
    <literal><![CDATA[
      x \ (y * L(y \ x,x \ y,a(z,u,w))) = a(x * y,x * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12508,a(flip),b,15737,a)].">
      <j1 rule="hyper" parents="63 12508 15737"/>
    </justification>
  </clause>

  <clause id="15739">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,y * a(z,u,w)) = a(x,y * (v5 * v5),a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8783,a(flip),b,15736,a)].">
      <j1 rule="hyper" parents="63 8783 15736"/>
    </justification>
  </clause>

  <clause id="15741">
    <literal><![CDATA[
      a(x,y * (z * z),a(u,w,v5)) = a(x,y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5385,a(flip),b,15739,a),flip(a)].">
      <j1 rule="hyper" parents="63 5385 15739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15742">
    <literal><![CDATA[
      a(x,(y \ 1) \ z,a(u,w,v5)) = a(x,y \ z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,11255,a(flip),b,15741,a)].">
      <j1 rule="hyper" parents="63 11255 15741"/>
    </justification>
  </clause>

  <clause id="15743">
    <literal><![CDATA[
      a(x,y \ 1,a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(229(a,1),15741(a,1,2)),flip(a)].">
      <j1 rule="para" parents="229 15741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15744">
    <literal><![CDATA[
      a(x,1 / y,a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(233(a,1),15741(a,1,2))].">
      <j1 rule="para" parents="233 15741"/>
    </justification>
  </clause>

  <clause id="15745">
    <literal><![CDATA[
      a(x,y \ (z \ 1),a(u,w,v5)) = a(x,y \ z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(584(a,1),15741(a,1,2)),flip(a)].">
      <j1 rule="para" parents="584 15741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15746">
    <literal><![CDATA[
      a(x,y \ (z \ (u \ 1)),a(w,v5,v6)) = a(x,y \ (z \ u),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(591(a,1),15741(a,1,2)),flip(a)].">
      <j1 rule="para" parents="591 15741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15748">
    <literal><![CDATA[
      a(x,y * (L(y,z,u) \ y),a(w,v5,v6)) = a(x,L(y \ 1,z,u),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(4459(a,1),15743(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4459 15743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15750">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),a(w,v5,v6)) = a(x,y * L(y,z,u),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(4590(a,1),15742(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4590 15742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15752">
    <literal><![CDATA[
      (x \ y) / (a(z,x \ y,a(u,w,v5)) * (x \ y)) = a(a(u,w,v5),(x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(15742(a,1),12884(a,1,2,1))].">
      <j1 rule="para" parents="15742 12884"/>
    </justification>
  </clause>

  <clause id="15753">
    <literal><![CDATA[
      a(x \ y,x \ y,a(z,u,w)) \ a(z,u,w) = L(a(z,u,w),(x \ 1) \ y,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(15742(a,1),13028(a,1,1))].">
      <j1 rule="para" parents="15742 13028"/>
    </justification>
  </clause>

  <clause id="15754">
    <literal><![CDATA[
      a(x,y \ z,a(u,w,v5)) * a(u,w,v5) = L(a(u,w,v5),(y \ 1) \ z,x)
    ]]></literal>
    <justification jstring="[para(15742(a,1),14597(a,1,1))].">
      <j1 rule="para" parents="15742 14597"/>
    </justification>
  </clause>

  <clause id="15755">
    <literal><![CDATA[
      a(x,y \ (z \ 1),a(u,w,v5)) = a(a(u,w,v5),y \ z,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,13734,a,b,15745,a),flip(a)].">
      <j1 rule="hyper" parents="316 13734 15745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15756">
    <literal><![CDATA[
      a(x,(y \ 1) \ (z \ (y \ 1)),a(u,w,v5)) = a(x,((y \ 1) * z) \ y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,11374,a(flip),b,15745,a)].">
      <j1 rule="hyper" parents="63 11374 15745"/>
    </justification>
  </clause>

  <clause id="15757">
    <literal><![CDATA[
      a(x,((y \ 1) * (((y \ 1) * z) \ z)) \ y,a(u,w,v5)) = a(x,1 / (((y \ 1) * z) \ z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(6277(a,1),15745(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6277 15745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15758">
    <literal><![CDATA[
      x \ (y * L(y \ x,x \ y,a(z,u,w))) = a(x \ y,x \ (y \ 1),a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,7320,a,b,15755,a)].">
      <j1 rule="hyper" parents="316 7320 15755"/>
    </justification>
  </clause>

  <clause id="15762">
    <literal><![CDATA[
      L(a(x,y,z),(u \ 1) \ w,v5) = L(a(x,y,z),u \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,14597,a(flip),b,15754,a),flip(a)].">
      <j1 rule="hyper" parents="63 14597 15754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15763">
    <literal><![CDATA[
      a(x,L(y \ 1,z,u),a(w,v5,v6)) = a(x,L(y,z,u),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,14005,a(flip),b,15748,a),flip(a)].">
      <j1 rule="hyper" parents="63 14005 15748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15765">
    <literal><![CDATA[
      (x \ y) \ (a(z,x \ y,a(u,w,v5)) \ (x \ y)) = a(a(u,w,v5),(x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5061,a(flip),b,15752,a)].">
      <j1 rule="hyper" parents="63 5061 15752"/>
    </justification>
  </clause>

  <clause id="15766">
    <literal><![CDATA[
      a(x,((y \ 1) * z) \ y,a(u,w,v5)) = a(x,y \ (z \ (y \ 1)),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,15742,a(flip),b,15756,a),flip(a)].">
      <j1 rule="hyper" parents="63 15742 15756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15767">
    <literal><![CDATA[
      a(x,((y \ 1) * z) \ y,a(u,w,v5)) = a(x,y \ (z \ y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,15746,a(flip),b,15766,a),flip(a)].">
      <j1 rule="hyper" parents="316 15746 15766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15768">
    <literal><![CDATA[
      a(x \ y,x \ (y \ 1),a(z,u,w)) = a(x * y,x * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15738,a(flip),b,15758,a),flip(a)].">
      <j1 rule="hyper" parents="63 15738 15758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15769">
    <literal><![CDATA[
      a(x \ y,x \ y,a(z,u,w)) = a(x * y,x * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15745,a(flip),b,15768,a)].">
      <j1 rule="hyper" parents="63 15745 15768"/>
    </justification>
  </clause>

  <clause id="15770">
    <literal><![CDATA[
      a(x \ y,z,a(u,x \ y,z)) = a(x * y,x * y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15342,a,b,15769,a)].">
      <j1 rule="hyper" parents="63 15342 15769"/>
    </justification>
  </clause>

  <clause id="15772">
    <literal><![CDATA[
      a(x * y,x * y,a(z,x,x)) = a(y,x,a(z,x \ y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9988,a(flip),b,15770,a),flip(a)].">
      <j1 rule="hyper" parents="63 9988 15770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15773">
    <literal><![CDATA[
      a(x * y,x * y,a(z,y,y)) = a(x,y,a(z,y \ x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,11225,a,b,15772,a)].">
      <j1 rule="hyper" parents="63 11225 15772"/>
    </justification>
  </clause>

  <clause id="15774">
    <literal><![CDATA[
      a(x,y,a(z,y \ x,y)) = a(z,y,a(x,y * x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15349,a(flip),b,15773,a),flip(a)].">
      <j1 rule="hyper" parents="63 15349 15773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15775">
    <literal><![CDATA[
      a(a(x,y,z),(u \ 1) \ w,v5) = a(a(x,y,z),u \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,9442,a(flip),b,15765,a),flip(a)].">
      <j1 rule="hyper" parents="63 9442 15765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15777">
    <literal><![CDATA[
      L(a(x,y,z),(u \ 1) \ w,(u \ 1) \ w) = L(a(x,y,z),u \ w,u \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14579,a(flip),b,15753,a),flip(a)].">
      <j1 rule="hyper" parents="63 14579 15753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15778">
    <literal><![CDATA[
      L(a(x,y,z),u \ w,u \ w) = L(a(x,y,z),u * w,u * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14241,a(flip),b,15777,a),flip(a)].">
      <j1 rule="hyper" parents="63 14241 15777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15782">
    <literal><![CDATA[
      L(x \ L(x,y * z,a(u,w,v5)),x,a(u,w,v5) * (y * z)) = a(x,(z \ 1) * y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,8853,a(flip),b,15719,a)].">
      <j1 rule="hyper" parents="63 8853 15719"/>
    </justification>
  </clause>

  <clause id="15783">
    <literal><![CDATA[
      a(x,(y \ 1) * z,a(u,w,v5)) = a(x,z * y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,5386,a(flip),b,15782,a),flip(a)].">
      <j1 rule="hyper" parents="63 5386 15782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15784">
    <literal><![CDATA[
      a(x,y * (z \ 1),a(u,w,v5)) = a(x,y * z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,11190,a,b,15783,a)].">
      <j1 rule="hyper" parents="63 11190 15783"/>
    </justification>
  </clause>

  <clause id="15785">
    <literal><![CDATA[
      a(x,(y * z) * z,a(u,w,v5)) = a(x,L(y,z,z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,11310,a(flip),b,15783,a),flip(a)].">
      <j1 rule="hyper" parents="63 11310 15783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15786">
    <literal><![CDATA[
      a(x,y * z,a(u,w,v5)) * a(u,w,v5) = L(a(u,w,v5),y * (z \ 1),x)
    ]]></literal>
    <justification jstring="[para(15784(a,1),14597(a,1,1))].">
      <j1 rule="para" parents="15784 14597"/>
    </justification>
  </clause>

  <clause id="15787">
    <literal><![CDATA[
      a(x,y * (z * y),a(u,w,v5)) = a(x,L(z,y,y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,11190,a,b,15785,a)].">
      <j1 rule="hyper" parents="63 11190 15785"/>
    </justification>
  </clause>

  <clause id="15788">
    <literal><![CDATA[
      a(x,L(y \ z,y,y),a(u,w,v5)) = a(x,y * z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,11270,a(flip),b,15785,a),flip(a)].">
      <j1 rule="hyper" parents="63 11270 15785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15789">
    <literal><![CDATA[
      a(x,L(((y \ 1) * z) \ u,y \ z,y \ z),a(w,v5,v6)) = a(x,((y \ 1) * z) * u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(14237(a,1),15788(a,1,2))].">
      <j1 rule="para" parents="14237 15788"/>
    </justification>
  </clause>

  <clause id="15790">
    <literal><![CDATA[
      L(a(x,y,z),u * (w \ 1),v5) = L(a(x,y,z),u * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,14597,a(flip),b,15786,a),flip(a)].">
      <j1 rule="hyper" parents="63 14597 15786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15791">
    <literal><![CDATA[
      L(a(x,y,z),(u \ 1) * w,v5) = L(a(x,y,z),w * u,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10797,a,b,15790,a)].">
      <j1 rule="hyper" parents="63 10797 15790"/>
    </justification>
  </clause>

  <clause id="15792">
    <literal><![CDATA[
      a(x,L(((y \ 1) * z) \ u,z * y,z * y),a(w,v5,v6)) = a(x,((y \ 1) * z) * u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,15073,a(flip),b,15789,a)].">
      <j1 rule="hyper" parents="63 15073 15789"/>
    </justification>
  </clause>

  <clause id="15793">
    <literal><![CDATA[
      a(x,((y \ 1) * (((y \ 1) * z) \ z)) \ y,a(u,w,v5)) = a(x,(((1 / y) * z) \ z) \ 1,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(2606(a,1),15757(a,2,2))].">
      <j1 rule="para" parents="2606 15757"/>
    </justification>
  </clause>

  <clause id="15794">
    <literal><![CDATA[
      a(x,((y \ 1) * (((y \ 1) * z) \ z)) \ y,a(u,w,v5)) = a(x,((1 / y) * z) \ z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,15743,a(flip),b,15793,a),flip(a)].">
      <j1 rule="hyper" parents="316 15743 15793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15795">
    <literal><![CDATA[
      a(x,((y \ 1) * (((y \ 1) * z) \ z)) \ y,a(u,w,v5)) = a(x,z \ ((1 / y) \ z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,11375,a(flip),b,15794,a),flip(a)].">
      <j1 rule="hyper" parents="316 11375 15794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15796">
    <literal><![CDATA[
      a(x,((y \ 1) * (((y \ 1) * z) \ z)) \ y,a(u,w,v5)) = a(x,z \ ((y \ 1) \ z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,11267,a(flip),b,15795,a),flip(a)].">
      <j1 rule="hyper" parents="316 11267 15795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15797">
    <literal><![CDATA[
      a(x,(((y / z) / y) * z) \ z,a(u,w,v5)) = a(x,y \ ((z \ 1) \ y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(11457(a,1),15796(a,1,2,1))].">
      <j1 rule="para" parents="11457 15796"/>
    </justification>
  </clause>

  <clause id="15798">
    <literal><![CDATA[
      a(x,y \ (((z / y) / z) \ y),a(u,w,v5)) = a(x,z \ ((y \ 1) \ z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,11375,a(flip),b,15797,a)].">
      <j1 rule="hyper" parents="63 11375 15797"/>
    </justification>
  </clause>

  <clause id="15799">
    <literal><![CDATA[
      a(x,y \ ((z \ (z / y)) \ y),a(u,w,v5)) = a(x,z \ ((y \ 1) \ z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,11267,a(flip),b,15798,a)].">
      <j1 rule="hyper" parents="63 11267 15798"/>
    </justification>
  </clause>

  <clause id="15800">
    <literal><![CDATA[
      a(x,y \ ((z / y) \ (z * y)),a(u,w,v5)) = a(x,z \ ((y \ 1) \ z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(12166(a,1),15799(a,1,2,2))].">
      <j1 rule="para" parents="12166 15799"/>
    </justification>
  </clause>

  <clause id="15811">
    <literal><![CDATA[
      (L(a(x,x,y),L(y,x,x),L(y,x,x) \ z) * z) \ (a(x,x,y) * z) = ((L(y,x,x) \ z) * y) \ (a(x,x,y) * ((y \ z) * y))
    ]]></literal>
    <justification jstring="[para(4409(a,1),6775(a,2,2,2))].">
      <j1 rule="para" parents="4409 6775"/>
    </justification>
  </clause>

  <clause id="15812">
    <literal><![CDATA[
      ((L(x,y,y) \ z) * x) \ (a(y,y,x) * ((x \ z) * x)) = ((z / L(x,y,y)) * (L(x,y,y) * a(y,y,x))) \ (a(y,y,x) * z)
    ]]></literal>
    <justification jstring="[para(2435(a,1),15811(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2435 15811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15814">
    <literal><![CDATA[
      ((L(x,y,y) \ z) * x) \ (a(y,y,x) * ((x \ z) * x)) = ((z / L(x,y,y)) * x) \ (a(y,y,x) * z)
    ]]></literal>
    <justification jstring="[para(4953(a,1),15812(a,2,1,2))].">
      <j1 rule="para" parents="4953 15812"/>
    </justification>
  </clause>

  <clause id="15815">
    <literal><![CDATA[
      ((L(x,y,y) \ z) * x) \ (a(y,y,x) * ((x \ z) * x)) = (x * (L(x,y,y) \ z)) \ (a(y,y,x) * z)
    ]]></literal>
    <justification jstring="[para(4327(a,1),15814(a,2,1))].">
      <j1 rule="para" parents="4327 15814"/>
    </justification>
  </clause>

  <clause id="15816">
    <literal><![CDATA[
      ((L(x,y,y) \ z) * x) \ (a(y,y,x) * ((x \ z) * x)) = x \ ((a(y,y,x) * z) / (L(x,y,y) \ z))
    ]]></literal>
    <justification jstring="[hyper(316,a,9615,a(flip),b,15815,a),flip(a)].">
      <j1 rule="hyper" parents="316 9615 15815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15817">
    <literal><![CDATA[
      x * (x \ ((a(y,y,x) * z) / (L(x,y,y) \ z))) = (z / L(x,y,y)) \ (z * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(15816(a,1),13311(a,1,2))].">
      <j1 rule="para" parents="15816 13311"/>
    </justification>
  </clause>

  <clause id="15818">
    <literal><![CDATA[
      (a(x,x,y) * z) / (L(y,x,x) \ z) = (z / L(y,x,x)) \ (z * a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(270,a,15817,a)].">
      <j1 rule="hyper" parents="270 15817"/>
    </justification>
  </clause>

  <clause id="15820">
    <literal><![CDATA[
      (x * (L(x,y,y) \ z)) \ (a(y,y,x) * z) = x \ ((z / L(x,y,y)) \ (z * a(y,y,x)))
    ]]></literal>
    <justification jstring="[para(15818(a,1),9615(a,2,2))].">
      <j1 rule="para" parents="15818 9615"/>
    </justification>
  </clause>

  <clause id="15821">
    <literal><![CDATA[
      (x * (L(x,y,y) \ z)) \ (z * a(y,y,x)) = x \ ((z / L(x,y,y)) \ (z * a(y,y,x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,2296,a(flip),b,15820,a)].">
      <j1 rule="hyper" parents="63 2296 15820"/>
    </justification>
  </clause>

  <clause id="15822">
    <literal><![CDATA[
      T(x \ ((y / L(x,z,z)) \ (y * a(z,z,x))),K(u,w)) = a(L(x,z,z) \ y,L(x,z,z),a(z,z,x))
    ]]></literal>
    <justification jstring="[para(15820(a,1),12760(a,1,1))].">
      <j1 rule="para" parents="15820 12760"/>
    </justification>
  </clause>

  <clause id="15823">
    <literal><![CDATA[
      x \ ((y / L(x,z,z)) \ (y * a(z,z,x))) = a(y,a(z,z,x),L(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7020,a(flip),b,15821,a),flip(a)].">
      <j1 rule="hyper" parents="63 7020 15821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15824">
    <literal><![CDATA[
      T(a(x,a(y,y,z),L(z,y,y)),K(u,w)) = a(L(z,y,y) \ x,L(z,y,y),a(y,y,z))
    ]]></literal>
    <justification jstring="[para(15823(a,1),15822(a,1,1))].">
      <j1 rule="para" parents="15823 15822"/>
    </justification>
  </clause>

  <clause id="15825">
    <literal><![CDATA[
      a(L(x,y,y) \ z,L(x,y,y),a(y,y,x)) = a(z,a(y,y,x),L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(10368,a,15824,a),flip(a)].">
      <j1 rule="hyper" parents="10368 15824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15827">
    <literal><![CDATA[
      a(L(x,y,y) \ z,a(y,y,x),L(x,y,y)) = a(z,a(y,y,x),L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8984,a(flip),b,15825,a)].">
      <j1 rule="hyper" parents="63 8984 15825"/>
    </justification>
  </clause>

  <clause id="15828">
    <literal><![CDATA[
      (x * (a(y,y,x) \ (L(x,y,y) \ z))) \ z = a(z,a(y,y,x),L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,9643,a(flip),b,15827,a)].">
      <j1 rule="hyper" parents="63 9643 15827"/>
    </justification>
  </clause>

  <clause id="15829">
    <literal><![CDATA[
      a(x,a(y,y,a(y,y,z) * z),L(a(y,y,z) * z,y,y)) = ((a(y,y,z) * z) * (a(y,y,a(y,y,z) * z) \ (z \ x))) \ x
    ]]></literal>
    <justification jstring="[para(8615(a,1),15828(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8615 15828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15830">
    <literal><![CDATA[
      a(x,a(y,y,a(y,y,z) * z),L(a(y,y,z) * z,y,y)) = ((a(y,y,z) * z) * (a(y,y,L(z,y,y)) \ (z \ x))) \ x
    ]]></literal>
    <justification jstring="[para(5101(a,1),15829(a,2,1,2,1))].">
      <j1 rule="para" parents="5101 15829"/>
    </justification>
  </clause>

  <clause id="15831">
    <literal><![CDATA[
      a(x,a(y,y,a(y,y,z) * z),L(a(y,y,z) * z,y,y)) = ((a(y,y,z) * z) * (a(y,y,z) \ (z \ x))) \ x
    ]]></literal>
    <justification jstring="[para(8519(a,1),15830(a,2,1,2,1))].">
      <j1 rule="para" parents="8519 15830"/>
    </justification>
  </clause>

  <clause id="15832">
    <literal><![CDATA[
      a(x,a(y,y,a(y,y,z) * z),L(a(y,y,z) * z,y,y)) = ((a(y,y,z) * z) * (z \ (a(y,y,z) \ x))) \ x
    ]]></literal>
    <justification jstring="[para(6920(a,1),15831(a,2,1,2))].">
      <j1 rule="para" parents="6920 15831"/>
    </justification>
  </clause>

  <clause id="15834">
    <literal><![CDATA[
      a(x,a(y,y,a(y,y,z) * z),L(a(y,y,z) * z,y,y)) = (a(y,y,z) * z) \ (x / (z \ (a(y,y,z) \ x)))
    ]]></literal>
    <justification jstring="[hyper(316,a,7235,a(flip),b,15832,a),flip(a)].">
      <j1 rule="hyper" parents="316 7235 15832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15835">
    <literal><![CDATA[
      a(x,a(y,y,a(y,y,z) * z),L(a(y,y,z) * z,y,y)) = (a(y,y,z) * z) \ (((a(y,y,z) \ x) / z) \ x)
    ]]></literal>
    <justification jstring="[para(8950(a,1),15834(a,2,2))].">
      <j1 rule="para" parents="8950 15834"/>
    </justification>
  </clause>

  <clause id="15836">
    <literal><![CDATA[
      (((x \ 1) * (x * y)) \ 1) \ R(y \ 1,y * (((x \ 1) * (x * y)) \ 1),y * ((x \ 1) * (x * y))) = (y * (((x \ 1) * (x * y)) \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(1711(a,1),8316(a,1,2))].">
      <j1 rule="para" parents="1711 8316"/>
    </justification>
  </clause>

  <clause id="15837">
    <literal><![CDATA[
      (((x \ 1) * (x * y)) \ 1) \ R(y \ 1,y * (((x \ 1) * (x * y)) \ 1),y * ((x * y) * x)) = (y * (((x \ 1) * (x * y)) \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(4749(a,1),15836(a,1,2))].">
      <j1 rule="para" parents="4749 15836"/>
    </justification>
  </clause>

  <clause id="15838">
    <literal><![CDATA[
      (((x \ 1) * (x * y)) \ 1) \ R(y \ 1,y * (((x \ 1) * (x * y)) \ 1),y * L(y,x,x)) = (y * (((x \ 1) * (x * y)) \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(4800(a,1),15837(a,1,2))].">
      <j1 rule="para" parents="4800 15837"/>
    </justification>
  </clause>

  <clause id="15839">
    <literal><![CDATA[
      (((x \ 1) * (x * y)) \ 1) \ L(y \ 1,y * (((x \ 1) * (x * y)) \ 1),y \ L(y,x,x)) = (y * (((x \ 1) * (x * y)) \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(9207(a,1),15838(a,1,2))].">
      <j1 rule="para" parents="9207 15838"/>
    </justification>
  </clause>

  <clause id="15840">
    <literal><![CDATA[
      (((x \ 1) * (x * y)) \ 1) \ L(y \ 1,y * (((x \ 1) * (x * y)) \ 1),a(y,x,x)) = (y * (((x \ 1) * (x * y)) \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(7484(a,1),15839(a,1,2))].">
      <j1 rule="para" parents="7484 15839"/>
    </justification>
  </clause>

  <clause id="15841">
    <literal><![CDATA[
      (x * (((y \ 1) * (y * x)) \ 1)) \ 1 = (((y \ 1) * (y * x)) \ 1) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(8399(a,1),15840(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8399 15840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15843">
    <literal><![CDATA[
      (x * (y \ ((y \ 1) \ (x \ 1)))) \ 1 = (((y \ 1) * (y * x)) \ 1) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(12178(a,1),15841(a,1,1,2))].">
      <j1 rule="para" parents="12178 15841"/>
    </justification>
  </clause>

  <clause id="15844">
    <literal><![CDATA[
      (x * (y \ ((y \ 1) \ (x \ 1)))) \ 1 = (y \ ((y \ 1) \ (x \ 1))) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(12178(a,1),15843(a,2,1))].">
      <j1 rule="para" parents="12178 15843"/>
    </justification>
  </clause>

  <clause id="15845">
    <literal><![CDATA[
      (x \ ((x \ 1) \ (y \ 1))) \ (y \ 1) = (x * (y / (x * y))) \ 1
    ]]></literal>
    <justification jstring="[para(12181(a,1),15844(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12181 15844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15846">
    <literal><![CDATA[
      (x \ ((x \ 1) \ (y \ 1))) \ (y \ 1) = y \ ((x \ 1) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(316,a,11398,a(flip),b,15845,a),flip(a)].">
      <j1 rule="hyper" parents="316 11398 15845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15848">
    <literal><![CDATA[
      R(x * K(y \ L(y,z,u),L(y,w,v5)),y \ L(y,z,u),L(y,w,v5)) = R(x,L(y,w,v5),y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7551,a(flip),b,11667,a),flip(a)].">
      <j1 rule="hyper" parents="63 7551 11667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15849">
    <literal><![CDATA[
      R(x,L(y,z,u),y * L(y,w,v5)) = R(x,y \ L(y,w,v5),L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5033(a,1),15848(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5033 15848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15850">
    <literal><![CDATA[
      R(x,L(y,z,u),y * L(y,w,v5)) = L(x,y \ L(y,w,v5),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,12814,a(flip),b,15849,a),flip(a)].">
      <j1 rule="hyper" parents="316 12814 15849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15851">
    <literal><![CDATA[
      L(x,L(y,z,u),y \ L(y,w,v5)) = L(x,y \ L(y,w,v5),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9207,a(flip),b,15850,a)].">
      <j1 rule="hyper" parents="63 9207 15850"/>
    </justification>
  </clause>

  <clause id="15852">
    <literal><![CDATA[
      (x * ((L(y,z \ L(z,u,w),L(z,v5,v6)) \ y) * v7)) / (x * v7) = L(L(y,L(z,v5,v6),z \ L(z,u,w)) \ y,v7,x)
    ]]></literal>
    <justification jstring="[para(15851(a,1),6657(a,1,1,2,1,1))].">
      <j1 rule="para" parents="15851 6657"/>
    </justification>
  </clause>

  <clause id="15853">
    <literal><![CDATA[
      L(L(x,y \ L(y,z,u),L(y,w,v5)) \ x,x,L(y,w,v5)) = a(y \ L(y,z,u),L(y,w,v5),x)
    ]]></literal>
    <justification jstring="[para(15851(a,1),9998(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="15851 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15854">
    <literal><![CDATA[
      L(L(x,L(y,z,u),y \ L(y,w,v5)) \ x,x,y \ L(y,w,v5)) = a(L(y,z,u),y \ L(y,w,v5),x)
    ]]></literal>
    <justification jstring="[para(15851(a,2),9998(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="15851 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15855">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),L(y,w,v5)) \ x = a(y \ L(y,z,u),L(y,w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9861,a(flip),b,15853,a)].">
      <j1 rule="hyper" parents="63 9861 15853"/>
    </justification>
  </clause>

  <clause id="15857">
    <literal><![CDATA[
      L(x,L(y,z,u),y \ L(y,w,v5)) \ x = a(L(y,z,u),y \ L(y,w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9861,a(flip),b,15854,a)].">
      <j1 rule="hyper" parents="63 9861 15854"/>
    </justification>
  </clause>

  <clause id="15859">
    <literal><![CDATA[
      L(L(x,L(y,z,u),y \ L(y,w,v5)) \ x,v6,v7) = L(L(x,y \ L(y,w,v5),L(y,z,u)) \ x,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,6657,a(flip),b,15852,a),flip(a)].">
      <j1 rule="hyper" parents="63 6657 15852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15860">
    <literal><![CDATA[
      L(L(x,y \ L(y,z,u),L(y,w,v5)) \ x,v6,v7) = L(a(L(y,w,v5),y \ L(y,z,u),x),v6,v7)
    ]]></literal>
    <justification jstring="[para(15857(a,1),15859(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15857 15859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15861">
    <literal><![CDATA[
      L(a(L(x,y,z),x \ L(x,u,w),v5),v6,v7) = L(a(x \ L(x,u,w),L(x,y,z),v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(15855(a,1),15860(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15855 15860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15862">
    <literal><![CDATA[
      a(L(x,y,z),x \ L(x,u,w),v5) = a(x \ L(x,u,w),L(x,y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(50,a,15861,a)].">
      <j1 rule="hyper" parents="50 15861"/>
    </justification>
  </clause>

  <clause id="15863">
    <literal><![CDATA[
      a(L(x,y,z),x * L(x,u,w),a(v5,v6,v7)) = a(x \ L(x,u,w),L(x,y,z),a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,15750,a(flip),b,15862,a)].">
      <j1 rule="hyper" parents="63 15750 15862"/>
    </justification>
  </clause>

  <clause id="15864">
    <literal><![CDATA[
      a(L(x,y,z),x * L(x,y,z),a(u,w,v5)) * a(u,w,v5) = L(a(u,w,v5),x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(15863(a,2),14657(a,1,1))].">
      <j1 rule="para" parents="15863 14657"/>
    </justification>
  </clause>

  <clause id="15865">
    <literal><![CDATA[
      L(a(x,y,z),u * L(u,w,v5),L(u,w,v5)) = L(a(x,y,z),u,u \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,14597,a(flip),b,15864,a)].">
      <j1 rule="hyper" parents="63 14597 15864"/>
    </justification>
  </clause>

  <clause id="15866">
    <literal><![CDATA[
      a(x \ y,(x \ y) \ L(x \ y,x,y \ (x \ y)),z) = (z * (((x \ y) / y) * x)) \ ((z / (x \ y)) * (L(1 / (x \ y),x,x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(9940(a,1),12587(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9940 12587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15867">
    <literal><![CDATA[
      a(x \ y,(x \ y) \ L(x \ y,x,y \ (x \ y)),z) = (z * (((x \ y) / y) * x)) \ ((z / (x \ y)) * (x \ ((1 / x) \ (x \ y))))
    ]]></literal>
    <justification jstring="[para(9931(a,1),15866(a,2,2,2))].">
      <j1 rule="para" parents="9931 15866"/>
    </justification>
  </clause>

  <clause id="15868">
    <literal><![CDATA[
      (x * (((y \ z) / z) * y)) \ ((x / (y \ z)) * (y \ ((1 / y) \ (y \ z)))) = a(y \ z,(y \ z) \ ((1 / y) * z),x)
    ]]></literal>
    <justification jstring="[para(8876(a,1),15867(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8876 15867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15869">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,x * a(z,y,y),x \ L(x,y,z)) = (u / (x * a(z,y,y))) * L(x * a(z,y,y),y,z)
    ]]></literal>
    <justification jstring="[para(9291(a,1),13889(a,1,2,3))].">
      <j1 rule="para" parents="9291 13889"/>
    </justification>
  </clause>

  <clause id="15870">
    <literal><![CDATA[
      (x \ L(x,x,y)) * L(z,x * a(y,x,x),a(x,x,y)) = (z / (x * a(y,x,x))) * L(x * a(y,x,x),x,y)
    ]]></literal>
    <justification jstring="[para(7488(a,1),15869(a,1,2))].">
      <j1 rule="para" parents="7488 15869"/>
    </justification>
  </clause>

  <clause id="15871">
    <literal><![CDATA[
      a(x * L(y,z,u),x * L(y,z,u),a(w,v5,v5)) * L(L(x * R(y,z,u),v5,w) \ (x * R(y,z,u)),v6,v7) = a(w,v5,L(x * R(y,z,u),v6,v7))
    ]]></literal>
    <justification jstring="[para(12989(a,1),15460(a,1,1))].">
      <j1 rule="para" parents="12989 15460"/>
    </justification>
  </clause>

  <clause id="15872">
    <literal><![CDATA[
      a(x,y,a(y,L(z,u,w) \ v5,L(z,u,w) \ v5)) * L(L(R(z,u,w) \ v5,y,x) \ (R(z,u,w) \ v5),v6,v7) = a(x,y,L(R(z,u,w) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(12624(a,1),15526(a,1,1,3))].">
      <j1 rule="para" parents="12624 15526"/>
    </justification>
  </clause>

  <clause id="15873">
    <literal><![CDATA[
      a(x * L(y,z,u),x * L(y,z,u),a(w,v5,v5)) * L(L(x * L(y,z,u),v5,w) \ (x * L(y,z,u)),v6,v7) = a(w,v5,L(x * R(y,z,u),v6,v7))
    ]]></literal>
    <justification jstring="[para(14933(a,1),15871(a,1,2,1))].">
      <j1 rule="para" parents="14933 15871"/>
    </justification>
  </clause>

  <clause id="15874">
    <literal><![CDATA[
      a(x,y,L(z * R(u,w,v5),v6,v7)) = a(x,y,L(z * L(u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,15429,a(flip),b,15873,a),flip(a)].">
      <j1 rule="hyper" parents="63 15429 15873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15877">
    <literal><![CDATA[
      (x * T(y,(z \ R(z,u,w)) * x)) \ T(y * (x * (z \ R(z,u,w))),1) = R(z \ R(z,u,w),x,T(y,(z \ R(z,u,w)) * x))
    ]]></literal>
    <justification jstring="[para(2195(a,1),4256(a,1,2,2))].">
      <j1 rule="para" parents="2195 4256"/>
    </justification>
  </clause>

  <clause id="15878">
    <literal><![CDATA[
      (x * T(y,(z \ R(z,u,w)) * x)) \ (y * (x * (z \ R(z,u,w)))) = R(z \ R(z,u,w),x,T(y,(z \ R(z,u,w)) * x))
    ]]></literal>
    <justification jstring="[para(211(a,1),15877(a,1,2))].">
      <j1 rule="para" parents="211 15877"/>
    </justification>
  </clause>

  <clause id="15880">
    <literal><![CDATA[
      (x * T(y,(z \ R(z,u,w)) * x)) \ (y * (x * (z \ R(z,u,w)))) = R(z \ R(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,4679,a(flip),b,15878,a),flip(a)].">
      <j1 rule="hyper" parents="316 4679 15878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15882">
    <literal><![CDATA[
      (x * T(y,x)) \ (y * (x * (z \ R(z,u,w)))) = R(z \ R(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[para(3729(a,1),15880(a,1,1,2))].">
      <j1 rule="para" parents="3729 15880"/>
    </justification>
  </clause>

  <clause id="15883">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z \ R(z,u,w)))) = R(z \ R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(114(a,1),15882(a,1,1))].">
      <j1 rule="para" parents="114 15882"/>
    </justification>
  </clause>

  <clause id="15885">
    <literal><![CDATA[
      R(x \ R(x,y,z),u,w) = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18,a,b,15883,a),flip(a)].">
      <j1 rule="hyper" parents="63 18 15883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15890">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w * (v5 * v5)) = R(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1701,a(flip),b,15885,a),flip(a)].">
      <j1 rule="hyper" parents="63 1701 15885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15891">
    <literal><![CDATA[
      L((x \ K(y,z)) \ R(x \ K(y,z),u,w),v5,v6) = R(x * R(x \ 1,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(9052(a,1),15885(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9052 15885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15892">
    <literal><![CDATA[
      x * ((R(y,z,u) \ y) * R((R(y,z,u) \ y) \ 1,w,v5)) = (y \ R(y,z,u)) \ (x * L(y \ R(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(15885(a,1),15031(a,2,2,2))].">
      <j1 rule="para" parents="15885 15031"/>
    </justification>
  </clause>

  <clause id="15894">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w * (v5 * v5)) = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,15885,a(flip),b,15890,a),flip(a)].">
      <j1 rule="hyper" parents="316 15885 15890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15896">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,(w \ 1) \ v5) = L(x \ R(x,y,z),u,w \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,1653,a(flip),b,15894,a)].">
      <j1 rule="hyper" parents="63 1653 15894"/>
    </justification>
  </clause>

  <clause id="15897">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w * (v5 * (v6 * v6))) = L(x \ R(x,y,z),u,w * v5)
    ]]></literal>
    <justification jstring="[para(32(a,1),15894(a,1,3))].">
      <j1 rule="para" parents="32 15894"/>
    </justification>
  </clause>

  <clause id="15898">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,(w \ 1) * v5) = L(x \ R(x,y,z),u,v5 * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,7724,a(flip),b,15897,a),flip(a)].">
      <j1 rule="hyper" parents="63 7724 15897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15899">
    <literal><![CDATA[
      R(x * R(x \ 1,y,z),u,w) = L(x * R(x \ 1,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(9052(a,1),15891(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9052 15891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15900">
    <literal><![CDATA[
      T((R(x \ 1,y,z) * ((x \ 1) \ u)) / u,x \ 1) = L(x * R(x \ 1,y,z),x \ 1,x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4791,a,b,15899,a)].">
      <j1 rule="hyper" parents="63 4791 15899"/>
    </justification>
  </clause>

  <clause id="15901">
    <literal><![CDATA[
      T((R(x \ 1,y,z) * ((x \ 1) \ u)) / u,x \ 1) = L(x * R(x \ 1,y,z),x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,8818,a(flip),b,15900,a),flip(a)].">
      <j1 rule="hyper" parents="316 8818 15900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15902">
    <literal><![CDATA[
      L((x \ 1) \ R(x \ 1,y,z),x \ 1,u) = L(x * R(x \ 1,y,z),x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14725,a(flip),b,15901,a)].">
      <j1 rule="hyper" parents="63 14725 15901"/>
    </justification>
  </clause>

  <clause id="15903">
    <literal><![CDATA[
      L(x * R(x \ 1,y,z),x \ 1,u) = L(x * R(x \ 1,y,z),x,x \ u)
    ]]></literal>
    <justification jstring="[para(1511(a,1),15902(a,1,1))].">
      <j1 rule="para" parents="1511 15902"/>
    </justification>
  </clause>

  <clause id="15904">
    <literal><![CDATA[
      L(x * R(x \ 1,y,z),x,x \ u) = L(x * R(x \ 1,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8818,a(flip),b,15903,a),flip(a)].">
      <j1 rule="hyper" parents="63 8818 15903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15905">
    <literal><![CDATA[
      L(x * R(x \ 1,y,z),x,u * x) = L(x * R(x \ 1,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1584,a(flip),b,15904,a),flip(a)].">
      <j1 rule="hyper" parents="63 1584 15904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15906">
    <literal><![CDATA[
      x * ((R(y,z,u) \ y) * R((R(y,z,u) \ y) \ 1,w,v5)) = (R(y,z,u) \ y) * (x * L(y \ R(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,14536,a(flip),b,15892,a),flip(a)].">
      <j1 rule="hyper" parents="316 14536 15892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15907">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (u * L(x \ R(x,y,z),w,v5)) = u * ((R(x,y,z) \ x) * R(x \ R(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(7651(a,1),15906(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7651 15906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15908">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (u * L(x \ R(x,y,z),w,v5)) = u * ((R(x,y,z) \ x) * L(x \ R(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(15885(a,1),15907(a,2,2,2))].">
      <j1 rule="para" parents="15885 15907"/>
    </justification>
  </clause>

  <clause id="15910">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (u * L(x \ R(x,y,z),w,v5)) = u * a(x \ L(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(15558(a,1),15908(a,2,2))].">
      <j1 rule="para" parents="15558 15908"/>
    </justification>
  </clause>

  <clause id="15911">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * L((x * (L(x,y,z) \ u)) \ (x * u),w,v5) = L(L(T(x,u),y,z),w,v5) * (L(T(x,u),y,z) \ (x * u))
    ]]></literal>
    <justification jstring="[para(4596(a,1),4597(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4596 4597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15912">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * L((x * (L(x,y,z) \ u)) \ (x * u),w,v5) = L(L(T(x,u),y,z),w,v5) * (L(x,y,z) \ (u * x))
    ]]></literal>
    <justification jstring="[para(4349(a,1),15911(a,2,2))].">
      <j1 rule="para" parents="4349 15911"/>
    </justification>
  </clause>

  <clause id="15913">
    <literal><![CDATA[
      L(L(T(x,y),z,u),w,v5) * (L(x,z,u) \ (y * x)) = (x * (L(x,z,u) \ y)) * L(L(T(x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(4596(a,1),15912(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4596 15912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15914">
    <literal><![CDATA[
      L(L(T(x,y),z,u),w,v5) * (L(x,z,u) \ (y * x)) = L(L(x,z,u),w,v5) * (x * (L(x,z,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(316,a,6525,a(flip),b,15913,a),flip(a)].">
      <j1 rule="hyper" parents="316 6525 15913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15926">
    <literal><![CDATA[
      (((x * (L(y,z,u) * y)) / y) \ (x * L(y,z,u))) \ (x * L(y,z,u)) = (x * (K(w,v5) * (y \ L(y,z,u)))) / (y \ K(w,v5))
    ]]></literal>
    <justification jstring="[para(12293(a,1),6800(a,1,1,1))].">
      <j1 rule="para" parents="12293 6800"/>
    </justification>
  </clause>

  <clause id="15927">
    <literal><![CDATA[
      (((x * (y * L(y,z,u))) / y) \ (x * L(y,z,u))) \ (x * L(y,z,u)) = (x * (K(w,v5) * (y \ L(y,z,u)))) / (y \ K(w,v5))
    ]]></literal>
    <justification jstring="[para(257(a,1),15926(a,1,1,1,1,2))].">
      <j1 rule="para" parents="257 15926"/>
    </justification>
  </clause>

  <clause id="15929">
    <literal><![CDATA[
      (x * (K(y,z) * (u \ L(u,w,v5)))) / (u \ K(y,z)) = (x * (u * L(u,w,v5))) / u
    ]]></literal>
    <justification jstring="[hyper(63,a,9085,a(flip),b,15927,a),flip(a)].">
      <j1 rule="hyper" parents="63 9085 15927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15930">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) / ((y \ K(w,v5)) * K(v5,w)) = (x * (y * L(y,z,u))) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,5118,a(flip),b,15929,a)].">
      <j1 rule="hyper" parents="63 5118 15929"/>
    </justification>
  </clause>

  <clause id="15931">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) / (y \ 1) = (x * (y * L(y,z,u))) / y
    ]]></literal>
    <justification jstring="[para(3828(a,1),15930(a,1,2))].">
      <j1 rule="para" parents="3828 15930"/>
    </justification>
  </clause>

  <clause id="15932">
    <literal><![CDATA[
      (x \ K(x * y,x \ 1)) \ (y * (x \ L(x,z,u))) = (y * (x * L(x,z,u))) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,11544,a,b,15931,a)].">
      <j1 rule="hyper" parents="63 11544 15931"/>
    </justification>
  </clause>

  <clause id="15933">
    <literal><![CDATA[
      ((x \ K(x * y,x \ 1)) \ y) * (x \ L(x,z,u)) = (y * (x * L(x,z,u))) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,13159,a(flip),b,15932,a)].">
      <j1 rule="hyper" parents="63 13159 15932"/>
    </justification>
  </clause>

  <clause id="15934">
    <literal><![CDATA[
      (x / (y \ 1)) * (y \ L(y,z,u)) = (x * (y * L(y,z,u))) / y
    ]]></literal>
    <justification jstring="[para(4206(a,1),15933(a,1,1))].">
      <j1 rule="para" parents="4206 15933"/>
    </justification>
  </clause>

  <clause id="15935">
    <literal><![CDATA[
      x \ ((x * (y * L(y,z,u))) / y) = L(x \ (x / (y \ 1)),z,u)
    ]]></literal>
    <justification jstring="[para(15934(a,1),13178(a,1,2))].">
      <j1 rule="para" parents="15934 13178"/>
    </justification>
  </clause>

  <clause id="15936">
    <literal><![CDATA[
      L(x,y,z) \ L(u \ (u / (x \ 1)),y,z) = a(u,x,L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(15935(a,1),8819(a,1,2))].">
      <j1 rule="para" parents="15935 8819"/>
    </justification>
  </clause>

  <clause id="15937">
    <literal><![CDATA[
      x * L(y \ L(y,y,z),u,w) = x * (a(z,y,L(y,u,w)) \ 1)
    ]]></literal>
    <justification jstring="[para(15936(a,1),2142(a,2,2))].">
      <j1 rule="para" parents="15936 2142"/>
    </justification>
  </clause>

  <clause id="15938">
    <literal><![CDATA[
      x * L(y \ L(y,y,z),u,w) = a(z,y,L(y,u,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,14393,a(flip),b,15937,a),flip(a)].">
      <j1 rule="hyper" parents="316 14393 15937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15939">
    <literal><![CDATA[
      L(x \ L(x,x,y),z,u) = x \ L(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(133,a,10018,a(flip),b,15938,a),flip(a)].">
      <j1 rule="hyper" parents="133 10018 15938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15940">
    <literal><![CDATA[
      x * L(R(y,z,z) \ y,u,w) = a(y,z,L(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(7660(a,2),15938(a,1,2,1))].">
      <j1 rule="para" parents="7660 15938"/>
    </justification>
  </clause>

  <clause id="15941">
    <literal><![CDATA[
      a(R(x,y,z) * L(L(x \ L(x,x,u),y,z),y,z),u,w) = R(x,y,z) \ R(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(15939(a,2),14919(a,1,1,2,1))].">
      <j1 rule="para" parents="15939 14919"/>
    </justification>
  </clause>

  <clause id="15942">
    <literal><![CDATA[
      a(x,x \ (L(R(y,z,z) \ y,u,w) \ v5),L(R(y,z,z) \ y,u,w)) = v5 / (x * (a(y,z,L(z,u,w)) \ (x \ (v5 / L(R(y,z,z) \ y,u,w)))))
    ]]></literal>
    <justification jstring="[para(15940(a,1),11269(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15940 11269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15943">
    <literal><![CDATA[
      a(R(x,y,z) * (x \ L(x,x,u)),u,w) = R(x,y,z) \ R(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14084,a(flip),b,15941,a)].">
      <j1 rule="hyper" parents="63 14084 15941"/>
    </justification>
  </clause>

  <clause id="15945">
    <literal><![CDATA[
      a(a(x,y,y) \ R(y,z,u),x,w) = R(y,z,u) \ R(R(y,z,u),x,w)
    ]]></literal>
    <justification jstring="[para(14455(a,1),15943(a,1,1))].">
      <j1 rule="para" parents="14455 15943"/>
    </justification>
  </clause>

  <clause id="15946">
    <literal><![CDATA[
      a(a(x,y,y) \ L(y,z,u),x,w) = R(y,z,u) \ R(R(y,z,u),x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,13965,a(flip),b,15945,a)].">
      <j1 rule="hyper" parents="63 13965 15945"/>
    </justification>
  </clause>

  <clause id="15947">
    <literal><![CDATA[
      a(a(x,y,y) * L(y,z,u),x,w) = R(y,z,u) \ R(R(y,z,u),x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14413,a(flip),b,15946,a)].">
      <j1 rule="hyper" parents="63 14413 15946"/>
    </justification>
  </clause>

  <clause id="15948">
    <literal><![CDATA[
      K(L(x,y,z) * (x \ 1),u * w) * ((u * (w * (L(x,y,z) * L(x \ 1,y,z)))) / v5) = ((L(x,y,z) * L(x \ 1,y,z)) * (u * w)) / v5
    ]]></literal>
    <justification jstring="[para(6534(a,1),7917(a,1,1))].">
      <j1 rule="para" parents="6534 7917"/>
    </justification>
  </clause>

  <clause id="15949">
    <literal><![CDATA[
      K(x \ L(x,y,z),u * w) * ((u * (w * (L(x,y,z) * L(x \ 1,y,z)))) / v5) = ((L(x,y,z) * L(x \ 1,y,z)) * (u * w)) / v5
    ]]></literal>
    <justification jstring="[para(969(a,1),15948(a,1,1,1))].">
      <j1 rule="para" parents="969 15948"/>
    </justification>
  </clause>

  <clause id="15951">
    <literal><![CDATA[
      1 * ((x * (y * (L(z,u,w) * L(z \ 1,u,w)))) / v5) = ((L(z,u,w) * L(z \ 1,u,w)) * (x * y)) / v5
    ]]></literal>
    <justification jstring="[para(5018(a,1),15949(a,1,1))].">
      <j1 rule="para" parents="5018 15949"/>
    </justification>
  </clause>

  <clause id="15952">
    <literal><![CDATA[
      (x * (y * (L(z,u,w) * L(z \ 1,u,w)))) / (x * y) = L(z,u,w) * L(z \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(131,a,15951,a,b,11,a(flip))].">
      <j1 rule="hyper" parents="131 15951 11"/>
    </justification>
  </clause>

  <clause id="15954">
    <literal><![CDATA[
      (((x * y) \ L(x * y,z,u)) * w) * a(x * y,(x * y) \ L(x * y,z,u),w) = ((y \ 1) * x) \ (L((y \ 1) * x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(14277(a,1),9594(a,1,2))].">
      <j1 rule="para" parents="14277 9594"/>
    </justification>
  </clause>

  <clause id="15955">
    <literal><![CDATA[
      ((x \ 1) * y) \ (L((x \ 1) * y,z,u) * w) = (y * x) \ (L(y * x,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8437,a(flip),b,15954,a),flip(a)].">
      <j1 rule="hyper" parents="63 8437 15954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15956">
    <literal><![CDATA[
      ((x \ 1) * y) \ (L((x \ 1) * y,z,u) * w) = (w / (y * x)) * L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,4382,a(flip),b,15955,a),flip(a)].">
      <j1 rule="hyper" parents="316 4382 15955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15957">
    <literal><![CDATA[
      (x / ((y \ 1) * z)) * L((y \ 1) * z,u,w) = (x / (z * y)) * L(z * y,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,4382,a(flip),b,15956,a)].">
      <j1 rule="hyper" parents="63 4382 15956"/>
    </justification>
  </clause>

  <clause id="15958">
    <literal><![CDATA[
      ((x \ y) / y) \ L(x \ (y \ 1),z,u) = ((y \ 1) / (x * y)) * L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12226,a(flip),b,15957,a)].">
      <j1 rule="hyper" parents="63 12226 15957"/>
    </justification>
  </clause>

  <clause id="15959">
    <literal><![CDATA[
      ((x \ 1) / (y * x)) * L(y * x,z,u) = x \ (y \ (x * L(x \ y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9779,a(flip),b,15958,a),flip(a)].">
      <j1 rule="hyper" parents="63 9779 15958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15960">
    <literal><![CDATA[
      (x \ 1) \ (x \ (y \ (x * L(x \ y,z,u)))) = x \ ((x / (y * x)) * L(y * x,z,u))
    ]]></literal>
    <justification jstring="[para(15959(a,1),8125(a,1,2))].">
      <j1 rule="para" parents="15959 8125"/>
    </justification>
  </clause>

  <clause id="15961">
    <literal><![CDATA[
      x \ ((x / (y * x)) * L(y * x,z,u)) = L(y \ (x * L(x \ y,z,u)),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12556,a(flip),b,15960,a),flip(a)].">
      <j1 rule="hyper" parents="63 12556 15960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15962">
    <literal><![CDATA[
      x \ ((x / (x * y)) * L(x * y,z,u)) = L(y \ (x * L(x \ y,z,u)),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8152,a(flip),b,15961,a)].">
      <j1 rule="hyper" parents="63 8152 15961"/>
    </justification>
  </clause>

  <clause id="15963">
    <literal><![CDATA[
      L(L(x * y,z,u) \ (x * y),y * x,y) = L(x \ (y * L(y \ x,z,u)),y,y) \ 1
    ]]></literal>
    <justification jstring="[para(15962(a,1),13440(a,2,1))].">
      <j1 rule="para" parents="15962 13440"/>
    </justification>
  </clause>

  <clause id="15964">
    <literal><![CDATA[
      L(L(x * y,z,u) \ (x * y),y * x,y) = L(L(x \ y,z,u) \ (x \ y),y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,12521,a(flip),b,15963,a),flip(a)].">
      <j1 rule="hyper" parents="316 12521 15963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15965">
    <literal><![CDATA[
      L(L(x * y,z,u) \ (x * y),y * x,y) = L(y \ (L(x / y,z,u) \ x),y,y)
    ]]></literal>
    <justification jstring="[para(13906(a,1),15964(a,2,1))].">
      <j1 rule="para" parents="13906 15964"/>
    </justification>
  </clause>

  <clause id="15966">
    <literal><![CDATA[
      L(x \ (L(y / x,x,z) \ y),x,x) = a(z,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10843,a(flip),b,15965,a),flip(a)].">
      <j1 rule="hyper" parents="63 10843 15965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15967">
    <literal><![CDATA[
      L(a(x,y,y \ z),y,y) = a(x,y,z * y)
    ]]></literal>
    <justification jstring="[para(13647(a,1),15966(a,1,1))].">
      <j1 rule="para" parents="13647 15966"/>
    </justification>
  </clause>

  <clause id="15968">
    <literal><![CDATA[
      L(L(x,y,z) \ x,y,y) = a(z,y,(x \ y) * y)
    ]]></literal>
    <justification jstring="[para(14509(a,1),15967(a,1,1))].">
      <j1 rule="para" parents="14509 15967"/>
    </justification>
  </clause>

  <clause id="15969">
    <literal><![CDATA[
      T((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,1 * (((x \ ((x * y) * z)) / z) / a(x,y,z))) = L(y * a(z \ (x \ ((x * y) * z)),y,y),y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3606,a(flip),b,12744,a)].">
      <j1 rule="hyper" parents="63 3606 12744"/>
    </justification>
  </clause>

  <clause id="15981">
    <literal><![CDATA[
      T((L(a(x,y,z),u,w) \ (v5 * v6)) / (L(a(x,y,z),u,w) \ v5),v5) = (L(a(x,y,z) \ 1,u,w) * (v6 * v5)) / (L(a(x,y,z) \ 1,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(14662(a,1),14679(a,1,1,2))].">
      <j1 rule="para" parents="14662 14679"/>
    </justification>
  </clause>

  <clause id="15982">
    <literal><![CDATA[
      (L(a(x,y,z) \ 1,u,w) * (v5 * v6)) / (L(a(x,y,z) \ 1,u,w) * v6) = (L(a(x,y,z),u,w) \ v6) \ (L(a(x,y,z),u,w) \ (v6 * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,6618,a(flip),b,15981,a),flip(a)].">
      <j1 rule="hyper" parents="63 6618 15981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15983">
    <literal><![CDATA[
      T((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,1 * (a(x,y,z) \ ((x \ ((x * y) * z)) / z))) = L(y * a(z \ (x \ ((x * y) * z)),y,y),y,y)
    ]]></literal>
    <justification jstring="[para(2276(a,1),15969(a,1,2,2))].">
      <j1 rule="para" parents="2276 15969"/>
    </justification>
  </clause>

  <clause id="15985">
    <literal><![CDATA[
      T((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,1 * y) = L(y * a(z \ (x \ ((x * y) * z)),y,y),y,y)
    ]]></literal>
    <justification jstring="[para(8477(a,1),15983(a,1,2,2))].">
      <j1 rule="para" parents="8477 15983"/>
    </justification>
  </clause>

  <clause id="15986">
    <literal><![CDATA[
      T((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,y) = L(y * a(z \ (x \ ((x * y) * z)),y,y),y,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),15985(a,1,2))].">
      <j1 rule="para" parents="7 15985"/>
    </justification>
  </clause>

  <clause id="15996">
    <literal><![CDATA[
      R(x,x,y) * ((y \ L(y,x,x)) * L((y \ L(y,x,x)) \ z,R(x,x,y),a(y,x,x))) = (y \ L(y,x,x)) * (R(x,x,y) * (x \ (R(x,x,y) * z)))
    ]]></literal>
    <justification jstring="[para(7484(a,1),7675(a,1,2,2))].">
      <j1 rule="para" parents="7484 7675"/>
    </justification>
  </clause>

  <clause id="15997">
    <literal><![CDATA[
      R(x,x,y) * ((y \ L(y,x,x)) * L((y \ L(y,x,x)) \ z,L(x,x,y),a(y,x,x))) = (y \ L(y,x,x)) * (R(x,x,y) * (x \ (R(x,x,y) * z)))
    ]]></literal>
    <justification jstring="[para(10977(a,1),15996(a,1,2,2))].">
      <j1 rule="para" parents="10977 15996"/>
    </justification>
  </clause>

  <clause id="15998">
    <literal><![CDATA[
      R(x,x,y) * ((y \ L(y,x,x)) * L((y \ L(y,x,x)) \ z,a(y,x,x),L(x,x,y))) = (y \ L(y,x,x)) * (R(x,x,y) * (x \ (R(x,x,y) * z)))
    ]]></literal>
    <justification jstring="[para(10635(a,1),15997(a,1,2,2))].">
      <j1 rule="para" parents="10635 15997"/>
    </justification>
  </clause>

  <clause id="15999">
    <literal><![CDATA[
      (x \ L(x,y,y)) * (R(y,y,x) * (y \ (R(y,y,x) * z))) = R(y,y,x) * ((x \ L(x,y,y)) * (R(y,y,x) * (y \ z)))
    ]]></literal>
    <justification jstring="[para(9855(a,1),15998(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9855 15998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16000">
    <literal><![CDATA[
      (x \ L(x,y,y)) * (R(y,y,x) * (y \ (R(y,y,x) * z))) = R(y,y,x) * (L(y,y,x) * (a(x,y,y) * (y \ z)))
    ]]></literal>
    <justification jstring="[para(11440(a,1),15999(a,2,2))].">
      <j1 rule="para" parents="11440 15999"/>
    </justification>
  </clause>

  <clause id="16001">
    <literal><![CDATA[
      (x \ L(x,y,y)) * (R(y,y,x) * (y \ (R(y,y,x) * z))) = R(y,y,x) * L(z,a(x,y,y),L(y,y,x))
    ]]></literal>
    <justification jstring="[para(10653(a,1),16000(a,2,2))].">
      <j1 rule="para" parents="10653 16000"/>
    </justification>
  </clause>

  <clause id="16002">
    <literal><![CDATA[
      (x \ L(x,y,y)) * (R(y,y,x) * (R(y,y,x) * (y \ z))) = R(y,y,x) * L(z,a(x,y,y),L(y,y,x))
    ]]></literal>
    <justification jstring="[para(1167(a,1),16001(a,1,2,2))].">
      <j1 rule="para" parents="1167 16001"/>
    </justification>
  </clause>

  <clause id="16003">
    <literal><![CDATA[
      L(x,x,y) * (a(y,x,x) * (R(x,x,y) * (x \ z))) = R(x,x,y) * L(z,a(y,x,x),L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,11440,a(flip),b,16002,a)].">
      <j1 rule="hyper" parents="63 11440 16002"/>
    </justification>
  </clause>

  <clause id="16005">
    <literal><![CDATA[
      L(x,y * a(z,y,y),(y * a(z,y,y)) \ L(y * a(z,y,y),y,z)) = ((a(z,y,y) \ 1) * (x * (y * a(z,y,y)))) / L(y * a(z,y,y),y,z)
    ]]></literal>
    <justification jstring="[para(6860(a,1),9056(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6860 9056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16006">
    <literal><![CDATA[
      L(x,y * a(z,y,y),(y * a(z,y,y)) \ L(y * a(z,y,y),y,z)) = (a(z,y,y) * (x * (y * (a(z,y,y) \ 1)))) / L(y * a(z,y,y),y,z)
    ]]></literal>
    <justification jstring="[para(9843(a,1),16005(a,2,1))].">
      <j1 rule="para" parents="9843 16005"/>
    </justification>
  </clause>

  <clause id="16008">
    <literal><![CDATA[
      L(x,y * a(z,y,y),(y * a(z,y,y)) \ L(y * a(z,y,y),y,z)) = (a(z,y,y) * (x * (a(z,y,y) \ y))) / L(y * a(z,y,y),y,z)
    ]]></literal>
    <justification jstring="[para(6859(a,1),16006(a,2,1,2,2))].">
      <j1 rule="para" parents="6859 16006"/>
    </justification>
  </clause>

  <clause id="16009">
    <literal><![CDATA[
      L(x,y * a(z,y,y),(y * a(z,y,y)) \ L(y * a(z,y,y),y,z)) = (a(z,y,y) * (x * (a(z,y,y) \ y))) / y
    ]]></literal>
    <justification jstring="[para(8470(a,1),16008(a,2,2))].">
      <j1 rule="para" parents="8470 16008"/>
    </justification>
  </clause>

  <clause id="16010">
    <literal><![CDATA[
      L(x,y * a(z,y,y),(y * a(z,y,y)) \ L(y * a(z,y,y),y,z)) = L(x,a(z,y,y) \ y,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,5446,a(flip),b,16009,a),flip(a)].">
      <j1 rule="hyper" parents="316 5446 16009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16011">
    <literal><![CDATA[
      L(x,y * a(z,y,y),(y * a(z,y,y)) \ y) = L(x,a(z,y,y) \ y,a(z,y,y))
    ]]></literal>
    <justification jstring="[para(8470(a,1),16010(a,1,3,2))].">
      <j1 rule="para" parents="8470 16010"/>
    </justification>
  </clause>

  <clause id="16012">
    <literal><![CDATA[
      L(x,y * a(z,y,y),a(z,y,y) \ 1) = L(x,a(z,y,y) \ y,a(z,y,y))
    ]]></literal>
    <justification jstring="[para(6860(a,1),16011(a,1,3))].">
      <j1 rule="para" parents="6860 16011"/>
    </justification>
  </clause>

  <clause id="16013">
    <literal><![CDATA[
      L(x,y * a(z,y,y),a(z,y,y) \ 1) = L(x,a(z,y,y),L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,10644,a(flip),b,16012,a),flip(a)].">
      <j1 rule="hyper" parents="316 10644 16012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16015">
    <literal><![CDATA[
      L(x,y * a(z,y,y),a(y,y,z)) = L(x,a(z,y,y),L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13656,a(flip),b,16013,a)].">
      <j1 rule="hyper" parents="63 13656 16013"/>
    </justification>
  </clause>

  <clause id="16016">
    <literal><![CDATA[
      (x / (y * a(z,y,y))) * L(y * a(z,y,y),y,z) = (y \ L(y,y,z)) * L(x,a(z,y,y),L(y,y,z))
    ]]></literal>
    <justification jstring="[para(16015(a,1),15870(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16015 15870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16017">
    <literal><![CDATA[
      (x \ L(x,x,y)) * L(z,a(y,x,x),L(x,x,y)) = (z / (x * a(y,x,x))) * x
    ]]></literal>
    <justification jstring="[para(8470(a,1),16016(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8470 16016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16018">
    <literal><![CDATA[
      (x \ L(x,x,y)) * L(z,a(y,x,x),L(x,x,y)) = x * ((x * a(y,x,x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,5295,a(flip),b,16017,a),flip(a)].">
      <j1 rule="hyper" parents="316 5295 16017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16019">
    <literal><![CDATA[
      (x \ L(x,x,y)) * L(z,a(y,x,x),L(x,x,y)) = (z / x) * L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,13832,a(flip),b,16018,a),flip(a)].">
      <j1 rule="hyper" parents="316 13832 16018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16020">
    <literal><![CDATA[
      L(x,a(y,z,z),L(z,z,y)) = L(x,z,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(34,a,13888,a,b,16019,a),flip(a)].">
      <j1 rule="hyper" parents="34 13888 16019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16021">
    <literal><![CDATA[
      L(x,x,y) * (a(y,x,x) * z) = x * L(z,x,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(16020(a,1),7311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16020 7311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16022">
    <literal><![CDATA[
      L(x,x,y) * (a(y,x,x) * (R(x,x,y) * (x \ z))) = R(x,x,y) * L(z,x,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(16020(a,1),16003(a,2,2))].">
      <j1 rule="para" parents="16020 16003"/>
    </justification>
  </clause>

  <clause id="16023">
    <literal><![CDATA[
      L(x,x,y) * (a(y,x,x) * z) = L(x * z,x,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,7493,a,b,16021,a),flip(a)].">
      <j1 rule="hyper" parents="316 7493 16021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16024">
    <literal><![CDATA[
      L(x,x,y) * (a(y,x,x) * (R(x,x,y) * (x \ z))) = x * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,8663,a(flip),b,16022,a),flip(a)].">
      <j1 rule="hyper" parents="316 8663 16022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16025">
    <literal><![CDATA[
      L(x * (R(x,x,y) * (x \ z)),x,a(x,x,y)) = x * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,16023,a(flip),b,16024,a)].">
      <j1 rule="hyper" parents="63 16023 16024"/>
    </justification>
  </clause>

  <clause id="16027">
    <literal><![CDATA[
      K((x * y) * z,a(x,y,z) \ K(z,y)) / (K(y,z) * a(x,y,z)) = (x * (z * y)) / ((x * (z * y)) / (1 / ((x * (z * y)) \ ((x * y) * z))))
    ]]></literal>
    <justification jstring="[para(13855(a,1),11122(a,1,1,2))].">
      <j1 rule="para" parents="13855 11122"/>
    </justification>
  </clause>

  <clause id="16028">
    <literal><![CDATA[
      (x * (y * z)) / ((x * (y * z)) / (1 / ((x * (y * z)) \ ((x * z) * y)))) = K((x * z) * y,K(y,z)) / (K(z,y) * a(x,z,y))
    ]]></literal>
    <justification jstring="[para(5290(a,1),16027(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5290 16027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16029">
    <literal><![CDATA[
      (x * (y * z)) / ((x * (y * z)) / (1 / ((x * (y * z)) \ ((x * z) * y)))) = K(y,K((x * z) * y,z)) / (K(z,y) * a(x,z,y))
    ]]></literal>
    <justification jstring="[para(4084(a,1),16028(a,2,1))].">
      <j1 rule="para" parents="4084 16028"/>
    </justification>
  </clause>

  <clause id="16031">
    <literal><![CDATA[
      (x * (y * z)) / ((x * (y * z)) / (1 / ((x * (y * z)) \ ((x * z) * y)))) = K(y,K(x * (z * y),z)) / (K(z,y) * a(x,z,y))
    ]]></literal>
    <justification jstring="[para(3552(a,1),16029(a,2,1,2))].">
      <j1 rule="para" parents="3552 16029"/>
    </justification>
  </clause>

  <clause id="16032">
    <literal><![CDATA[
      (x * (y * z)) / ((x * (y * z)) / (1 / ((x * (y * z)) \ ((x * z) * y)))) = K(z,K(y,x * (z * y))) / (K(z,y) * a(x,z,y))
    ]]></literal>
    <justification jstring="[para(4086(a,1),16031(a,2,1))].">
      <j1 rule="para" parents="4086 16031"/>
    </justification>
  </clause>

  <clause id="16033">
    <literal><![CDATA[
      (x * (y * z)) / ((x * (y * z)) / (1 / ((x * (y * z)) \ ((x * z) * y)))) = K(z,K(y,x * y)) / (K(z,y) * a(x,z,y))
    ]]></literal>
    <justification jstring="[para(10540(a,1),16032(a,2,1))].">
      <j1 rule="para" parents="10540 16032"/>
    </justification>
  </clause>

  <clause id="16034">
    <literal><![CDATA[
      (x * (y * z)) / ((x * (y * z)) / (1 / ((x * (y * z)) \ ((x * z) * y)))) = K(x,K(z,y)) / (K(z,y) * a(x,z,y))
    ]]></literal>
    <justification jstring="[para(4101(a,1),16033(a,2,1))].">
      <j1 rule="para" parents="4101 16033"/>
    </justification>
  </clause>

  <clause id="16035">
    <literal><![CDATA[
      (x * (y * z)) / ((x * (y * z)) / (1 / ((x * (y * z)) \ ((x * z) * y)))) = (K(x,K(z,y)) / a(x,z,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,10180,a(flip),b,16034,a),flip(a)].">
      <j1 rule="hyper" parents="316 10180 16034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16036">
    <literal><![CDATA[
      (x * (y * z)) / ((x * (y * z)) / (1 / ((x * (y * z)) \ ((x * z) * y)))) = (a(x,z,y) \ K(x,K(z,y))) * K(y,z)
    ]]></literal>
    <justification jstring="[para(2276(a,1),16035(a,2,1))].">
      <j1 rule="para" parents="2276 16035"/>
    </justification>
  </clause>

  <clause id="16037">
    <literal><![CDATA[
      (x * (y * z)) / ((x * (y * z)) / (1 / ((x * (y * z)) \ ((x * z) * y)))) = K(x,K(z,y)) * (a(x,z,y) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,14424,a(flip),b,16036,a),flip(a)].">
      <j1 rule="hyper" parents="316 14424 16036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16038">
    <literal><![CDATA[
      (x * (y * z)) / ((x * (y * z)) / (1 / ((x * (y * z)) \ ((x * z) * y)))) = a(x,z,y) \ K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,10443,a(flip),b,16037,a),flip(a)].">
      <j1 rule="hyper" parents="316 10443 16037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16039">
    <literal><![CDATA[
      (x * (y * z)) / ((x * (y * z)) / (1 / ((x * (y * z)) \ ((x * z) * y)))) = T(a(x,z,y) \ K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,5331,a,b,16038,a),flip(a)].">
      <j1 rule="hyper" parents="316 5331 16038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16040">
    <literal><![CDATA[
      (x * (y * z)) / ((x * (y * z)) / (1 / (K(z,y) * a(x,z,y)))) = T(a(x,z,y) \ K(y,z),x)
    ]]></literal>
    <justification jstring="[para(10561(a,1),16039(a,1,2,2,2))].">
      <j1 rule="para" parents="10561 16039"/>
    </justification>
  </clause>

  <clause id="16041">
    <literal><![CDATA[
      (x * (y * z)) / ((x * (y * z)) / ((1 / a(x,z,y)) * K(y,z))) = T(a(x,z,y) \ K(y,z),x)
    ]]></literal>
    <justification jstring="[para(10180(a,1),16040(a,1,2,2))].">
      <j1 rule="para" parents="10180 16040"/>
    </justification>
  </clause>

  <clause id="16042">
    <literal><![CDATA[
      (x * (y * z)) / ((x * (y * z)) / (a(x,z,y) \ K(y,z))) = T(a(x,z,y) \ K(y,z),x)
    ]]></literal>
    <justification jstring="[para(14392(a,1),16041(a,1,2,2))].">
      <j1 rule="para" parents="14392 16041"/>
    </justification>
  </clause>

  <clause id="16043">
    <literal><![CDATA[
      (x * (y * z)) / (a(x,z,y) * ((x * (y * z)) * K(z,y))) = T(a(x,z,y) \ K(y,z),x)
    ]]></literal>
    <justification jstring="[para(14452(a,1),16042(a,1,2))].">
      <j1 rule="para" parents="14452 16042"/>
    </justification>
  </clause>

  <clause id="16044">
    <literal><![CDATA[
      (x * (y * z)) / (a(x,z,y) * (x * (z * y))) = T(a(x,z,y) \ K(y,z),x)
    ]]></literal>
    <justification jstring="[para(3933(a,1),16043(a,1,2,2))].">
      <j1 rule="para" parents="3933 16043"/>
    </justification>
  </clause>

  <clause id="16045">
    <literal><![CDATA[
      (x * (y * z)) / ((x * z) * y) = T(a(x,z,y) \ K(y,z),x)
    ]]></literal>
    <justification jstring="[para(2330(a,1),16044(a,1,2))].">
      <j1 rule="para" parents="2330 16044"/>
    </justification>
  </clause>

  <clause id="16047">
    <literal><![CDATA[
      K(a(x,y,z) * a(u,w,v5),v6) * (v7 * ((a(x,y,z) * a(u,w,v5)) * v8)) = ((a(u,w,v5) * a(x,y,z)) * v8) * T(v7,v8 * (a(u,w,v5) * a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(5337(a,1),5457(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5337 5457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16048">
    <literal><![CDATA[
      K(a(x,y,z) * a(u,w,v5),v6) * (v7 * ((a(x,y,z) * a(u,w,v5)) * v8)) = ((a(u,w,v5) * a(x,y,z)) * v8) * T(v7,v8 * a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(5259(a,1),16047(a,2,2))].">
      <j1 rule="para" parents="5259 16047"/>
    </justification>
  </clause>

  <clause id="16050">
    <literal><![CDATA[
      K(a(x,y,z) * a(u,w,v5),v6) * (v7 * ((a(x,y,z) * a(u,w,v5)) * v8)) = ((a(u,w,v5) * a(x,y,z)) * v8) * T(v7,v8)
    ]]></literal>
    <justification jstring="[para(5243(a,1),16048(a,2,2))].">
      <j1 rule="para" parents="5243 16048"/>
    </justification>
  </clause>

  <clause id="16052">
    <literal><![CDATA[
      ((a(x,y,z) * a(u,w,v5)) * v6) * T(v7,v6) = v7 * ((a(u,w,v5) * a(x,y,z)) * v6)
    ]]></literal>
    <justification jstring="[hyper(223,a,16050,a),flip(a)].">
      <j1 rule="hyper" parents="223 16050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16054">
    <literal><![CDATA[
      (x * ((a(y,z,u) * a(w,v5,v6)) * v7)) / ((x * v7) * (a(y,z,u) * a(w,v5,v6))) = a(a(w,v5,v6) * a(y,z,u),v7,x)
    ]]></literal>
    <justification jstring="[para(16052(a,1),5701(a,1,1))].">
      <j1 rule="para" parents="16052 5701"/>
    </justification>
  </clause>

  <clause id="16055">
    <literal><![CDATA[
      T(a(x,y,a(z,u,w) * a(v5,v6,v7)) \ K(a(z,u,w) * a(v5,v6,v7),y),x) = a(a(v5,v6,v7) * a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,16045,a(flip),b,16054,a)].">
      <j1 rule="hyper" parents="63 16045 16054"/>
    </justification>
  </clause>

  <clause id="16056">
    <literal><![CDATA[
      T(a(x,y,a(z,u,w) * a(v5,v6,v7)) \ K(a(z,u,w),y),x) = a(a(v5,v6,v7) * a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(5280(a,1),16055(a,1,1,2))].">
      <j1 rule="para" parents="5280 16055"/>
    </justification>
  </clause>

  <clause id="16057">
    <literal><![CDATA[
      T(a(x,y,a(z,u,w) * a(v5,v6,v7)) \ 1,x) = a(a(v5,v6,v7) * a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(2303(a,1),16056(a,1,1,2))].">
      <j1 rule="para" parents="2303 16056"/>
    </justification>
  </clause>

  <clause id="16059">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * a(v5,v6,v7)) \ 1 = a(a(v5,v6,v7) * a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4997,a(flip),b,16057,a)].">
      <j1 rule="hyper" parents="63 4997 16057"/>
    </justification>
  </clause>

  <clause id="16062">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * a(v5,v6,v7)) \ v8 = a(a(v5,v6,v7) * a(z,u,w),y,x) * v8
    ]]></literal>
    <justification jstring="[hyper(138,a,16059,a(flip),b,14398,a),flip(a)].">
      <j1 rule="hyper" parents="138 16059 14398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16064">
    <literal><![CDATA[
      L(x,a(y,z,u) \ w,a(y,z,u) * a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,7035,a(flip),b,9433,a),flip(a)].">
      <j1 rule="hyper" parents="35 7035 9433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16065">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,10834,a(flip),b,16064,a)].">
      <j1 rule="hyper" parents="63 10834 16064"/>
    </justification>
  </clause>

  <clause id="16067">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ u) \ ((a(x,y,z) * a(x,y,z)) * w) = (a(x,y,z) \ u) \ w
    ]]></literal>
    <justification jstring="[hyper(63,a,6672,a(flip),b,16064,a)].">
      <j1 rule="hyper" parents="63 6672 16064"/>
    </justification>
  </clause>

  <clause id="16068">
    <literal><![CDATA[
      ((a(x,y,z) * a(x,y,z)) * u) \ w = u \ ((a(x,y,z) * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1677,a(flip),b,16065,a)].">
      <j1 rule="hyper" parents="63 1677 16065"/>
    </justification>
  </clause>

  <clause id="16069">
    <literal><![CDATA[
      ((a(x,y,z) * a(x,y,z)) * u) * w = (a(x,y,z) * a(x,y,z)) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(139,a,16065,a(flip),b,7635,a(flip))].">
      <j1 rule="hyper" parents="139 16065 7635"/>
    </justification>
  </clause>

  <clause id="16070">
    <literal><![CDATA[
      ((a(x,y,z) * a(x,y,z)) * (u * w)) \ (((a(x,y,z) * a(x,y,z)) * u) * (w * v5)) = L(v5,L(w,u,a(x,y,z) * a(x,y,z)),(a(x,y,z) * a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(16065(a,1),459(a,1,2,2,1))].">
      <j1 rule="para" parents="16065 459"/>
    </justification>
  </clause>

  <clause id="16071">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * ((a(x,y,z) \ u) * w) = ((a(x,y,z) \ 1) \ u) * w
    ]]></literal>
    <justification jstring="[para(6305(a,1),16069(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6305 16069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16075">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) \ u) \ w) * (a(x,y,z) * a(x,y,z)) = (a(x,y,z) \ u) \ w
    ]]></literal>
    <justification jstring="[hyper(63,a,5363,a(flip),b,16067,a)].">
      <j1 rule="hyper" parents="63 5363 16067"/>
    </justification>
  </clause>

  <clause id="16076">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u * L(z,w,v5)) = ((a(x,y,z) \ 1) \ u) * L(z,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,6995,a(flip),b,16071,a)].">
      <j1 rule="hyper" parents="63 6995 16071"/>
    </justification>
  </clause>

  <clause id="16077">
    <literal><![CDATA[
      a(x,x,L(y,y,z)) * (a(x,x,y) \ z) = ((a(x,x,y) \ 1) \ (z / y)) * L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11877,a(flip),b,16076,a)].">
      <j1 rule="hyper" parents="63 11877 16076"/>
    </justification>
  </clause>

  <clause id="16080">
    <literal><![CDATA[
      (x / ((a(y,z,u) \ 1) \ w)) * (w * (a(y,z,u) * a(y,z,u))) = w * ((a(y,z,u) \ w) \ x)
    ]]></literal>
    <justification jstring="[para(16075(a,1),12885(a,2,2))].">
      <j1 rule="para" parents="16075 12885"/>
    </justification>
  </clause>

  <clause id="16081">
    <literal><![CDATA[
      ((a(x,y,z) * u) \ w) * (a(x,y,z) * a(x,y,z)) = (a(x,y,z) \ u) \ w
    ]]></literal>
    <justification jstring="[para(14400(a,1),16075(a,1,1,1))].">
      <j1 rule="para" parents="14400 16075"/>
    </justification>
  </clause>

  <clause id="16082">
    <literal><![CDATA[
      ((a(x,y,z) * u) \ w) * (a(x,y,z) * a(x,y,z)) = ((a(x,y,z) \ 1) * u) \ w
    ]]></literal>
    <justification jstring="[para(14391(a,2),16081(a,2,1))].">
      <j1 rule="para" parents="14391 16081"/>
    </justification>
  </clause>

  <clause id="16083">
    <literal><![CDATA[
      L(x \ ((a(y,z,u) \ 1) \ w),x,a(y,z,u)) = ((a(y,z,u) \ 1) * x) \ w
    ]]></literal>
    <justification jstring="[hyper(63,a,9059,a,b,16082,a)].">
      <j1 rule="hyper" parents="63 9059 16082"/>
    </justification>
  </clause>

  <clause id="16084">
    <literal><![CDATA[
      ((x * a(y,z,u)) \ w) * (a(y,z,u) * a(y,z,u)) = ((a(y,z,u) \ 1) * x) \ w
    ]]></literal>
    <justification jstring="[hyper(63,a,2395,a(flip),b,16082,a)].">
      <j1 rule="hyper" parents="63 2395 16082"/>
    </justification>
  </clause>

  <clause id="16085">
    <literal><![CDATA[
      L(((a(x,y,z) \ 1) \ u) / w,w,a(x,y,z)) * w = w * (((a(x,y,z) \ 1) * w) \ u)
    ]]></literal>
    <justification jstring="[para(16083(a,1),602(a,2,2))].">
      <j1 rule="para" parents="16083 602"/>
    </justification>
  </clause>

  <clause id="16086">
    <literal><![CDATA[
      L(x \ (a(y,z,u) * w),x,a(y,z,u)) = ((a(y,z,u) \ 1) * x) \ L(w,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(7604(a,1),16083(a,1,1,2))].">
      <j1 rule="para" parents="7604 16083"/>
    </justification>
  </clause>

  <clause id="16087">
    <literal><![CDATA[
      L(x \ (a(y,z,u) \ (w * (v5 * a(y,z,u)))),x,a(y,z,u)) = ((a(y,z,u) \ 1) * x) \ (w * (v5 * (a(y,z,u) \ 1)))
    ]]></literal>
    <justification jstring="[para(7882(a,1),16083(a,1,1,2))].">
      <j1 rule="para" parents="7882 16083"/>
    </justification>
  </clause>

  <clause id="16088">
    <literal><![CDATA[
      (x * a(y,z,u)) * (((a(y,z,u) \ 1) * x) \ w) = w * (a(y,z,u) * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,16084,a(flip),b,388,a)].">
      <j1 rule="hyper" parents="139 16084 388"/>
    </justification>
  </clause>

  <clause id="16089">
    <literal><![CDATA[
      a(x,((a(y,z,u) \ 1) * w) \ v5,v6) = a(x,(w * a(y,z,u)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(16084(a,1),13059(a,1,2))].">
      <j1 rule="para" parents="16084 13059"/>
    </justification>
  </clause>

  <clause id="16090">
    <literal><![CDATA[
      a(x,(a(y,z,u) \ w) \ v5,v6) = a(x,(w * a(y,z,u)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(14391(a,1),16089(a,1,2,1))].">
      <j1 rule="para" parents="14391 16089"/>
    </justification>
  </clause>

  <clause id="16091">
    <literal><![CDATA[
      (x * a(y,z,u)) * ((a(y,z,u) \ x) \ w) = w * (a(y,z,u) * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(14391(a,1),16088(a,1,2,1))].">
      <j1 rule="para" parents="14391 16088"/>
    </justification>
  </clause>

  <clause id="16092">
    <literal><![CDATA[
      a(x,y,((z * a(u,w,v5)) * ((a(u,w,v5) \ z) \ v6)) * v7) = a(x,y,v6 * v7)
    ]]></literal>
    <justification jstring="[para(16091(a,2),5874(a,1,3,1))].">
      <j1 rule="para" parents="16091 5874"/>
    </justification>
  </clause>

  <clause id="16093">
    <literal><![CDATA[
      a(x,y,((a(z,u,w) \ v5) * v6) * v7) = a(x,y,((v5 * a(z,u,w)) * v6) * v7)
    ]]></literal>
    <justification jstring="[para(9(a,1),16092(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="9 16092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16094">
    <literal><![CDATA[
      a(x,y,(((z * u) \ (a(z,u,u) \ w)) * v5) * v6) = a(x,y,((((z * u) \ w) * a(z,u,u)) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(7407(a,1),16093(a,1,3,1,1))].">
      <j1 rule="para" parents="7407 16093"/>
    </justification>
  </clause>

  <clause id="16095">
    <literal><![CDATA[
      (a(x,x,y) \ z) \ (((a(x,x,y) \ 1) \ (z / y)) * L(y,x,x)) = a(x,x,L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,16077,a(flip),b,2290,a(flip))].">
      <j1 rule="hyper" parents="133 16077 2290"/>
    </justification>
  </clause>

  <clause id="16096">
    <literal><![CDATA[
      (a(x,x,y) \ z) \ L(z,y,a(y,x,x)) = a(x,x,L(y,y,z))
    ]]></literal>
    <justification jstring="[para(13727(a,1),16095(a,1,2))].">
      <j1 rule="para" parents="13727 16095"/>
    </justification>
  </clause>

  <clause id="16097">
    <literal><![CDATA[
      (x / (y * (a(z,u,w) \ 1))) * y = y * (((a(z,u,w) \ 1) * y) \ x)
    ]]></literal>
    <justification jstring="[para(7032(a,1),16085(a,1,1))].">
      <j1 rule="para" parents="7032 16085"/>
    </justification>
  </clause>

  <clause id="16098">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,u * a(x,y,z)) \ 1 = u * (((a(x,y,z) \ 1) * u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,13303,a,b,16097,a)].">
      <j1 rule="hyper" parents="63 13303 16097"/>
    </justification>
  </clause>

  <clause id="16099">
    <literal><![CDATA[
      L(a(x,y,z),u,u * a(x,y,z)) = u * (((a(x,y,z) \ 1) * u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,13445,a(flip),b,16098,a)].">
      <j1 rule="hyper" parents="63 13445 16098"/>
    </justification>
  </clause>

  <clause id="16100">
    <literal><![CDATA[
      L(a(x,y,z),u,u * a(x,y,z)) = u * ((a(x,y,z) \ u) \ 1)
    ]]></literal>
    <justification jstring="[para(14391(a,1),16099(a,2,2,1))].">
      <j1 rule="para" parents="14391 16099"/>
    </justification>
  </clause>

  <clause id="16101">
    <literal><![CDATA[
      (x / ((a(y,z,u) \ 1) \ w)) * (u * (L(L(u,z,y),z,y) \ w)) = w * ((a(y,z,u) \ w) \ x)
    ]]></literal>
    <justification jstring="[para(14074(a,2),16080(a,1,2))].">
      <j1 rule="para" parents="14074 16080"/>
    </justification>
  </clause>

  <clause id="16102">
    <literal><![CDATA[
      (x / (a(y,z,u) * w)) * (u * (L(L(u,z,y),z,y) \ w)) = w * ((a(y,z,u) \ w) \ x)
    ]]></literal>
    <justification jstring="[para(14400(a,1),16101(a,1,1,2))].">
      <j1 rule="para" parents="14400 16101"/>
    </justification>
  </clause>

  <clause id="16103">
    <literal><![CDATA[
      L(x \ (a(y,z,u) * w),x,a(y,z,u)) = (a(y,z,u) \ x) \ L(w,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(14391(a,1),16086(a,2,1))].">
      <j1 rule="para" parents="14391 16086"/>
    </justification>
  </clause>

  <clause id="16104">
    <literal><![CDATA[
      L(x \ (a(y,z,u) * w),x,a(y,z,u)) = (a(y,z,u) \ x) \ w
    ]]></literal>
    <justification jstring="[para(14381(a,1),16103(a,2,2))].">
      <j1 rule="para" parents="14381 16103"/>
    </justification>
  </clause>

  <clause id="16105">
    <literal><![CDATA[
      L(x \ (a(y,z,u) * w),x,a(y,z,u)) = (x * (a(y,z,u) \ 1)) \ w
    ]]></literal>
    <justification jstring="[para(14393(a,2),16104(a,2,1))].">
      <j1 rule="para" parents="14393 16104"/>
    </justification>
  </clause>

  <clause id="16106">
    <literal><![CDATA[
      L(x \ a(y,z,u),x,a(y,z,u)) = (x * (a(y,z,u) \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(8(a,1),16105(a,1,1,2))].">
      <j1 rule="para" parents="8 16105"/>
    </justification>
  </clause>

  <clause id="16107">
    <literal><![CDATA[
      L((a(x,y,z) * u) * a(w,a(v5,v6,v7),v8),a(v8,a(v7,v6,v5),w),a(x,y,z)) = (a(v8,a(v7,v6,v5),w) * (a(x,y,z) \ 1)) \ u
    ]]></literal>
    <justification jstring="[para(14414(a,1),16105(a,1,1))].">
      <j1 rule="para" parents="14414 16105"/>
    </justification>
  </clause>

  <clause id="16108">
    <literal><![CDATA[
      (x * (a(y,z,x) \ 1)) \ 1 = x \ a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11699,a(flip),b,16106,a),flip(a)].">
      <j1 rule="hyper" parents="63 11699 16106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16110">
    <literal><![CDATA[
      (a(x,y,z) \ z) \ 1 = z \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(6859(a,1),16108(a,1,1))].">
      <j1 rule="para" parents="6859 16108"/>
    </justification>
  </clause>

  <clause id="16112">
    <literal><![CDATA[
      T(a(x,y,z) \ z,z \ 1) = (z \ a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(16110(a,1),5296(a,2,1))].">
      <j1 rule="para" parents="16110 5296"/>
    </justification>
  </clause>

  <clause id="16113">
    <literal><![CDATA[
      (x \ 1) \ (a(y,z,x) \ 1) = (x \ a(y,z,x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,6963,a(flip),b,16112,a)].">
      <j1 rule="hyper" parents="63 6963 16112"/>
    </justification>
  </clause>

  <clause id="16114">
    <literal><![CDATA[
      ((x \ a(y,z,x)) \ 1) \ L(x,z,y) = ((a(y,z,x) \ x) \ 1) * L(x,z,y)
    ]]></literal>
    <justification jstring="[para(16113(a,1),14926(a,1,1))].">
      <j1 rule="para" parents="16113 14926"/>
    </justification>
  </clause>

  <clause id="16115">
    <literal><![CDATA[
      ((x \ a(y,z,x)) \ 1) \ L(x,z,y) = (x \ a(y,z,x)) * L(x,z,y)
    ]]></literal>
    <justification jstring="[para(16110(a,1),16114(a,2,1))].">
      <j1 rule="para" parents="16110 16114"/>
    </justification>
  </clause>

  <clause id="16116">
    <literal><![CDATA[
      a(x,y,((T(z / (u \ 1),u) \ (a(u \ z,u * u,u * u) \ w)) * v5) * v6) = a(x,y,(((((u \ z) * (u * u)) \ w) * a(u \ z,u * u,u * u)) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(613(a,2),16094(a,1,3,1,1,1))].">
      <j1 rule="para" parents="613 16094"/>
    </justification>
  </clause>

  <clause id="16117">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * u) \ (w * (v5 * (a(x,y,z) \ 1))) = (a(x,y,z) * u) \ (w * (v5 * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,298,a(flip),b,16087,a),flip(a)].">
      <j1 rule="hyper" parents="63 298 16087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16118">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * u) \ (u * (w * (a(x,y,z) \ 1))) = L(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,2496,a(flip),b,16117,a),flip(a)].">
      <j1 rule="hyper" parents="316 2496 16117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16119">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (w * ((a(x,y,z) \ ((a(x,y,z) \ 1) \ v5)) * a(x,y,z))) = ((a(x,y,z) \ 1) * u) \ (w * (a(x,y,z) \ v5))
    ]]></literal>
    <justification jstring="[para(6303(a,1),16117(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6303 16117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16120">
    <literal><![CDATA[
      L(x,a(y,z,u) \ 1,w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9504,a(flip),b,16118,a)].">
      <j1 rule="hyper" parents="63 9504 16118"/>
    </justification>
  </clause>

  <clause id="16121">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) \ u,a(x,y,z),w) = ((a(x,y,z) \ 1) * w) \ (w * u)
    ]]></literal>
    <justification jstring="[para(4993(a,1),16118(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4993 16118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16123">
    <literal><![CDATA[
      R(x,a(y,z,u) \ 1,w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8256,a,b,16120,a)].">
      <j1 rule="hyper" parents="63 8256 16120"/>
    </justification>
  </clause>

  <clause id="16124">
    <literal><![CDATA[
      L(x,a(y,z,u),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,13661,a(flip),b,16120,a)].">
      <j1 rule="hyper" parents="63 13661 16120"/>
    </justification>
  </clause>

  <clause id="16127">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * u) * L(w,a(x,y,z),u) = u * (T(a(x,y,z) \ 1,u) * w)
    ]]></literal>
    <justification jstring="[hyper(139,a,16120,a(flip),b,3286,a(flip))].">
      <j1 rule="hyper" parents="139 16120 3286"/>
    </justification>
  </clause>

  <clause id="16128">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * ((a(y,z,u) \ 1) * w) = (x * (a(y,z,u) \ 1)) * w
    ]]></literal>
    <justification jstring="[para(16120(a,1),8255(a,1,1))].">
      <j1 rule="para" parents="16120 8255"/>
    </justification>
  </clause>

  <clause id="16129">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u) \ w) * w = (x * (a(y,z,u) \ 1)) * ((a(y,z,u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(16120(a,1),12355(a,1,1))].">
      <j1 rule="para" parents="16120 12355"/>
    </justification>
  </clause>

  <clause id="16131">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),a(u,z,y),w) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,14118,a(flip),b,16124,a),flip(a)].">
      <j1 rule="hyper" parents="316 14118 16124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16132">
    <literal><![CDATA[
      L(x,a(y \ z,y,z),u) = L(x,a(z,y,z * y),u)
    ]]></literal>
    <justification jstring="[para(9946(a,1),16124(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9946 16124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16133">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (w * a(u,z,y)) = (x * a(u,z,y)) * w
    ]]></literal>
    <justification jstring="[para(16124(a,1),10597(a,1,1))].">
      <j1 rule="para" parents="16124 10597"/>
    </justification>
  </clause>

  <clause id="16135">
    <literal><![CDATA[
      L(x,a(y,z,u),(x * a(y,z,u)) \ w) \ w = (a(y,z,u) \ 1) * ((x * (a(y,z,u) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(16123(a,1),4833(a,1,1))].">
      <j1 rule="para" parents="16123 4833"/>
    </justification>
  </clause>

  <clause id="16136">
    <literal><![CDATA[
      L(x,a(y,y,x),z) \ (L(x,y,y) * z) = (x \ L(x,y,y)) * z
    ]]></literal>
    <justification jstring="[para(16123(a,1),5097(a,1,1))].">
      <j1 rule="para" parents="16123 5097"/>
    </justification>
  </clause>

  <clause id="16138">
    <literal><![CDATA[
      L(a(x,y,a(z,u,u)) \ y,x,a(u \ z,u,z)) = L(y,a(z,u,z * u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8903,a,b,16132,a)].">
      <j1 rule="hyper" parents="63 8903 16132"/>
    </justification>
  </clause>

  <clause id="16141">
    <literal><![CDATA[
      L(x,a(y,x,x),z) * (z * a(x,x,y)) = R(x,x,y) * z
    ]]></literal>
    <justification jstring="[para(7332(a,1),16133(a,2,1))].">
      <j1 rule="para" parents="7332 16133"/>
    </justification>
  </clause>

  <clause id="16142">
    <literal><![CDATA[
      L(x,a(y,y,x),z) \ (L(x,y,y) * z) = a(y,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(316,a,14426,a(flip),b,16136,a),flip(a)].">
      <j1 rule="hyper" parents="316 14426 16136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16143">
    <literal><![CDATA[
      L(x,y,a(z,x,y)) \ (L(x,y,y) * z) = a(y,y,x) \ z
    ]]></literal>
    <justification jstring="[para(15373(a,1),16142(a,1,1))].">
      <j1 rule="para" parents="15373 16142"/>
    </justification>
  </clause>

  <clause id="16144">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),w) = ((a(x,y,z) \ 1) * w) \ (w * u)
    ]]></literal>
    <justification jstring="[para(14400(a,1),16121(a,1,1))].">
      <j1 rule="para" parents="14400 16121"/>
    </justification>
  </clause>

  <clause id="16145">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),w) = (a(x,y,z) \ w) \ (w * u)
    ]]></literal>
    <justification jstring="[para(14391(a,1),16144(a,2,1))].">
      <j1 rule="para" parents="14391 16144"/>
    </justification>
  </clause>

  <clause id="16146">
    <literal><![CDATA[
      L(a(x,y,z) * (u \ w),a(x,y,z),u) = (a(x,y,z) \ u) \ w
    ]]></literal>
    <justification jstring="[hyper(316,a,168,a(flip),b,16145,a),flip(a)].">
      <j1 rule="hyper" parents="316 168 16145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16147">
    <literal><![CDATA[
      L((a(x,y,z) \ u) \ w,a(z,y,x),u) = a(x,y,z) * (u \ w)
    ]]></literal>
    <justification jstring="[hyper(41,a,16131,a,b,16146,a)].">
      <j1 rule="hyper" parents="41 16131 16146"/>
    </justification>
  </clause>

  <clause id="16149">
    <literal><![CDATA[
      a(x,y,z) * (u \ ((a(x,y,z) \ u) * w)) = L(w,a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),16147(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 16147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16151">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (a(y,z,u) \ w) = (x * (a(y,z,u) \ 1)) * w
    ]]></literal>
    <justification jstring="[para(14391(a,1),16128(a,1,2))].">
      <j1 rule="para" parents="14391 16128"/>
    </justification>
  </clause>

  <clause id="16152">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (a(y,z,u) \ w) = (a(y,z,u) \ x) * w
    ]]></literal>
    <justification jstring="[para(14393(a,1),16151(a,2,1))].">
      <j1 rule="para" parents="14393 16151"/>
    </justification>
  </clause>

  <clause id="16153">
    <literal><![CDATA[
      (a(x,y,z) \ L(u,a(z,y,x),w)) * w = u * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(16131(a,1),16152(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16131 16152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16154">
    <literal><![CDATA[
      L(x * a(a(y,z,z),x,u),u,a(z \ y,z,y)) = L(x,a(y,z,y * z),u)
    ]]></literal>
    <justification jstring="[para(9445(a,1),16138(a,1,1))].">
      <j1 rule="para" parents="9445 16138"/>
    </justification>
  </clause>

  <clause id="16159">
    <literal><![CDATA[
      L(x * a(a(y,z,z),x,u),u,a(y,z,z)) = L(x,a(y,z,y * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11095,a(flip),b,16154,a)].">
      <j1 rule="hyper" parents="63 11095 16154"/>
    </justification>
  </clause>

  <clause id="16160">
    <literal><![CDATA[
      L(x,a(y,z,y * z),u) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9456,a(flip),b,16159,a),flip(a)].">
      <j1 rule="hyper" parents="63 9456 16159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16161">
    <literal><![CDATA[
      (x \ y) * a(z,x \ y,a(x,y,y)) = L(x \ y,a(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13521,a,b,16160,a)].">
      <j1 rule="hyper" parents="63 13521 16160"/>
    </justification>
  </clause>

  <clause id="16163">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * u) * L(w,a(x,y,z),u) = u * ((a(x,y,z) \ 1) * w)
    ]]></literal>
    <justification jstring="[para(4997(a,1),16127(a,2,2,1))].">
      <j1 rule="para" parents="4997 16127"/>
    </justification>
  </clause>

  <clause id="16165">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(w,a(x,y,z),u) = u * ((a(x,y,z) \ 1) * w)
    ]]></literal>
    <justification jstring="[para(14391(a,1),16163(a,1,1))].">
      <j1 rule="para" parents="14391 16163"/>
    </justification>
  </clause>

  <clause id="16166">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(w,a(x,y,z),u) = u * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(14391(a,1),16165(a,2,2))].">
      <j1 rule="para" parents="14391 16165"/>
    </justification>
  </clause>

  <clause id="16172">
    <literal><![CDATA[
      (x * (a(y,z,u) \ 1)) * ((a(y,z,u) \ 1) \ w) = (x * a(y,z,u)) * (a(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,7249,a(flip),b,16129,a),flip(a)].">
      <j1 rule="hyper" parents="63 7249 16129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16173">
    <literal><![CDATA[
      (a(x,y,z) \ u) * ((a(x,y,z) \ 1) \ w) = (u * a(x,y,z)) * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(14393(a,1),16172(a,1,1))].">
      <j1 rule="para" parents="14393 16172"/>
    </justification>
  </clause>

  <clause id="16174">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (w * a(x,y,z)) = (u * a(x,y,z)) * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(14394(a,1),16173(a,1,2))].">
      <j1 rule="para" parents="14394 16173"/>
    </justification>
  </clause>

  <clause id="16175">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * ((u * (a(x,y,z) \ 1)) \ w) = a(x,y,z) * ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10627,a(flip),b,16135,a),flip(a)].">
      <j1 rule="hyper" parents="63 10627 16135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16177">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * ((a(x,y,z) \ u) \ w) = a(x,y,z) * ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(14393(a,1),16175(a,1,2,1))].">
      <j1 rule="para" parents="14393 16175"/>
    </justification>
  </clause>

  <clause id="16178">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) \ u) \ w) = a(x,y,z) * ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14391,a(flip),b,16177,a)].">
      <j1 rule="hyper" parents="63 14391 16177"/>
    </justification>
  </clause>

  <clause id="16179">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * u) \ (w * (a(x,y,z) \ v5)) = (a(x,y,z) * u) \ (w * ((a(x,y,z) \ 1) \ v5))
    ]]></literal>
    <justification jstring="[para(2274(a,1),16119(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2274 16119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16181">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (w * ((a(x,y,z) \ 1) \ v5)) = (a(x,y,z) \ u) \ (w * (a(x,y,z) \ v5))
    ]]></literal>
    <justification jstring="[para(14391(a,1),16179(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14391 16179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16182">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (w * (a(x,y,z) \ v5)) = (a(x,y,z) * u) \ (w * (a(x,y,z) * v5))
    ]]></literal>
    <justification jstring="[para(14400(a,1),16181(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14400 16181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16183">
    <literal><![CDATA[
      x \ ((a(y,z,u) * w) \ (w * (a(y,z,u) * x))) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(16182(a,1),14774(a,1,2))].">
      <j1 rule="para" parents="16182 14774"/>
    </justification>
  </clause>

  <clause id="16186">
    <literal><![CDATA[
      x \ R(x,a(y,z,u),w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(10592(a,1),16183(a,1,2))].">
      <j1 rule="para" parents="10592 16183"/>
    </justification>
  </clause>

  <clause id="16187">
    <literal><![CDATA[
      L(x,a(y,a(z,u,w),x),a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(39,a,13932,a,b,16186,a)].">
      <j1 rule="hyper" parents="39 13932 16186"/>
    </justification>
  </clause>

  <clause id="16188">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * x = R(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,16186,a)].">
      <j1 rule="hyper" parents="38 2295 16186"/>
    </justification>
  </clause>

  <clause id="16189">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(10628(a,1),16186(a,1,2))].">
      <j1 rule="para" parents="10628 16186"/>
    </justification>
  </clause>

  <clause id="16190">
    <literal><![CDATA[
      (a(x,y,z) * (a(u,a(x,y,z),w) * w)) / w = a(x,y,z) * a(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(209,a,16187,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="209 16187 18"/>
    </justification>
  </clause>

  <clause id="16191">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ w = L(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(133,a,16187,a(flip),b,11630,a)].">
      <j1 rule="hyper" parents="133 16187 11630"/>
    </justification>
  </clause>

  <clause id="16192">
    <literal><![CDATA[
      L(x,a(y,z,u),w) \ x = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(133,a,16187,a(flip),b,11629,a)].">
      <j1 rule="hyper" parents="133 16187 11629"/>
    </justification>
  </clause>

  <clause id="16195">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),w) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,14124,a,b,16189,a),flip(a)].">
      <j1 rule="hyper" parents="316 14124 16189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16196">
    <literal><![CDATA[
      x * a(x,a(y,z,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(152,a,16189,a)].">
      <j1 rule="hyper" parents="152 16189"/>
    </justification>
  </clause>

  <clause id="16197">
    <literal><![CDATA[
      x * a(y,a(z,u,w),x) = L(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(139,a,14124,a,b,16189,a)].">
      <j1 rule="hyper" parents="139 14124 16189"/>
    </justification>
  </clause>

  <clause id="16198">
    <literal><![CDATA[
      x * a(y,a(z,u,w),x) = L(x,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(139,a,14123,a,b,16189,a)].">
      <j1 rule="hyper" parents="139 14123 16189"/>
    </justification>
  </clause>

  <clause id="16199">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,u),w),v5,v6) = a(L(x,v5,v6),a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2136,a(flip),b,16189,a)].">
      <j1 rule="hyper" parents="63 2136 16189"/>
    </justification>
  </clause>

  <clause id="16200">
    <literal><![CDATA[
      x \ (y * L(y \ x,a(z,u,w),v5)) = a(x \ y,a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,1252,a(flip),b,16189,a)].">
      <j1 rule="hyper" parents="63 1252 16189"/>
    </justification>
  </clause>

  <clause id="16202">
    <literal><![CDATA[
      a(x,y,z * L(z,a(u,w,v5),v6)) = a(x,y,a(z,a(u,w,v5),v6))
    ]]></literal>
    <justification jstring="[para(16189(a,1),5566(a,1,3)),flip(a)].">
      <j1 rule="para" parents="16189 5566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16203">
    <literal><![CDATA[
      x \ L(x,a(y,z,y * z),u) = a(x,a(y,z,z \ y),u)
    ]]></literal>
    <justification jstring="[para(9946(a,1),16189(a,1,2,2))].">
      <j1 rule="para" parents="9946 16189"/>
    </justification>
  </clause>

  <clause id="16205">
    <literal><![CDATA[
      (L(x,x,a(y,z,u)) \ (((1 / x) \ a(y,z,u)) * w)) / w = a(y,z,u) * a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(16189(a,1),15029(a,2,2))].">
      <j1 rule="para" parents="16189 15029"/>
    </justification>
  </clause>

  <clause id="16206">
    <literal><![CDATA[
      a(x * L(x,y,z),a(u,w,v5),v6) = a(a(x,a(v5,w,u),v6),y,z)
    ]]></literal>
    <justification jstring="[para(16189(a,1),15296(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16189 15296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16207">
    <literal><![CDATA[
      a(x \ L(x,y,z),a(u,w,v5),v6) \ v6 = L(v6,a(u,w,v5),x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,10633,a(flip),b,16191,a),flip(a)].">
      <j1 rule="hyper" parents="316 10633 16191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16214">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * a(w,a(u,z,y),x) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,13658,a,b,16192,a)].">
      <j1 rule="hyper" parents="139 13658 16192"/>
    </justification>
  </clause>

  <clause id="16215">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w) \ x,v5,v6) = a(w,a(y,z,u),L(x,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,13383,a(flip),b,16192,a)].">
      <j1 rule="hyper" parents="63 13383 16192"/>
    </justification>
  </clause>

  <clause id="16217">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ (x * a(y,x,a(z,u,w))) = a(y,a(z,u,w),x * a(y,x,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(8919(a,1),16192(a,1,1))].">
      <j1 rule="para" parents="8919 16192"/>
    </justification>
  </clause>

  <clause id="16218">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * w = L(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,16195,a)].">
      <j1 rule="hyper" parents="38 2295 16195"/>
    </justification>
  </clause>

  <clause id="16220">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * w = L(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,14126,a,b,16196,a)].">
      <j1 rule="hyper" parents="63 14126 16196"/>
    </justification>
  </clause>

  <clause id="16222">
    <literal><![CDATA[
      a(x \ y,a(x,y,y),z) = a(z,x \ y,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(34,a,16161,a,b,16196,a),flip(a)].">
      <j1 rule="hyper" parents="34 16161 16196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16225">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ u) * a(R(x,y,z) \ u,a(w,v5,v6),v7)) = R(x,y,z) * L(R(x,y,z) \ u,a(w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(16196(a,1),12620(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16196 12620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16227">
    <literal><![CDATA[
      (x \ y) * a(x,a(z,u,w),y) = x \ L(y,a(w,u,z),x)
    ]]></literal>
    <justification jstring="[hyper(133,a,16198,a(flip),b,8417,a),flip(a)].">
      <j1 rule="hyper" parents="133 16198 8417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16231">
    <literal><![CDATA[
      (a(x,y,z) \ ((R(u,u,a(x,y,z)) \ ((u \ ((u * u) * a(x,y,z))) * w)) / w)) * w = L(w,a(z,y,x),L(u,u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(8767(a,2),16220(a,1,1))].">
      <j1 rule="para" parents="8767 16220"/>
    </justification>
  </clause>

  <clause id="16232">
    <literal><![CDATA[
      a(x,a(y,z,z \ y),u) = x \ L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(16160(a,1),16203(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16160 16203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16233">
    <literal><![CDATA[
      a(x,a(y,z,z \ y),u) = a(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,16189,a(flip),b,16232,a),flip(a)].">
      <j1 rule="hyper" parents="316 16189 16232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16234">
    <literal><![CDATA[
      a(x,y \ z,a(z,y,y)) \ 1 = a(y \ z,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9951,a(flip),b,16233,a)].">
      <j1 rule="hyper" parents="63 9951 16233"/>
    </justification>
  </clause>

  <clause id="16235">
    <literal><![CDATA[
      a(x,a(y,z,y * z),u) = a(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(9946(a,1),16233(a,1,2))].">
      <j1 rule="para" parents="9946 16233"/>
    </justification>
  </clause>

  <clause id="16237">
    <literal><![CDATA[
      L(x,y \ (1 / z),(y \ (1 / z)) \ L(y \ (1 / z),y,z)) = x * a(y \ z,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[para(16235(a,1),15090(a,2,2))].">
      <j1 rule="para" parents="16235 15090"/>
    </justification>
  </clause>

  <clause id="16238">
    <literal><![CDATA[
      a(x \ y,(x \ y) \ ((1 / x) * y),z) = a(x \ y,a(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14194,a,b,16234,a)].">
      <j1 rule="hyper" parents="63 14194 16234"/>
    </justification>
  </clause>

  <clause id="16239">
    <literal><![CDATA[
      a(a(x,y,y),y \ x,z) = a(y \ x,a(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13732,a(flip),b,16234,a)].">
      <j1 rule="hyper" parents="63 13732 16234"/>
    </justification>
  </clause>

  <clause id="16241">
    <literal><![CDATA[
      a(L(x,y,z),a(u,w,v5),v6) = L(a(x,a(u,w,v5),v6),y,z)
    ]]></literal>
    <justification jstring="[para(16189(a,1),16199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16189 16199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16243">
    <literal><![CDATA[
      a(x,a(y,z,u),w * L(w,v5,v6)) = a(v6,v5,a(w,a(u,z,y),x))
    ]]></literal>
    <justification jstring="[hyper(63,a,15434,a,b,16202,a)].">
      <j1 rule="hyper" parents="63 15434 16202"/>
    </justification>
  </clause>

  <clause id="16246">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) * a(y,a(z,u,y),L(x,w,v5)) = x * a(x \ L(x,a(z,u,y),y),w,v5)
    ]]></literal>
    <justification jstring="[para(16215(a,1),15274(a,1,2))].">
      <j1 rule="para" parents="16215 15274"/>
    </justification>
  </clause>

  <clause id="16247">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,v6)) = L(a(x,a(y,z,u),w),v5,v6)
    ]]></literal>
    <justification jstring="[para(16192(a,1),16215(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16192 16215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16248">
    <literal><![CDATA[
      a(L(x,y,z),a(u,w,v5),v6) = a(x,a(u,w,v5),L(v6,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,16241,a,b,16247,a)].">
      <j1 rule="hyper" parents="316 16241 16247"/>
    </justification>
  </clause>

  <clause id="16249">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5 * a(x,a(y,z,u),w),v6)) = L(a(x,a(y,z,u),w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,14779,a(flip),b,16247,a),flip(a)].">
      <j1 rule="hyper" parents="316 14779 16247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16250">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,v6)) = L(a(x,a(u,z,y),w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,13658,a,b,16247,a)].">
      <j1 rule="hyper" parents="63 13658 16247"/>
    </justification>
  </clause>

  <clause id="16251">
    <literal><![CDATA[
      a(x,a(x,y,z),L(u,w,v5)) = L(a(u,x,a(z,y,x)),w,v5)
    ]]></literal>
    <justification jstring="[para(13675(a,1),16247(a,2,1))].">
      <j1 rule="para" parents="13675 16247"/>
    </justification>
  </clause>

  <clause id="16252">
    <literal><![CDATA[
      a(L(x,y,z),a(u,w,v5),v6) = a(x,a(v5,w,u),L(v6,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,13658,a,b,16248,a),flip(a)].">
      <j1 rule="hyper" parents="316 13658 16248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16253">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,v6)) = a(w,a(u,z,y),L(x,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,14123,a,b,16248,a)].">
      <j1 rule="hyper" parents="63 14123 16248"/>
    </justification>
  </clause>

  <clause id="16255">
    <literal><![CDATA[
      x * a(y,a(z,u,w),L(x,v5,v6)) = L(x,a(z,u,w),L(y,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(139,a,16248,a(flip),b,16195,a)].">
      <j1 rule="hyper" parents="139 16248 16195"/>
    </justification>
  </clause>

  <clause id="16257">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,x,a(y,z,u))) = x \ L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,14903,a(flip),b,16250,a),flip(a)].">
      <j1 rule="hyper" parents="316 14903 16250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16258">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * a(x,a(x,y,z),L(y,u,w)) = L(1 / R(x \ L(x,y,z),u,w),x,y) \ 1
    ]]></literal>
    <justification jstring="[para(16250(a,2),15022(a,1,2))].">
      <j1 rule="para" parents="16250 15022"/>
    </justification>
  </clause>

  <clause id="16259">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5 * a(x,a(y,z,u),w),v5)) \ a(x,a(u,z,y),w) = a(v5,v5 * a(x,a(u,z,y),w),a(x,a(u,z,y),w))
    ]]></literal>
    <justification jstring="[para(16250(a,2),13779(a,1,1))].">
      <j1 rule="para" parents="16250 13779"/>
    </justification>
  </clause>

  <clause id="16260">
    <literal><![CDATA[
      a(x,a(x,y,z),L(y,u,w)) = L(a(x,x,a(y,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(15345(a,1),16251(a,2,1))].">
      <j1 rule="para" parents="15345 16251"/>
    </justification>
  </clause>

  <clause id="16262">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,v6)) \ v7 = v7 * a(w,a(y,z,u),L(x,v5,v6))
    ]]></literal>
    <justification jstring="[para(16252(a,1),14414(a,1,1))].">
      <j1 rule="para" parents="16252 14414"/>
    </justification>
  </clause>

  <clause id="16263">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,v6)) \ w = L(w,a(u,z,y),L(x,v5,v6))
    ]]></literal>
    <justification jstring="[para(16252(a,1),16191(a,1,1))].">
      <j1 rule="para" parents="16252 16191"/>
    </justification>
  </clause>

  <clause id="16264">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,y)) = a(y,a(w,v5,y),L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,13672,a,b,16253,a)].">
      <j1 rule="hyper" parents="316 13672 16253"/>
    </justification>
  </clause>

  <clause id="16265">
    <literal><![CDATA[
      a(x,y,z) * a(u,a(z,y,x),L(z,w,v5)) = L(a(x,y,z),z,L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(139,a,16253,a,b,11612,a)].">
      <j1 rule="hyper" parents="139 16253 11612"/>
    </justification>
  </clause>

  <clause id="16268">
    <literal><![CDATA[
      a(x,a(x,y,z),L(y,u,w)) = a(x,x,L(a(y,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,11868,a,b,16260,a),flip(a)].">
      <j1 rule="hyper" parents="316 11868 16260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16270">
    <literal><![CDATA[
      a(x,L(y,z,x),a(u,w,y)) = a(y,a(u,w,y),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,5574,a(flip),b,16264,a),flip(a)].">
      <j1 rule="hyper" parents="316 5574 16264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16271">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,y) \ a(x,a(z,y,x),y) = L(a(z,y,x),u,y)
    ]]></literal>
    <justification jstring="[para(16270(a,1),14734(a,1,2))].">
      <j1 rule="para" parents="16270 14734"/>
    </justification>
  </clause>

  <clause id="16274">
    <literal><![CDATA[
      a(x,a(x,y,z),L(y,u,w)) = a(x,x,a(y,y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5178,a,b,16268,a),flip(a)].">
      <j1 rule="hyper" parents="316 5178 16268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16277">
    <literal><![CDATA[
      R(x,a(y,z,u),w * L(w,v5,v6)) = a(v6,v5,a(w,a(u,z,y),x)) * x
    ]]></literal>
    <justification jstring="[para(16243(a,1),16188(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16243 16188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16281">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,x,a(y,z,u))) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,16189,a(flip),b,16257,a),flip(a)].">
      <j1 rule="hyper" parents="316 16189 16257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16283">
    <literal><![CDATA[
      (x * (((y \ z) / z) * y)) \ ((x / (y \ z)) * (y \ ((1 / y) \ (y \ z)))) = a(y \ z,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,15868,a,b,16238,a)].">
      <j1 rule="hyper" parents="63 15868 16238"/>
    </justification>
  </clause>

  <clause id="16284">
    <literal><![CDATA[
      a(x,a(x,y,z),L(y,u,w)) \ 1 = a(y,x,L(a(z,y,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,14814,a(flip),b,16262,a),flip(a)].">
      <j1 rule="hyper" parents="316 14814 16262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16285">
    <literal><![CDATA[
      a(x,a(x,y,z),L(y,u,w)) = a(y,x,L(a(z,y,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14122,a(flip),b,16284,a)].">
      <j1 rule="hyper" parents="63 14122 16284"/>
    </justification>
  </clause>

  <clause id="16286">
    <literal><![CDATA[
      a(x,y,L(a(z,x,y),u,w)) = a(y,y,a(x,x,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16274,a(flip),b,16285,a),flip(a)].">
      <j1 rule="hyper" parents="63 16274 16285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16287">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),x,y)) = a(x,y,L(a(z,x,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,15345,a,b,16286,a)].">
      <j1 rule="hyper" parents="316 15345 16286"/>
    </justification>
  </clause>

  <clause id="16288">
    <literal><![CDATA[
      L(a(x,x,a(y,y,L(z,u,w))) \ x,y,L(a(z,y,x),u,w)) = L(x,L(a(z,y,x),u,w),y)
    ]]></literal>
    <justification jstring="[para(16286(a,1),12725(a,1,1,1))].">
      <j1 rule="para" parents="16286 12725"/>
    </justification>
  </clause>

  <clause id="16290">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),x,y)) * L(L(y,x,z) \ y,u,w) = L(a(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[para(16287(a,2),14500(a,1,1))].">
      <j1 rule="para" parents="16287 14500"/>
    </justification>
  </clause>

  <clause id="16291">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,y) \ a(x,x,a(z,y,y)) = L(a(z,y,x),u,y)
    ]]></literal>
    <justification jstring="[para(15362(a,1),16271(a,1,2))].">
      <j1 rule="para" parents="15362 16271"/>
    </justification>
  </clause>

  <clause id="16292">
    <literal><![CDATA[
      R(x,a(y,z,u),w * L(w,v5,v6)) = x * a(a(x,a(u,z,y),w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,14024,a(flip),b,16277,a),flip(a)].">
      <j1 rule="hyper" parents="316 14024 16277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16293">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L(L(x,z,y) \ x,u,z) = L(a(y,z,x),u,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14736,a(flip),b,16291,a)].">
      <j1 rule="hyper" parents="63 14736 16291"/>
    </justification>
  </clause>

  <clause id="16294">
    <literal><![CDATA[
      R(x,a(y,z,u),y * L(y,w,v5)) = x * a(a(x,y,a(u,z,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(7011(a,1),16292(a,2,2,1))].">
      <j1 rule="para" parents="7011 16292"/>
    </justification>
  </clause>

  <clause id="16295">
    <literal><![CDATA[
      a(x,y,L(z,u,y)) = L(a(x,y,z),u,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15429,a(flip),b,16293,a)].">
      <j1 rule="hyper" parents="63 15429 16293"/>
    </justification>
  </clause>

  <clause id="16296">
    <literal><![CDATA[
      a(x,y,L(z,x,y)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,14606,a(flip),b,16295,a),flip(a)].">
      <j1 rule="hyper" parents="316 14606 16295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16297">
    <literal><![CDATA[
      L(a(L(x,x,y),y,z),u,y) = x \ R(x,y,L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14759,a(flip),b,16295,a),flip(a)].">
      <j1 rule="hyper" parents="63 14759 16295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16298">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,y) = a(x,y,L(z,u,y)) \ 1
    ]]></literal>
    <justification jstring="[para(16295(a,2),13442(a,2,1))].">
      <j1 rule="para" parents="16295 13442"/>
    </justification>
  </clause>

  <clause id="16299">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,L(z,u,y)) \ w) = a(a(x,y,z),u,y) * w
    ]]></literal>
    <justification jstring="[para(16295(a,2),14793(a,1,2,1))].">
      <j1 rule="para" parents="16295 14793"/>
    </justification>
  </clause>

  <clause id="16300">
    <literal><![CDATA[
      (L(a(x,y,z),u,y) \ a(x,y,z)) * w = a(x,y,z) * (a(x,y,L(z,u,y)) \ w)
    ]]></literal>
    <justification jstring="[para(16295(a,2),14796(a,2,2,1))].">
      <j1 rule="para" parents="16295 14796"/>
    </justification>
  </clause>

  <clause id="16301">
    <literal><![CDATA[
      L(a(x,y * z,z * R(z \ 1,u,w)),z,y * z) = a(x,y * z,L(z * R(z \ 1,u,w),z,y))
    ]]></literal>
    <justification jstring="[para(15905(a,1),16295(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15905 16295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16303">
    <literal><![CDATA[
      R(x,y,L(z,x,y)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,11862,a(flip),b,16296,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 11862 16296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16304">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),x,y)) = x \ L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(5371(a,1),16296(a,2,2))].">
      <j1 rule="para" parents="5371 16296"/>
    </justification>
  </clause>

  <clause id="16305">
    <literal><![CDATA[
      x \ R(x,y,z * L(z,u,y)) = a(x,y,z * L(z,u,y))
    ]]></literal>
    <justification jstring="[para(9864(a,1),16296(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9864 16296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16309">
    <literal><![CDATA[
      (a(x,y,L(z,u,w)) \ v5) * (u \ R(u,w,z * L(z,y,x))) = a(x,y,u \ (w \ ((w * z) * u))) \ v5
    ]]></literal>
    <justification jstring="[para(16296(a,1),15643(a,1,2))].">
      <j1 rule="para" parents="16296 15643"/>
    </justification>
  </clause>

  <clause id="16310">
    <literal><![CDATA[
      a(x,y,z * L(u,w,L(v5,u,w))) = a(x,y,z * (u * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(16303(a,1),7272(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="16303 7272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16315">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,y),x,y) = R(x,y,L(z,u,y)) \ x
    ]]></literal>
    <justification jstring="[para(16298(a,2),14627(a,1,1))].">
      <j1 rule="para" parents="16298 14627"/>
    </justification>
  </clause>

  <clause id="16316">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,y) = x \ R(x,y,L(z,u,y))
    ]]></literal>
    <justification jstring="[para(14759(a,1),16297(a,1,1))].">
      <j1 rule="para" parents="14759 16297"/>
    </justification>
  </clause>

  <clause id="16317">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ w) * (u \ L(u,w,a(x,y,z))) = u \ ((a(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(16304(a,1),14913(a,1,2))].">
      <j1 rule="para" parents="16304 14913"/>
    </justification>
  </clause>

  <clause id="16319">
    <literal><![CDATA[
      a(x,y,z * L(z,u,y)) * x = R(x,y,z * L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,16305,a)].">
      <j1 rule="hyper" parents="38 2295 16305"/>
    </justification>
  </clause>

  <clause id="16320">
    <literal><![CDATA[
      a(x,y,z * L(z,u,y)) * x = L(x,y,z \ L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,9207,a(flip),b,16319,a),flip(a)].">
      <j1 rule="hyper" parents="316 9207 16319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16321">
    <literal><![CDATA[
      L(R(x,y,z) \ x,u,y) = R(x,y,L(z,u,y)) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,14630,a(flip),b,16315,a)].">
      <j1 rule="hyper" parents="63 14630 16315"/>
    </justification>
  </clause>

  <clause id="16322">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * (u * L(R(x,z,y) \ x,w,z)) = a(x,z,L(y,w,z)) \ u
    ]]></literal>
    <justification jstring="[para(16321(a,2),15408(a,1,2,2))].">
      <j1 rule="para" parents="16321 15408"/>
    </justification>
  </clause>

  <clause id="16324">
    <literal><![CDATA[
      a(L(x,y,z),z,y) \ a(u,w,y * (y * a(y,z,x))) = a(L(x,y,z),z,L(y,w,u)) \ 1
    ]]></literal>
    <justification jstring="[para(16310(a,1),15635(a,1,2))].">
      <j1 rule="para" parents="16310 15635"/>
    </justification>
  </clause>

  <clause id="16325">
    <literal><![CDATA[
      L(a(x,y,z),L(z,u,w),v5) = L(a(x,y,z),z,L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14596,a(flip),b,16265,a)].">
      <j1 rule="hyper" parents="63 14596 16265"/>
    </justification>
  </clause>

  <clause id="16326">
    <literal><![CDATA[
      L(a(x,y,z \ u),z \ u,L(w,z,z)) = L(a(x,y,z \ u),(z \ 1) * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10993,a(flip),b,16325,a),flip(a)].">
      <j1 rule="hyper" parents="63 10993 16325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16327">
    <literal><![CDATA[
      L(a(x,y,z),z,L(u,w,z)) = L(a(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,7639,a(flip),b,16325,a),flip(a)].">
      <j1 rule="hyper" parents="63 7639 16325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16329">
    <literal><![CDATA[
      L(L(a(x,y,z),z,L(u,w,v5)),z,y) = L(L(z,y,x) \ z,L(z,w,v5),u)
    ]]></literal>
    <justification jstring="[para(16325(a,1),13408(a,1,1))].">
      <j1 rule="para" parents="16325 13408"/>
    </justification>
  </clause>

  <clause id="16330">
    <literal><![CDATA[
      L(a(x,y,z),z,u \ z) = L(a(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11637,a(flip),b,16327,a)].">
      <j1 rule="hyper" parents="63 11637 16327"/>
    </justification>
  </clause>

  <clause id="16333">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,u,w),v5) = L(L(x,y,z) \ x,x,L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,13408,a(flip),b,16329,a),flip(a)].">
      <j1 rule="hyper" parents="63 13408 16329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16335">
    <literal><![CDATA[
      R(L(L(x,y,z) \ x,x,L(u,w,v5)),v6,v7) = L(R(L(x,y,z) \ x,v6,v7),L(x,w,v5),u)
    ]]></literal>
    <justification jstring="[para(16333(a,1),29(a,1,1))].">
      <j1 rule="para" parents="16333 29"/>
    </justification>
  </clause>

  <clause id="16341">
    <literal><![CDATA[
      a(x,y,z * L(z,a(u,w,v5),v6)) \ v6 = L(v6,a(u,w,v5),z * L(z,y,x))
    ]]></literal>
    <justification jstring="[para(15295(a,1),16207(a,1,1))].">
      <j1 rule="para" parents="15295 16207"/>
    </justification>
  </clause>

  <clause id="16345">
    <literal><![CDATA[
      L(x,a(y,z,u),w * L(w,v5,v6)) = a(v6,v5,a(w,a(y,z,u),x)) \ x
    ]]></literal>
    <justification jstring="[para(16202(a,1),16341(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16202 16341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16346">
    <literal><![CDATA[
      L(x,a(y,z,u),w * L(w,v5,v6)) = x * a(v6,v5,a(w,a(y,z,u),x))
    ]]></literal>
    <justification jstring="[hyper(316,a,14470,a(flip),b,16345,a),flip(a)].">
      <j1 rule="hyper" parents="316 14470 16345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16350">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * L(L(y,x,z) \ y,u,a(w,v5,z)) = L(a(z,x,y),u,a(w,v5,z))
    ]]></literal>
    <justification jstring="[para(6853(a,1),16290(a,1,1,3,1))].">
      <j1 rule="para" parents="6853 16290"/>
    </justification>
  </clause>

  <clause id="16351">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * L(L(y,x,z) \ y,u,a(z,w,v5)) = L(a(z,x,y),u,a(z,w,v5))
    ]]></literal>
    <justification jstring="[para(8397(a,1),16290(a,1,1,3,1))].">
      <j1 rule="para" parents="8397 16290"/>
    </justification>
  </clause>

  <clause id="16353">
    <literal><![CDATA[
      L(a(x,y,z \ u),z \ u,L(w,z,z)) = L(a(x,y,z \ u),u * z,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,15791,a(flip),b,16326,a),flip(a)].">
      <j1 rule="hyper" parents="316 15791 16326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16354">
    <literal><![CDATA[
      L(a(x,y,z \ u),z \ u,u \ (z \ u)) = L(a(x,y,z \ u),u * z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11639,a(flip),b,16353,a)].">
      <j1 rule="hyper" parents="63 11639 16353"/>
    </justification>
  </clause>

  <clause id="16355">
    <literal><![CDATA[
      L(a(x,y,z \ u),z \ u,u) = L(a(x,y,z \ u),u * z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16330,a(flip),b,16354,a)].">
      <j1 rule="hyper" parents="63 16330 16354"/>
    </justification>
  </clause>

  <clause id="16356">
    <literal><![CDATA[
      L(a(x,y,z \ u),z \ u,z) = L(a(x,y,z \ u),u * z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9120,a(flip),b,16355,a)].">
      <j1 rule="hyper" parents="63 9120 16355"/>
    </justification>
  </clause>

  <clause id="16357">
    <literal><![CDATA[
      x \ (L(a(y,z,x \ u),u * x,u) \ u) = a(y,z,x \ u) \ (x \ u)
    ]]></literal>
    <justification jstring="[para(16355(a,1),14684(a,1,2,1))].">
      <j1 rule="para" parents="16355 14684"/>
    </justification>
  </clause>

  <clause id="16358">
    <literal><![CDATA[
      x \ (a(y,z,u) * (x * a(w,a(y,z,u),x))) = a(y,z,u) * a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5447,a(flip),b,16190,a)].">
      <j1 rule="hyper" parents="63 5447 16190"/>
    </justification>
  </clause>

  <clause id="16359">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5 * a(x,a(y,z,u),w),v6)) = a(x,a(u,z,y),L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,16250,a,b,16249,a),flip(a)].">
      <j1 rule="hyper" parents="316 16250 16249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16360">
    <literal><![CDATA[
      (a(x,y,L(z,u,y)) \ a(x,y,z)) * w = a(x,y,z) * (a(x,y,L(z,u,y)) \ w)
    ]]></literal>
    <justification jstring="[para(16295(a,2),16300(a,1,1,1))].">
      <j1 rule="para" parents="16295 16300"/>
    </justification>
  </clause>

  <clause id="16361">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * (u * L(R(x,z,y) \ x,y,z)) = (L(y,z,x) \ y) \ u
    ]]></literal>
    <justification jstring="[para(14510(a,1),16322(a,2,1))].">
      <j1 rule="para" parents="14510 16322"/>
    </justification>
  </clause>

  <clause id="16362">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * (u * L(R(x,z,y) \ x,y,z)) = u * (y \ L(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,14358,a(flip),b,16361,a),flip(a)].">
      <j1 rule="hyper" parents="316 14358 16361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16363">
    <literal><![CDATA[
      x \ ((x * a(y,z,u)) * w) = a(y,z,u) * (w * a(x,a(y,z,u),w))
    ]]></literal>
    <justification jstring="[hyper(38,a,8450,a,b,16358,a)].">
      <j1 rule="hyper" parents="38 8450 16358"/>
    </justification>
  </clause>

  <clause id="16364">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (u * w) = a(x,y,z) * (w * a(a(x,y,z) \ u,a(x,y,z),w))
    ]]></literal>
    <justification jstring="[para(2274(a,1),16363(a,1,2,1))].">
      <j1 rule="para" parents="2274 16363"/>
    </justification>
  </clause>

  <clause id="16365">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (u * w) = a(x,y,z) * (w * a(a(x,y,z) * u,a(x,y,z),w))
    ]]></literal>
    <justification jstring="[para(14413(a,1),16364(a,2,2,2))].">
      <j1 rule="para" parents="14413 16364"/>
    </justification>
  </clause>

  <clause id="16366">
    <literal><![CDATA[
      a(x,y,z) * (u * a(x * a(z,y,x),a(x,y,z),u)) = (a(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[para(14923(a,1),16365(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14923 16365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16367">
    <literal><![CDATA[
      L(R(L(x,y,z) \ x,u,w),L(x,v5,v6),v7) = L(R(L(x,y,z) \ x,u,w),x,L(v7,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,29,a(flip),b,16335,a),flip(a)].">
      <j1 rule="hyper" parents="63 29 16335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16368">
    <literal><![CDATA[
      a(x,y,L(z,u,a(w,v5,x))) = L(a(x,y,z),u,a(w,v5,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,15455,a(flip),b,16350,a)].">
      <j1 rule="hyper" parents="63 15455 16350"/>
    </justification>
  </clause>

  <clause id="16369">
    <literal><![CDATA[
      a(x,y,L(z,u,a(x,w,v5))) = L(a(x,y,z),u,a(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,15455,a(flip),b,16351,a)].">
      <j1 rule="hyper" parents="63 15455 16351"/>
    </justification>
  </clause>

  <clause id="16371">
    <literal><![CDATA[
      L(R(L(x,y,z) \ x,u,w),L(x,v5,v6),v7) = L(L(L(x,y,z) \ x,u,w),x,L(v7,v5,v6))
    ]]></literal>
    <justification jstring="[para(11560(a,1),16367(a,2,1))].">
      <j1 rule="para" parents="11560 16367"/>
    </justification>
  </clause>

  <clause id="16372">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),L(x,v5,v6),v7) = L(L(L(x,y,z) \ x,u,w),x,L(v7,v5,v6))
    ]]></literal>
    <justification jstring="[para(11560(a,1),16371(a,1,1))].">
      <j1 rule="para" parents="11560 16371"/>
    </justification>
  </clause>

  <clause id="16376">
    <literal><![CDATA[
      L(L(x,x,a(y,y,L(z,u,w))),y,L(a(z,y,x),u,w)) = L(x,L(a(z,y,x),u,w),y)
    ]]></literal>
    <justification jstring="[para(14022(a,1),16288(a,1,1))].">
      <j1 rule="para" parents="14022 16288"/>
    </justification>
  </clause>

  <clause id="16377">
    <literal><![CDATA[
      a(L(x,y,z),z,y) \ a(u,w,L(a(y,z,x),y,y)) = a(L(x,y,z),z,L(y,w,u)) \ 1
    ]]></literal>
    <justification jstring="[para(5810(a,1),16324(a,1,2))].">
      <j1 rule="para" parents="5810 16324"/>
    </justification>
  </clause>

  <clause id="16378">
    <literal><![CDATA[
      a(L(x,y,z),z,y) \ a(u,w,a(y,z,x)) = a(L(x,y,z),z,L(y,w,u)) \ 1
    ]]></literal>
    <justification jstring="[para(8510(a,1),16377(a,1,2,3))].">
      <j1 rule="para" parents="8510 16377"/>
    </justification>
  </clause>

  <clause id="16380">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ a(y,x,a(z,u,w))) = a(y,a(z,u,w),x * a(y,x,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,1129,a(flip),b,16217,a)].">
      <j1 rule="hyper" parents="63 1129 16217"/>
    </justification>
  </clause>

  <clause id="16381">
    <literal><![CDATA[
      L(x,y \ (1 / z),y \ ((1 / z) * L((1 / z) \ y,y,z))) = x * a(y \ z,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[para(1252(a,1),16237(a,1,3))].">
      <j1 rule="para" parents="1252 16237"/>
    </justification>
  </clause>

  <clause id="16382">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) * a(y,a(z,u,y),L(x,w,v5)) = x * a(a(x,y,a(z,u,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(11688(a,1),16246(a,2,2,1))].">
      <j1 rule="para" parents="11688 16246"/>
    </justification>
  </clause>

  <clause id="16383">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ a(y,x,a(z,u,w))) = a(y,a(z,u,w),L(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,13644,a(flip),b,16380,a),flip(a)].">
      <j1 rule="hyper" parents="316 13644 16380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16384">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ a(y,x,a(z,u,w))) = a(y,a(z,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,16281,a(flip),b,16383,a),flip(a)].">
      <j1 rule="hyper" parents="316 16281 16383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16385">
    <literal><![CDATA[
      L(x,y \ (1 / z),y \ ((z \ 1) * L((z \ 1) \ y,y,z))) = x * a(y \ z,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[para(4979(a,1),16381(a,1,3,2))].">
      <j1 rule="para" parents="4979 16381"/>
    </justification>
  </clause>

  <clause id="16386">
    <literal><![CDATA[
      L(x,y \ (1 / z),y \ (z * L(z \ y,y,z))) = x * a(y \ z,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[para(1350(a,1),16385(a,1,3,2))].">
      <j1 rule="para" parents="1350 16385"/>
    </justification>
  </clause>

  <clause id="16387">
    <literal><![CDATA[
      L(x,y \ (1 / z),a(z,y,z * y) \ 1) = x * a(y \ z,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[para(9981(a,1),16386(a,1,3))].">
      <j1 rule="para" parents="9981 16386"/>
    </justification>
  </clause>

  <clause id="16392">
    <literal><![CDATA[
      (x * (((y \ z) / z) * y)) \ ((y \ z) * (L(y \ z,y,y \ 1) \ x)) = a(y \ z,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[para(13618(a,1),16283(a,1,2))].">
      <j1 rule="para" parents="13618 16283"/>
    </justification>
  </clause>

  <clause id="16393">
    <literal><![CDATA[
      (x * (((y \ z) / z) * y)) \ ((y \ z) * (((1 / y) * z) \ x)) = a(y \ z,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[para(887(a,1),16392(a,1,2,2,1))].">
      <j1 rule="para" parents="887 16392"/>
    </justification>
  </clause>

  <clause id="16394">
    <literal><![CDATA[
      a(x \ y,a(y,x,x),z) = a(y * x,a(x,x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12348,a(flip),b,16393,a),flip(a)].">
      <j1 rule="hyper" parents="63 12348 16393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16395">
    <literal><![CDATA[
      a(a(x,y,y),y \ x,z) = a(x * y,a(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,16239,a,b,16394,a)].">
      <j1 rule="hyper" parents="63 16239 16394"/>
    </justification>
  </clause>

  <clause id="16396">
    <literal><![CDATA[
      a(x \ y,a(x,x,y),z) = a(y * x,a(x,x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13658,a,b,16394,a)].">
      <j1 rule="hyper" parents="63 13658 16394"/>
    </justification>
  </clause>

  <clause id="16397">
    <literal><![CDATA[
      (x \ y) * a(y * x,a(x,x,y),z) = L(x \ y,a(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(139,a,16394,a(flip),b,16189,a)].">
      <j1 rule="hyper" parents="139 16394 16189"/>
    </justification>
  </clause>

  <clause id="16398">
    <literal><![CDATA[
      (((x / y) * (y * a(z,y \ x,y))) / a(z,y \ x,y)) \ x = a(x * y,a(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,15579,a,b,16396,a)].">
      <j1 rule="hyper" parents="63 15579 16396"/>
    </justification>
  </clause>

  <clause id="16399">
    <literal><![CDATA[
      (a(x \ y,x,a(z,x \ y,x)) * y) \ y = a(y * x,a(x,x,y),z)
    ]]></literal>
    <justification jstring="[para(14566(a,1),16398(a,1,1))].">
      <j1 rule="para" parents="14566 16398"/>
    </justification>
  </clause>

  <clause id="16400">
    <literal><![CDATA[
      (a(x,y,a(z,y \ x,y)) * x) \ x = a(x * y,a(y,y,x),z)
    ]]></literal>
    <justification jstring="[para(9988(a,1),16399(a,1,1,1))].">
      <j1 rule="para" parents="9988 16399"/>
    </justification>
  </clause>

  <clause id="16401">
    <literal><![CDATA[
      L(x,y,a(y,y \ x,z)) \ x = a(x * y,a(y,y,x),z)
    ]]></literal>
    <justification jstring="[para(13697(a,1),16400(a,1,1))].">
      <j1 rule="para" parents="13697 16400"/>
    </justification>
  </clause>

  <clause id="16402">
    <literal><![CDATA[
      a(x * y,a(y,y,x),z) = a(y,a(y,y \ x,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11771,a(flip),b,16401,a),flip(a)].">
      <j1 rule="hyper" parents="63 11771 16401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16403">
    <literal><![CDATA[
      a(x \ y,a(x,x,y),z) = a(x,a(x,x \ y,z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16396,a,b,16402,a)].">
      <j1 rule="hyper" parents="63 16396 16402"/>
    </justification>
  </clause>

  <clause id="16404">
    <literal><![CDATA[
      a(a(x,y,y),y \ x,z) = a(y,a(y,y \ x,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,16395,a,b,16402,a)].">
      <j1 rule="hyper" parents="63 16395 16402"/>
    </justification>
  </clause>

  <clause id="16405">
    <literal><![CDATA[
      a(x,a(x,x \ y,z),y) = a(z,y * x,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13709,a(flip),b,16402,a),flip(a)].">
      <j1 rule="hyper" parents="63 13709 16402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16406">
    <literal><![CDATA[
      (x \ y) * a(x,a(x,x \ y,z),y) = L(x \ y,a(y,x,x),z)
    ]]></literal>
    <justification jstring="[para(16402(a,1),16397(a,1,2))].">
      <j1 rule="para" parents="16402 16397"/>
    </justification>
  </clause>

  <clause id="16407">
    <literal><![CDATA[
      a(x,x,a(x \ y,x \ y,z)) = a(x,a(x,x \ y,z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15346,a,b,16403,a)].">
      <j1 rule="hyper" parents="63 15346 16403"/>
    </justification>
  </clause>

  <clause id="16408">
    <literal><![CDATA[
      x \ L(y,a(z,x \ y,x),x) = L(x \ y,a(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,16227,a(flip),b,16406,a)].">
      <j1 rule="hyper" parents="63 16227 16406"/>
    </justification>
  </clause>

  <clause id="16409">
    <literal><![CDATA[
      x \ L(y,x,a(z,x \ y,x)) = L(x \ y,a(y,x,x),z)
    ]]></literal>
    <justification jstring="[para(6997(a,1),16408(a,1,2))].">
      <j1 rule="para" parents="6997 16408"/>
    </justification>
  </clause>

  <clause id="16410">
    <literal><![CDATA[
      L(x \ y,x,a(z,x \ y,x)) = L(x \ y,a(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11697,a,b,16409,a)].">
      <j1 rule="hyper" parents="63 11697 16409"/>
    </justification>
  </clause>

  <clause id="16411">
    <literal><![CDATA[
      a(x * (y \ z),y,a(x,y \ z,y)) = z \ (y * L(y \ z,a(z,y,y),x))
    ]]></literal>
    <justification jstring="[para(16410(a,1),14846(a,2,2,2))].">
      <j1 rule="para" parents="16410 14846"/>
    </justification>
  </clause>

  <clause id="16412">
    <literal><![CDATA[
      a(x * (y \ z),y,a(x,y \ z,y)) = a(z \ y,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[hyper(316,a,16200,a(flip),b,16411,a),flip(a)].">
      <j1 rule="hyper" parents="316 16200 16411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16413">
    <literal><![CDATA[
      a(x \ y,x,a(z,x \ y,x)) = a(y \ x,a(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13937,a(flip),b,16412,a)].">
      <j1 rule="hyper" parents="63 13937 16412"/>
    </justification>
  </clause>

  <clause id="16414">
    <literal><![CDATA[
      a(x \ y,a(x,y,y),z) = a(x,y,a(z,y \ x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,9988,a(flip),b,16413,a),flip(a)].">
      <j1 rule="hyper" parents="63 9988 16413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16415">
    <literal><![CDATA[
      a(x,y \ z,a(y,z,z)) = a(y,z,a(x,z \ y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16222,a(flip),b,16414,a)].">
      <j1 rule="hyper" parents="63 16222 16414"/>
    </justification>
  </clause>

  <clause id="16416">
    <literal><![CDATA[
      L(a(x,y * z,z * L(z \ 1,u,w)),z,y * z) = a(x,y * z,L(z * R(z \ 1,u,w),z,y))
    ]]></literal>
    <justification jstring="[para(7272(a,1),16301(a,1,1))].">
      <j1 rule="para" parents="7272 16301"/>
    </justification>
  </clause>

  <clause id="16417">
    <literal><![CDATA[
      L(a(x,y * z,z \ L(z,u,w)),z,y * z) = a(x,y * z,L(z * R(z \ 1,u,w),z,y))
    ]]></literal>
    <justification jstring="[para(1064(a,1),16416(a,1,1,3))].">
      <j1 rule="para" parents="1064 16416"/>
    </justification>
  </clause>

  <clause id="16418">
    <literal><![CDATA[
      L(a(x,y * z,z * L(z,u,w)),z,y * z) = a(x,y * z,L(z * R(z \ 1,u,w),z,y))
    ]]></literal>
    <justification jstring="[para(5566(a,1),16417(a,1,1))].">
      <j1 rule="para" parents="5566 16417"/>
    </justification>
  </clause>

  <clause id="16419">
    <literal><![CDATA[
      a(x,y * z,L(z * R(z \ 1,u,w),z,y)) = a(x,y * z,L(z * L(z,u,w),z,y * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16295,a,b,16418,a),flip(a)].">
      <j1 rule="hyper" parents="63 16295 16418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16420">
    <literal><![CDATA[
      (a(x,y,L(z,u,w)) \ v5) * (u \ L(u,w,z \ L(z,y,x))) = a(x,y,u \ (w \ ((w * z) * u))) \ v5
    ]]></literal>
    <justification jstring="[para(9207(a,1),16309(a,1,2,2))].">
      <j1 rule="para" parents="9207 16309"/>
    </justification>
  </clause>

  <clause id="16421">
    <literal><![CDATA[
      (a(x,y,L(z,u,w)) \ v5) * (u \ L(u,w,z \ L(z,y,x))) = a(x,y,L(L(z,u,w),w,u)) \ v5
    ]]></literal>
    <justification jstring="[para(11904(a,1),16420(a,2,1))].">
      <j1 rule="para" parents="11904 16420"/>
    </justification>
  </clause>

  <clause id="16422">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * a(x,a(x,y,z),L(y,u,w)) = L(1 / L(x \ L(x,y,z),u,w),x,y) \ 1
    ]]></literal>
    <justification jstring="[para(8380(a,1),16258(a,2,1,1,2))].">
      <j1 rule="para" parents="8380 16258"/>
    </justification>
  </clause>

  <clause id="16423">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * a(x,a(x,y,z),L(y,u,w)) = L(L(x \ L(x,y,z),u,w) \ 1,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(5019(a,1),16422(a,2,1,1))].">
      <j1 rule="para" parents="5019 16422"/>
    </justification>
  </clause>

  <clause id="16424">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * a(x,a(x,y,z),L(y,u,w)) = L(L(L(x,y,z) \ x,u,w),x,y) \ 1
    ]]></literal>
    <justification jstring="[para(13378(a,1),16423(a,2,1,1))].">
      <j1 rule="para" parents="13378 16423"/>
    </justification>
  </clause>

  <clause id="16425">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * a(x,a(x,y,z),L(y,u,w)) = L(a(z,y,x),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(10006(a,1),16424(a,2,1))].">
      <j1 rule="para" parents="10006 16424"/>
    </justification>
  </clause>

  <clause id="16426">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * a(x,a(x,y,z),L(y,u,w)) = L(a(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,13442,a,b,16425,a),flip(a)].">
      <j1 rule="hyper" parents="316 13442 16425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16427">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * a(x,x,a(y,y,L(z,u,w))) = L(a(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(16274(a,1),16426(a,1,2))].">
      <j1 rule="para" parents="16274 16426"/>
    </justification>
  </clause>

  <clause id="16428">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) * a(y \ x,y \ x,a(z,z,L(u,y \ x,y))) = L(a(u,z,y \ x) \ 1,y \ x,y)
    ]]></literal>
    <justification jstring="[para(475(a,1),16427(a,1,1))].">
      <j1 rule="para" parents="475 16427"/>
    </justification>
  </clause>

  <clause id="16429">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) * a(x * y,x * y,a(z,z,L(u,x,y))) = L(a(u,z,x * y) \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(10113(a,1),16427(a,1,1))].">
      <j1 rule="para" parents="10113 16427"/>
    </justification>
  </clause>

  <clause id="16430">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) * a(x \ y,y * x,a(z,z,u)) = L(a(u,z,x * y) \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(14100(a,1),16429(a,1,2))].">
      <j1 rule="para" parents="14100 16429"/>
    </justification>
  </clause>

  <clause id="16433">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ u) * a(L(x,y,z) \ u,a(w,v5,v6),v7)) = R(x,y,z) * L(R(x,y,z) \ u,a(w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(6771(a,1),16225(a,1,2,2))].">
      <j1 rule="para" parents="6771 16225"/>
    </justification>
  </clause>

  <clause id="16434">
    <literal><![CDATA[
      R(x,y,z) * L(R(x,y,z) \ u,a(w,v5,v6),v7) = L(x,y,z) * L(L(x,y,z) \ u,a(w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(16196(a,1),16433(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16196 16433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16435">
    <literal><![CDATA[
      (a(x,y,z) \ ((L(u,u,a(x,y,z)) \ ((u \ ((u * u) * a(x,y,z))) * w)) / w)) * w = L(w,a(z,y,x),L(u,u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(5264(a,1),16231(a,1,1,2,1,1))].">
      <j1 rule="para" parents="5264 16231"/>
    </justification>
  </clause>

  <clause id="16436">
    <literal><![CDATA[
      (a(x,y,z) \ ((L(u,u,a(x,y,z)) \ (((u \ a(x,y,z)) * (u * u)) * w)) / w)) * w = L(w,a(z,y,x),L(u,u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(2300(a,1),16435(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="2300 16435"/>
    </justification>
  </clause>

  <clause id="16437">
    <literal><![CDATA[
      (a(x,y,z) \ ((L(u,u,a(x,y,z)) \ (((1 / u) \ a(x,y,z)) * w)) / w)) * w = L(w,a(z,y,x),L(u,u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(5359(a,1),16436(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="5359 16436"/>
    </justification>
  </clause>

  <clause id="16438">
    <literal><![CDATA[
      L(x,a(y,z,u),L(w,w,a(u,z,y))) = (a(u,z,y) \ (a(u,z,y) * a(w,a(u,z,y),x))) * x
    ]]></literal>
    <justification jstring="[para(16205(a,1),16437(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16205 16437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16439">
    <literal><![CDATA[
      L(x,a(y,z,u),L(w,w,a(u,z,y))) = a(w,a(u,z,y),x) * x
    ]]></literal>
    <justification jstring="[para(9(a,1),16438(a,2,1))].">
      <j1 rule="para" parents="9 16438"/>
    </justification>
  </clause>

  <clause id="16440">
    <literal><![CDATA[
      L(x,a(y,z,u),L(w,w,a(u,z,y))) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(316,a,16220,a(flip),b,16439,a),flip(a)].">
      <j1 rule="hyper" parents="316 16220 16439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16442">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,w),a(u,z,y),w) = L(x,L(w,w,a(y,z,u)),a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15514,a(flip),b,16440,a),flip(a)].">
      <j1 rule="hyper" parents="63 15514 16440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16443">
    <literal><![CDATA[
      L(x,L(y,y,a(z,u,w)),a(w,u,z)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14027,a(flip),b,16442,a),flip(a)].">
      <j1 rule="hyper" parents="63 14027 16442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16444">
    <literal><![CDATA[
      a(x,x * a(y,a(z,u,w),v5),a(y,a(z,u,w),v5)) = a(y,a(z,u,w),L(v5,x,x)) \ a(y,a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(16359(a,1),16259(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16359 16259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16445">
    <literal><![CDATA[
      (((x \ y) * (y \ x)) * y) \ L(((x \ (y * ((x \ y) \ 1))) \ 1) * y,z,u) = (x * (1 / (y \ x))) \ L(y * (x \ (y * ((x \ y) \ 1))),z,u)
    ]]></literal>
    <justification jstring="[para(7421(a,1),9593(a,1,1,1))].">
      <j1 rule="para" parents="7421 9593"/>
    </justification>
  </clause>

  <clause id="16446">
    <literal><![CDATA[
      (x / ((x \ y) \ 1)) \ L(((x \ (y * ((x \ y) \ 1))) \ 1) * y,z,u) = (x * (1 / (y \ x))) \ L(y * (x \ (y * ((x \ y) \ 1))),z,u)
    ]]></literal>
    <justification jstring="[para(9336(a,1),16445(a,1,1))].">
      <j1 rule="para" parents="9336 16445"/>
    </justification>
  </clause>

  <clause id="16447">
    <literal><![CDATA[
      (x * (1 / (y \ x))) \ L(y * (x \ (y * ((x \ y) \ 1))),z,u) = (x / ((x \ y) \ 1)) \ L(((x \ y) * (y \ x)) * y,z,u)
    ]]></literal>
    <justification jstring="[para(7421(a,1),16446(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7421 16446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16448">
    <literal><![CDATA[
      (x * (1 / (y \ x))) \ L(y * (x \ (y * ((x \ y) \ 1))),z,u) = (x / ((x \ y) \ 1)) \ L(x / ((x \ y) \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(9336(a,1),16447(a,2,2,1))].">
      <j1 rule="para" parents="9336 16447"/>
    </justification>
  </clause>

  <clause id="16449">
    <literal><![CDATA[
      (x * (1 / (y \ x))) \ L(y * (x \ (y * ((x \ y) \ 1))),z,u) = ((x \ y) \ 1) \ (x * L(x \ ((x \ y) \ 1),z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5189,a(flip),b,16448,a),flip(a)].">
      <j1 rule="hyper" parents="316 5189 16448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16450">
    <literal><![CDATA[
      (x * (1 / (y \ x))) \ L(y * (x \ (y * ((x \ y) \ 1))),z,u) = (x \ y) \ (x * L(x \ (x \ y),z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,9495,a(flip),b,16449,a),flip(a)].">
      <j1 rule="hyper" parents="316 9495 16449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16451">
    <literal><![CDATA[
      (x * (1 / (y \ x))) \ L(y * (x \ (y * ((x \ y) \ 1))),z,u) = (x \ y) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1363(a,1),16450(a,2,2))].">
      <j1 rule="para" parents="1363 16450"/>
    </justification>
  </clause>

  <clause id="16452">
    <literal><![CDATA[
      (x * (1 / (y \ x))) \ L(x * (1 / (y \ x)),z,u) = (x \ y) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7438(a,1),16451(a,1,2,1))].">
      <j1 rule="para" parents="7438 16451"/>
    </justification>
  </clause>

  <clause id="16453">
    <literal><![CDATA[
      K(x,y) * ((z * (1 / (x \ z))) * L((z * (1 / (x \ z))) \ K(y,x),u,w)) = T(z * (1 / (x \ z)),y) \ L(K(x,y) * (z * (1 / (x \ z))),u,w)
    ]]></literal>
    <justification jstring="[para(2967(a,1),11448(a,1,2,2,1,2))].">
      <j1 rule="para" parents="2967 11448"/>
    </justification>
  </clause>

  <clause id="16454">
    <literal><![CDATA[
      K(x,y) * (z * ((1 / (x \ z)) * L((1 / (x \ z)) \ (z \ K(y,x)),u,w))) = T(z * (1 / (x \ z)),y) \ L(K(x,y) * (z * (1 / (x \ z))),u,w)
    ]]></literal>
    <justification jstring="[para(879(a,1),16453(a,1,2))].">
      <j1 rule="para" parents="879 16453"/>
    </justification>
  </clause>

  <clause id="16455">
    <literal><![CDATA[
      K(x,y) * (z * (((x \ z) \ 1) * L(((x \ z) \ 1) \ (z \ K(y,x)),u,w))) = T(z * (1 / (x \ z)),y) \ L(K(x,y) * (z * (1 / (x \ z))),u,w)
    ]]></literal>
    <justification jstring="[para(4979(a,1),16454(a,1,2,2))].">
      <j1 rule="para" parents="4979 16454"/>
    </justification>
  </clause>

  <clause id="16456">
    <literal><![CDATA[
      T(x * (1 / (y \ x)),z) \ L(K(y,z) * (x * (1 / (y \ x))),u,w) = K(y,z) * (x * ((y \ x) * L((y \ x) \ (x \ K(z,y)),u,w)))
    ]]></literal>
    <justification jstring="[para(1350(a,1),16455(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1350 16455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16457">
    <literal><![CDATA[
      T(x * (1 / (y \ x)),z) \ L(K(y,z) * (x * (1 / (y \ x))),u,w) = (x * (y \ x)) \ L(x * (y \ x),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,5199,a(flip),b,16456,a),flip(a)].">
      <j1 rule="hyper" parents="316 5199 16456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16459">
    <literal><![CDATA[
      T(x * (1 / (y \ x)),z) \ L(T(x * (1 / (y \ x)),z),u,w) = (x * (y \ x)) \ L(x * (y \ x),u,w)
    ]]></literal>
    <justification jstring="[para(11447(a,1),16457(a,1,2,1))].">
      <j1 rule="para" parents="11447 16457"/>
    </justification>
  </clause>

  <clause id="16460">
    <literal><![CDATA[
      (x * (1 / (y \ x))) \ L(x * (1 / (y \ x)),z,u) = (x * (y \ x)) \ L(x * (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4346,a(flip),b,16459,a)].">
      <j1 rule="hyper" parents="63 4346 16459"/>
    </justification>
  </clause>

  <clause id="16461">
    <literal><![CDATA[
      (x * (y \ x)) \ L(x * (y \ x),z,u) = (x \ y) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16452,a(flip),b,16460,a),flip(a)].">
      <j1 rule="hyper" parents="63 16452 16460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16462">
    <literal><![CDATA[
      ((x \ y) * y) \ L((x \ y) * y,z,u) = (y \ x) \ (y \ L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4877,a,b,16461,a)].">
      <j1 rule="hyper" parents="63 4877 16461"/>
    </justification>
  </clause>

  <clause id="16463">
    <literal><![CDATA[
      L((x \ y) * y,z,u) \ ((x \ y) * y) = ((y \ x) \ (y \ L(x,z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(16462(a,1),1894(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16462 1894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16464">
    <literal><![CDATA[
      L((x \ y) * y,z,u) \ ((x \ y) * y) = (y \ L(x,z,u)) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,13975,a(flip),b,16463,a),flip(a)].">
      <j1 rule="hyper" parents="316 13975 16463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16465">
    <literal><![CDATA[
      (x \ L(y,z,z)) \ (x \ y) = a(z,z,(y \ x) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4952,a(flip),b,16464,a),flip(a)].">
      <j1 rule="hyper" parents="63 4952 16464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16477">
    <literal><![CDATA[
      (a(x,y,z) * (u \ (w * a(x,y,z)))) \ (u \ ((w * a(x,y,z)) * ((v5 * a(x,y,z)) / v5))) = a(u,u \ (w * ((v5 * a(x,y,z)) / v5)),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(2287(a,1),7227(a,1,1,2,2,2))].">
      <j1 rule="para" parents="2287 7227"/>
    </justification>
  </clause>

  <clause id="16478">
    <literal><![CDATA[
      a(x,x \ (y * ((z * a(u,w,v5)) / z)),a(u,w,v5)) = (a(u,w,v5) * (x \ (y * a(u,w,v5)))) \ (x \ ((y * a(u,w,v5)) * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(2287(a,1),16477(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2287 16477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16482">
    <literal><![CDATA[
      a(x,x \ (y * ((z * a(u,w,v5)) / z)),a(u,w,v5)) = (a(u,w,v5) * (x \ (y * a(u,w,v5)))) \ (x \ (v5 * (L(L(v5,w,u),w,u) \ y)))
    ]]></literal>
    <justification jstring="[para(14726(a,1),16478(a,2,2,2))].">
      <j1 rule="para" parents="14726 16478"/>
    </justification>
  </clause>

  <clause id="16483">
    <literal><![CDATA[
      a(x,x \ (y * ((z * a(u,w,v5)) / z)),a(u,w,v5)) = (a(u,w,v5) * (x \ (y * a(u,w,v5)))) \ ((x \ y) * (a(u,w,v5) * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(14075(a,1),16482(a,2,2))].">
      <j1 rule="para" parents="14075 16482"/>
    </justification>
  </clause>

  <clause id="16484">
    <literal><![CDATA[
      a(x,x \ (y * ((z * a(u,w,v5)) / z)),a(u,w,v5)) = ((a(u,w,v5) * (x \ (y * a(u,w,v5)))) \ (x \ y)) * (a(u,w,v5) * a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,388,a(flip),b,16483,a),flip(a)].">
      <j1 rule="hyper" parents="316 388 16483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16485">
    <literal><![CDATA[
      a(x,x \ (y * ((z * a(u,w,v5)) / z)),a(u,w,v5)) = (a(u,w,v5) \ (x \ (y * a(u,w,v5)))) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(316,a,16081,a(flip),b,16484,a),flip(a)].">
      <j1 rule="hyper" parents="316 16081 16484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16486">
    <literal><![CDATA[
      a(x,x \ (y * ((z * a(u,w,v5)) / z)),a(u,w,v5)) = (a(u,w,v5) * (x \ (a(u,w,v5) \ y))) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(14787(a,1),16485(a,2,1))].">
      <j1 rule="para" parents="14787 16485"/>
    </justification>
  </clause>

  <clause id="16487">
    <literal><![CDATA[
      a(x,x \ (y * ((z * a(u,w,v5)) / z)),a(u,w,v5)) = a(x,x \ y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,14852,a(flip),b,16486,a),flip(a)].">
      <j1 rule="hyper" parents="316 14852 16486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16489">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),L(L(x,u,w),y,z) * (L(L(x,u,w),y,z) \ L(x,u,w)),w * u) = ((w * u) * L(L(x,u,w),y,z)) \ (w * (u * x))
    ]]></literal>
    <justification jstring="[para(13383(a,1),14884(a,1,1))].">
      <j1 rule="para" parents="13383 14884"/>
    </justification>
  </clause>

  <clause id="16490">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),L(x,u,w),w * u) = ((w * u) * L(L(x,u,w),y,z)) \ (w * (u * x))
    ]]></literal>
    <justification jstring="[para(10(a,1),16489(a,1,2))].">
      <j1 rule="para" parents="10 16489"/>
    </justification>
  </clause>

  <clause id="16491">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),x,L(w * u,u,w)) = ((w * u) * L(L(x,u,w),y,z)) \ (w * (u * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,16372,a(flip),b,16490,a)].">
      <j1 rule="hyper" parents="63 16372 16490"/>
    </justification>
  </clause>

  <clause id="16493">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),x,L(w * u,u,w)) = (w * (u * L(x,y,z))) \ (w * (u * x))
    ]]></literal>
    <justification jstring="[para(403(a,1),16491(a,2,1))].">
      <j1 rule="para" parents="403 16491"/>
    </justification>
  </clause>

  <clause id="16494">
    <literal><![CDATA[
      L(L(L(x,x,y) \ x,R(y,x,x),z),x,L(z * R(y,x,x),R(y,x,x),z)) = (z * (y * x)) \ (z * (R(y,x,x) * x))
    ]]></literal>
    <justification jstring="[para(7155(a,1),16493(a,2,1,2))].">
      <j1 rule="para" parents="7155 16493"/>
    </justification>
  </clause>

  <clause id="16495">
    <literal><![CDATA[
      L(L(a(x,y,y),R(x,y,y),z),y,L(z * R(x,y,y),R(x,y,y),z)) = (z * (x * y)) \ (z * (R(x,y,y) * y))
    ]]></literal>
    <justification jstring="[para(7290(a,1),16494(a,1,1,1))].">
      <j1 rule="para" parents="7290 16494"/>
    </justification>
  </clause>

  <clause id="16496">
    <literal><![CDATA[
      L(L(a(x,y,y),L(x,y,y),z),y,L(z * R(x,y,y),R(x,y,y),z)) = (z * (x * y)) \ (z * (R(x,y,y) * y))
    ]]></literal>
    <justification jstring="[para(10977(a,1),16495(a,1,1))].">
      <j1 rule="para" parents="10977 16495"/>
    </justification>
  </clause>

  <clause id="16497">
    <literal><![CDATA[
      L(a(x,y,L(y,L(x,y,y),z)),y,L(z * R(x,y,y),R(x,y,y),z)) = (z * (x * y)) \ (z * (R(x,y,y) * y))
    ]]></literal>
    <justification jstring="[para(13562(a,2),16496(a,1,1))].">
      <j1 rule="para" parents="13562 16496"/>
    </justification>
  </clause>

  <clause id="16498">
    <literal><![CDATA[
      L(L(x,y,z) \ (L(x,y,z) \ x),y,z) * (a(u,w,L(x,y,z) \ (L(x,y,z) \ x)) \ v5) = a(u,w,L(x,L(x,y,z),L(x,y,z))) \ ((L(x,y,z) \ 1) * v5)
    ]]></literal>
    <justification jstring="[para(8608(a,1),7000(a,2,1))].">
      <j1 rule="para" parents="8608 7000"/>
    </justification>
  </clause>

  <clause id="16499">
    <literal><![CDATA[
      L(L(x,y,z) \ (L(x,y,z) \ x),y,z) * (a(u,w,L(x,y,z) \ (L(x,y,z) \ x)) \ v5) = a(u,w,L(x,L(x,y,z),x)) \ ((L(x,y,z) \ 1) * v5)
    ]]></literal>
    <justification jstring="[para(7995(a,1),16498(a,2,1,3))].">
      <j1 rule="para" parents="7995 16498"/>
    </justification>
  </clause>

  <clause id="16500">
    <literal><![CDATA[
      L(L(x,y,z) \ (L(x,y,z) \ x),y,z) * (a(u,w,L(x,y,z) \ (L(x,y,z) \ x)) \ v5) = a(u,w,x) \ ((L(x,y,z) \ 1) * v5)
    ]]></literal>
    <justification jstring="[para(5574(a,1),16499(a,2,1))].">
      <j1 rule="para" parents="5574 16499"/>
    </justification>
  </clause>

  <clause id="16502">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * (a(u,w,L(x,y,z) \ (L(x,y,z) \ x)) \ v5) = a(u,w,x) \ ((L(x,y,z) \ 1) * v5)
    ]]></literal>
    <justification jstring="[para(1371(a,1),16500(a,1,1))].">
      <j1 rule="para" parents="1371 16500"/>
    </justification>
  </clause>

  <clause id="16504">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * (a(u,w,L(x,L(x,y,z),L(x,y,z))) \ v5) = a(u,w,x) \ ((L(x,y,z) \ 1) * v5)
    ]]></literal>
    <justification jstring="[para(8608(a,1),16502(a,1,2,1))].">
      <j1 rule="para" parents="8608 16502"/>
    </justification>
  </clause>

  <clause id="16505">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * (a(u,w,L(x,L(x,y,z),x)) \ v5) = a(u,w,x) \ ((L(x,y,z) \ 1) * v5)
    ]]></literal>
    <justification jstring="[para(7995(a,1),16504(a,1,2,1,3))].">
      <j1 rule="para" parents="7995 16504"/>
    </justification>
  </clause>

  <clause id="16506">
    <literal><![CDATA[
      a(x,y,z) \ ((L(z,u,w) \ 1) * v5) = (L(z,u,w) \ 1) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(5574(a,1),16505(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5574 16505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16508">
    <literal><![CDATA[
      a(x,y,z) * (R(x,y,z) \ L(u,L(x,y,z) \ 1,L(x,y,z))) = (L(x,y,z) \ 1) * (a(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14729,a,b,16506,a)].">
      <j1 rule="hyper" parents="63 14729 16506"/>
    </justification>
  </clause>

  <clause id="16510">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * (a(z,y,x) \ u) = a(x,y,z) * ((R(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(12614(a,1),16508(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12614 16508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16511">
    <literal><![CDATA[
      a(x,y,z) * ((R(x,y,z) \ 1) * x) = (x \ a(z,y,x)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14887,a(flip),b,16510,a),flip(a)].">
      <j1 rule="hyper" parents="63 14887 16510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16512">
    <literal><![CDATA[
      (R(x,y,z) \ a(x,y,z)) * x = (x \ a(z,y,x)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8659,a(flip),b,16511,a)].">
      <j1 rule="hyper" parents="63 8659 16511"/>
    </justification>
  </clause>

  <clause id="16513">
    <literal><![CDATA[
      (x \ a(y,z,x)) * L(x,z,y) = a(x \ a(z,z,y),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,15437,a(flip),b,16512,a),flip(a)].">
      <j1 rule="hyper" parents="63 15437 16512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16514">
    <literal><![CDATA[
      L(x,y,z) = ((x \ a(z,y,x)) \ 1) * a(x \ a(y,y,z),x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,16513,a(flip),b,16115,a),flip(a)].">
      <j1 rule="hyper" parents="139 16513 16115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16515">
    <literal><![CDATA[
      ((x \ a(y,a(z,u,w),x)) \ 1) * a(x \ 1,x,x) = L(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(14385(a,1),16514(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="14385 16514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16516">
    <literal><![CDATA[
      ((x \ a(a(y,z,a(u,w,v5)),u,x)) \ 1) * a(x \ 1,x,x) = L(x,u,a(y,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(15239(a,1),16514(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="15239 16514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16517">
    <literal><![CDATA[
      L(x,a(y,z,u),w * L(w,v5,v6)) = ((x \ a(a(w,a(u,z,y),x),v5,v6)) \ 1) * a(x \ 1,x,x)
    ]]></literal>
    <justification jstring="[para(16206(a,1),16515(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16206 16515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16518">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w) * a(R(x,u,w),L(x \ L(x,y,z),u,w),v5),v5,R(x,u,w)) = (R(x,u,w) * v5) \ (L(R(x,u,w),y,z) * v5)
    ]]></literal>
    <justification jstring="[para(4992(a,1),8895(a,2,2,2))].">
      <j1 rule="para" parents="4992 8895"/>
    </justification>
  </clause>

  <clause id="16519">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w) * a(R(x,u,w),L(x \ L(x,y,z),u,w),v5),v5,R(x,u,w)) = v5 \ ((v5 / R(x,u,w)) * L(R(x,u,w),y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,7107,a(flip),b,16518,a),flip(a)].">
      <j1 rule="hyper" parents="316 7107 16518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16520">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w) * a(L(x,u,w),L(x \ L(x,y,z),u,w),v5),v5,R(x,u,w)) = v5 \ ((v5 / R(x,u,w)) * L(R(x,u,w),y,z))
    ]]></literal>
    <justification jstring="[para(4643(a,1),16519(a,1,1,2))].">
      <j1 rule="para" parents="4643 16519"/>
    </justification>
  </clause>

  <clause id="16521">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w) * a(L(x,u,w),L(x \ L(x,y,z),u,w),v5),v5,L(x,u,w)) = v5 \ ((v5 / R(x,u,w)) * L(R(x,u,w),y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4628,a(flip),b,16520,a)].">
      <j1 rule="hyper" parents="63 4628 16520"/>
    </justification>
  </clause>

  <clause id="16522">
    <literal><![CDATA[
      (L(x,y,z) * u) \ ((L(x,y,z) * L(x \ L(x,w,v5),y,z)) * T(u,x \ L(x,w,v5))) = u \ ((u / R(x,y,z)) * L(R(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,8632,a(flip),b,16521,a)].">
      <j1 rule="hyper" parents="63 8632 16521"/>
    </justification>
  </clause>

  <clause id="16523">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (L(L(x,w,v5),y,z) * T(u,x \ L(x,w,v5))) = u \ ((u / R(x,y,z)) * L(R(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(2139(a,1),16522(a,1,2,1))].">
      <j1 rule="para" parents="2139 16522"/>
    </justification>
  </clause>

  <clause id="16524">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (L(L(x,w,v5),y,z) * u) = u \ ((u / R(x,y,z)) * L(R(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(4992(a,1),16523(a,1,2,2))].">
      <j1 rule="para" parents="4992 16523"/>
    </justification>
  </clause>

  <clause id="16525">
    <literal><![CDATA[
      (x / R(y,z,u)) * L(R(y,z,u),w,v5) = (x / L(y,z,u)) * L(L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(38,a,7115,a(flip),b,16524,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 7115 16524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16526">
    <literal><![CDATA[
      (x / L(y,z,(z * y) \ x)) * L(L(y,z,(z * y) \ x),u,w) = (L(y,u,w) * z) * ((y * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9798,a(flip),b,16525,a),flip(a)].">
      <j1 rule="hyper" parents="63 9798 16525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16528">
    <literal><![CDATA[
      K(x,y) * ((z / L(x,u,w)) * L(L(x,u,w),v5,v6)) = L(R(T(x,y),u,w),v5,v6) * (R(x,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(16525(a,1),9501(a,1,2))].">
      <j1 rule="para" parents="16525 9501"/>
    </justification>
  </clause>

  <clause id="16529">
    <literal><![CDATA[
      K(x,y) * ((z / R(y,u,w)) * L(R(y,u,w),v5,v6)) = L(T(y,x),u,w) \ (L(L(y,u,w),v5,v6) * z)
    ]]></literal>
    <justification jstring="[para(16525(a,2),10424(a,1,2))].">
      <j1 rule="para" parents="16525 10424"/>
    </justification>
  </clause>

  <clause id="16530">
    <literal><![CDATA[
      ((x / (y * z)) * y) * L(L(z,y,(y * z) \ x),u,w) = (L(z,u,w) * y) * ((z * y) \ x)
    ]]></literal>
    <justification jstring="[para(1605(a,1),16526(a,1,1))].">
      <j1 rule="para" parents="1605 16526"/>
    </justification>
  </clause>

  <clause id="16531">
    <literal><![CDATA[
      (x / (y * z)) * (y * L(z,u,w)) = (L(z,u,w) * y) * ((z * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1608,a(flip),b,16530,a)].">
      <j1 rule="hyper" parents="63 1608 16530"/>
    </justification>
  </clause>

  <clause id="16533">
    <literal><![CDATA[
      ((x / (y * z)) * y) * L(L(z,y,y \ (z \ x)),u,w) = (L(z,u,w) * y) * ((z * y) \ x)
    ]]></literal>
    <justification jstring="[para(14643(a,1),16530(a,1,2,1))].">
      <j1 rule="para" parents="14643 16530"/>
    </justification>
  </clause>

  <clause id="16534">
    <literal><![CDATA[
      L(R(T(x,y),z,u),w,v5) * (R(x,z,u) \ v6) = L(L(T(x,y),z,u),w,v5) * (L(x,z,u) \ v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,9499,a(flip),b,16528,a),flip(a)].">
      <j1 rule="hyper" parents="63 9499 16528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16535">
    <literal><![CDATA[
      L(L(T(x,y),z,u),w,v5) * (L(x,z,u) \ (y * x)) = L(R(x,z,u),w,v5) * (R(x,z,u) \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,9791,a(flip),b,16534,a),flip(a)].">
      <j1 rule="hyper" parents="63 9791 16534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16536">
    <literal><![CDATA[
      R(T(x,y),z,u) \ (L(R(x,z,u),w,v5) * v6) = L(T(x,y),z,u) \ (L(L(x,z,u),w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,4417,a(flip),b,16529,a)].">
      <j1 rule="hyper" parents="63 4417 16529"/>
    </justification>
  </clause>

  <clause id="16537">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (L(L(x,z,u),w,v5) * T(v6,x)) = R(T(x,y),z,u) \ (v6 * L(R(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(4354(a,1),16536(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4354 16536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16538">
    <literal><![CDATA[
      a(x,(L(T(y,z),u,w) \ (L(L(y,u,w),v5,v6) * v7)) * R(T(y,z),u,w),v8) = a(x,L(R(y,u,w),v5,v6) * v7,v8)
    ]]></literal>
    <justification jstring="[para(16536(a,1),11191(a,1,2,1))].">
      <j1 rule="para" parents="16536 11191"/>
    </justification>
  </clause>

  <clause id="16539">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (R(x,y,z) \ (x * v5)) = L(L(x,y,z),u,w) * (x * (L(x,y,z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,15914,a(flip),b,16535,a),flip(a)].">
      <j1 rule="hyper" parents="63 15914 16535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16540">
    <literal><![CDATA[
      R(x,y,z) * (L(L(x,y,z),u,w) * (x * (L(x,y,z) \ v5))) = L(R(x,y,z),u,w) * (x * v5)
    ]]></literal>
    <justification jstring="[hyper(139,a,16539,a(flip),b,1126,a)].">
      <j1 rule="hyper" parents="139 16539 1126"/>
    </justification>
  </clause>

  <clause id="16541">
    <literal><![CDATA[
      R(x,y,z) * (x * (L(L(x,y,z),u,w) * (L(x,y,z) \ v5))) = L(R(x,y,z),u,w) * (x * v5)
    ]]></literal>
    <justification jstring="[para(1844(a,1),16540(a,1,2))].">
      <j1 rule="para" parents="1844 16540"/>
    </justification>
  </clause>

  <clause id="16542">
    <literal><![CDATA[
      x * (R(x,y,z) * (L(L(x,y,z),u,w) * (L(x,y,z) \ v5))) = L(R(x,y,z),u,w) * (x * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,1166,a(flip),b,16541,a)].">
      <j1 rule="hyper" parents="63 1166 16541"/>
    </justification>
  </clause>

  <clause id="16543">
    <literal><![CDATA[
      R(T(x,y),z,u) \ (w * L(R(x,z,u),v5,v6)) = L(T(x,y),z,u) \ (w * L(L(x,v5,v6),z,u))
    ]]></literal>
    <justification jstring="[para(4584(a,1),16537(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4584 16537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16544">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (R(T(x,v5),y,z) \ v5) = K(x,v6) * (L(T(x,v6),y,z) \ (v5 * L(L(x,u,w),y,z)))
    ]]></literal>
    <justification jstring="[para(16543(a,1),9386(a,2,2))].">
      <j1 rule="para" parents="16543 9386"/>
    </justification>
  </clause>

  <clause id="16545">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (R(T(x,v5),y,z) \ v5) = L(x,y,z) \ (v5 * L(L(x,u,w),y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,4290,a(flip),b,16544,a),flip(a)].">
      <j1 rule="hyper" parents="316 4290 16544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16546">
    <literal><![CDATA[
      (x * (L(x,y,z) \ (u * L(L(x,w,v5),y,z)))) / x = (u * L(R(x,y,z),w,v5)) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(16545(a,1),9057(a,1,1,2))].">
      <j1 rule="para" parents="16545 9057"/>
    </justification>
  </clause>

  <clause id="16547">
    <literal><![CDATA[
      (x * L(R(y,z,u),w,v5)) / R(y,z,u) = (x * L(L(y,w,v5),z,u)) / L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4333,a(flip),b,16546,a),flip(a)].">
      <j1 rule="hyper" parents="63 4333 16546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16548">
    <literal><![CDATA[
      (x * L(R(y,z,u),w,v5)) / R(y,z,u) = L(L(y,z,u),w,v5) * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,4411,a(flip),b,16547,a),flip(a)].">
      <j1 rule="hyper" parents="316 4411 16547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16549">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (R(x,y,z) \ v5) = L(L(x,y,z),u,w) * (L(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,4377,a(flip),b,16548,a)].">
      <j1 rule="hyper" parents="63 4377 16548"/>
    </justification>
  </clause>

  <clause id="16550">
    <literal><![CDATA[
      R(x,y,z) * (L(L(x,y,z),u,w) * (L(x,y,z) \ v5)) = L(R(x,y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[hyper(139,a,16549,a(flip),b,1126,a)].">
      <j1 rule="hyper" parents="139 16549 1126"/>
    </justification>
  </clause>

  <clause id="16551">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (x * v5) = x * (L(R(x,y,z),u,w) * v5)
    ]]></literal>
    <justification jstring="[para(16550(a,1),16542(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16550 16542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16552">
    <literal><![CDATA[
      ((x * (L(R(x,y,z),u,w) * v5)) / v5) \ (x * L(R(x,y,z),u,w)) = a(L(L(x,y,z),u,w),x,v5)
    ]]></literal>
    <justification jstring="[para(16551(a,1),8983(a,1,1,1))].">
      <j1 rule="para" parents="16551 8983"/>
    </justification>
  </clause>

  <clause id="16553">
    <literal><![CDATA[
      a(L(L(x,y,z),u,w),x,v5) = a(x,L(R(x,y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,6925,a,b,16552,a),flip(a)].">
      <j1 rule="hyper" parents="63 6925 16552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16554">
    <literal><![CDATA[
      a(L(L(x,y,z),u,w),x,v5) = a(x,L(L(x,y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,11332,a(flip),b,16553,a),flip(a)].">
      <j1 rule="hyper" parents="316 11332 16553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16555">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ R(L(L(x,y,z),u,w),x,v5) = a(x,L(L(x,y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,14633,a,b,16554,a)].">
      <j1 rule="hyper" parents="63 14633 16554"/>
    </justification>
  </clause>

  <clause id="16556">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(R(L(x,y,z),x,v5),u,w) = a(x,L(L(x,y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(29(a,1),16555(a,1,2))].">
      <j1 rule="para" parents="29 16555"/>
    </justification>
  </clause>

  <clause id="16557">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(L(R(x,x,v5),y,z),u,w) = a(x,L(L(x,y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(29(a,1),16556(a,1,2,1))].">
      <j1 rule="para" parents="29 16556"/>
    </justification>
  </clause>

  <clause id="16558">
    <literal><![CDATA[
      a(x,L(y,z,u) * (L(T(y,w),z,u) \ (L(L(y,z,u),v5,v6) * v7)),v8) = a(x,L(R(y,z,u),v5,v6) * v7,v8)
    ]]></literal>
    <justification jstring="[hyper(63,a,12038,a(flip),b,16538,a)].">
      <j1 rule="hyper" parents="63 12038 16538"/>
    </justification>
  </clause>

  <clause id="16560">
    <literal><![CDATA[
      a(x,K(y,z) * (L(L(z,u,w),v5,v6) * v7),v8) = a(x,L(R(z,u,w),v5,v6) * v7,v8)
    ]]></literal>
    <justification jstring="[para(4367(a,1),16558(a,1,2))].">
      <j1 rule="para" parents="4367 16558"/>
    </justification>
  </clause>

  <clause id="16561">
    <literal><![CDATA[
      a(x,L(R(y,z,u),w,v5) * v6,v7) = a(x,L(L(y,z,u),w,v5) * v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,11200,a(flip),b,16560,a),flip(a)].">
      <j1 rule="hyper" parents="63 11200 16560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16564">
    <literal><![CDATA[
      a(x,L(L(y,z,u),w,v5) * (w * v5),v6) = a(x,v5 * (w * R(y,z,u)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,11284,a(flip),b,16561,a),flip(a)].">
      <j1 rule="hyper" parents="63 11284 16561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16565">
    <literal><![CDATA[
      a(x,y * (z * R(u,w,v5)),v6) = a(x,y * (z * L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,11284,a(flip),b,16564,a),flip(a)].">
      <j1 rule="hyper" parents="63 11284 16564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16566">
    <literal><![CDATA[
      a(x,L(y,y,z * R(u,w,v5)) * (z * L(u,w,v5)),v6) = a(x,(y \ 1) \ (z * R(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,11287,a(flip),b,16565,a),flip(a)].">
      <j1 rule="hyper" parents="63 11287 16565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16567">
    <literal><![CDATA[
      a(x,y * ((R(z,u,w) \ v5) * L(z,u,w)),v6) = a(x,y * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,11211,a(flip),b,16565,a),flip(a)].">
      <j1 rule="hyper" parents="63 11211 16565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16568">
    <literal><![CDATA[
      a(x,((y * R(z,u,w)) \ v5) * (y * L(z,u,w)),v6) = a(x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,11191,a(flip),b,16565,a),flip(a)].">
      <j1 rule="hyper" parents="63 11191 16565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16569">
    <literal><![CDATA[
      a(x,((y * R(z,u,w)) \ (v5 \ (y * R(z,u,w)))) * (y * L(z,u,w)),v6) = a(x,(T(1 / v5,y * R(z,u,w)) \ 1) \ (y * R(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[para(4181(a,2),16565(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4181 16565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16570">
    <literal><![CDATA[
      a(x,y * (L(z,u,w) * (R(z,u,w) \ v5)),v6) = a(x,y * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,11206,a,b,16567,a)].">
      <j1 rule="hyper" parents="63 11206 16567"/>
    </justification>
  </clause>

  <clause id="16571">
    <literal><![CDATA[
      a(x,y * (L(z \ 1,z,z \ R(u,w,v5)) * L(u,w,v5)),v6) = a(x,y * (R(u,w,v5) / z),v6)
    ]]></literal>
    <justification jstring="[para(1603(a,2),16567(a,1,2,2,1))].">
      <j1 rule="para" parents="1603 16567"/>
    </justification>
  </clause>

  <clause id="16572">
    <literal><![CDATA[
      a(x,y * (L(z,a(u,w,z),w) \ L(z,w,u)),v5) = a(x,y * a(z,w,u),v5)
    ]]></literal>
    <justification jstring="[para(14113(a,1),16570(a,1,2,2))].">
      <j1 rule="para" parents="14113 16570"/>
    </justification>
  </clause>

  <clause id="16573">
    <literal><![CDATA[
      a(x,y * (a(z,u,w) \ 1),v5) = a(x,y * a(w,u,z),v5)
    ]]></literal>
    <justification jstring="[para(11632(a,1),16572(a,1,2,2))].">
      <j1 rule="para" parents="11632 16572"/>
    </justification>
  </clause>

  <clause id="16574">
    <literal><![CDATA[
      a(x,y * a(z,u,w),v5) = a(x,y * a(w,u,z),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,13058,a(flip),b,16573,a)].">
      <j1 rule="hyper" parents="63 13058 16573"/>
    </justification>
  </clause>

  <clause id="16575">
    <literal><![CDATA[
      a(x,a(y,z,u) * w,v5) = a(x,w * a(u,z,y),v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,11190,a,b,16574,a)].">
      <j1 rule="hyper" parents="316 11190 16574"/>
    </justification>
  </clause>

  <clause id="16576">
    <literal><![CDATA[
      a(x,L(y,y,z * L(u,w,v5)) * (z * L(u,w,v5)),v6) = a(x,(y \ 1) \ (z * R(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(7496(a,1),16566(a,1,2,1))].">
      <j1 rule="para" parents="7496 16566"/>
    </justification>
  </clause>

  <clause id="16577">
    <literal><![CDATA[
      a(x,y * (L(z \ 1,z,z \ L(u,w,v5)) * L(u,w,v5)),v6) = a(x,y * (R(u,w,v5) / z),v6)
    ]]></literal>
    <justification jstring="[para(7482(a,1),16571(a,1,2,2,1))].">
      <j1 rule="para" parents="7482 16571"/>
    </justification>
  </clause>

  <clause id="16578">
    <literal><![CDATA[
      a(x,(y \ 1) \ (z * R(u,w,v5)),v6) = a(x,(y \ 1) \ (z * L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,11287,a(flip),b,16576,a),flip(a)].">
      <j1 rule="hyper" parents="63 11287 16576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16579">
    <literal><![CDATA[
      a(x,y * ((L(z,u,w) / v5) * (v5 * T(v5 \ 1,z))),v6) = a(x,y * (R(z,u,w) / v5),v6)
    ]]></literal>
    <justification jstring="[para(4575(a,1),16577(a,1,2,2))].">
      <j1 rule="para" parents="4575 16577"/>
    </justification>
  </clause>

  <clause id="16580">
    <literal><![CDATA[
      a(x,y * ((L(z,u,w) / v5) * K(v5 \ 1,z)),v6) = a(x,y * (R(z,u,w) / v5),v6)
    ]]></literal>
    <justification jstring="[para(2814(a,1),16579(a,1,2,2,2))].">
      <j1 rule="para" parents="2814 16579"/>
    </justification>
  </clause>

  <clause id="16581">
    <literal><![CDATA[
      a(x,y * (R(z,u,w) / v5),v6) = a(x,y * (L(z,u,w) / v5),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,11204,a(flip),b,16580,a),flip(a)].">
      <j1 rule="hyper" parents="63 11204 16580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16583">
    <literal><![CDATA[
      a(x,y * (R(z,u,w) / v5),v6) = a(x,y * (v5 \ L(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,11198,a(flip),b,16581,a),flip(a)].">
      <j1 rule="hyper" parents="316 11198 16581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16584">
    <literal><![CDATA[
      a(x,y * (z \ R(u,w,v5)),v6) = a(x,y * (z \ L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,11198,a(flip),b,16583,a)].">
      <j1 rule="hyper" parents="63 11198 16583"/>
    </justification>
  </clause>

  <clause id="16585">
    <literal><![CDATA[
      a(x,y * (z \ L(u,w,v5)),v6) * L(x,a(v6,y * (z \ R(u,w,v5)),x),y * (z \ R(u,w,v5))) = R(x,y * (z \ R(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(16584(a,1),13928(a,2,1)),flip(a)].">
      <j1 rule="para" parents="16584 13928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16586">
    <literal><![CDATA[
      a(x,y * (z \ L(u,w,v5)),v6) \ L(v6,v6,a(x,y * (z \ R(u,w,v5)),y * (z \ L(u,w,v5)))) = L(v6,y * (z \ R(u,w,v5)),x)
    ]]></literal>
    <justification jstring="[para(16584(a,1),15396(a,1,1))].">
      <j1 rule="para" parents="16584 15396"/>
    </justification>
  </clause>

  <clause id="16587">
    <literal><![CDATA[
      a(x,y * (z \ L(u,w,v5)),v6) * L(x,a(v6,y * (z \ L(u,w,v5)),x),y * (z \ R(u,w,v5))) = R(x,y * (z \ R(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(16584(a,1),16585(a,1,2,2))].">
      <j1 rule="para" parents="16584 16585"/>
    </justification>
  </clause>

  <clause id="16588">
    <literal><![CDATA[
      a(x,y * (z \ L(u,w,v5)),v6) \ L(v6,v6,a(x,y * (z \ L(u,w,v5)),y * (z \ L(u,w,v5)))) = L(v6,y * (z \ R(u,w,v5)),x)
    ]]></literal>
    <justification jstring="[para(16584(a,1),16586(a,1,2,3))].">
      <j1 rule="para" parents="16584 16586"/>
    </justification>
  </clause>

  <clause id="16589">
    <literal><![CDATA[
      a(x,y * (z \ L(u,w,v5)),v6) * L(x,a(v6,y * (z \ L(u,w,v5)),x),y * (z \ L(u,w,v5))) = R(x,y * (z \ R(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(10708(a,1),16587(a,1,2))].">
      <j1 rule="para" parents="10708 16587"/>
    </justification>
  </clause>

  <clause id="16590">
    <literal><![CDATA[
      L(x,y * (z \ R(u,w,v5)),v6) = L(x,y * (z \ L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,15380,a(flip),b,16588,a),flip(a)].">
      <j1 rule="hyper" parents="63 15380 16588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16591">
    <literal><![CDATA[
      L(x,(L(y \ R(z,u,w),v5,v6) \ (y \ R(z,u,w))) * (y \ L(z,u,w)),v7) = L(x,L(1 / (y \ R(z,u,w)),v5,v6) \ 1,v7)
    ]]></literal>
    <justification jstring="[para(6592(a,2),16590(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6592 16590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16592">
    <literal><![CDATA[
      L(x,(L(y \ R(z,u,w),v5,v6) \ (y \ R(z,u,w))) * (y \ L(z,u,w)),v7) = L(x,L((y \ R(z,u,w)) \ 1,v5,v6) \ 1,v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,10827,a(flip),b,16591,a),flip(a)].">
      <j1 rule="hyper" parents="316 10827 16591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16593">
    <literal><![CDATA[
      L(x,(R(y,z,u) \ (L(w / R(y,z,u),v5,v6) \ w)) * (w \ L(y,z,u)),v7) = L(x,L((w \ R(y,z,u)) \ 1,v5,v6) \ 1,v7)
    ]]></literal>
    <justification jstring="[para(13906(a,1),16592(a,1,2,1))].">
      <j1 rule="para" parents="13906 16592"/>
    </justification>
  </clause>

  <clause id="16594">
    <literal><![CDATA[
      R(x,y * (z \ R(u,w,v5)),v6) = R(x,y * (z \ L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,13928,a,b,16589,a),flip(a)].">
      <j1 rule="hyper" parents="63 13928 16589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16595">
    <literal><![CDATA[
      R(x,y * (L(z,z,a(u,u,w)) \ R(z,u,w)),v5) = R(x,y * (a(w,u,z) \ 1),v5)
    ]]></literal>
    <justification jstring="[para(15388(a,1),16594(a,2,2,2))].">
      <j1 rule="para" parents="15388 16594"/>
    </justification>
  </clause>

  <clause id="16596">
    <literal><![CDATA[
      R(x,y * (a(z,u,w) \ 1),v5) = R(x,y * a(w,u,z),v5)
    ]]></literal>
    <justification jstring="[para(15389(a,1),16595(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15389 16595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16597">
    <literal><![CDATA[
      R(x,a(y,z,u) \ w,v5) = R(x,w * a(u,z,y),v5)
    ]]></literal>
    <justification jstring="[para(14393(a,1),16596(a,1,2))].">
      <j1 rule="para" parents="14393 16596"/>
    </justification>
  </clause>

  <clause id="16598">
    <literal><![CDATA[
      R(x,y * a(z,u,w),v5) = R(x,y * a(w,u,z),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,15622,a(flip),b,16597,a)].">
      <j1 rule="hyper" parents="63 15622 16597"/>
    </justification>
  </clause>

  <clause id="16599">
    <literal><![CDATA[
      (L(x \ 1,y,z) * y) \ R(x \ 1,y * a(x,y,z),y * a(z,y,x)) = (a(z,y,x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(16597(a,1),14551(a,1,2))].">
      <j1 rule="para" parents="16597 14551"/>
    </justification>
  </clause>

  <clause id="16600">
    <literal><![CDATA[
      a(x,((y * R(z,u,w)) \ (v5 \ (y * R(z,u,w)))) * (y * L(z,u,w)),v6) = a(x,(T(1 / v5,y * z) \ 1) \ (y * R(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[para(3483(a,1),16569(a,2,2,1,1))].">
      <j1 rule="para" parents="3483 16569"/>
    </justification>
  </clause>

  <clause id="16601">
    <literal><![CDATA[
      a(x,((y * R(z,u,w)) \ (v5 \ (y * R(z,u,w)))) * (y * L(z,u,w)),v6) = a(x,(T(1 / v5,y * z) \ 1) \ (y * L(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,16578,a(flip),b,16600,a),flip(a)].">
      <j1 rule="hyper" parents="316 16578 16600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16603">
    <literal><![CDATA[
      a(x,((y * R(z,u,w)) \ (v5 \ (y * R(z,u,w)))) * (y * L(z,u,w)),v6) = a(x,((1 / v5) \ 1) \ (y * L(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,11247,a(flip),b,16601,a),flip(a)].">
      <j1 rule="hyper" parents="316 11247 16601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16605">
    <literal><![CDATA[
      a(x,((y * R(z,u,w)) \ (v5 \ (y * R(z,u,w)))) * (y * L(z,u,w)),v6) = a(x,v5 \ (y * L(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[para(83(a,1),16603(a,2,2,1))].">
      <j1 rule="para" parents="83 16603"/>
    </justification>
  </clause>

  <clause id="16606">
    <literal><![CDATA[
      a(x,y \ (z * R(u,w,v5)),v6) = a(x,y \ (z * L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,16568,a(flip),b,16605,a)].">
      <j1 rule="hyper" parents="63 16568 16605"/>
    </justification>
  </clause>

  <clause id="16609">
    <literal><![CDATA[
      a(x,y \ (K(z,u) * L(w,v5,v6)),v7) = a(x,y \ R(w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,11208,a(flip),b,16606,a),flip(a)].">
      <j1 rule="hyper" parents="63 11208 16606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16610">
    <literal><![CDATA[
      a(x,y \ R(z,u,w),v5) = a(x,y \ L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11208,a(flip),b,16609,a),flip(a)].">
      <j1 rule="hyper" parents="63 11208 16609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16611">
    <literal><![CDATA[
      a(x,y \ L(z,u,w),a(v5,v6,v7)) * a(v5,v6,v7) = L(a(v5,v6,v7),y \ R(z,u,w),x)
    ]]></literal>
    <justification jstring="[para(16610(a,1),14597(a,1,1))].">
      <j1 rule="para" parents="16610 14597"/>
    </justification>
  </clause>

  <clause id="16613">
    <literal><![CDATA[
      L(a(x,y,z),u \ R(w,v5,v6),v7) = L(a(x,y,z),u \ L(w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,14597,a(flip),b,16611,a),flip(a)].">
      <j1 rule="hyper" parents="63 14597 16611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16614">
    <literal><![CDATA[
      L(a(x,y,z \ L(u,w,v5)),z \ L(u,w,v5),y) = R(u,w,v5) \ (L(z / R(u,w,v5),y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13908,a(flip),b,16613,a),flip(a)].">
      <j1 rule="hyper" parents="63 13908 16613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16617">
    <literal><![CDATA[
      L(x \ L(y,z,u),w,v5) \ (x \ L(y,z,u)) = R(y,z,u) \ (L(x / R(y,z,u),w,v5) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13403,a(flip),b,16614,a)].">
      <j1 rule="hyper" parents="63 13403 16614"/>
    </justification>
  </clause>

  <clause id="16618">
    <literal><![CDATA[
      R(x,y,z) \ (L(u / R(x,y,z),w,v5) \ u) = L(x,y,z) \ (L(u / L(x,y,z),w,v5) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13906,a(flip),b,16617,a),flip(a)].">
      <j1 rule="hyper" parents="63 13906 16617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16619">
    <literal><![CDATA[
      L(x,(L(y,z,u) \ (L(w / L(y,z,u),v5,v6) \ w)) * (w \ L(y,z,u)),v7) = L(x,L((w \ R(y,z,u)) \ 1,v5,v6) \ 1,v7)
    ]]></literal>
    <justification jstring="[para(16618(a,1),16593(a,1,2,1))].">
      <j1 rule="para" parents="16618 16593"/>
    </justification>
  </clause>

  <clause id="16636">
    <literal><![CDATA[
      L(x,L(1 / (y \ L(z,u,w)),v5,v6) \ 1,v7) = L(x,L((y \ R(z,u,w)) \ 1,v5,v6) \ 1,v7)
    ]]></literal>
    <justification jstring="[para(13915(a,1),16619(a,1,2))].">
      <j1 rule="para" parents="13915 16619"/>
    </justification>
  </clause>

  <clause id="16637">
    <literal><![CDATA[
      L(x,L((y \ R(z,u,w)) \ 1,v5,v6) \ 1,v7) = L(x,L((y \ L(z,u,w)) \ 1,v5,v6) \ 1,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,10827,a(flip),b,16636,a),flip(a)].">
      <j1 rule="hyper" parents="63 10827 16636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16639">
    <literal><![CDATA[
      L((L(x * K(y,z),u,w) \ L(L(x,v5,v6),u,w)) * K(y,z),L(x * K(y,z),u,w),v7) \ v7 = L(x,u,w) * (K(y,z) * (L(L(x * K(y,z),u,w),v5,v6) \ v7))
    ]]></literal>
    <justification jstring="[para(7878(a,1),10473(a,1,1,1))].">
      <j1 rule="para" parents="7878 10473"/>
    </justification>
  </clause>

  <clause id="16640">
    <literal><![CDATA[
      L((R(x * K(y,z),u,w) \ L(R(x,u,w),v5,v6)) * K(y,z),R(x * K(y,z),u,w),v7) \ v7 = R(x,u,w) * (K(y,z) * (L(R(x * K(y,z),u,w),v5,v6) \ v7))
    ]]></literal>
    <justification jstring="[para(4875(a,1),10474(a,1,1,1))].">
      <j1 rule="para" parents="4875 10474"/>
    </justification>
  </clause>

  <clause id="16641">
    <literal><![CDATA[
      L((x \ (a(y,z,u) \ w)) \ ((a(y,z,u) * x) \ w),T(x,v5) \ (a(y,z,u) \ w),x * a(y,z,u)) = a(T(x,v5) \ (a(y,z,u) \ w),x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(10298(a,1),10930(a,1,1))].">
      <j1 rule="para" parents="10298 10930"/>
    </justification>
  </clause>

  <clause id="16642">
    <literal><![CDATA[
      L((x \ (a(y,z,u) \ w)) \ ((a(y,z,u) * x) \ w),x \ (a(y,z,u) \ w),x * a(y,z,u)) = a(T(x,v5) \ (a(y,z,u) \ w),x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10801,a(flip),b,16641,a)].">
      <j1 rule="hyper" parents="63 10801 16641"/>
    </justification>
  </clause>

  <clause id="16645">
    <literal><![CDATA[
      a(T(x,y) \ (a(z,u,w) \ v5),x,a(z,u,w)) = ((a(z,u,w) * x) * (x \ (a(z,u,w) \ v5))) \ v5
    ]]></literal>
    <justification jstring="[hyper(63,a,1677,a(flip),b,16642,a),flip(a)].">
      <j1 rule="hyper" parents="63 1677 16642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16646">
    <literal><![CDATA[
      a(T(x,y) \ (a(z,u,w) \ v5),x,a(z,u,w)) = (a(z,u,w) * x) \ (v5 / (x \ (a(z,u,w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,7235,a(flip),b,16645,a),flip(a)].">
      <j1 rule="hyper" parents="316 7235 16645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16647">
    <literal><![CDATA[
      a(T(x,y) \ (a(z,u,w) \ v5),x,a(z,u,w)) = (a(z,u,w) * x) \ (((a(z,u,w) \ v5) / x) \ v5)
    ]]></literal>
    <justification jstring="[para(8950(a,1),16646(a,2,2))].">
      <j1 rule="para" parents="8950 16646"/>
    </justification>
  </clause>

  <clause id="16648">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (((a(x,y,z) \ w) / u) \ w) = a(u \ (a(x,y,z) \ w),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2908,a(flip),b,16647,a),flip(a)].">
      <j1 rule="hyper" parents="63 2908 16647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16649">
    <literal><![CDATA[
      a(x,a(y,y,a(y,y,z) * z),L(a(y,y,z) * z,y,y)) = a(z \ (a(y,y,z) \ x),z,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15835,a,b,16648,a)].">
      <j1 rule="hyper" parents="63 15835 16648"/>
    </justification>
  </clause>

  <clause id="16650">
    <literal><![CDATA[
      a(x \ (a(y,y,x) \ z),x,a(y,y,x)) = a(z,a(y,y,L(x,y,y)),L(a(y,y,x) * x,y,y))
    ]]></literal>
    <justification jstring="[para(5101(a,1),16649(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5101 16649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16651">
    <literal><![CDATA[
      a(x \ (a(y,y,x) \ z),x,a(y,y,x)) = a(z,a(y,y,x),L(a(y,y,x) * x,y,y))
    ]]></literal>
    <justification jstring="[para(8519(a,1),16650(a,2,2))].">
      <j1 rule="para" parents="8519 16650"/>
    </justification>
  </clause>

  <clause id="16653">
    <literal><![CDATA[
      a(x \ (a(y,y,x) \ z),x,a(y,y,x)) = a(z,a(y,y,x),x)
    ]]></literal>
    <justification jstring="[para(8615(a,1),16651(a,2,3))].">
      <j1 rule="para" parents="8615 16651"/>
    </justification>
  </clause>

  <clause id="16654">
    <literal><![CDATA[
      a(x \ (a(y,y,x) \ z),x,a(y,y,x)) = a(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,7011,a(flip),b,16653,a),flip(a)].">
      <j1 rule="hyper" parents="316 7011 16653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16655">
    <literal><![CDATA[
      a(a(x,x,y) \ z,y,a(y,x,x)) = a(z,y,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,9989,a(flip),b,16654,a)].">
      <j1 rule="hyper" parents="63 9989 16654"/>
    </justification>
  </clause>

  <clause id="16656">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) \ x = ((a(z,z,y) \ x) / y) * (y * a(z,z,y))
    ]]></literal>
    <justification jstring="[para(16655(a,1),10074(a,1,1))].">
      <j1 rule="para" parents="16655 10074"/>
    </justification>
  </clause>

  <clause id="16657">
    <literal><![CDATA[
      a(x,a(y,y,x),z) * z = ((a(y,y,x) \ z) / x) * (x * a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9452,a(flip),b,16656,a)].">
      <j1 rule="hyper" parents="63 9452 16656"/>
    </justification>
  </clause>

  <clause id="16658">
    <literal><![CDATA[
      a(x,a(y,y,x),z) * z = (x * a(y,y,x)) * (x \ (a(y,y,x) \ z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5353,a(flip),b,16657,a),flip(a)].">
      <j1 rule="hyper" parents="316 5353 16657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16659">
    <literal><![CDATA[
      (x * a(y,y,x)) * (x \ (a(y,y,x) \ z)) = L(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13481,a(flip),b,16658,a),flip(a)].">
      <j1 rule="hyper" parents="63 13481 16658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16660">
    <literal><![CDATA[
      x * (L(x,y,y) \ (a(y,y,x) \ z)) = L(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13791,a(flip),b,16659,a)].">
      <j1 rule="hyper" parents="63 13791 16659"/>
    </justification>
  </clause>

  <clause id="16661">
    <literal><![CDATA[
      (a(x,x,y) \ z) \ L(z,y,a(y,x,x)) = a(x,x,L(y,L(y,x,x),z))
    ]]></literal>
    <justification jstring="[para(16660(a,1),11869(a,1,2))].">
      <j1 rule="para" parents="16660 11869"/>
    </justification>
  </clause>

  <clause id="16662">
    <literal><![CDATA[
      a(x,x,L(y,L(y,x,x),z)) = a(x,x,L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16096,a(flip),b,16661,a),flip(a)].">
      <j1 rule="hyper" parents="63 16096 16661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16663">
    <literal><![CDATA[
      L(L(x,y,y),a(y,y,x),z) = a(y,y,L(x,x,z)) \ x
    ]]></literal>
    <justification jstring="[para(16662(a,1),11963(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16662 11963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16664">
    <literal><![CDATA[
      L(x,y * (((z \ K(u,w)) \ 1) * (v5 * T(z \ K(u,w),K(w,u) * (z * v5)))),v6) = L(x,y * ((z \ 1) * (v5 * T((z \ K(u,w)) \ 1,(z \ K(u,w)) \ v5))),v6)
    ]]></literal>
    <justification jstring="[para(3695(a,1),11011(a,1,2,2,2,2))].">
      <j1 rule="para" parents="3695 11011"/>
    </justification>
  </clause>

  <clause id="16673">
    <literal><![CDATA[
      (x * (y * (L(L(z,u,w),u,w) \ z))) \ (x * (y * (z * (L(L(z,u,w),u,w) \ v5)))) = L(L(v5,L(L(z,u,w),u,w) \ z,y),z * (L(L(z,u,w),u,w) \ y),x)
    ]]></literal>
    <justification jstring="[para(10068(a,1),14092(a,1,2,2,2))].">
      <j1 rule="para" parents="10068 14092"/>
    </justification>
  </clause>

  <clause id="16674">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) \ ((L(x,z,y) \ x) * (L(L(x,z,y) \ x,u,w) \ a(x,x,a(y,z,z)))) = a(y,z,L(x,u,w)) \ (x * (L(x,z,y) \ a(x,x,a(y,z,z))))
    ]]></literal>
    <justification jstring="[para(8670(a,1),15458(a,2,2))].">
      <j1 rule="para" parents="8670 15458"/>
    </justification>
  </clause>

  <clause id="16675">
    <literal><![CDATA[
      ((a(x,y,z) * a(x,y,z)) * (u * w)) \ ((a(x,y,z) * a(x,y,z)) * (u * (w * v5))) = L(v5,L(w,u,a(x,y,z) * a(x,y,z)),(a(x,y,z) * a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(16069(a,1),16070(a,1,2))].">
      <j1 rule="para" parents="16069 16070"/>
    </justification>
  </clause>

  <clause id="16676">
    <literal><![CDATA[
      a(x,y,(((((z \ u) * (z * z)) \ w) * a(z \ u,z * z,z * z)) * v5) * v6) = a(x,y,((T(u / (z \ 1),z) \ (1 \ w)) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(466(a,1),16116(a,1,3,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="466 16116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16677">
    <literal><![CDATA[
      a(x,y,(((((z \ u) * (z * z)) \ w) * a(z \ u,z * z,z * z)) * v5) * v6) = a(x,y,((T(u / (z \ 1),z) \ w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(66(a,1),16676(a,2,3,1,1,2))].">
      <j1 rule="para" parents="66 16676"/>
    </justification>
  </clause>

  <clause id="16679">
    <literal><![CDATA[
      a(x,y,(((((z \ u) * (z * z)) \ w) * a(z \ u,z * z,z * z)) * v5) * v6) = a(x,y,(((u / (z \ 1)) \ w) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,5548,a(flip),b,16677,a),flip(a)].">
      <j1 rule="hyper" parents="316 5548 16677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16681">
    <literal><![CDATA[
      a(x,y,(((((z \ u) * (z * z)) \ w) * a(z \ u,z * z,z * z)) * v5) * v6) = a(x,y,((((z \ 1) \ u) \ w) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,5551,a(flip),b,16679,a),flip(a)].">
      <j1 rule="hyper" parents="316 5551 16679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16682">
    <literal><![CDATA[
      a(x,y,(((((z \ u) * (z * z)) \ w) * 1) * v5) * v6) = a(x,y,((((z \ 1) \ u) \ w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(466(a,1),16681(a,1,3,1,1,2))].">
      <j1 rule="para" parents="466 16681"/>
    </justification>
  </clause>

  <clause id="16683">
    <literal><![CDATA[
      a(x,y,((((z \ u) * (z * z)) \ w) * v5) * v6) = a(x,y,((((z \ 1) \ u) \ w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(8(a,1),16682(a,1,3,1,1))].">
      <j1 rule="para" parents="8 16682"/>
    </justification>
  </clause>

  <clause id="16685">
    <literal><![CDATA[
      a(x,y,((((z \ 1) \ u) \ w) * v5) * v6) = a(x,y,v6 * (v5 * ((z \ u) \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11460,a(flip),b,16683,a),flip(a)].">
      <j1 rule="hyper" parents="63 11460 16683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16687">
    <literal><![CDATA[
      a(x,y,z * ((((u \ 1) \ w) \ v5) * v6)) = a(x,y,z * (v6 * ((u \ w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,16685,a)].">
      <j1 rule="hyper" parents="63 5469 16685"/>
    </justification>
  </clause>

  <clause id="16688">
    <literal><![CDATA[
      a(x,y,R(z,z,(((u \ 1) \ w) \ v5) * v6) * (v6 * ((u \ w) \ v5))) = a(x,y,z \ ((((u \ 1) \ w) \ v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5844,a(flip),b,16687,a),flip(a)].">
      <j1 rule="hyper" parents="63 5844 16687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16689">
    <literal><![CDATA[
      a(x,y,R(z,z,u * ((w \ v5) \ v6)) * (u * ((w \ v5) \ v6))) = a(x,y,z \ ((((w \ 1) \ v5) \ v6) * u))
    ]]></literal>
    <justification jstring="[para(7596(a,1),16688(a,1,3,1))].">
      <j1 rule="para" parents="7596 16688"/>
    </justification>
  </clause>

  <clause id="16690">
    <literal><![CDATA[
      a(x,y,z \ ((((u \ 1) \ w) \ v5) * v6)) = a(x,y,z \ (v6 * ((u \ w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5844,a(flip),b,16689,a),flip(a)].">
      <j1 rule="hyper" parents="63 5844 16689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16691">
    <literal><![CDATA[
      a(x,y,z \ ((u / (w \ 1)) * (L(u / (w \ 1),w \ 1,w) \ v5))) = a(x,y,z \ ((u * w) * ((w \ u) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14301,a,b,16690,a)].">
      <j1 rule="hyper" parents="63 14301 16690"/>
    </justification>
  </clause>

  <clause id="16692">
    <literal><![CDATA[
      a(x,y,z \ (((u \ 1) \ w) * (L((u \ 1) \ w,u \ 1,u) \ v5))) = a(x,y,z \ ((w * u) * ((u \ w) \ v5)))
    ]]></literal>
    <justification jstring="[para(10576(a,1),16691(a,1,3,2))].">
      <j1 rule="para" parents="10576 16691"/>
    </justification>
  </clause>

  <clause id="16693">
    <literal><![CDATA[
      a(x,y,z \ (((u \ 1) \ w) * ((u * w) \ v5))) = a(x,y,z \ ((w * u) * ((u \ w) \ v5)))
    ]]></literal>
    <justification jstring="[para(474(a,1),16692(a,1,3,2,2,1))].">
      <j1 rule="para" parents="474 16692"/>
    </justification>
  </clause>

  <clause id="16694">
    <literal><![CDATA[
      a(x,y,z \ (((u * w) \ v5) * (u \ w))) = a(x,y,z \ ((w * u) * ((u \ w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6692,a(flip),b,16693,a)].">
      <j1 rule="hyper" parents="63 6692 16693"/>
    </justification>
  </clause>

  <clause id="16699">
    <literal><![CDATA[
      L((K(x,y) * (L(z,u,w) \ L(L(z,v5,v6),u,w))) * K(y,x),L(z * K(y,x),u,w),v7) \ v7 = L(z,u,w) * (K(y,x) * (L(L(z * K(y,x),u,w),v5,v6) \ v7))
    ]]></literal>
    <justification jstring="[para(10244(a,1),16639(a,1,1,1,1))].">
      <j1 rule="para" parents="10244 16639"/>
    </justification>
  </clause>

  <clause id="16700">
    <literal><![CDATA[
      L((K(x,y) * (R(z,u,w) \ L(R(z,u,w),v5,v6))) * K(y,x),R(z * K(y,x),u,w),v7) \ v7 = R(z,u,w) * (K(y,x) * (L(R(z * K(y,x),u,w),v5,v6) \ v7))
    ]]></literal>
    <justification jstring="[para(10243(a,1),16640(a,1,1,1,1))].">
      <j1 rule="para" parents="10243 16640"/>
    </justification>
  </clause>

  <clause id="16701">
    <literal><![CDATA[
      L(x,y * (((z \ K(u,w)) \ 1) * (v5 * T(K(u,w) * (z \ 1),z * v5))),v6) = L(x,y * ((z \ 1) * (v5 * T((z \ K(u,w)) \ 1,(z \ K(u,w)) \ v5))),v6)
    ]]></literal>
    <justification jstring="[para(10356(a,1),16664(a,1,2,2,2,2))].">
      <j1 rule="para" parents="10356 16664"/>
    </justification>
  </clause>

  <clause id="16702">
    <literal><![CDATA[
      L(x,y * ((z \ 1) * (u * T((z \ K(w,v5)) \ 1,(z \ K(w,v5)) \ u))),v6) = L(x,y * (((z \ K(w,v5)) \ 1) * (u * (K(w,v5) * (z \ 1)))),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,10914,a(flip),b,16701,a),flip(a)].">
      <j1 rule="hyper" parents="63 10914 16701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16704">
    <literal><![CDATA[
      L(x,y * ((z \ 1) * (u * T((z \ K(w,v5)) \ 1,(z \ K(w,v5)) \ u))),v6) = L(x,y * ((u * (z \ 1)) * ((z \ K(w,v5)) \ 1)),v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,11023,a(flip),b,16702,a),flip(a)].">
      <j1 rule="hyper" parents="316 11023 16702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16706">
    <literal><![CDATA[
      L(x,y * ((z \ 1) * (u * T((z \ K(w,v5)) \ 1,(z \ K(w,v5)) \ u))),v6) = L(x,y * ((u * (1 / z)) * (K(v5,w) * z)),v6)
    ]]></literal>
    <justification jstring="[para(11475(a,1),16704(a,2,2,2))].">
      <j1 rule="para" parents="11475 16704"/>
    </justification>
  </clause>

  <clause id="16707">
    <literal><![CDATA[
      L(x,y * ((z \ 1) * (u * T((z \ K(w,v5)) \ 1,(z \ K(w,v5)) \ u))),v6) = L(x,y * ((u * (1 / z)) * z),v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,10902,a(flip),b,16706,a),flip(a)].">
      <j1 rule="hyper" parents="316 10902 16706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16709">
    <literal><![CDATA[
      L(x,y * ((z \ 1) * (u * T((z \ K(w,v5)) \ 1,(z \ K(w,v5)) \ u))),v6) = L(x,y * R(u,z \ 1,z),v6)
    ]]></literal>
    <justification jstring="[para(2569(a,1),16707(a,2,2,2))].">
      <j1 rule="para" parents="2569 16707"/>
    </justification>
  </clause>

  <clause id="16710">
    <literal><![CDATA[
      L(x,y * ((z \ 1) * (u * T((z \ K(w,v5)) \ 1,K(v5,w) * (z * u)))),v6) = L(x,y * R(u,z \ 1,z),v6)
    ]]></literal>
    <justification jstring="[para(3695(a,1),16709(a,1,2,2,2,2))].">
      <j1 rule="para" parents="3695 16709"/>
    </justification>
  </clause>

  <clause id="16711">
    <literal><![CDATA[
      L(x,y * ((z \ 1) * (u * T(((z \ 1) \ 1) * K(w,v5),z * u))),v6) = L(x,y * R(u,z \ 1,z),v6)
    ]]></literal>
    <justification jstring="[para(11085(a,1),16710(a,1,2,2,2,2))].">
      <j1 rule="para" parents="11085 16710"/>
    </justification>
  </clause>

  <clause id="16712">
    <literal><![CDATA[
      L(x,y * ((z \ 1) * (u * T((z \ 1) \ K(w,v5),z * u))),v6) = L(x,y * R(u,z \ 1,z),v6)
    ]]></literal>
    <justification jstring="[para(3780(a,1),16711(a,1,2,2,2,2,1))].">
      <j1 rule="para" parents="3780 16711"/>
    </justification>
  </clause>

  <clause id="16713">
    <literal><![CDATA[
      L(x,y * ((z \ 1) * (u * ((z \ 1) \ K(w,v5)))),v6) = L(x,y * R(u,z \ 1,z),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,10914,a(flip),b,16712,a)].">
      <j1 rule="hyper" parents="63 10914 16712"/>
    </justification>
  </clause>

  <clause id="16715">
    <literal><![CDATA[
      L(x,y * ((1 / z) * (u * (z * K(w,v5)))),v6) = L(x,y * R(u,z \ 1,z),v6)
    ]]></literal>
    <justification jstring="[para(4926(a,1),16713(a,1,2,2))].">
      <j1 rule="para" parents="4926 16713"/>
    </justification>
  </clause>

  <clause id="16716">
    <literal><![CDATA[
      L(x,((1 / y) * (z * y)) * u,w) = L(x,u * R(z,y \ 1,y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11470,a(flip),b,16715,a)].">
      <j1 rule="hyper" parents="63 11470 16715"/>
    </justification>
  </clause>

  <clause id="16717">
    <literal><![CDATA[
      L(x,((y \ 1) * (z * y)) * u,w) = L(x,u * R(z,y \ 1,y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10812,a(flip),b,16716,a)].">
      <j1 rule="hyper" parents="63 10812 16716"/>
    </justification>
  </clause>

  <clause id="16718">
    <literal><![CDATA[
      L(x,y * R(z,u \ 1,u),w) = L(x,y * R(z,u,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10923,a(flip),b,16717,a),flip(a)].">
      <j1 rule="hyper" parents="63 10923 16717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16719">
    <literal><![CDATA[
      L(x,y * R(y * z,z,z),u) = L(x,y * (L(y,z,z) * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12676,a(flip),b,16718,a),flip(a)].">
      <j1 rule="hyper" parents="63 12676 16718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16720">
    <literal><![CDATA[
      L(x,y * L(y * z,z,z),u) = L(x,y * (L(y,z,z) * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11976,a(flip),b,16719,a)].">
      <j1 rule="hyper" parents="63 11976 16719"/>
    </justification>
  </clause>

  <clause id="16721">
    <literal><![CDATA[
      L(x,y * L(y * z,z,z),u) = L(x,y * (z * R(y,z,z)),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,12677,a(flip),b,16720,a),flip(a)].">
      <j1 rule="hyper" parents="316 12677 16720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16722">
    <literal><![CDATA[
      a(x,y,L(z,L(1 / u,w * u,w * u),v5)) = a(x,y,L(z,w * L(w * u,u,u),v5))
    ]]></literal>
    <justification jstring="[para(16720(a,2),12678(a,2,3))].">
      <j1 rule="para" parents="16720 12678"/>
    </justification>
  </clause>

  <clause id="16723">
    <literal><![CDATA[
      a(x,y,L(z,L(L(u,u,w),R(w,u,u),R(w,u,u)),v5)) = a(x,y,L(z,w * L(w * u,u,u),v5))
    ]]></literal>
    <justification jstring="[para(16721(a,2),12029(a,2,3))].">
      <j1 rule="para" parents="16721 12029"/>
    </justification>
  </clause>

  <clause id="16724">
    <literal><![CDATA[
      a(x,y,L(z,L(u \ 1,w * u,w * u),v5)) = a(x,y,L(z,w * L(w * u,u,u),v5))
    ]]></literal>
    <justification jstring="[para(10835(a,1),16722(a,1,3))].">
      <j1 rule="para" parents="10835 16722"/>
    </justification>
  </clause>

  <clause id="16725">
    <literal><![CDATA[
      a(x,y,L(z,L(u,w * u,w * u),v5)) = a(x,y,L(z,w * L(w * u,u,u),v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,8930,a(flip),b,16724,a)].">
      <j1 rule="hyper" parents="63 8930 16724"/>
    </justification>
  </clause>

  <clause id="16726">
    <literal><![CDATA[
      a(x,y,L(z,L(L(u,u,w),R(w,u,u),R(w,u,u)),v5)) = a(x,y,L(z,L(u,w * u,w * u),v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,16725,a,b,16723,a),flip(a)].">
      <j1 rule="hyper" parents="316 16725 16723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16727">
    <literal><![CDATA[
      a(x,y,L(z,L(L(u,u,w),R(w,u,u),L(w,u,u)),v5)) = a(x,y,L(z,L(u,w * u,w * u),v5))
    ]]></literal>
    <justification jstring="[para(4628(a,1),16726(a,1,3,2))].">
      <j1 rule="para" parents="4628 16726"/>
    </justification>
  </clause>

  <clause id="16728">
    <literal><![CDATA[
      a(x,y,L(z,L(L(u,u,w),L(w,u,u),L(w,u,u)),v5)) = a(x,y,L(z,L(u,w * u,w * u),v5))
    ]]></literal>
    <justification jstring="[para(10977(a,1),16727(a,1,3,2))].">
      <j1 rule="para" parents="10977 16727"/>
    </justification>
  </clause>

  <clause id="16729">
    <literal><![CDATA[
      a(x,y,L(z,L(L(u,u,w),w,w),v5)) = a(x,y,L(z,L(u,w * u,w * u),v5))
    ]]></literal>
    <justification jstring="[para(13874(a,1),16728(a,1,3))].">
      <j1 rule="para" parents="13874 16728"/>
    </justification>
  </clause>

  <clause id="16730">
    <literal><![CDATA[
      a(x,y,L(z,L(u,w * u,w * u),v5)) = a(x,y,L(z,(u \ w) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,12389,a(flip),b,16729,a),flip(a)].">
      <j1 rule="hyper" parents="63 12389 16729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16732">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u * x,u * x) = a(z,y,L((x \ u) * u,(x \ u) * u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14971,a(flip),b,16730,a)].">
      <j1 rule="hyper" parents="63 14971 16730"/>
    </justification>
  </clause>

  <clause id="16733">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u * x,u * x) = L((x \ u) * u,y,z) \ ((x \ u) * u)
    ]]></literal>
    <justification jstring="[hyper(316,a,14510,a(flip),b,16732,a),flip(a)].">
      <j1 rule="hyper" parents="316 14510 16732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16734">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u * x,u * x) = (u \ L(x,y,z)) \ (u \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,16464,a(flip),b,16733,a),flip(a)].">
      <j1 rule="hyper" parents="316 16464 16733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16735">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x * u,x * u) = (u \ L(x,y,z)) \ (u \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10844,a,b,16734,a)].">
      <j1 rule="hyper" parents="63 10844 16734"/>
    </justification>
  </clause>

  <clause id="16736">
    <literal><![CDATA[
      a(x,y,((z \ L(u,w,v5)) \ (z \ u)) * ((z * u) * (u * z))) = a(x,y,(z * u) * ((u * z) * (L(u,w,v5) \ u)))
    ]]></literal>
    <justification jstring="[para(16734(a,1),10848(a,1,3,1))].">
      <j1 rule="para" parents="16734 10848"/>
    </justification>
  </clause>

  <clause id="16737">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ L(L(x,y,z) \ x,u,w),v5 * x,v5 * x) * (v6 * a(w,u,a(L(x,y,z) \ x,L(x,y,z) \ x,u))) = a(w,u,(v5 \ L(x,y,z)) \ (v5 \ x)) \ v6
    ]]></literal>
    <justification jstring="[para(16734(a,1),15598(a,2,1,3))].">
      <j1 rule="para" parents="16734 15598"/>
    </justification>
  </clause>

  <clause id="16738">
    <literal><![CDATA[
      a(x,y,(z * u) * ((u * z) * (L(u,w,v5) \ u))) = a(x,y,(z \ L(u,w,v5)) \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5816,a(flip),b,16736,a),flip(a)].">
      <j1 rule="hyper" parents="63 5816 16736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16740">
    <literal><![CDATA[
      a(x,y,(z * u) * ((u * z) * (L(u,w,v5) \ u))) = a(x,y,(z \ u) \ (z \ L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,13976,a(flip),b,16738,a),flip(a)].">
      <j1 rule="hyper" parents="316 13976 16738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16741">
    <literal><![CDATA[
      a(x,y,(z * u) * (u * (z * (L(u,w,v5) \ u)))) = a(x,y,(z \ u) \ (z \ L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(5151(a,1),16740(a,1,3,2))].">
      <j1 rule="para" parents="5151 16740"/>
    </justification>
  </clause>

  <clause id="16742">
    <literal><![CDATA[
      a(x,y,(z * u) * (u * (z * (u \ L(u,w,v5))))) = a(x,y,(z \ u) \ (z \ L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7984,a(flip),b,16741,a)].">
      <j1 rule="hyper" parents="63 7984 16741"/>
    </justification>
  </clause>

  <clause id="16743">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (z \ L(u,w,v5))) = a(x,y,z * (u * (L(u,w,v5) \ z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14135,a(flip),b,16742,a),flip(a)].">
      <j1 rule="hyper" parents="63 14135 16742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16744">
    <literal><![CDATA[
      a(x,y,(z \ L(u,w,v5)) \ (z \ u)) = a(x,y,z * (u * (L(u,w,v5) \ z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13976,a,b,16743,a)].">
      <j1 rule="hyper" parents="63 13976 16743"/>
    </justification>
  </clause>

  <clause id="16745">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) \ ((L(x,z,y) \ x) * (L(L(x,z,y) \ x,u,w) \ a(x,x,a(y,z,z)))) = a(y,z,L(x,u,w)) \ (L(x,z,y) \ R(x,x,a(y,z,z)))
    ]]></literal>
    <justification jstring="[para(7334(a,1),16674(a,2,2))].">
      <j1 rule="para" parents="7334 16674"/>
    </justification>
  </clause>

  <clause id="16746">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) \ ((L(x,z,y) \ x) * (L(L(x,z,y) \ x,u,w) \ a(x,x,a(y,z,z)))) = a(y,z,L(x,u,w)) \ (L(x,z,y) \ L(x,x,a(y,z,z)))
    ]]></literal>
    <justification jstring="[para(5264(a,1),16745(a,2,2,2))].">
      <j1 rule="para" parents="5264 16745"/>
    </justification>
  </clause>

  <clause id="16747">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) \ ((L(x,z,y) \ x) * (L(L(x,z,y) \ x,u,w) \ a(x,x,a(y,z,z)))) = a(y,z,L(x,u,w)) \ a(y,z,x)
    ]]></literal>
    <justification jstring="[para(15381(a,1),16746(a,2,2))].">
      <j1 rule="para" parents="15381 16746"/>
    </justification>
  </clause>

  <clause id="16748">
    <literal><![CDATA[
      (((a(x,y,z) * a(x,y,z)) * (u * w)) \ (u * (w * v5))) * (a(x,y,z) * a(x,y,z)) = L(v5,L(w,u,a(x,y,z) * a(x,y,z)),(a(x,y,z) * a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5363,a(flip),b,16675,a)].">
      <j1 rule="hyper" parents="63 5363 16675"/>
    </justification>
  </clause>

  <clause id="16749">
    <literal><![CDATA[
      L((K(x,y) * L(z \ L(z,u,w),v5,v6)) * K(y,x),L(z * K(y,x),v5,v6),v7) \ v7 = L(z,v5,v6) * (K(y,x) * (L(L(z * K(y,x),v5,v6),u,w) \ v7))
    ]]></literal>
    <justification jstring="[para(2138(a,1),16699(a,1,1,1,1,2))].">
      <j1 rule="para" parents="2138 16699"/>
    </justification>
  </clause>

  <clause id="16750">
    <literal><![CDATA[
      L(L(K(x,y) * (z \ L(z,u,w)),v5,v6) * K(y,x),L(z * K(y,x),v5,v6),v7) \ v7 = L(z,v5,v6) * (K(y,x) * (L(L(z * K(y,x),v5,v6),u,w) \ v7))
    ]]></literal>
    <justification jstring="[para(4850(a,2),16749(a,1,1,1,1))].">
      <j1 rule="para" parents="4850 16749"/>
    </justification>
  </clause>

  <clause id="16751">
    <literal><![CDATA[
      L(L((K(x,y) * (z \ L(z,u,w))) * K(y,x),v5,v6),L(z * K(y,x),v5,v6),v7) \ v7 = L(z,v5,v6) * (K(y,x) * (L(L(z * K(y,x),v5,v6),u,w) \ v7))
    ]]></literal>
    <justification jstring="[para(4837(a,2),16750(a,1,1,1))].">
      <j1 rule="para" parents="4837 16750"/>
    </justification>
  </clause>

  <clause id="16752">
    <literal><![CDATA[
      L(L(K(x,y) * ((z \ L(z,u,w)) * K(y,x)),v5,v6),L(z * K(y,x),v5,v6),v7) \ v7 = L(z,v5,v6) * (K(y,x) * (L(L(z * K(y,x),v5,v6),u,w) \ v7))
    ]]></literal>
    <justification jstring="[para(406(a,1),16751(a,1,1,1,1))].">
      <j1 rule="para" parents="406 16751"/>
    </justification>
  </clause>

  <clause id="16753">
    <literal><![CDATA[
      L(L(K(x,y) * (z * L(z \ K(y,x),u,w)),v5,v6),L(z * K(y,x),v5,v6),v7) \ v7 = L(z,v5,v6) * (K(y,x) * (L(L(z * K(y,x),v5,v6),u,w) \ v7))
    ]]></literal>
    <justification jstring="[para(4852(a,1),16752(a,1,1,1,1,2))].">
      <j1 rule="para" parents="4852 16752"/>
    </justification>
  </clause>

  <clause id="16754">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),L(x * K(v5,v6),u,w),v7) \ v7 = L(x,u,w) * (K(v5,v6) * (L(L(x * K(v5,v6),u,w),y,z) \ v7))
    ]]></literal>
    <justification jstring="[para(5196(a,1),16753(a,1,1,1,1))].">
      <j1 rule="para" parents="5196 16753"/>
    </justification>
  </clause>

  <clause id="16756">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),L(x,u,w),v5) \ v5 = L(x,u,w) * (K(v6,v7) * (L(L(x * K(v6,v7),u,w),y,z) \ v5))
    ]]></literal>
    <justification jstring="[para(10872(a,1),16754(a,1,1))].">
      <j1 rule="para" parents="10872 16754"/>
    </justification>
  </clause>

  <clause id="16758">
    <literal><![CDATA[
      L((K(x,y) * L(z \ L(z,u,w),v5,v6)) * K(y,x),R(z * K(y,x),v5,v6),v7) \ v7 = R(z,v5,v6) * (K(y,x) * (L(R(z * K(y,x),v5,v6),u,w) \ v7))
    ]]></literal>
    <justification jstring="[para(8381(a,1),16700(a,1,1,1,1,2))].">
      <j1 rule="para" parents="8381 16700"/>
    </justification>
  </clause>

  <clause id="16759">
    <literal><![CDATA[
      L(L(K(x,y) * (z \ L(z,u,w)),v5,v6) * K(y,x),R(z * K(y,x),v5,v6),v7) \ v7 = R(z,v5,v6) * (K(y,x) * (L(R(z * K(y,x),v5,v6),u,w) \ v7))
    ]]></literal>
    <justification jstring="[para(4850(a,2),16758(a,1,1,1,1))].">
      <j1 rule="para" parents="4850 16758"/>
    </justification>
  </clause>

  <clause id="16760">
    <literal><![CDATA[
      L(L((K(x,y) * (z \ L(z,u,w))) * K(y,x),v5,v6),R(z * K(y,x),v5,v6),v7) \ v7 = R(z,v5,v6) * (K(y,x) * (L(R(z * K(y,x),v5,v6),u,w) \ v7))
    ]]></literal>
    <justification jstring="[para(4837(a,2),16759(a,1,1,1))].">
      <j1 rule="para" parents="4837 16759"/>
    </justification>
  </clause>

  <clause id="16761">
    <literal><![CDATA[
      L(L(K(x,y) * ((z \ L(z,u,w)) * K(y,x)),v5,v6),R(z * K(y,x),v5,v6),v7) \ v7 = R(z,v5,v6) * (K(y,x) * (L(R(z * K(y,x),v5,v6),u,w) \ v7))
    ]]></literal>
    <justification jstring="[para(406(a,1),16760(a,1,1,1,1))].">
      <j1 rule="para" parents="406 16760"/>
    </justification>
  </clause>

  <clause id="16762">
    <literal><![CDATA[
      L(L(K(x,y) * (z * L(z \ K(y,x),u,w)),v5,v6),R(z * K(y,x),v5,v6),v7) \ v7 = R(z,v5,v6) * (K(y,x) * (L(R(z * K(y,x),v5,v6),u,w) \ v7))
    ]]></literal>
    <justification jstring="[para(4852(a,1),16761(a,1,1,1,1,2))].">
      <j1 rule="para" parents="4852 16761"/>
    </justification>
  </clause>

  <clause id="16763">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),R(x * K(v5,v6),u,w),v7) \ v7 = R(x,u,w) * (K(v5,v6) * (L(R(x * K(v5,v6),u,w),y,z) \ v7))
    ]]></literal>
    <justification jstring="[para(5196(a,1),16762(a,1,1,1,1))].">
      <j1 rule="para" parents="5196 16762"/>
    </justification>
  </clause>

  <clause id="16765">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),L(x * K(v5,v6),u,w),v7) \ v7 = R(x,u,w) * (K(v5,v6) * (L(R(x * K(v5,v6),u,w),y,z) \ v7))
    ]]></literal>
    <justification jstring="[para(10977(a,1),16763(a,1,1))].">
      <j1 rule="para" parents="10977 16763"/>
    </justification>
  </clause>

  <clause id="16766">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),L(x,u,w),v5) \ v5 = R(x,u,w) * (K(v6,v7) * (L(R(x * K(v6,v7),u,w),y,z) \ v5))
    ]]></literal>
    <justification jstring="[para(10872(a,1),16765(a,1,1))].">
      <j1 rule="para" parents="10872 16765"/>
    </justification>
  </clause>

  <clause id="16768">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),L(x,u,w),v5) \ v5 = R(x,u,w) * (K(v6,v7) * (K(v7,v6) * (L(R(x,u,w),y,z) \ v5)))
    ]]></literal>
    <justification jstring="[para(10506(a,1),16766(a,2,2,2))].">
      <j1 rule="para" parents="10506 16766"/>
    </justification>
  </clause>

  <clause id="16769">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),L(x,u,w),v5) \ v5 = R(x,u,w) * (L(R(x,u,w),y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(669(a,1),16768(a,2,2))].">
      <j1 rule="para" parents="669 16768"/>
    </justification>
  </clause>

  <clause id="16770">
    <literal><![CDATA[
      L(x,y,z) * (K(u,w) * (L(L(x * K(u,w),y,z),v5,v6) \ v7)) = R(x,y,z) * (L(R(x,y,z),v5,v6) \ v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,16756,a(flip),b,16769,a)].">
      <j1 rule="hyper" parents="63 16756 16769"/>
    </justification>
  </clause>

  <clause id="16771">
    <literal><![CDATA[
      L(x,y,z) * (K(u,w) * (K(w,u) * (L(L(x,v5,v6),y,z) \ v7))) = R(x,y,z) * (L(R(x,y,z),v5,v6) \ v7)
    ]]></literal>
    <justification jstring="[para(11083(a,1),16770(a,1,2,2))].">
      <j1 rule="para" parents="11083 16770"/>
    </justification>
  </clause>

  <clause id="16772">
    <literal><![CDATA[
      R(x,y,z) * (L(R(x,y,z),u,w) \ v5) = L(x,y,z) * (L(L(x,u,w),y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(669(a,1),16771(a,1,2)),flip(a)].">
      <j1 rule="para" parents="669 16771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16774">
    <literal><![CDATA[
      (L(R(x,y,z),u,w) \ L(x,u,w)) * R(x,y,z) = L(x,y,z) * (L(L(x,u,w),y,z) \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,4396,a,b,16772,a)].">
      <j1 rule="hyper" parents="63 4396 16772"/>
    </justification>
  </clause>

  <clause id="16777">
    <literal><![CDATA[
      (L(R(x,y,z),u,w) \ L(x,u,w)) * R(x,y,z) = L(x,y,z) * L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(13383(a,1),16774(a,2,2))].">
      <j1 rule="para" parents="13383 16774"/>
    </justification>
  </clause>

  <clause id="16778">
    <literal><![CDATA[
      (L(R(x,y,z),u,w) \ L(x,u,w)) * R(x,y,z) = x * a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,15266,a(flip),b,16777,a),flip(a)].">
      <j1 rule="hyper" parents="316 15266 16777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16779">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,w),y,z) = (x * a(x \ L(x,u,w),y,z)) \ R(x,u,w)
    ]]></literal>
    <justification jstring="[para(16778(a,1),14855(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16778 14855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16780">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,w),y,z) = a(x \ L(x,u,w),y,z) \ (x \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,14476,a(flip),b,16779,a),flip(a)].">
      <j1 rule="hyper" parents="316 14476 16779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16781">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,w),y,z) = a(x \ L(x,u,w),y,z) * (x \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,14438,a(flip),b,16780,a),flip(a)].">
      <j1 rule="hyper" parents="316 14438 16780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16782">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,w),y,z) = L(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,15560,a(flip),b,16781,a),flip(a)].">
      <j1 rule="hyper" parents="316 15560 16781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16783">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,w),y,z) = L(R(x,u,w) \ x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,13512,a,b,16782,a),flip(a)].">
      <j1 rule="hyper" parents="316 13512 16782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16784">
    <literal><![CDATA[
      R(x,y,z) \ R(R(x,y,z),u,w) = L(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12497,a,b,16782,a)].">
      <j1 rule="hyper" parents="63 12497 16782"/>
    </justification>
  </clause>

  <clause id="16785">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,u \ (x \ 1)) = (1 / (u * x)) * (u * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15174,a(flip),b,16782,a),flip(a)].">
      <j1 rule="hyper" parents="63 15174 16782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16786">
    <literal><![CDATA[
      L(R(T(x,y),z,x) \ R(R(T(x,y),z,x),x,u),w,v5) = a(x,L(x,w,v5),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15085,a(flip),b,16782,a),flip(a)].">
      <j1 rule="hyper" parents="63 15085 16782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16787">
    <literal><![CDATA[
      L(x \ R(x,L(x,y,z),u),w,v5) = a(L(x,w,v5),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14272,a(flip),b,16782,a),flip(a)].">
      <j1 rule="hyper" parents="63 14272 16782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16788">
    <literal><![CDATA[
      L(x \ R(x,y \ 1,y),z,u) = a(L(x,z,u),y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2390,a(flip),b,16782,a),flip(a)].">
      <j1 rule="hyper" parents="63 2390 16782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16789">
    <literal><![CDATA[
      L(x \ R(x,y,y),z,u) = a(L(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2384,a(flip),b,16782,a),flip(a)].">
      <j1 rule="hyper" parents="63 2384 16782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16790">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(L(R(x,v5,v6),y,z),u,w) = L(L(x,y,z) \ R(L(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(29(a,1),16782(a,1,2,1))].">
      <j1 rule="para" parents="29 16782"/>
    </justification>
  </clause>

  <clause id="16791">
    <literal><![CDATA[
      L(x,y,z) \ R(L(x,y,z),u,w) = L(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(29(a,2),16782(a,1,2))].">
      <j1 rule="para" parents="29 16782"/>
    </justification>
  </clause>

  <clause id="16792">
    <literal><![CDATA[
      L(x,y,L(z \ R(z,u,w),v5,v6)) = L(x,y,L(z \ L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(16782(a,1),7495(a,1,3))].">
      <j1 rule="para" parents="16782 7495"/>
    </justification>
  </clause>

  <clause id="16793">
    <literal><![CDATA[
      R(L(x \ R(x,y,z),u,w),L(x,u,w),w * u) = (w * (u * x)) \ ((w * u) * R(L(x,u,w),y,z))
    ]]></literal>
    <justification jstring="[para(16782(a,1),9496(a,1,1))].">
      <j1 rule="para" parents="16782 9496"/>
    </justification>
  </clause>

  <clause id="16794">
    <literal><![CDATA[
      (L(x,y,z) / u) \ L(R(x,w,v5),y,z) = L(x \ R(x,w,v5),y,z) / (u \ 1)
    ]]></literal>
    <justification jstring="[para(16782(a,1),13007(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16782 13007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16795">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) * a(x,x,a(y,y,z)) = a(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(16782(a,1),15617(a,1,1))].">
      <j1 rule="para" parents="16782 15617"/>
    </justification>
  </clause>

  <clause id="16796">
    <literal><![CDATA[
      a(L(x,y,z),u,u) = L(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[para(2380(a,1),16789(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2380 16789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16797">
    <literal><![CDATA[
      a(L(x,y,z),u,u) = a(x,u,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,13562,a,b,16796,a),flip(a)].">
      <j1 rule="hyper" parents="316 13562 16796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16800">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) \ y = L(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(16797(a,1),7297(a,1,1))].">
      <j1 rule="para" parents="16797 7297"/>
    </justification>
  </clause>

  <clause id="16801">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u,w,v5)) = L(a(x,u,L(u,y,z)),w,v5)
    ]]></literal>
    <justification jstring="[para(16797(a,1),13562(a,2,1))].">
      <j1 rule="para" parents="16797 13562"/>
    </justification>
  </clause>

  <clause id="16802">
    <literal><![CDATA[
      a(L(x,y,z),u,w) \ L(w,w,a(x,u,L(u,y,z))) = L(w,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(16797(a,1),15380(a,1,2,3))].">
      <j1 rule="para" parents="16797 15380"/>
    </justification>
  </clause>

  <clause id="16803">
    <literal><![CDATA[
      L(x,L(x,y,z),u) = L(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10018,a(flip),b,16800,a)].">
      <j1 rule="hyper" parents="63 10018 16800"/>
    </justification>
  </clause>

  <clause id="16804">
    <literal><![CDATA[
      L(x \ L(x,x,y),z,u) = x \ L(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,16800,a(flip),b,15938,a),flip(a)].">
      <j1 rule="hyper" parents="133 16800 15938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16805">
    <literal><![CDATA[
      L((x \ 1) * L(x,x,y),z,u) = (x \ 1) * L(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(16800(a,1),13983(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16800 13983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16807">
    <literal><![CDATA[
      R(L(x,x,L(y,z,u)),w,v5) = L(R(x,w,v5),L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(16803(a,1),29(a,1,1))].">
      <j1 rule="para" parents="16803 29"/>
    </justification>
  </clause>

  <clause id="16808">
    <literal><![CDATA[
      L(L(x,y,z),L(x,u,w),v5) = L(L(x,x,L(v5,u,w)),y,z)
    ]]></literal>
    <justification jstring="[para(16803(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16803 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16809">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),L(T(1 / (1 / y),x),z,u),w) = L(1 / (K(x,y) / y),1 / (K(x,y) / y),L(w,z,u))
    ]]></literal>
    <justification jstring="[para(6638(a,2),16803(a,1,2))].">
      <j1 rule="para" parents="6638 16803"/>
    </justification>
  </clause>

  <clause id="16810">
    <literal><![CDATA[
      L(x,x,L(y,z,a(u,w,x))) = L(x,x,y)
    ]]></literal>
    <justification jstring="[para(6853(a,1),16803(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6853 16803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16811">
    <literal><![CDATA[
      L(x,x,L(y,z,u)) \ L(R(x,w,v5),L(x,z,u),y) = L(x \ R(x,w,v5),L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(16803(a,1),16782(a,1,1))].">
      <j1 rule="para" parents="16803 16782"/>
    </justification>
  </clause>

  <clause id="16813">
    <literal><![CDATA[
      x \ L(x \ L(x,x,y),z,u) = L(x \ 1,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,16804,a,b,1064,a)].">
      <j1 rule="hyper" parents="133 16804 1064"/>
    </justification>
  </clause>

  <clause id="16814">
    <literal><![CDATA[
      a(L(x,y,z),u \ 1,u) = L(a(x,u \ 1,u),y,z)
    ]]></literal>
    <justification jstring="[para(2387(a,1),16788(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2387 16788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16815">
    <literal><![CDATA[
      a(L(x,y,z),u \ 1,u) = a(x,u \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,13878,a,b,16814,a),flip(a)].">
      <j1 rule="hyper" parents="316 13878 16814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16816">
    <literal><![CDATA[
      a(x,y \ 1,L(y,z,u)) \ y = L(y,y \ 1,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(16815(a,1),7385(a,1,1))].">
      <j1 rule="para" parents="16815 7385"/>
    </justification>
  </clause>

  <clause id="16817">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u,w,v5)) = a(x,u,L(L(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,13557,a,b,16801,a),flip(a)].">
      <j1 rule="hyper" parents="316 13557 16801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16818">
    <literal><![CDATA[
      L(R(x,y,z),L(x,u,w),v5) = L(R(x,y,z),x,L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,29,a(flip),b,16807,a),flip(a)].">
      <j1 rule="hyper" parents="63 29 16807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16819">
    <literal><![CDATA[
      L(L(x,y,z),L(x,u,w),v5) = L(L(x,y,z),x,L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,30,a,b,16808,a),flip(a)].">
      <j1 rule="hyper" parents="316 30 16808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16820">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),L(a(x,y,z),v5,v6),v7) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14418(a,1),16808(a,2,1))].">
      <j1 rule="para" parents="14418 16808"/>
    </justification>
  </clause>

  <clause id="16822">
    <literal><![CDATA[
      x * L(x \ L(x,x \ 1,y),z,u) = L(x,x \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14769,a,b,16816,a)].">
      <j1 rule="hyper" parents="63 14769 16816"/>
    </justification>
  </clause>

  <clause id="16823">
    <literal><![CDATA[
      R(L(L(x,y,z),x,L(u,w,v5)),v6,v7) = L(R(L(x,y,z),v6,v7),L(x,w,v5),u)
    ]]></literal>
    <justification jstring="[para(16819(a,1),29(a,1,1))].">
      <j1 rule="para" parents="16819 29"/>
    </justification>
  </clause>

  <clause id="16825">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),z,L(y,u,w))) = L(L(z,u,w),y,x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[para(16819(a,1),14510(a,1,3))].">
      <j1 rule="para" parents="16819 14510"/>
    </justification>
  </clause>

  <clause id="16826">
    <literal><![CDATA[
      L(L(x,y,z),x,L(u,w,v5)) \ L(R(L(x,y,z),v6,v7),L(x,w,v5),u) = L(L(x,y,z) \ R(L(x,y,z),v6,v7),L(x,w,v5),u)
    ]]></literal>
    <justification jstring="[para(16819(a,1),16782(a,1,1))].">
      <j1 rule="para" parents="16819 16782"/>
    </justification>
  </clause>

  <clause id="16827">
    <literal><![CDATA[
      a(a(x,y,y) * L(y,z,u),x,w) = L(y \ R(y,x,w),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15947,a,b,16784,a)].">
      <j1 rule="hyper" parents="63 15947 16784"/>
    </justification>
  </clause>

  <clause id="16828">
    <literal><![CDATA[
      (1 / x) \ a(a(y,z,z) * L(z,u,w),y,v5) = L(z \ R(z,y,v5),u,w) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(16827(a,1),5315(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16827 5315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16829">
    <literal><![CDATA[
      L(x,y,a(a(z,u,u) * L(u,w,v5),z,y)) = L(x,L(u \ R(u,z,y),w,v5),y)
    ]]></literal>
    <justification jstring="[para(16827(a,1),6997(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16827 6997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16830">
    <literal><![CDATA[
      a(a(x,y \ R(y,z,u),y \ R(y,z,u)) * L(y \ R(y,z,u),w,v5),x,v6) = L((y \ R(y,z,u)) \ L(y \ R(y,z,u),x,v6),w,v5)
    ]]></literal>
    <justification jstring="[para(15885(a,1),16827(a,2,1,2))].">
      <j1 rule="para" parents="15885 16827"/>
    </justification>
  </clause>

  <clause id="16832">
    <literal><![CDATA[
      a(L(x,y,z),L(x,u,w),v5) = L(a(x,L(x,u,w),v5),y,z)
    ]]></literal>
    <justification jstring="[para(13951(a,1),16787(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13951 16787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16833">
    <literal><![CDATA[
      a(L(x,y,z),L(x,u,w),v5) = a(x,L(x,u,w),L(v5,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,15595,a,b,16832,a),flip(a)].">
      <j1 rule="hyper" parents="316 15595 16832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16835">
    <literal><![CDATA[
      a(x,L(x,y,z),L(u,w,v5)) \ u = L(u,L(x,y,z),L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(16833(a,1),15583(a,1,1))].">
      <j1 rule="para" parents="16833 15583"/>
    </justification>
  </clause>

  <clause id="16836">
    <literal><![CDATA[
      x * L((x \ 1) * L(x,x,y),z,u) = L(x,x \ 1,L(x * y,z,u))
    ]]></literal>
    <justification jstring="[para(7181(a,1),16822(a,1,2,1))].">
      <j1 rule="para" parents="7181 16822"/>
    </justification>
  </clause>

  <clause id="16837">
    <literal><![CDATA[
      L(R(x,y,z),u,w) \ L(x,u,w) = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(39,a,7701,a,b,16783,a(flip))].">
      <j1 rule="hyper" parents="39 7701 16783"/>
    </justification>
  </clause>

  <clause id="16838">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * (u * L(R(x,z,y) \ x,w,v5)) = a(L(x,w,v5),z,y) \ u
    ]]></literal>
    <justification jstring="[para(16837(a,1),15573(a,1,2,2))].">
      <j1 rule="para" parents="16837 15573"/>
    </justification>
  </clause>

  <clause id="16842">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) * a(z,y,x) = a(L(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,15578,a(flip),b,16795,a)].">
      <j1 rule="hyper" parents="63 15578 16795"/>
    </justification>
  </clause>

  <clause id="16843">
    <literal><![CDATA[
      a(x,y,z) \ a(L(x,u,w),y,z) = a(z,y,x * L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(133,a,16795,a(flip),b,15577,a(flip))].">
      <j1 rule="hyper" parents="133 16795 15577"/>
    </justification>
  </clause>

  <clause id="16844">
    <literal><![CDATA[
      a(L(x,y,z),T(z,y),u) \ L(u,u,a(x,T(z,y),T(z,z * y))) = L(u,T(z,y),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(544(a,1),16802(a,1,2,3,3))].">
      <j1 rule="para" parents="544 16802"/>
    </justification>
  </clause>

  <clause id="16846">
    <literal><![CDATA[
      a(L(x,y * (z * z),u),w,v5) \ L(v5,v5,a(x,w,L(w,y,u))) = L(v5,w,L(x,y * (z * z),u))
    ]]></literal>
    <justification jstring="[para(7517(a,1),16802(a,1,2,3))].">
      <j1 rule="para" parents="7517 16802"/>
    </justification>
  </clause>

  <clause id="16847">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),z,L(y,u,w))) = L(L(z,y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,13383,a(flip),b,16825,a),flip(a)].">
      <j1 rule="hyper" parents="316 13383 16825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16848">
    <literal><![CDATA[
      a(x,y,L(z,z,L(y,u,a(w,v5,z)))) = L(L(z,y,x) \ z,u,a(w,v5,z))
    ]]></literal>
    <justification jstring="[para(6853(a,1),16847(a,1,3,1))].">
      <j1 rule="para" parents="6853 16847"/>
    </justification>
  </clause>

  <clause id="16849">
    <literal><![CDATA[
      a(x,y,L(L(z,z,z \ u),z,L(y,z,L(z,w,v5) \ u))) = L(L(z,y,x) \ z,z,L(z,w,v5) \ u)
    ]]></literal>
    <justification jstring="[para(15148(a,1),16847(a,1,3,1))].">
      <j1 rule="para" parents="15148 16847"/>
    </justification>
  </clause>

  <clause id="16851">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,a(w,v5,x)) = a(z,y,L(x,x,y))
    ]]></literal>
    <justification jstring="[para(16810(a,1),16848(a,1,3)),flip(a)].">
      <j1 rule="para" parents="16810 16848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16852">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,a(w,v5,x)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,14510,a(flip),b,16851,a),flip(a)].">
      <j1 rule="hyper" parents="316 14510 16851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16854">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,y,z),z * y) = L((z * (y * x)) \ ((z * y) * x),u,a(w,v5,x))
    ]]></literal>
    <justification jstring="[para(16852(a,1),897(a,1,1))].">
      <j1 rule="para" parents="16852 897"/>
    </justification>
  </clause>

  <clause id="16855">
    <literal><![CDATA[
      L(L(T(x,y) \ R(T(x,y),x,z),u,x),w,v5) = a(x,L(x,w,v5),z)
    ]]></literal>
    <justification jstring="[para(16784(a,1),16786(a,1,1))].">
      <j1 rule="para" parents="16784 16786"/>
    </justification>
  </clause>

  <clause id="16856">
    <literal><![CDATA[
      L(L(x \ R(x,x,y),z,x),u,w) = a(x,L(x,u,w),y)
    ]]></literal>
    <justification jstring="[para(3104(a,1),16855(a,1,1,1))].">
      <j1 rule="para" parents="3104 16855"/>
    </justification>
  </clause>

  <clause id="16857">
    <literal><![CDATA[
      a(x,L(x,y,z),u) = L(a(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(14608(a,2),16856(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14608 16856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16860">
    <literal><![CDATA[
      a(x,L(x,y,z),u) = a(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,11868,a,b,16857,a),flip(a)].">
      <j1 rule="hyper" parents="316 11868 16857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16864">
    <literal><![CDATA[
      a(x,x,L(y,z,a(x,u,w))) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(8397(a,1),16860(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8397 16860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16865">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ y = L(y,x,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(16860(a,1),13816(a,1,1))].">
      <j1 rule="para" parents="16860 13816"/>
    </justification>
  </clause>

  <clause id="16867">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u),w,v5)) \ y = L(y,L(x,w,v5),L(x,z,u))
    ]]></literal>
    <justification jstring="[para(16860(a,1),16835(a,1,1))].">
      <j1 rule="para" parents="16860 16835"/>
    </justification>
  </clause>

  <clause id="16869">
    <literal><![CDATA[
      a(x,x,y) \ L(y,z,a(x,u,w)) = L(L(y,z,a(x,u,w)),x,x)
    ]]></literal>
    <justification jstring="[para(16864(a,1),4950(a,1,1))].">
      <j1 rule="para" parents="16864 4950"/>
    </justification>
  </clause>

  <clause id="16870">
    <literal><![CDATA[
      L(L(x,y,y),a(y,y,x),z) = L(x,y,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16663,a,b,16865,a)].">
      <j1 rule="hyper" parents="63 16663 16865"/>
    </justification>
  </clause>

  <clause id="16871">
    <literal><![CDATA[
      L(x,y,L(y,x,x \ z)) \ z = (x \ z) * a(y,y,x)
    ]]></literal>
    <justification jstring="[para(16870(a,1),7799(a,1,1))].">
      <j1 rule="para" parents="16870 7799"/>
    </justification>
  </clause>

  <clause id="16874">
    <literal><![CDATA[
      L(L(x,x,a(y,y,z)),y,y) = L(a(y,y,x) \ 1,x,z) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,15546,a(flip),b,16869,a),flip(a)].">
      <j1 rule="hyper" parents="63 15546 16869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16875">
    <literal><![CDATA[
      L(L(x,x,a(y,y,z)),y,y) = a(y,y,L(x,x,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,14427,a(flip),b,16874,a),flip(a)].">
      <j1 rule="hyper" parents="316 14427 16874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16876">
    <literal><![CDATA[
      L(L(x,x,a(y,y,z)),y,y) = L(x,y,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,16865,a(flip),b,16875,a),flip(a)].">
      <j1 rule="hyper" parents="316 16865 16875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16877">
    <literal><![CDATA[
      L(R(L(x,y,z),u,w),L(x,v5,v6),v7) = L(R(L(x,y,z),u,w),x,L(v7,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,29,a(flip),b,16823,a),flip(a)].">
      <j1 rule="hyper" parents="63 29 16823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16878">
    <literal><![CDATA[
      L(R(L(x,y,z),u,w),L(x,v5,v6),v7) = L(L(R(x,u,w),y,z),x,L(v7,v5,v6))
    ]]></literal>
    <justification jstring="[para(29(a,1),16877(a,2,1))].">
      <j1 rule="para" parents="29 16877"/>
    </justification>
  </clause>

  <clause id="16879">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,u) / ((u * x) \ 1) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12723,a(flip),b,16794,a),flip(a)].">
      <j1 rule="hyper" parents="63 12723 16794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16880">
    <literal><![CDATA[
      a(L(x,y,z),z,y) \ u = u * (y \ L(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,16362,a(flip),b,16838,a),flip(a)].">
      <j1 rule="hyper" parents="63 16362 16838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16881">
    <literal><![CDATA[
      a(L(x,y,z),z,u) \ w = a(x,z,L(u,y,z)) \ w
    ]]></literal>
    <justification jstring="[hyper(63,a,16322,a(flip),b,16838,a),flip(a)].">
      <j1 rule="hyper" parents="63 16322 16838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16882">
    <literal><![CDATA[
      a(L(x,y,z),z,u) = a(x,z,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(39,a,16322,a(flip),b,16838,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 16322 16838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16883">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (z \ L(z,u,w)) = a(L(w,z,u),u,L(z,y,x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,16378,a(flip),b,16880,a),flip(a)].">
      <j1 rule="hyper" parents="63 16378 16880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16884">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (z \ L(z,u,w)) = a(w,u,L(L(z,y,x),z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,16881,a(flip),b,16883,a),flip(a)].">
      <j1 rule="hyper" parents="316 16881 16883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16885">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (z \ L(z,u,w)) = L(a(w,u,L(z,y,x)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,16298,a,b,16884,a),flip(a)].">
      <j1 rule="hyper" parents="316 16298 16884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16886">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * L(z,u,w) = z * L(a(w,u,L(z,y,x)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(16885(a,1),15552(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16885 15552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16887">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),z,y) \ z = a(w,u,a(z,y,x)) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,14675,a(flip),b,16886,a)].">
      <j1 rule="hyper" parents="316 14675 16886"/>
    </justification>
  </clause>

  <clause id="16888">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) / (v5 \ 1) = (1 / v5) \ L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(16827(a,1),16828(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16827 16828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16889">
    <literal><![CDATA[
      (1 / (x * y)) * (x * R(y,z,u)) = L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,16879,a(flip),b,16888,a(flip))].">
      <j1 rule="hyper" parents="139 16879 16888"/>
    </justification>
  </clause>

  <clause id="16890">
    <literal><![CDATA[
      L(a(x,y,z),y * x,y * x) = L(x \ R(x,y,z),y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14626,a,b,16889,a)].">
      <j1 rule="hyper" parents="63 14626 16889"/>
    </justification>
  </clause>

  <clause id="16892">
    <literal><![CDATA[
      L(x,x,L(y,z,u)) \ L(R(x,w,v5),x,L(y,z,u)) = L(x \ R(x,w,v5),L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(16818(a,1),16811(a,1,2))].">
      <j1 rule="para" parents="16818 16811"/>
    </justification>
  </clause>

  <clause id="16893">
    <literal><![CDATA[
      L(x \ R(x,y,z),L(x,u,w),v5) = L(x \ R(x,y,z),x,L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16782,a(flip),b,16892,a),flip(a)].">
      <j1 rule="hyper" parents="63 16782 16892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16894">
    <literal><![CDATA[
      L((x * (y * z)) \ ((x * y) * z),u,a(w,v5,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1561,a,b,16854,a),flip(a)].">
      <j1 rule="hyper" parents="63 1561 16854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16896">
    <literal><![CDATA[
      L(a(x,y,z),u,a(w,v5,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(14(a,2),16894(a,1,1))].">
      <j1 rule="para" parents="14 16894"/>
    </justification>
  </clause>

  <clause id="16897">
    <literal><![CDATA[
      a(a(x,y,y) * z,x,y) = a(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9251,a(flip),b,16896,a)].">
      <j1 rule="hyper" parents="63 9251 16896"/>
    </justification>
  </clause>

  <clause id="16901">
    <literal><![CDATA[
      a(L(x,y,z),z,u) \ L(u,u,a(x,T(z,y),T(z,z * y))) = L(u,T(z,y),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(11194(a,1),16844(a,1,1))].">
      <j1 rule="para" parents="11194 16844"/>
    </justification>
  </clause>

  <clause id="16903">
    <literal><![CDATA[
      L(x,T(y,z),L(u,z,y)) = a(L(u,z,y),y,x) \ L(x,x,a(u,y,y))
    ]]></literal>
    <justification jstring="[para(11221(a,1),16901(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="11221 16901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16904">
    <literal><![CDATA[
      L(x,T(y,z),L(u,z,y)) = a(u,y,L(x,z,y)) \ L(x,x,a(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,16881,a(flip),b,16903,a),flip(a)].">
      <j1 rule="hyper" parents="316 16881 16903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16906">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(L(R(x,v5,v6),y,z),u,w) = L(L(x \ R(x,v5,v6),y,z),u,w)
    ]]></literal>
    <justification jstring="[para(16791(a,1),16790(a,2,1))].">
      <j1 rule="para" parents="16791 16790"/>
    </justification>
  </clause>

  <clause id="16907">
    <literal><![CDATA[
      L(L(x \ R(x,x,y),z,u),w,v5) = a(x,L(L(x,z,u),w,v5),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16557,a(flip),b,16906,a),flip(a)].">
      <j1 rule="hyper" parents="63 16557 16906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16908">
    <literal><![CDATA[
      a(x,L(L(x,y,z),u,w),v5) = L(L(a(x,x,v5),y,z),u,w)
    ]]></literal>
    <justification jstring="[para(7329(a,1),16907(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7329 16907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16909">
    <literal><![CDATA[
      a(x,L(L(x,y,z),u,w),v5) = L(a(x,x,L(v5,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(11868(a,2),16908(a,2,1))].">
      <j1 rule="para" parents="11868 16908"/>
    </justification>
  </clause>

  <clause id="16910">
    <literal><![CDATA[
      a(x,L(L(x,y,z),u,w),v5) = a(x,x,L(L(v5,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,11868,a,b,16909,a),flip(a)].">
      <j1 rule="hyper" parents="316 11868 16909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16911">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u),w,v5)) \ y = L(y,x,L(L(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(16910(a,1),10099(a,1,1))].">
      <j1 rule="para" parents="16910 10099"/>
    </justification>
  </clause>

  <clause id="16912">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y,w,v5)) = L(x,y,L(L(y,w,v5),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16867,a(flip),b,16911,a)].">
      <j1 rule="hyper" parents="63 16867 16911"/>
    </justification>
  </clause>

  <clause id="16915">
    <literal><![CDATA[
      L(x,y,L(z,u * (w * w),v5)) = a(L(z,u,v5),y,x) \ L(x,x,a(z,y,L(y,u,v5)))
    ]]></literal>
    <justification jstring="[para(8843(a,1),16846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8843 16846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16916">
    <literal><![CDATA[
      L(x,y,L(z,u * (w * w),v5)) = L(x,y,L(z,u,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,16802,a(flip),b,16915,a),flip(a)].">
      <j1 rule="hyper" parents="316 16802 16915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16919">
    <literal><![CDATA[
      L(x,y,L(z,(u \ 1) \ w,v5)) = L(x,y,L(z,u \ w,v5))
    ]]></literal>
    <justification jstring="[para(10965(a,1),16916(a,1,3))].">
      <j1 rule="para" parents="10965 16916"/>
    </justification>
  </clause>

  <clause id="16920">
    <literal><![CDATA[
      L(R(x \ R(x,y,z),L(x,u,w),w * u),u,w) = (w * (u * x)) \ ((w * u) * R(L(x,u,w),y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,29,a(flip),b,16793,a)].">
      <j1 rule="hyper" parents="63 29 16793"/>
    </justification>
  </clause>

  <clause id="16921">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),L(x,u,w),w * u),u,w) = (w * (u * x)) \ ((w * u) * R(L(x,u,w),y,z))
    ]]></literal>
    <justification jstring="[para(15885(a,1),16920(a,1,1))].">
      <j1 rule="para" parents="15885 16920"/>
    </justification>
  </clause>

  <clause id="16922">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),x,L(u * w,w,u)),w,u) = (u * (w * x)) \ ((u * w) * R(L(x,w,u),y,z))
    ]]></literal>
    <justification jstring="[para(16893(a,1),16921(a,1,1))].">
      <j1 rule="para" parents="16893 16921"/>
    </justification>
  </clause>

  <clause id="16925">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),1 / (K(x,y) / y),L(z,u,w)) = L(1 / (K(x,y) / y),L(1 / (1 / y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10810,a(flip),b,16809,a),flip(a)].">
      <j1 rule="hyper" parents="63 10810 16809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16927">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),1 / (K(x,y) / y),L(z,u,w)) = L(1 / (K(x,y) / y),L((1 / y) \ 1,u,w),z)
    ]]></literal>
    <justification jstring="[hyper(316,a,10835,a(flip),b,16925,a),flip(a)].">
      <j1 rule="hyper" parents="316 10835 16925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16928">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),1 / (K(x,y) / y),L(z,u,w)) = L(1 / (K(x,y) / y),L(y,u,w),z)
    ]]></literal>
    <justification jstring="[para(83(a,1),16927(a,2,2,1))].">
      <j1 rule="para" parents="83 16927"/>
    </justification>
  </clause>

  <clause id="16929">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),(K(x,y) / y) \ 1,L(z,u,w)) = L(1 / (K(x,y) / y),L(y,u,w),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10798,a(flip),b,16928,a)].">
      <j1 rule="hyper" parents="63 10798 16928"/>
    </justification>
  </clause>

  <clause id="16930">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),T(y,x),L(z,u,w)) = L(1 / (K(x,y) / y),L(y,u,w),z)
    ]]></literal>
    <justification jstring="[para(2965(a,2),16929(a,1,2))].">
      <j1 rule="para" parents="2965 16929"/>
    </justification>
  </clause>

  <clause id="16931">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),L(y,z,u),w) = L(1 / (K(x,y) / y),y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(10874,a,16930,a),flip(a)].">
      <j1 rule="hyper" parents="10874 16930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16933">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),L(y,z,u),w) = L(T(y,x),y \ 1,L(w,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,12780,a(flip),b,16931,a),flip(a)].">
      <j1 rule="hyper" parents="316 12780 16931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16934">
    <literal><![CDATA[
      L(L(x,y,z),x,L(u,w,v5)) \ L(L(R(x,v6,v7),y,z),x,L(u,w,v5)) = L(L(x,y,z) \ R(L(x,y,z),v6,v7),L(x,w,v5),u)
    ]]></literal>
    <justification jstring="[para(16878(a,1),16826(a,1,2))].">
      <j1 rule="para" parents="16878 16826"/>
    </justification>
  </clause>

  <clause id="16935">
    <literal><![CDATA[
      L(L(x,y,z) \ R(L(x,y,z),u,w),L(x,v5,v6),v7) = L(L(x \ R(x,u,w),y,z),x,L(v7,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,16906,a(flip),b,16934,a),flip(a)].">
      <j1 rule="hyper" parents="63 16906 16934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16936">
    <literal><![CDATA[
      L(L(x,y,z) \ L(R(x,u,w),y,z),L(x,v5,v6),v7) = L(L(x \ R(x,u,w),y,z),x,L(v7,v5,v6))
    ]]></literal>
    <justification jstring="[para(29(a,1),16935(a,1,1,2))].">
      <j1 rule="para" parents="29 16935"/>
    </justification>
  </clause>

  <clause id="16937">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),x,L(v5,u,w)) = v5 \ (L(R(x,y,z),u,w) * (L(x,u,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,14937,a(flip),b,16936,a),flip(a)].">
      <j1 rule="hyper" parents="63 14937 16936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16938">
    <literal><![CDATA[
      a(a(x,y \ R(y,z,u),y \ L(y,z,u)) * L(y \ R(y,z,u),w,v5),x,v6) = L((y \ R(y,z,u)) \ L(y \ R(y,z,u),x,v6),w,v5)
    ]]></literal>
    <justification jstring="[para(7390(a,1),16830(a,1,1,1))].">
      <j1 rule="para" parents="7390 16830"/>
    </justification>
  </clause>

  <clause id="16940">
    <literal><![CDATA[
      a(a(x,y \ R(y,z,u),y * L(y,z,u)) * L(y \ R(y,z,u),w,v5),x,v6) = L((y \ R(y,z,u)) \ L(y \ R(y,z,u),x,v6),w,v5)
    ]]></literal>
    <justification jstring="[para(5566(a,1),16938(a,1,1,1))].">
      <j1 rule="para" parents="5566 16938"/>
    </justification>
  </clause>

  <clause id="16941">
    <literal><![CDATA[
      a(a(x,y \ L(y,z,u),y * L(y,z,u)) * L(y \ R(y,z,u),w,v5),x,v6) = L((y \ R(y,z,u)) \ L(y \ R(y,z,u),x,v6),w,v5)
    ]]></literal>
    <justification jstring="[para(12041(a,1),16940(a,1,1,1))].">
      <j1 rule="para" parents="12041 16940"/>
    </justification>
  </clause>

  <clause id="16942">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ L(x \ R(x,y,z),u,w),v5,v6) = a(1 * L(x \ R(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(14380(a,1),16941(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14380 16941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16943">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ L(x \ R(x,y,z),u,w),v5,v6) = a(L(x \ R(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,1807,a(flip),b,16942,a),flip(a)].">
      <j1 rule="hyper" parents="316 1807 16942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16945">
    <literal><![CDATA[
      a(L(x \ R(x,y,z),u,w),v5,v6) = L(a(z,y,x * L(x,v5,v6)),u,w)
    ]]></literal>
    <justification jstring="[para(15567(a,1),16943(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15567 16943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16946">
    <literal><![CDATA[
      a(L(x \ R(x,y,z),u,w),v5,v6) = a(z,y,L(x * L(x,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,15231,a,b,16945,a),flip(a)].">
      <j1 rule="hyper" parents="316 15231 16945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16956">
    <literal><![CDATA[
      ((x * y) \ ((a(z,u,w) * a(z,u,w)) \ (x * (y * v5)))) * (a(z,u,w) * a(z,u,w)) = L(v5,L(y,x,a(z,u,w) * a(z,u,w)),(a(z,u,w) * a(z,u,w)) * x)
    ]]></literal>
    <justification jstring="[para(16068(a,1),16748(a,1,1))].">
      <j1 rule="para" parents="16068 16748"/>
    </justification>
  </clause>

  <clause id="16957">
    <literal><![CDATA[
      ((x * y) \ (x * ((a(z,u,w) * a(z,u,w)) \ (y * v5)))) * (a(z,u,w) * a(z,u,w)) = L(v5,L(y,x,a(z,u,w) * a(z,u,w)),(a(z,u,w) * a(z,u,w)) * x)
    ]]></literal>
    <justification jstring="[para(7034(a,1),16956(a,1,1,2))].">
      <j1 rule="para" parents="7034 16956"/>
    </justification>
  </clause>

  <clause id="16958">
    <literal><![CDATA[
      ((x * y) \ (x * (y * ((a(z,u,w) * a(z,u,w)) \ v5)))) * (a(z,u,w) * a(z,u,w)) = L(v5,L(y,x,a(z,u,w) * a(z,u,w)),(a(z,u,w) * a(z,u,w)) * x)
    ]]></literal>
    <justification jstring="[para(7034(a,1),16957(a,1,1,2,2))].">
      <j1 rule="para" parents="7034 16957"/>
    </justification>
  </clause>

  <clause id="16959">
    <literal><![CDATA[
      L(x,L(y,z,a(u,w,v5) * a(u,w,v5)),(a(u,w,v5) * a(u,w,v5)) * z) = L((a(u,w,v5) * a(u,w,v5)) \ x,y,z) * (a(u,w,v5) * a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(18(a,2),16958(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 16958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16960">
    <literal><![CDATA[
      L(x,L(y,z,a(u,w,v5) * a(u,w,v5)),(a(u,w,v5) * a(u,w,v5)) * z) = L(((a(u,w,v5) * a(u,w,v5)) \ x) * (a(u,w,v5) * a(u,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,1058,a,b,16959,a),flip(a)].">
      <j1 rule="hyper" parents="316 1058 16959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16961">
    <literal><![CDATA[
      L(x,L(y,z,a(u,w,v5) * a(u,w,v5)),(a(u,w,v5) * a(u,w,v5)) * z) = L(T(x,a(u,w,v5) * a(u,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[para(582(a,1),16960(a,2,1))].">
      <j1 rule="para" parents="582 16960"/>
    </justification>
  </clause>

  <clause id="16962">
    <literal><![CDATA[
      L(x,L(y,z,a(u,w,v5) * a(u,w,v5)),(a(u,w,v5) * a(u,w,v5)) * z) = L(T(x,a(u,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[para(5239(a,1),16961(a,2,1))].">
      <j1 rule="para" parents="5239 16961"/>
    </justification>
  </clause>

  <clause id="16963">
    <literal><![CDATA[
      L(x,L(y,z,a(u,w,v5) * a(u,w,v5)),(a(u,w,v5) * a(u,w,v5)) * z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2281,a(flip),b,16962,a),flip(a)].">
      <j1 rule="hyper" parents="316 2281 16962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16967">
    <literal><![CDATA[
      L(x,y,(a(z,u,w) * a(z,u,w)) * v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10985,a(flip),b,16963,a)].">
      <j1 rule="hyper" parents="63 10985 16963"/>
    </justification>
  </clause>

  <clause id="16969">
    <literal><![CDATA[
      L(x,y,z * (a(u,w,v5) * a(u,w,v5))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1668,a,b,16967,a)].">
      <j1 rule="hyper" parents="63 1668 16967"/>
    </justification>
  </clause>

  <clause id="16970">
    <literal><![CDATA[
      L(x,y,z \ ((a(u,w,v5) \ 1) \ v6)) = L(x,y,z \ (a(u,w,v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,11124,a(flip),b,16967,a)].">
      <j1 rule="hyper" parents="63 11124 16967"/>
    </justification>
  </clause>

  <clause id="16971">
    <literal><![CDATA[
      L(x,y,z * (u * (a(w,v5,v6) * a(w,v5,v6)))) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3160,a(flip),b,16967,a)].">
      <j1 rule="hyper" parents="63 3160 16967"/>
    </justification>
  </clause>

  <clause id="16972">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ v5) = L(x,y,a(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(14397(a,1),16967(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14397 16967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16973">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ 1) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(229(a,1),16969(a,1,3)),flip(a)].">
      <j1 rule="para" parents="229 16969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16974">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w),u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(13995(a,1),16969(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13995 16969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16975">
    <literal><![CDATA[
      L(x,y,z * (L(L(u,w,v5),w,v5) \ u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(13997(a,2),16969(a,1,3,2))].">
      <j1 rule="para" parents="13997 16969"/>
    </justification>
  </clause>

  <clause id="16978">
    <literal><![CDATA[
      L(x,y,z * a(u,z,z)) = L(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[para(8470(a,1),16974(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="8470 16974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16980">
    <literal><![CDATA[
      (x * L(L(x,y,z),y,z)) * L(u,x,x) = x * (L(L(x,y,z),y,z) * u)
    ]]></literal>
    <justification jstring="[para(16974(a,1),9001(a,1,2))].">
      <j1 rule="para" parents="16974 9001"/>
    </justification>
  </clause>

  <clause id="16981">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,w)) = L(x,y,L(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(9873(a,1),16974(a,1,3,1))].">
      <j1 rule="para" parents="9873 16974"/>
    </justification>
  </clause>

  <clause id="16984">
    <literal><![CDATA[
      (x * (a(y,z,u) \ 1)) \ (((x * (a(y,z,u) \ 1)) / x) * w) = L(x \ w,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1612,a,b,16973,a)].">
      <j1 rule="hyper" parents="63 1612 16973"/>
    </justification>
  </clause>

  <clause id="16985">
    <literal><![CDATA[
      L(x,y \ (1 / z),a(z,y,z * y)) = x * a(y \ z,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,16387,a(flip),b,16973,a),flip(a)].">
      <j1 rule="hyper" parents="63 16387 16973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16986">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13656,a(flip),b,16973,a)].">
      <j1 rule="hyper" parents="63 13656 16973"/>
    </justification>
  </clause>

  <clause id="16988">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) * u,u,a(x,y,z)) = 1 / (u \ ((a(x,y,z) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,9895,a(flip),b,16973,a),flip(a)].">
      <j1 rule="hyper" parents="63 9895 16973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16989">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) \ u,x,a(x,y,z)) = (a(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8857,a(flip),b,16973,a),flip(a)].">
      <j1 rule="hyper" parents="63 8857 16973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16990">
    <literal><![CDATA[
      L((a(x,y,x * y) \ 1) \ z,x * y,a(x,y,x * y)) = (x * y) * (L(x * y,y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2669,a(flip),b,16973,a),flip(a)].">
      <j1 rule="hyper" parents="63 2669 16973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16991">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * u) * L(w,u,a(x,y,z)) = (a(x,y,z) \ 1) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(139,a,16973,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="139 16973 18"/>
    </justification>
  </clause>

  <clause id="16992">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (R(x,y,z) * T(u,x * a(y * z,x,a(x,y,z)))) = L(u,R(x,y,z),a(x,y,z)) * ((a(x,y,z) \ 1) * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(16973(a,1),8734(a,2,1))].">
      <j1 rule="para" parents="16973 8734"/>
    </justification>
  </clause>

  <clause id="16993">
    <literal><![CDATA[
      L(x,y \ 1,a(z,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,15699,a,b,16986,a)].">
      <j1 rule="hyper" parents="316 15699 16986"/>
    </justification>
  </clause>

  <clause id="16994">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),v5,v6) = L(L(x,v5,v6),y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,30,a,b,16986,a)].">
      <j1 rule="hyper" parents="316 30 16986"/>
    </justification>
  </clause>

  <clause id="16995">
    <literal><![CDATA[
      L(a(x,y,z),u,a(z,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,16896,a(flip),b,16986,a),flip(a)].">
      <j1 rule="hyper" parents="316 16896 16986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16998">
    <literal><![CDATA[
      L(x,y,a(z,x,y)) = L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,15427,a(flip),b,16986,a),flip(a)].">
      <j1 rule="hyper" parents="316 15427 16986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16999">
    <literal><![CDATA[
      L((a(x,y,z) * u) \ w,u,a(z,y,x)) = u \ (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(316,a,14058,a(flip),b,16986,a),flip(a)].">
      <j1 rule="hyper" parents="316 14058 16986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17000">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(w,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,14055,a(flip),b,16986,a),flip(a)].">
      <j1 rule="hyper" parents="316 14055 16986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17002">
    <literal><![CDATA[
      (a(x,y,z) * u) / L(w,w \ u,a(z,y,x)) = a(x,y,z) * (u / w)
    ]]></literal>
    <justification jstring="[hyper(209,a,16986,a,b,10606,a(flip))].">
      <j1 rule="hyper" parents="209 16986 10606"/>
    </justification>
  </clause>

  <clause id="17003">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * a(v5,v6,v7) = a(v5,v6,v7) * L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,16986,a,b,2275,a),flip(a)].">
      <j1 rule="hyper" parents="139 16986 2275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17004">
    <literal><![CDATA[
      x * L(y,z,a(u,w,v5)) = x * L(y,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,16986,a,b,9,a)].">
      <j1 rule="hyper" parents="139 16986 9"/>
    </justification>
  </clause>

  <clause id="17006">
    <literal><![CDATA[
      x \ L(y,z,a(u,w,v5)) = x \ L(y,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,16986,a,b,10,a)].">
      <j1 rule="hyper" parents="133 16986 10"/>
    </justification>
  </clause>

  <clause id="17007">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ a(u,z,y) = a(u,z,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(16986(a,1),11606(a,1,1))].">
      <j1 rule="para" parents="16986 11606"/>
    </justification>
  </clause>

  <clause id="17008">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ x = x \ L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(16986(a,1),14060(a,1,1))].">
      <j1 rule="para" parents="16986 14060"/>
    </justification>
  </clause>

  <clause id="17009">
    <literal><![CDATA[
      a(x,y,z) * (u * L(w,u,a(z,y,x))) = (a(x,y,z) * u) * w
    ]]></literal>
    <justification jstring="[para(16986(a,1),14054(a,1,2,2))].">
      <j1 rule="para" parents="16986 14054"/>
    </justification>
  </clause>

  <clause id="17011">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * y = a(w,u,z) * (x * (a(w,u,z) \ y))
    ]]></literal>
    <justification jstring="[para(16986(a,1),14838(a,1,1))].">
      <j1 rule="para" parents="16986 14838"/>
    </justification>
  </clause>

  <clause id="17014">
    <literal><![CDATA[
      a(x,y,z) * (a(u,w,x) * v5) = a(u,w,x) * (v5 * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(16995(a,1),5382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16995 5382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17017">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),w,a(u,z,y)) = x * a(a(y,z,u),x,w)
    ]]></literal>
    <justification jstring="[hyper(41,a,9456,a,b,17000,a),flip(a)].">
      <j1 rule="hyper" parents="41 9456 17000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17018">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) * y) * a(w,u,z) = x * (y * a(w,u,z))
    ]]></literal>
    <justification jstring="[para(17000(a,1),5383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17000 5383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17019">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z,u) \ 1) = L(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7344,a,b,16978,a)].">
      <j1 rule="hyper" parents="63 7344 16978"/>
    </justification>
  </clause>

  <clause id="17020">
    <literal><![CDATA[
      a(x,y,z) * L(1 / u,u,a(z,y,x)) = a(x,y,z) / u
    ]]></literal>
    <justification jstring="[hyper(139,a,16993,a(flip),b,7645,a(flip))].">
      <j1 rule="hyper" parents="139 16993 7645"/>
    </justification>
  </clause>

  <clause id="17021">
    <literal><![CDATA[
      x \ ((a(y,z,u) \ x) * (w * a(y,z,u))) = L(w,a(y,z,u),a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2512,a,b,16972,a)].">
      <j1 rule="hyper" parents="63 2512 16972"/>
    </justification>
  </clause>

  <clause id="17022">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * v5) = L(x,y,v5 * a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15554,a(flip),b,16972,a),flip(a)].">
      <j1 rule="hyper" parents="63 15554 16972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17023">
    <literal><![CDATA[
      L(x,y,z \ L(L(u,w,v5),w,v5)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(10072(a,1),16975(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10072 16975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17024">
    <literal><![CDATA[
      L(x,L(y \ z,y,z \ u) \ 1,L((y \ z) \ 1,y,z \ u)) = L(x,u \ ((z \ u) * y),u \ ((z \ u) * y))
    ]]></literal>
    <justification jstring="[hyper(316,a,15159,a(flip),b,16981,a),flip(a)].">
      <j1 rule="hyper" parents="316 15159 16981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17025">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ v5,L(z,u,w),L(z \ 1,v6,v7)) \ (v5 * (1 / L(z,v6,v7)))) = a(x,y,L(z,v6,v7) \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(16981(a,2),9806(a,1,3,1))].">
      <j1 rule="para" parents="16981 9806"/>
    </justification>
  </clause>

  <clause id="17026">
    <literal><![CDATA[
      a(x,y,(z * (L(u,w,a(v5,v6,v7)) * v8)) * v9) = a(x,y,(z * (v8 * L(u,w,a(v7,v6,v5)))) * v9)
    ]]></literal>
    <justification jstring="[para(17004(a,1),5691(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="17004 5691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17027">
    <literal><![CDATA[
      L(x,y,L(z \ u,z \ u,z)) = L(x,y,(u \ z) \ 1)
    ]]></literal>
    <justification jstring="[para(356(a,1),17019(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="356 17019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17028">
    <literal><![CDATA[
      L(L(x,y,z * a(u,w,v5)) \ x,x,y) = a(a(v5,w,u) * z,y,x)
    ]]></literal>
    <justification jstring="[para(17022(a,1),9998(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="17022 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17029">
    <literal><![CDATA[
      L(x,y,L(z,u,u) * (u \ 1)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3335,a(flip),b,17023,a)].">
      <j1 rule="hyper" parents="63 3335 17023"/>
    </justification>
  </clause>

  <clause id="17030">
    <literal><![CDATA[
      L(x,y,L(z * (u \ 1),u,u)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11073,a,b,17029,a)].">
      <j1 rule="hyper" parents="63 11073 17029"/>
    </justification>
  </clause>

  <clause id="17031">
    <literal><![CDATA[
      L(x,y,L((z \ 1) * u,z,z)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1671,a,b,17030,a)].">
      <j1 rule="hyper" parents="63 1671 17030"/>
    </justification>
  </clause>

  <clause id="17032">
    <literal><![CDATA[
      L(x,L(y \ z,y \ z,y),(z \ y) \ 1) = L(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14208,a(flip),b,17027,a),flip(a)].">
      <j1 rule="hyper" parents="63 14208 17027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17033">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ a(u,z,y) = (x \ 1) * a(u,z,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2290,a(flip),b,17007,a),flip(a)].">
      <j1 rule="hyper" parents="316 2290 17007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17034">
    <literal><![CDATA[
      L(x \ L(x,L(1 / y,y,a(z,u,w)),a(w,u,z)),x,a(w,u,z) / y) = a(x,L(1 / y,y,a(z,u,w)),a(w,u,z))
    ]]></literal>
    <justification jstring="[para(17020(a,1),5386(a,1,3))].">
      <j1 rule="para" parents="17020 5386"/>
    </justification>
  </clause>

  <clause id="17036">
    <literal><![CDATA[
      L(x,y,z * (L(L(u,w,v5),w,v5) \ v6)) = L(x,y,(u \ v6) * z)
    ]]></literal>
    <justification jstring="[para(14087(a,1),16971(a,1,3,2))].">
      <j1 rule="para" parents="14087 16971"/>
    </justification>
  </clause>

  <clause id="17037">
    <literal><![CDATA[
      L((a(x,x,y) * y) \ z,x,a(y,y,x)) = y \ (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,15376,a,b,16999,a)].">
      <j1 rule="hyper" parents="63 15376 16999"/>
    </justification>
  </clause>

  <clause id="17039">
    <literal><![CDATA[
      L(x / y,y,a(y,z,u)) * y = L(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,14831,a(flip),b,17011,a),flip(a)].">
      <j1 rule="hyper" parents="316 14831 17011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17040">
    <literal><![CDATA[
      a(x,y,z) * L(u,x,a(z,y,x)) = (u / x) * (x * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(17039(a,1),14061(a,1,2))].">
      <j1 rule="para" parents="17039 14061"/>
    </justification>
  </clause>

  <clause id="17041">
    <literal><![CDATA[
      L(a(x,y,z),u,a(w,v5,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,2307,a,b,17014,a)].">
      <j1 rule="hyper" parents="35 2307 17014"/>
    </justification>
  </clause>

  <clause id="17042">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,16986,a,b,17041,a)].">
      <j1 rule="hyper" parents="63 16986 17041"/>
    </justification>
  </clause>

  <clause id="17043">
    <literal><![CDATA[
      a(x,y,L(z,u,a(w,v5,x))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,16368,a,b,17041,a)].">
      <j1 rule="hyper" parents="63 16368 17041"/>
    </justification>
  </clause>

  <clause id="17044">
    <literal><![CDATA[
      a(x,y,L(z,u,a(x,w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,16369,a,b,17042,a)].">
      <j1 rule="hyper" parents="63 16369 17042"/>
    </justification>
  </clause>

  <clause id="17046">
    <literal><![CDATA[
      a(x,y,z) \ (u * a(x,w,v5)) = (a(x,y,z) \ u) * a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(17042(a,1),456(a,1,2,2))].">
      <j1 rule="para" parents="17042 456"/>
    </justification>
  </clause>

  <clause id="17054">
    <literal><![CDATA[
      x \ L(L(x,a(y,z,u),w),w,a(y,z,u)) = a(a(y,z,u),x,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,16986,a,b,17017,a(flip))].">
      <j1 rule="hyper" parents="133 16986 17017"/>
    </justification>
  </clause>

  <clause id="17056">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(w,v5,z * L(z,y,x)) = a(x,y,z) * (u * a(w,v5,z * L(z,y,x)))
    ]]></literal>
    <justification jstring="[para(13859(a,1),17018(a,1,1,1))].">
      <j1 rule="para" parents="13859 17018"/>
    </justification>
  </clause>

  <clause id="17057">
    <literal><![CDATA[
      L(x,y,(z \ u) * L(z,w,v5)) = L(x,y,z * (L(z,w,v5) \ u))
    ]]></literal>
    <justification jstring="[para(13617(a,1),17036(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13617 17036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17058">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,w,v5)) * (a(y,w,v5) \ a(y,z,u)) = (a(y,w,v5) \ x) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14753,a,b,17046,a)].">
      <j1 rule="hyper" parents="63 14753 17046"/>
    </justification>
  </clause>

  <clause id="17060">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,x * (L(x,u,w) \ v5)) = L(L(x,y,z) \ x,x,L(x,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,9112,a(flip),b,17057,a),flip(a)].">
      <j1 rule="hyper" parents="63 9112 17057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17061">
    <literal><![CDATA[
      L(x,y,z * (L(z,u,w) \ (R(z,z,v5) \ v5))) = L(x,y,((z * z) \ v5) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(4656(a,1),17057(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4656 17057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17062">
    <literal><![CDATA[
      a(a(x,y,z) * u,w,v5) = a(u * a(z,y,x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,9998,a,b,17028,a),flip(a)].">
      <j1 rule="hyper" parents="63 9998 17028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17065">
    <literal><![CDATA[
      L(x,y,z \ (a(u,w,v5) \ v6)) = L(x,y,z \ (v6 * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(14394(a,1),16970(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="14394 16970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17067">
    <literal><![CDATA[
      L(x,y,z \ ((u \ w) * L(u,w,v5))) = L(x,y,z \ (w * a(v5,w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13760,a,b,17065,a)].">
      <j1 rule="hyper" parents="63 13760 17065"/>
    </justification>
  </clause>

  <clause id="17068">
    <literal><![CDATA[
      L(x,y \ (1 / z),a(y,y,z)) = x * a(y \ z,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9227,a(flip),b,16985,a)].">
      <j1 rule="hyper" parents="63 9227 16985"/>
    </justification>
  </clause>

  <clause id="17069">
    <literal><![CDATA[
      L(x,y \ (z \ 1),a(y,y,z)) = x * a(y \ z,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10865,a(flip),b,17068,a)].">
      <j1 rule="hyper" parents="63 10865 17068"/>
    </justification>
  </clause>

  <clause id="17070">
    <literal><![CDATA[
      x * a(y \ z,a(z,y,y),x) = L(x,y \ z,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15700,a(flip),b,17069,a),flip(a)].">
      <j1 rule="hyper" parents="63 15700 17069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17071">
    <literal><![CDATA[
      x * a(y * z,a(z,z,y),x) = L(x,z \ y,a(z,z,y))
    ]]></literal>
    <justification jstring="[para(16394(a,1),17070(a,1,2))].">
      <j1 rule="para" parents="16394 17070"/>
    </justification>
  </clause>

  <clause id="17072">
    <literal><![CDATA[
      L(x,y \ z,a(y,y,z)) = L(x,z * y,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13494,a(flip),b,17071,a),flip(a)].">
      <j1 rule="hyper" parents="63 13494 17071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17073">
    <literal><![CDATA[
      L(x,y \ z,a(z,y,y)) = L(x,z * y,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16986,a,b,17072,a)].">
      <j1 rule="hyper" parents="63 16986 17072"/>
    </justification>
  </clause>

  <clause id="17074">
    <literal><![CDATA[
      a(a(x,y,y),y \ x,z) \ 1 = z \ L(z,x * y,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(17073(a,1),15530(a,2,2))].">
      <j1 rule="para" parents="17073 15530"/>
    </justification>
  </clause>

  <clause id="17075">
    <literal><![CDATA[
      a(a(x,y,y),y \ x,z) \ 1 = a(z,x * y,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,9235,a(flip),b,17074,a),flip(a)].">
      <j1 rule="hyper" parents="316 9235 17074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17076">
    <literal><![CDATA[
      a(x,a(x,x \ y,z),y) \ 1 = a(z,y * x,a(y,x,x))
    ]]></literal>
    <justification jstring="[para(16404(a,1),17075(a,1,1))].">
      <j1 rule="para" parents="16404 17075"/>
    </justification>
  </clause>

  <clause id="17077">
    <literal><![CDATA[
      1 * a(x,a(y,z \ x,z),z) = a(y,x * z,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14414,a(flip),b,17076,a)].">
      <j1 rule="hyper" parents="63 14414 17076"/>
    </justification>
  </clause>

  <clause id="17078">
    <literal><![CDATA[
      1 * a(x,y,a(z,y \ x,y)) = a(z,x * y,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(7011(a,1),17077(a,1,2))].">
      <j1 rule="para" parents="7011 17077"/>
    </justification>
  </clause>

  <clause id="17079">
    <literal><![CDATA[
      a(x,y * z,a(y,z,z)) = a(y,z,a(x,z \ y,z))
    ]]></literal>
    <justification jstring="[hyper(141,a,17078,a),flip(a)].">
      <j1 rule="hyper" parents="141 17078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17080">
    <literal><![CDATA[
      L((a(x,y,x * y) \ 1) \ z,x,a(y,y,x)) = (a(x,y,x * y) \ x) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9227,a(flip),b,16989,a)].">
      <j1 rule="hyper" parents="63 9227 16989"/>
    </justification>
  </clause>

  <clause id="17081">
    <literal><![CDATA[
      a(x,y,z) * L(u,u,a(z,y,x)) = (1 / u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5327,a(flip),b,17003,a),flip(a)].">
      <j1 rule="hyper" parents="63 5327 17003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17082">
    <literal><![CDATA[
      L(x,y,z \ (a(u,w,v5) * w)) = L(x,y,z \ (w * a(v5,w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14765,a(flip),b,17067,a)].">
      <j1 rule="hyper" parents="63 14765 17067"/>
    </justification>
  </clause>

  <clause id="17083">
    <literal><![CDATA[
      L(x,(y * z) \ (a(u,z,y) * z),(y * z) \ (z * a(y,z,u))) = L(x,L(y,z,u) \ 1,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,14314,a(flip),b,17082,a),flip(a)].">
      <j1 rule="hyper" parents="63 14314 17082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17084">
    <literal><![CDATA[
      L((x * L(L(x,y,z),y,z)) * u,x,x) = x * (L(L(x,y,z),y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10060,a,b,16980,a)].">
      <j1 rule="hyper" parents="63 10060 16980"/>
    </justification>
  </clause>

  <clause id="17085">
    <literal><![CDATA[
      L(x,y,z) * (L(x,y,z) * u) = x * (L(L(x,y,z),y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14214,a(flip),b,17084,a)].">
      <j1 rule="hyper" parents="63 14214 17084"/>
    </justification>
  </clause>

  <clause id="17086">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) * u,u,a(x,y,z)) = 1 / (u \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(2301(a,1),16988(a,2,2,2))].">
      <j1 rule="para" parents="2301 16988"/>
    </justification>
  </clause>

  <clause id="17087">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) * u,u,a(x,y,z)) = (a(x,y,z) / u) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,5298,a(flip),b,17086,a),flip(a)].">
      <j1 rule="hyper" parents="316 5298 17086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17089">
    <literal><![CDATA[
      L(a(x,y,z) \ u,u,a(x,y,z)) = (a(x,y,z) / u) \ 1
    ]]></literal>
    <justification jstring="[para(14391(a,1),17087(a,1,1))].">
      <j1 rule="para" parents="14391 17087"/>
    </justification>
  </clause>

  <clause id="17090">
    <literal><![CDATA[
      L((a(x,y,z) / u) \ 1,u,a(x,y,z)) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(41,a,14055,a,b,17089,a)].">
      <j1 rule="hyper" parents="41 14055 17089"/>
    </justification>
  </clause>

  <clause id="17091">
    <literal><![CDATA[
      L((a(x,y,z) / (u / w)) \ 1,w \ u,a(x,y,z)) = a(x,y,z) \ (u / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10798,a(flip),b,17090,a)].">
      <j1 rule="hyper" parents="63 10798 17090"/>
    </justification>
  </clause>

  <clause id="17092">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(w,u,a(x,y,z)) = (a(x,y,z) \ 1) * (u * w)
    ]]></literal>
    <justification jstring="[para(14391(a,1),16991(a,1,1))].">
      <j1 rule="para" parents="14391 16991"/>
    </justification>
  </clause>

  <clause id="17093">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(w,u,a(x,y,z)) = a(x,y,z) \ (u * w)
    ]]></literal>
    <justification jstring="[hyper(316,a,14391,a(flip),b,17092,a),flip(a)].">
      <j1 rule="hyper" parents="316 14391 17092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17095">
    <literal><![CDATA[
      L(x,a(y,z,u) \ w,a(y,z,u)) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(34,a,14053,a,b,17093,a)].">
      <j1 rule="hyper" parents="34 14053 17093"/>
    </justification>
  </clause>

  <clause id="17097">
    <literal><![CDATA[
      L(x,L(y \ 1,y,a(z,u,w)),a(z,u,w)) = L(x,y \ a(z,u,w),a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,10953,a,b,17095,a)].">
      <j1 rule="hyper" parents="63 10953 17095"/>
    </justification>
  </clause>

  <clause id="17098">
    <literal><![CDATA[
      L(x,y * a(z,u,w),a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,10834,a(flip),b,17095,a),flip(a)].">
      <j1 rule="hyper" parents="63 10834 17095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17099">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,a(y,z,u)) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7644,a(flip),b,17095,a),flip(a)].">
      <j1 rule="hyper" parents="63 7644 17095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17100">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,y) = a(x,y * a(z,u,w),a(z,u,w))
    ]]></literal>
    <justification jstring="[para(17098(a,1),14865(a,1,1,2))].">
      <j1 rule="para" parents="17098 14865"/>
    </justification>
  </clause>

  <clause id="17101">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,a(u,z,y)) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16986,a,b,17099,a)].">
      <j1 rule="hyper" parents="63 16986 17099"/>
    </justification>
  </clause>

  <clause id="17102">
    <literal><![CDATA[
      L(x,y \ (z \ ((z * a(u,w,v5)) * y)),a(v5,w,u)) = L(x,a(z,a(u,w,v5),y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(8450(a,2),17101(a,1,2))].">
      <j1 rule="para" parents="8450 17101"/>
    </justification>
  </clause>

  <clause id="17103">
    <literal><![CDATA[
      L((a(x,y,z) / (1 / u)) \ 1,u,a(x,y,z)) = a(x,y,z) \ (1 / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15699,a(flip),b,17091,a)].">
      <j1 rule="hyper" parents="63 15699 17091"/>
    </justification>
  </clause>

  <clause id="17104">
    <literal><![CDATA[
      L(((L(x,y,z) \ x) / (1 / u)) \ 1,u,a(z,y,L(x,x,y))) = a(z,y,L(x,x,y)) \ (1 / u)
    ]]></literal>
    <justification jstring="[para(14510(a,1),17103(a,1,1,1,1))].">
      <j1 rule="para" parents="14510 17103"/>
    </justification>
  </clause>

  <clause id="17105">
    <literal><![CDATA[
      x \ ((x * a(y,z,u)) * (a(y,z,u) \ w)) = L(w,a(y,z,u),a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(16174(a,1),17021(a,1,2))].">
      <j1 rule="para" parents="16174 17021"/>
    </justification>
  </clause>

  <clause id="17106">
    <literal><![CDATA[
      L(x,L(y,y,a(z,u,w)),a(z,u,w)) = L(x,y \ a(z,u,w),a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15728,a(flip),b,17097,a)].">
      <j1 rule="hyper" parents="63 15728 17097"/>
    </justification>
  </clause>

  <clause id="17109">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),a(y,z,u) * w) = a(a(y,z,u) \ x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(17105(a,1),14125(a,1,2))].">
      <j1 rule="para" parents="17105 14125"/>
    </justification>
  </clause>

  <clause id="17110">
    <literal><![CDATA[
      a(a(x,y,z) \ u,a(z,y,x),w) = a(u,a(x,y,z),a(x,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,16189,a(flip),b,17109,a),flip(a)].">
      <j1 rule="hyper" parents="63 16189 17109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17111">
    <literal><![CDATA[
      a(x * a(y,z,u),a(u,z,y),w) = a(x,a(y,z,u),a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14477,a(flip),b,17110,a)].">
      <j1 rule="hyper" parents="63 14477 17110"/>
    </justification>
  </clause>

  <clause id="17112">
    <literal><![CDATA[
      a(x,y,z) * (u * a(x,a(z,y,x),a(z,y,x) * u)) = (a(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[para(17111(a,1),16366(a,1,2,2))].">
      <j1 rule="para" parents="17111 16366"/>
    </justification>
  </clause>

  <clause id="17114">
    <literal><![CDATA[
      L(x * a(y,z,z * y),y,a(z,z,y)) = (a(y,z,y * z) \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(14474(a,1),17080(a,1,1))].">
      <j1 rule="para" parents="14474 17080"/>
    </justification>
  </clause>

  <clause id="17116">
    <literal><![CDATA[
      L(x,y,z * (L(z,u,w) \ (R(z,z,v5) \ v5))) = L(x,y,v5 * ((z * z) \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,15604,a(flip),b,17061,a),flip(a)].">
      <j1 rule="hyper" parents="316 15604 17061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17117">
    <literal><![CDATA[
      L(x,y,z * (L(z,u,w) \ (R(z,z,v5) \ v5))) = L(x,y,v5 * L((z * z) \ z,u,w))
    ]]></literal>
    <justification jstring="[para(1120(a,2),17116(a,2,3,2))].">
      <j1 rule="para" parents="1120 17116"/>
    </justification>
  </clause>

  <clause id="17118">
    <literal><![CDATA[
      L(x,y,z * (L(z,u,w) \ (R(z,z,v5) \ v5))) = L(x,y,v5 * L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,1692,a(flip),b,17117,a),flip(a)].">
      <j1 rule="hyper" parents="316 1692 17117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17119">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ L(v5,z,z)) = L(x,y,v5 * L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(4660(a,1),17118(a,1,3))].">
      <j1 rule="para" parents="4660 17118"/>
    </justification>
  </clause>

  <clause id="17120">
    <literal><![CDATA[
      L(x,y,z * L(u \ 1,w,v5)) = L(x,y,z * (L(u,w,v5) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,14215,a(flip),b,17119,a),flip(a)].">
      <j1 rule="hyper" parents="63 14215 17119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17121">
    <literal><![CDATA[
      L(x,y,(1 / (K(z,L(u,w,v5) \ 1) / z)) * L(u \ 1,w,v5)) = L(x,y,(L(u,w,v5) \ 1) * (1 / (1 / z)))
    ]]></literal>
    <justification jstring="[para(4072(a,1),17120(a,2,3))].">
      <j1 rule="para" parents="4072 17120"/>
    </justification>
  </clause>

  <clause id="17122">
    <literal><![CDATA[
      L(x \ y,x,a(z,u,w)) = (x * (a(z,u,w) \ 1)) \ ((a(z,u,w) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(5004(a,1),16984(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5004 16984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17123">
    <literal><![CDATA[
      (x * (a(y,z,u) \ 1)) \ ((a(y,z,u) \ 1) * w) = (a(y,z,u) * x) \ (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2299,a(flip),b,17122,a),flip(a)].">
      <j1 rule="hyper" parents="63 2299 17122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17125">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(x,u,w) \ v5) = L(L(x,y,z) \ x,x,L(x,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,9098,a(flip),b,17060,a)].">
      <j1 rule="hyper" parents="63 9098 17060"/>
    </justification>
  </clause>

  <clause id="17126">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ ((a(x,y,z) \ 1) * w) = (a(x,y,z) * u) \ (w * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14393(a,1),17123(a,1,1))].">
      <j1 rule="para" parents="14393 17123"/>
    </justification>
  </clause>

  <clause id="17127">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (a(x,y,z) \ w) = (a(x,y,z) * u) \ (w * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14391(a,1),17126(a,1,2))].">
      <j1 rule="para" parents="14391 17126"/>
    </justification>
  </clause>

  <clause id="17128">
    <literal><![CDATA[
      a(x,y,z) \ (L(L(z,y,x),a(x,y,z),y) \ u) = (a(x,y,z) * z) \ (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14709,a,b,17127,a)].">
      <j1 rule="hyper" parents="63 14709 17127"/>
    </justification>
  </clause>

  <clause id="17129">
    <literal><![CDATA[
      a(x,y,z) \ (L(L(z,y,x),a(x,y,z),y) \ u) = L(z \ u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,2299,a,b,17128,a),flip(a)].">
      <j1 rule="hyper" parents="316 2299 17128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17130">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) \ z) \ u) = L(z \ u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(14705(a,1),17129(a,1,2,1))].">
      <j1 rule="para" parents="14705 17129"/>
    </justification>
  </clause>

  <clause id="17131">
    <literal><![CDATA[
      a(x,y,z) * ((z * a(x,y,z)) \ u) = L(z \ u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16178,a(flip),b,17130,a)].">
      <j1 rule="hyper" parents="63 16178 17130"/>
    </justification>
  </clause>

  <clause id="17132">
    <literal><![CDATA[
      a(x,y,z) * ((z * a(x,y,z)) \ (z * u)) = L(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),17131(a,2,1))].">
      <j1 rule="para" parents="9 17131"/>
    </justification>
  </clause>

  <clause id="17133">
    <literal><![CDATA[
      a(x,y,z) * (z * ((a(x,y,z) * z) \ u)) = L(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(11700(a,1),17132(a,1,2))].">
      <j1 rule="para" parents="11700 17132"/>
    </justification>
  </clause>

  <clause id="17134">
    <literal><![CDATA[
      ((a(x,y,z) \ u) / z) * (z * a(x,y,z)) = L(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14097,a,b,17133,a)].">
      <j1 rule="hyper" parents="63 14097 17133"/>
    </justification>
  </clause>

  <clause id="17135">
    <literal><![CDATA[
      ((x / a(y,z,u)) / u) * (u * a(y,z,u)) = L(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(2276(a,2),17134(a,1,1,1))].">
      <j1 rule="para" parents="2276 17134"/>
    </justification>
  </clause>

  <clause id="17136">
    <literal><![CDATA[
      ((x / a(y,z,u)) / u) * (u * a(y,z,u)) = x * a(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,11690,a,b,17135,a),flip(a)].">
      <j1 rule="hyper" parents="316 11690 17135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17137">
    <literal><![CDATA[
      a(a(x,y,z),z,z \ (a(x,y,z) * u)) = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,14968,a,b,17136,a(flip))].">
      <j1 rule="hyper" parents="34 14968 17136"/>
    </justification>
  </clause>

  <clause id="17138">
    <literal><![CDATA[
      a(x,a(y,z,x),a(y,z,x) * u) = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,11624,a(flip),b,17137,a)].">
      <j1 rule="hyper" parents="63 11624 17137"/>
    </justification>
  </clause>

  <clause id="17139">
    <literal><![CDATA[
      a(x,y,z) * (u * a(u,x,a(z,y,x))) = (a(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[para(17138(a,1),17112(a,1,2,2))].">
      <j1 rule="para" parents="17138 17112"/>
    </justification>
  </clause>

  <clause id="17140">
    <literal><![CDATA[
      a(x,y,z) * L(u,x,a(z,y,x)) = (a(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[para(11690(a,1),17139(a,1,2))].">
      <j1 rule="para" parents="11690 17139"/>
    </justification>
  </clause>

  <clause id="17141">
    <literal><![CDATA[
      (a(x,y,z) \ x) \ (x * u) = (u / x) * (x * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17040,a(flip),b,17140,a),flip(a)].">
      <j1 rule="hyper" parents="63 17040 17140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17142">
    <literal><![CDATA[
      L(x * a(y,z,z * y),y,a(z,z,y)) = (x / y) * (y * a(y,z,y * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17114,a,b,17141,a)].">
      <j1 rule="hyper" parents="63 17114 17141"/>
    </justification>
  </clause>

  <clause id="17143">
    <literal><![CDATA[
      L(x * a(y,z,z * y),y,a(z,z,y)) = (x / y) * R(y,z,z * y)
    ]]></literal>
    <justification jstring="[para(9245(a,1),17142(a,2,2))].">
      <j1 rule="para" parents="9245 17142"/>
    </justification>
  </clause>

  <clause id="17144">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,w,v5)) = L(x,a(y,w,v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,16152,a,b,17058,a)].">
      <j1 rule="hyper" parents="35 16152 17058"/>
    </justification>
  </clause>

  <clause id="17145">
    <literal><![CDATA[
      L(x,a(y,z,u),a(w,v5,y)) = L(x,a(y,v5,w),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,16986,a,b,17144,a)].">
      <j1 rule="hyper" parents="316 16986 17144"/>
    </justification>
  </clause>

  <clause id="17154">
    <literal><![CDATA[
      L(x,L(L(a(y,z,u),w,v5),v5,w),a(u,z,y)) = L(x,a(v5,a(y,z,u),w),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(13508(a,1),17102(a,1,2))].">
      <j1 rule="para" parents="13508 17102"/>
    </justification>
  </clause>

  <clause id="17155">
    <literal><![CDATA[
      L((a(x,y,x * y) \ 1) \ z,x * y,a(y,y,x)) = (x * y) * (L(x * y,y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9227,a(flip),b,16990,a)].">
      <j1 rule="hyper" parents="63 9227 16990"/>
    </justification>
  </clause>

  <clause id="17156">
    <literal><![CDATA[
      L(x * a(y,z,z * y),y * z,a(z,z,y)) = (y * z) * (L(y * z,z,y) \ x)
    ]]></literal>
    <justification jstring="[para(14474(a,1),17155(a,1,1))].">
      <j1 rule="para" parents="14474 17155"/>
    </justification>
  </clause>

  <clause id="17157">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ ((a(x,y,z) * a(x,y,z)) * v5) = a(x,y,z) * (v5 * a(w,u,z * L(z,y,x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15641,a,b,17056,a)].">
      <j1 rule="hyper" parents="63 15641 17056"/>
    </justification>
  </clause>

  <clause id="17158">
    <literal><![CDATA[
      L(1 / ((L(x,y,z) / u) \ x),u,a(z,y,L(x,x,y))) = a(z,y,L(x,x,y)) \ (1 / u)
    ]]></literal>
    <justification jstring="[para(13328(a,1),17104(a,1,1))].">
      <j1 rule="para" parents="13328 17104"/>
    </justification>
  </clause>

  <clause id="17159">
    <literal><![CDATA[
      L(1 / ((L(x,y,z) / u) \ x),u,L(x,y,z) \ x) = a(z,y,L(x,x,y)) \ (1 / u)
    ]]></literal>
    <justification jstring="[para(14510(a,1),17158(a,1,3))].">
      <j1 rule="para" parents="14510 17158"/>
    </justification>
  </clause>

  <clause id="17160">
    <literal><![CDATA[
      L(1 / ((L(x,y,z) / u) \ x),u,x \ L(x,y,z)) = a(z,y,L(x,x,y)) \ (1 / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9212,a(flip),b,17159,a)].">
      <j1 rule="hyper" parents="63 9212 17159"/>
    </justification>
  </clause>

  <clause id="17161">
    <literal><![CDATA[
      L(1 / ((L(x,y,z) / u) \ x),u,x \ L(x,y,z)) = (L(x,y,z) \ x) \ (1 / u)
    ]]></literal>
    <justification jstring="[para(14510(a,1),17160(a,2,1))].">
      <j1 rule="para" parents="14510 17160"/>
    </justification>
  </clause>

  <clause id="17162">
    <literal><![CDATA[
      L(1 / ((L(x,y,z) / u) \ x),u,x \ L(x,y,z)) = (1 / u) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,14358,a(flip),b,17161,a),flip(a)].">
      <j1 rule="hyper" parents="316 14358 17161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17163">
    <literal><![CDATA[
      L((x \ L(x,y,z)) / u,u,x \ L(x,y,z)) = (1 / u) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(9764(a,1),17162(a,1,1))].">
      <j1 rule="para" parents="9764 17162"/>
    </justification>
  </clause>

  <clause id="17164">
    <literal><![CDATA[
      1 / (x * (L(y,z,u) \ y)) = (1 / x) * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9215,a(flip),b,17163,a)].">
      <j1 rule="hyper" parents="63 9215 17163"/>
    </justification>
  </clause>

  <clause id="17165">
    <literal><![CDATA[
      ((1 / x) * (y \ L(y,z,u))) \ 1 = x * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(204,a,17164,a)].">
      <j1 rule="hyper" parents="204 17164"/>
    </justification>
  </clause>

  <clause id="17166">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) \ 1 = (x \ 1) * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(80(a,1),17165(a,1,1,1))].">
      <j1 rule="para" parents="80 17165"/>
    </justification>
  </clause>

  <clause id="17167">
    <literal><![CDATA[
      ((a(x,y,a(z,x,y)) * u) \ 1) * (L(y,x,z) \ y) = (a(z,x,y) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(15202(a,1),17166(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15202 17166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17168">
    <literal><![CDATA[
      (a(x,y,L(z,u,w)) \ v5) * (a(x,y,z) * a(x,y,z)) = a(x,y,z) * (v5 * a(w,u,z * L(z,y,x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5363,a(flip),b,17157,a)].">
      <j1 rule="hyper" parents="63 5363 17157"/>
    </justification>
  </clause>

  <clause id="17169">
    <literal><![CDATA[
      x * (a(y,z,L(u,w,v5)) \ (a(y,z,u) * a(y,z,u))) = a(y,z,u) * (x * a(v5,w,u * L(u,z,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14752,a(flip),b,17168,a)].">
      <j1 rule="hyper" parents="63 14752 17168"/>
    </justification>
  </clause>

  <clause id="17170">
    <literal><![CDATA[
      x * (a(y,z,u) * (a(y,z,L(u,w,v5)) \ a(y,z,u))) = a(y,z,u) * (x * a(v5,w,u * L(u,z,y)))
    ]]></literal>
    <justification jstring="[para(14691(a,1),17169(a,1,2))].">
      <j1 rule="para" parents="14691 17169"/>
    </justification>
  </clause>

  <clause id="17172">
    <literal><![CDATA[
      L(x,y,(1 / (K(z,L(u,w,v5) \ 1) / z)) * L(u \ 1,w,v5)) = L(x,y,(L(u,w,v5) \ 1) * ((1 / z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(316,a,1682,a(flip),b,17121,a),flip(a)].">
      <j1 rule="hyper" parents="316 1682 17121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17175">
    <literal><![CDATA[
      L(x,y,(1 / (K(z,L(u,w,v5) \ 1) / z)) * L(u \ 1,w,v5)) = L(x,y,(L(u,w,v5) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(83(a,1),17172(a,2,3,2))].">
      <j1 rule="para" parents="83 17172"/>
    </justification>
  </clause>

  <clause id="17176">
    <literal><![CDATA[
      L(x,y,(1 / (K(z,u \ 1) / z)) * L(u \ 1,w,v5)) = L(x,y,(L(u,w,v5) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3745(a,1),17175(a,1,3,1,2,1))].">
      <j1 rule="para" parents="3745 17175"/>
    </justification>
  </clause>

  <clause id="17178">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,w) * (1 / (1 / v5))) = L(x,y,(L(z,u,w) \ 1) * v5)
    ]]></literal>
    <justification jstring="[para(4302(a,1),17176(a,1,3))].">
      <j1 rule="para" parents="4302 17176"/>
    </justification>
  </clause>

  <clause id="17179">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,w) * ((1 / v5) \ 1)) = L(x,y,(L(z,u,w) \ 1) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,1682,a(flip),b,17178,a)].">
      <j1 rule="hyper" parents="63 1682 17178"/>
    </justification>
  </clause>

  <clause id="17180">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,w) * v5) = L(x,y,(L(z,u,w) \ 1) * v5)
    ]]></literal>
    <justification jstring="[para(83(a,1),17179(a,1,3,2))].">
      <j1 rule="para" parents="83 17179"/>
    </justification>
  </clause>

  <clause id="17181">
    <literal><![CDATA[
      L(x \ L(x,L(y \ 1,y,a(z,u,w)),a(w,u,z)),x,a(w,u,z) / y) = a(x,L(1 / y,y,a(z,u,w)),a(w,u,z))
    ]]></literal>
    <justification jstring="[para(10835(a,1),17034(a,1,1,2))].">
      <j1 rule="para" parents="10835 17034"/>
    </justification>
  </clause>

  <clause id="17183">
    <literal><![CDATA[
      L(x \ L(x,L(y,y,a(z,u,w)),a(w,u,z)),x,a(w,u,z) / y) = a(x,L(1 / y,y,a(z,u,w)),a(w,u,z))
    ]]></literal>
    <justification jstring="[para(15728(a,1),17181(a,1,1,2))].">
      <j1 rule="para" parents="15728 17181"/>
    </justification>
  </clause>

  <clause id="17184">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,a(z,u,w) / y) = a(x,L(1 / y,y,a(w,u,z)),a(z,u,w))
    ]]></literal>
    <justification jstring="[para(16443(a,1),17183(a,1,1,2))].">
      <j1 rule="para" parents="16443 17183"/>
    </justification>
  </clause>

  <clause id="17185">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,a(z,u,w) / y) = a(x,L(1 / y,y,a(w,u,z)),a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,13660,a,b,17184,a),flip(a)].">
      <j1 rule="hyper" parents="316 13660 17184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17187">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,y \ a(z,u,w)) = a(x,L(1 / y,y,a(w,u,z)),a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1586,a(flip),b,17185,a)].">
      <j1 rule="hyper" parents="63 1586 17185"/>
    </justification>
  </clause>

  <clause id="17189">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ v5,L(z,u,w),L(z \ 1,v6,v7)) \ (v5 * (L(z,v6,v7) \ 1))) = a(x,y,L(z,v6,v7) \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5599,a(flip),b,17025,a)].">
      <j1 rule="hyper" parents="63 5599 17025"/>
    </justification>
  </clause>

  <clause id="17190">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ v5,L(z,u,w),L(z \ 1,v6,v7)) \ (L(z,v6,v7) * v5)) = a(x,y,L(z,v6,v7) \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6680,a(flip),b,17189,a)].">
      <j1 rule="hyper" parents="63 6680 17189"/>
    </justification>
  </clause>

  <clause id="17191">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ v5,L(z,u,w),L(z,v6,v7)) \ (L(z,v6,v7) * v5)) = a(x,y,L(z,v6,v7) \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9547,a(flip),b,17190,a)].">
      <j1 rule="hyper" parents="63 9547 17190"/>
    </justification>
  </clause>

  <clause id="17192">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ v5,z,L(L(z,v6,v7),u,w)) \ (L(z,v6,v7) * v5)) = a(x,y,L(z,v6,v7) \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(16912(a,1),17191(a,1,3,1))].">
      <j1 rule="para" parents="16912 17191"/>
    </justification>
  </clause>

  <clause id="17193">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (R(x,y,z) * T(u,x * a(y * z,x,a(x,y,z)))) = L(u,L(x,y,z),a(x,y,z)) * ((a(x,y,z) \ 1) * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(10977(a,1),16992(a,2,1))].">
      <j1 rule="para" parents="10977 16992"/>
    </justification>
  </clause>

  <clause id="17194">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (R(x,y,z) * T(u,x * a(y * z,x,a(x,y,z)))) = L(u,L(x,y,z),a(x,y,z)) * (a(x,y,z) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(8410(a,1),17193(a,2,2))].">
      <j1 rule="para" parents="8410 17193"/>
    </justification>
  </clause>

  <clause id="17195">
    <literal><![CDATA[
      L(x,L(y,z,u),a(y,z,u)) * (a(y,z,u) \ R(y,z,u)) = (a(y,z,u) \ 1) * (R(y,z,u) * T(x,y))
    ]]></literal>
    <justification jstring="[para(5243(a,1),17194(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5243 17194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17196">
    <literal><![CDATA[
      L(x,L(y,z,u),a(y,z,u)) * (a(y,z,u) \ R(y,z,u)) = (a(y,z,u) \ 1) * (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(2842(a,1),17195(a,2,2))].">
      <j1 rule="para" parents="2842 17195"/>
    </justification>
  </clause>

  <clause id="17199">
    <literal><![CDATA[
      L(x,L(y,z,u),a(y,z,u)) * L(y,a(u,z,y),z) = (a(y,z,u) \ 1) * (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(13927(a,1),17196(a,1,2))].">
      <j1 rule="para" parents="13927 17196"/>
    </justification>
  </clause>

  <clause id="17200">
    <literal><![CDATA[
      L(x,L(y,z,u),a(y,z,u)) * L(y,a(u,z,y),z) = a(y,z,u) \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,14391,a(flip),b,17199,a),flip(a)].">
      <j1 rule="hyper" parents="316 14391 17199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17201">
    <literal><![CDATA[
      L(x,L(y,z,u),a(y,z,u)) * L(y,a(u,z,y),z) = (a(y,z,u) \ x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,8431,a(flip),b,17200,a),flip(a)].">
      <j1 rule="hyper" parents="316 8431 17200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17202">
    <literal><![CDATA[
      L(x,L(y,z,u),a(y,z,u)) * L(y,y,a(z,z,u)) = (a(y,z,u) \ x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(15378(a,1),17201(a,1,2))].">
      <j1 rule="para" parents="15378 17201"/>
    </justification>
  </clause>

  <clause id="17203">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ L(L(x,y,z) \ x,u,w),L(x,y,z) \ x,v5) = (L(x,y,z) \ x) * L((L(x,y,z) \ x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(14505(a,1),14672(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="14505 14672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17204">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ L(L(x,y,z) \ x,u,w),L(x,y,z) \ x,v5) = (L(x,y,z) \ x) * L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(5076(a,1),17203(a,2,2,1))].">
      <j1 rule="para" parents="5076 17203"/>
    </justification>
  </clause>

  <clause id="17206">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ L(L(x,y,z) \ x,u,w),L(x,y,z) \ x,v5) = a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,15235,a(flip),b,17204,a),flip(a)].">
      <j1 rule="hyper" parents="316 15235 17204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17208">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * ((L(x,y,z) \ x) \ v5) = v5 * a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,17206,a(flip),b,7098,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 17206 7098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17209">
    <literal><![CDATA[
      L(L(x,y,z) \ (x * L(x \ L(x,y,z),u,w)),L(x,y,z) \ x,v5) = a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1252(a,1),17206(a,1,1))].">
      <j1 rule="para" parents="1252 17206"/>
    </justification>
  </clause>

  <clause id="17210">
    <literal><![CDATA[
      (x * a(y \ L(y,z,u),w,v5)) * (L(y,z,u) \ y) = x * L(L(y,z,u) \ y,w,v5)
    ]]></literal>
    <justification jstring="[hyper(138,a,17208,a(flip),b,4377,a)].">
      <j1 rule="hyper" parents="138 17208 4377"/>
    </justification>
  </clause>

  <clause id="17211">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * L(L(x,y,z) \ x,w,v5)) = u * a(x \ L(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(35,a,14361,a,b,17210,a)].">
      <j1 rule="hyper" parents="35 14361 17210"/>
    </justification>
  </clause>

  <clause id="17212">
    <literal><![CDATA[
      (a(x,y,z * L(z,u,w)) * v5) * (L(z,u,w) \ z) = v5 * L(L(z,u,w) \ z,y,x)
    ]]></literal>
    <justification jstring="[para(13773(a,2),17210(a,1,1))].">
      <j1 rule="para" parents="13773 17210"/>
    </justification>
  </clause>

  <clause id="17213">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (L(x \ L(x,y,z),u,w) \ v5) = v5 * a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14736(a,2),17211(a,1,2))].">
      <j1 rule="para" parents="14736 17211"/>
    </justification>
  </clause>

  <clause id="17214">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ u) * (L(x \ L(x,y,z),w,v5) \ (x \ L(x,y,z))) = u * L(L(x,y,z) \ x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,15645,a,b,17212,a)].">
      <j1 rule="hyper" parents="63 15645 17212"/>
    </justification>
  </clause>

  <clause id="17215">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(L(x,y,z) \ x,u,w) \ v5) = v5 * a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9609,a,b,17213,a)].">
      <j1 rule="hyper" parents="63 9609 17213"/>
    </justification>
  </clause>

  <clause id="17216">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) \ (a(x,x,a(y,z,z)) * a(x \ L(x,z,y),u,w)) = a(y,z,L(x,u,w)) \ a(y,z,x)
    ]]></literal>
    <justification jstring="[para(17215(a,1),16747(a,1,2))].">
      <j1 rule="para" parents="17215 16747"/>
    </justification>
  </clause>

  <clause id="17217">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ L(x \ L(x,y,z),u,w)),L(x,y,z) \ x,v5) = a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1129(a,1),17209(a,1,1))].">
      <j1 rule="para" parents="1129 17209"/>
    </justification>
  </clause>

  <clause id="17219">
    <literal><![CDATA[
      L(a(x \ L(x,y,z),u,w),L(x,y,z) \ x,v5) = a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(15261(a,1),17217(a,1,1))].">
      <j1 rule="para" parents="15261 17217"/>
    </justification>
  </clause>

  <clause id="17220">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (L(R(x,y,z) \ x,u,w) \ v5) = v5 * a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(17219(a,1),15624(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17219 15624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17221">
    <literal><![CDATA[
      L(R(x,y,z) \ x,u,w) \ v5 = v5 * L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(34,a,15910,a,b,17220,a),flip(a)].">
      <j1 rule="hyper" parents="34 15910 17220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17223">
    <literal><![CDATA[
      (1 / x) * (L(R(y,z,u) \ y,w,v5) \ x) = L(L(y \ R(y,z,u),w,v5),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,17221,a,b,886,a)].">
      <j1 rule="hyper" parents="139 17221 886"/>
    </justification>
  </clause>

  <clause id="17224">
    <literal><![CDATA[
      L(R(x,y,z) \ x,u,w) \ v5 = L(x \ R(x,y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[hyper(34,a,2231,a,b,17223,a),flip(a)].">
      <j1 rule="hyper" parents="34 2231 17223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17225">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) \ v5 = L(R(x,y,z) \ x,u,w) * v5
    ]]></literal>
    <justification jstring="[hyper(320,a,17224,a),flip(a)].">
      <j1 rule="hyper" parents="320 17224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17226">
    <literal><![CDATA[
      x / L(R(y,z,u) \ y,w,v5) = L(y \ R(y,z,u),w,v5) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,4359,a,b,17224,a)].">
      <j1 rule="hyper" parents="63 4359 17224"/>
    </justification>
  </clause>

  <clause id="17227">
    <literal><![CDATA[
      a(x,x \ (L(R(y,z,z) \ y,u,w) \ v5),L(R(y,z,z) \ y,u,w)) = v5 / (x * (a(y,z,L(z,u,w)) \ (x \ (L(y \ R(y,z,z),u,w) * v5))))
    ]]></literal>
    <justification jstring="[para(17226(a,1),15942(a,2,2,2,2,2))].">
      <j1 rule="para" parents="17226 15942"/>
    </justification>
  </clause>

  <clause id="17228">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * (L(y \ L(y,z,u),w,v5) \ (y \ L(y,z,u))) = x * L(L(y,z,u) \ y,w,v5)
    ]]></literal>
    <justification jstring="[para(14351(a,1),17214(a,1,1))].">
      <j1 rule="para" parents="14351 17214"/>
    </justification>
  </clause>

  <clause id="17229">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * a(w,v5,y * L(y,z,u)) = x * L(L(y,z,u) \ y,v5,w)
    ]]></literal>
    <justification jstring="[para(15220(a,1),17228(a,1,2))].">
      <j1 rule="para" parents="15220 17228"/>
    </justification>
  </clause>

  <clause id="17230">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,w) * (v5 * (L(x,y,z) \ x)) = v5 * L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,13775,a,b,17229,a)].">
      <j1 rule="hyper" parents="63 13775 17229"/>
    </justification>
  </clause>

  <clause id="17231">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) * (v5 * (L(z,y,x) \ z)) = v5 * L(L(z,y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(15295(a,1),17230(a,1,1))].">
      <j1 rule="para" parents="15295 17230"/>
    </justification>
  </clause>

  <clause id="17232">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,z) = a(z \ L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(322,a,17216,a),flip(a)].">
      <j1 rule="hyper" parents="322 17216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17234">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,z) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,15295,a(flip),b,17232,a),flip(a)].">
      <j1 rule="hyper" parents="316 15295 17232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17236">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,L(z,u,y)) \ w) = a(z \ L(z,y,x),u,y) * w
    ]]></literal>
    <justification jstring="[para(17232(a,1),16360(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17232 16360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17237">
    <literal><![CDATA[
      a(x,y,z) * (u * a(w,v5,z * L(z,y,x))) = u * (a(x,y,z) * a(z \ L(z,y,x),v5,w))
    ]]></literal>
    <justification jstring="[para(17232(a,1),17170(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="17232 17170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17238">
    <literal><![CDATA[
      a(x,x * a(y,a(z,u,w),v5),a(y,a(z,u,w),v5)) = a(y,a(z,u,w),v5 * L(v5,x,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,16444,a,b,17234,a)].">
      <j1 rule="hyper" parents="63 16444 17234"/>
    </justification>
  </clause>

  <clause id="17239">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(v5,v6,v7 * L(v7,v8,v9)) * a(v5,v6,v7)) = a(v5,v6,L(v7,v8,v9)) * a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(17234(a,1),14856(a,1,2,1))].">
      <j1 rule="para" parents="17234 14856"/>
    </justification>
  </clause>

  <clause id="17240">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,y) = a(a(z,y,x),u,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,16299,a(flip),b,17236,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 16299 17236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17241">
    <literal><![CDATA[
      a(x,y,z * L(z,u,y)) = a(a(x,y,z),u,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15295,a(flip),b,17240,a)].">
      <j1 rule="hyper" parents="63 15295 17240"/>
    </justification>
  </clause>

  <clause id="17242">
    <literal><![CDATA[
      a(x,y,z * L(z,x,u)) = a(a(u,x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13642,a(flip),b,17240,a)].">
      <j1 rule="hyper" parents="63 13642 17240"/>
    </justification>
  </clause>

  <clause id="17244">
    <literal><![CDATA[
      L(x,y,z \ L(z,u,y)) = a(a(x,y,z),u,y) * x
    ]]></literal>
    <justification jstring="[para(17241(a,1),16320(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17241 16320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17245">
    <literal><![CDATA[
      a(x,y \ L(y,z,x),u) = a(a(u,x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,15300,a,b,17242,a)].">
      <j1 rule="hyper" parents="63 15300 17242"/>
    </justification>
  </clause>

  <clause id="17246">
    <literal><![CDATA[
      L(x,y,L(z \ L(z,u,y),w,v5)) = a(a(x,y,L(z,w,v5)),u,y) * x
    ]]></literal>
    <justification jstring="[para(2136(a,1),17244(a,1,3))].">
      <j1 rule="para" parents="2136 17244"/>
    </justification>
  </clause>

  <clause id="17247">
    <literal><![CDATA[
      a(x,x * a(y,a(z,u,w),v5),a(y,a(z,u,w),v5)) = a(y,a(z,u,w),a(x,x,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,4962,a(flip),b,17238,a),flip(a)].">
      <j1 rule="hyper" parents="316 4962 17238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17248">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w),v5,v5) = a(x,a(y,z,u),a(v5,v5,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14834,a(flip),b,17247,a)].">
      <j1 rule="hyper" parents="63 14834 17247"/>
    </justification>
  </clause>

  <clause id="17249">
    <literal><![CDATA[
      a(x,a(y,z,u),a(w,w,v5)) = a(w,w,a(v5,a(y,z,u),x))
    ]]></literal>
    <justification jstring="[hyper(63,a,14012,a(flip),b,17248,a),flip(a)].">
      <j1 rule="hyper" parents="63 14012 17248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17250">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) * a(x,y,z) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(34,a,15580,a,b,17239,a),flip(a)].">
      <j1 rule="hyper" parents="34 15580 17239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17251">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,L(z,u,w)) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(35,a,2274,a,b,17250,a)].">
      <j1 rule="hyper" parents="35 2274 17250"/>
    </justification>
  </clause>

  <clause id="17252">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,L(z,u,w)) = a(z \ L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,15295,a,b,17251,a),flip(a)].">
      <j1 rule="hyper" parents="316 15295 17251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17253">
    <literal><![CDATA[
      a(x,y,z) * a(z \ L(z,y,x),u,w) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,15295,a,b,17251,a)].">
      <j1 rule="hyper" parents="139 15295 17251"/>
    </justification>
  </clause>

  <clause id="17254">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,z * L(z,y,x)) = a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,13642,a(flip),b,17252,a)].">
      <j1 rule="hyper" parents="139 13642 17252"/>
    </justification>
  </clause>

  <clause id="17255">
    <literal><![CDATA[
      a(x,y,z) * (u * a(w,v5,z * L(z,y,x))) = u * a(x,y,L(z,v5,w))
    ]]></literal>
    <justification jstring="[para(17253(a,1),17237(a,2,2))].">
      <j1 rule="para" parents="17253 17237"/>
    </justification>
  </clause>

  <clause id="17259">
    <literal><![CDATA[
      a(x,x \ (L(R(y,z,z) \ y,u,w) \ v5),L(R(y,z,z) \ y,u,w)) = v5 / (x * (a(y,z,L(z,u,w)) \ (x \ (L(a(y,z,z),u,w) * v5))))
    ]]></literal>
    <justification jstring="[para(2380(a,1),17227(a,2,2,2,2,2,1,1))].">
      <j1 rule="para" parents="2380 17227"/>
    </justification>
  </clause>

  <clause id="17260">
    <literal><![CDATA[
      a(x,x \ (L(R(y,z,z) \ y,u,w) \ v5),L(R(y,z,z) \ y,u,w)) = v5 / (x * (a(y,z,L(z,u,w)) \ (x \ (a(y,z,L(z,u,w)) * v5))))
    ]]></literal>
    <justification jstring="[para(13562(a,2),17259(a,2,2,2,2,2,1))].">
      <j1 rule="para" parents="13562 17259"/>
    </justification>
  </clause>

  <clause id="17261">
    <literal><![CDATA[
      a(x,x \ (L(R(y,z,z) \ y,u,w) \ v5),L(R(y,z,z) \ y,u,w)) = v5 / (x * (a(y,z,L(z,u,w)) * (x \ (a(y,z,L(z,u,w)) \ v5))))
    ]]></literal>
    <justification jstring="[para(14775(a,1),17260(a,2,2,2))].">
      <j1 rule="para" parents="14775 17260"/>
    </justification>
  </clause>

  <clause id="17269">
    <literal><![CDATA[
      R(x,a(y,x,a(z,u,x)),a(y,x,a(z,u,x))) \ ((x * a(y,x,a(z,u,x))) * w) = L(w * a(y,x,a(z,u,x)),a(y,x,a(z,u,x)) \ 1,L(x,a(z,u,x),y))
    ]]></literal>
    <justification jstring="[para(14394(a,1),13485(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14394 13485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17270">
    <literal><![CDATA[
      R(x,a(y,x,a(z,u,x)),a(y,x,a(z,u,x))) \ ((x * a(y,x,a(z,u,x))) * w) = L(w * a(y,x,a(z,u,x)),a(y,x,a(z,u,x)),L(x,a(z,u,x),y))
    ]]></literal>
    <justification jstring="[hyper(316,a,16120,a(flip),b,17269,a),flip(a)].">
      <j1 rule="hyper" parents="316 16120 17269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17271">
    <literal><![CDATA[
      R(x,a(y,x,a(z,u,x)),a(y,x,a(z,u,x))) \ ((x * a(y,x,a(z,u,x))) * w) = L(w * a(y,x,a(z,u,x)),x,a(x,a(z,u,x),y))
    ]]></literal>
    <justification jstring="[hyper(316,a,14248,a(flip),b,17270,a),flip(a)].">
      <j1 rule="hyper" parents="316 14248 17270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17272">
    <literal><![CDATA[
      L(x * a(y,z,a(u,w,z)),z,a(z,a(u,w,z),y)) = z \ ((z * a(y,z,a(u,w,z))) * x)
    ]]></literal>
    <justification jstring="[para(13754(a,1),17271(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13754 17271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17273">
    <literal><![CDATA[
      L(x * a(y,z,a(u,w,z)),z,a(z,a(u,w,z),y)) = z \ (L(z,a(u,w,z),y) * x)
    ]]></literal>
    <justification jstring="[para(13475(a,1),17272(a,2,2,1))].">
      <j1 rule="para" parents="13475 17272"/>
    </justification>
  </clause>

  <clause id="17274">
    <literal><![CDATA[
      L(x * a(y,z,a(u,w,z)),z,a(z,a(u,w,z),y)) = (x / z) * L(z,a(u,w,z),y)
    ]]></literal>
    <justification jstring="[hyper(316,a,4382,a(flip),b,17273,a),flip(a)].">
      <j1 rule="hyper" parents="316 4382 17273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17275">
    <literal><![CDATA[
      L(x * a(y,z,a(u,w,z)),z,a(z,a(u,w,z),y)) = z * (L(z,a(u,w,z),y) \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,14121,a(flip),b,17274,a),flip(a)].">
      <j1 rule="hyper" parents="316 14121 17274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17289">
    <literal><![CDATA[
      a(x,y,z * ((L(u * (w * w),v5,v6) \ (w * w)) * L(v7,L(u,v5,v6) \ 1,L(u,v5,v6) \ 1))) = a(x,y,((L(u * (w * w),v5,v6) \ (w * w)) \ v7) * z)
    ]]></literal>
    <justification jstring="[para(11715(a,1),8689(a,1,3,2,2))].">
      <j1 rule="para" parents="11715 8689"/>
    </justification>
  </clause>

  <clause id="17290">
    <literal><![CDATA[
      a(x,y,((L(z * (u * u),w,v5) \ (u * u)) \ v6) * v7) = a(x,y,(L(v6,L(z,w,v5) \ 1,L(z,w,v5) \ 1) * L(z * (u * u),w,v5)) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,6088,a(flip),b,17289,a),flip(a)].">
      <j1 rule="hyper" parents="63 6088 17289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17293">
    <literal><![CDATA[
      a(x,y,((L(z * (u * u),w,v5) \ (u * u)) \ v6) * v7) = a(x,y,(L(v6,L(z,w,v5) \ 1,L(z,w,v5) \ 1) * L(z,w,v5)) * v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,5997,a(flip),b,17290,a),flip(a)].">
      <j1 rule="hyper" parents="316 5997 17290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17295">
    <literal><![CDATA[
      a(x,y,((L(z * (u * u),w,v5) \ (u * u)) \ v6) * v7) = a(x,y,(L(v6,L(z,w,v5) \ 1,L(z,w,v5)) * L(z,w,v5)) * v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,7429,a(flip),b,17293,a),flip(a)].">
      <j1 rule="hyper" parents="316 7429 17293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17296">
    <literal><![CDATA[
      a(x,y,((L(z * (u * u),w,v5) \ (u * u)) \ v6) * v7) = a(x,y,(L(v6,L(z,w,v5),L(z,w,v5)) * L(z,w,v5)) * v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,7575,a(flip),b,17295,a),flip(a)].">
      <j1 rule="hyper" parents="316 7575 17295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17297">
    <literal><![CDATA[
      a(x,y,((L(z * (u * u),w,v5) \ (u * u)) \ v6) * v7) = a(x,y,(L(z,w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,8683,a(flip),b,17296,a),flip(a)].">
      <j1 rule="hyper" parents="316 8683 17296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17298">
    <literal><![CDATA[
      a(x,y,(L(z * (u * u),w,v5) \ v6) * v7) = a(x,y,(L(z,w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,7209,a(flip),b,17297,a)].">
      <j1 rule="hyper" parents="63 7209 17297"/>
    </justification>
  </clause>

  <clause id="17300">
    <literal><![CDATA[
      a(x,y,(L((z \ (z \ 1)) \ u,w,v5) \ v6) * v7) = a(x,y,(L(u,w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,6330,a,b,17298,a)].">
      <j1 rule="hyper" parents="63 6330 17298"/>
    </justification>
  </clause>

  <clause id="17302">
    <literal><![CDATA[
      a(x,y,(L((1 / z) * u,w,v5) \ v6) * v7) = a(x,y,(L(z * u,w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,12810,a(flip),b,17300,a),flip(a)].">
      <j1 rule="hyper" parents="63 12810 17300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17304">
    <literal><![CDATA[
      a(x,y,(L(z * (u \ 1),w,v5) \ v6) * v7) = a(x,y,(L(u * z,w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,12098,a(flip),b,17302,a)].">
      <j1 rule="hyper" parents="63 12098 17302"/>
    </justification>
  </clause>

  <clause id="17306">
    <literal><![CDATA[
      T(x \ T(x * (L(y,z,u) * L(y \ 1,w,v5)),(y \ L(y,z,u)) * (y \ L(y,w,v5))),x * ((y \ L(y,z,u)) * (y \ L(y,w,v5)))) = L(y,z,u) * L(y \ 1,w,v5)
    ]]></literal>
    <justification jstring="[para(5133(a,1),6311(a,1,1,2,1,2))].">
      <j1 rule="para" parents="5133 6311"/>
    </justification>
  </clause>

  <clause id="17307">
    <literal><![CDATA[
      T(x \ T(x * (L(y,z,u) * L(y \ 1,w,v5)),L(y,z,u) * L(y \ 1,w,v5)),x * ((y \ L(y,z,u)) * (y \ L(y,w,v5)))) = L(y,z,u) * L(y \ 1,w,v5)
    ]]></literal>
    <justification jstring="[para(5133(a,1),17306(a,1,1,2,2))].">
      <j1 rule="para" parents="5133 17306"/>
    </justification>
  </clause>

  <clause id="17308">
    <literal><![CDATA[
      T(x \ T(x * (L(y,z,u) * L(y \ 1,w,v5)),L(y,z,u) * (y \ 1)),x * ((y \ L(y,z,u)) * (y \ L(y,w,v5)))) = L(y,z,u) * L(y \ 1,w,v5)
    ]]></literal>
    <justification jstring="[para(6514(a,1),17307(a,1,1,2))].">
      <j1 rule="para" parents="6514 17307"/>
    </justification>
  </clause>

  <clause id="17309">
    <literal><![CDATA[
      T(x \ (x * (L(y,z,u) * L(y \ 1,w,v5))),x * ((y \ L(y,z,u)) * (y \ L(y,w,v5)))) = L(y,z,u) * L(y \ 1,w,v5)
    ]]></literal>
    <justification jstring="[para(4991(a,1),17308(a,1,1,2))].">
      <j1 rule="para" parents="4991 17308"/>
    </justification>
  </clause>

  <clause id="17311">
    <literal><![CDATA[
      T(L(x,y,z) * L(x \ 1,u,w),v5 * ((x \ L(x,y,z)) * (x \ L(x,u,w)))) = L(x,y,z) * L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),17309(a,1,1))].">
      <j1 rule="para" parents="9 17309"/>
    </justification>
  </clause>

  <clause id="17313">
    <literal><![CDATA[
      T(L(x,y,z) * L(x \ 1,u,w),v5) = L(x,y,z) * L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3485,a(flip),b,17311,a)].">
      <j1 rule="hyper" parents="63 3485 17311"/>
    </justification>
  </clause>

  <clause id="17317">
    <literal><![CDATA[
      ((L(x,y,z) * L(x \ 1,u,w)) * v5) * v6 = (v5 * (L(x,y,z) * L(x \ 1,u,w))) * v6
    ]]></literal>
    <justification jstring="[para(17313(a,1),239(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="17313 239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17318">
    <literal><![CDATA[
      ((L(x,y,z) * L(x \ 1,y,z)) * u) * w = u * (w * (L(x,y,z) * L(x \ 1,y,z)))
    ]]></literal>
    <justification jstring="[hyper(316,a,12321,a(flip),b,17317,a),flip(a)].">
      <j1 rule="hyper" parents="316 12321 17317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17319">
    <literal><![CDATA[
      (x * (y * (L(z,u,w) * L(z \ 1,u,w)))) / (x * y) = R(L(z,u,w) * L(z \ 1,u,w),x,y)
    ]]></literal>
    <justification jstring="[hyper(136,a,17318,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="136 17318 109"/>
    </justification>
  </clause>

  <clause id="17321">
    <literal><![CDATA[
      R(L(x,y,z) * L(x \ 1,y,z),u,w) = L(x,y,z) * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,15952,a(flip),b,17319,a),flip(a)].">
      <j1 rule="hyper" parents="63 15952 17319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17323">
    <literal><![CDATA[
      a(L(x,y,z) * L(x \ 1,y,z),u,w) = 1
    ]]></literal>
    <justification jstring="[hyper(132,a,17321,a(flip),b,16303,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="132 17321 16303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17326">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * L(z \ 1,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,17323,a)].">
      <j1 rule="hyper" parents="52 17323"/>
    </justification>
  </clause>

  <clause id="17327">
    <literal><![CDATA[
      (((L(x,y,z) * L(x \ 1,y,z)) \ u) * w) * 1 = u * ((L(x,y,z) * L(x \ 1,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(17323(a,1),9832(a,1,2))].">
      <j1 rule="para" parents="17323 9832"/>
    </justification>
  </clause>

  <clause id="17329">
    <literal><![CDATA[
      ((L(x,y,z) * L(x \ 1,y,z)) \ u) * w = u * ((L(x,y,z) * L(x \ 1,y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(146,a,17327,a)].">
      <j1 rule="hyper" parents="146 17327"/>
    </justification>
  </clause>

  <clause id="17331">
    <literal><![CDATA[
      (x * ((L(y,z,u) * L(y \ 1,z,u)) \ w)) * v5 = (x * w) * ((L(y,z,u) * L(y \ 1,z,u)) \ v5)
    ]]></literal>
    <justification jstring="[para(9830(a,1),17329(a,1,1))].">
      <j1 rule="para" parents="9830 17329"/>
    </justification>
  </clause>

  <clause id="17332">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * ((L(v5,v6,v7) * L(v5 \ 1,v6,v7)) \ v8))) = a(x,y,z * (v8 * (((L(v5,v6,v7) * L(v5 \ 1,v6,v7)) \ w) * u)))
    ]]></literal>
    <justification jstring="[para(17329(a,1),9835(a,1,3,2))].">
      <j1 rule="para" parents="17329 9835"/>
    </justification>
  </clause>

  <clause id="17334">
    <literal><![CDATA[
      (x * y) * ((L(z,u,w) * L(z \ 1,u,w)) \ v5) = (x * (y * (L(L(z,u,w),u,w) \ z))) * v5
    ]]></literal>
    <justification jstring="[para(10046(a,1),17331(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10046 17331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17335">
    <literal><![CDATA[
      (x * (y * (L(L(z,u,w),u,w) \ z))) * v5 = (x * y) * (v5 * (L(L(z,u,w),u,w) \ z))
    ]]></literal>
    <justification jstring="[para(10046(a,1),17334(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10046 17334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17336">
    <literal><![CDATA[
      (x * (y * (L(L(y,z,u),z,u) \ w))) * v5 = (x * w) * (v5 * (L(L(y,z,u),z,u) \ y))
    ]]></literal>
    <justification jstring="[para(14088(a,1),17335(a,1,1,2))].">
      <j1 rule="para" parents="14088 17335"/>
    </justification>
  </clause>

  <clause id="17337">
    <literal><![CDATA[
      (x * (y * (L(L(y,z,u),z,u) \ w))) * v5 = (x * w) * (v5 * (a(u,z,y) * a(u,z,y)))
    ]]></literal>
    <justification jstring="[para(13997(a,1),17336(a,2,2,2))].">
      <j1 rule="para" parents="13997 17336"/>
    </justification>
  </clause>

  <clause id="17339">
    <literal><![CDATA[
      a(x,y,z * (u * (((L(w,v5,v6) * L(w \ 1,v5,v6)) \ v7) * v8))) = a(x,y,z * ((v8 * v7) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6321,a(flip),b,17332,a),flip(a)].">
      <j1 rule="hyper" parents="63 6321 17332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17341">
    <literal><![CDATA[
      a(x,y,z * (u * (w * ((L(v5,v6,v7) * L(v5 \ 1,v6,v7)) \ v8)))) = a(x,y,z * ((v8 * w) * u))
    ]]></literal>
    <justification jstring="[para(17329(a,1),17339(a,1,3,2,2))].">
      <j1 rule="para" parents="17329 17339"/>
    </justification>
  </clause>

  <clause id="17342">
    <literal><![CDATA[
      a(x,y,z * (u * (L(w,v5,v6) * ((L(v7,v8,v9) * L(v7 \ 1,v8,v9)) \ v10)))) = a(x,y,z * ((v10 * R(w,v5,v6)) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9688,a(flip),b,17341,a)].">
      <j1 rule="hyper" parents="63 9688 17341"/>
    </justification>
  </clause>

  <clause id="17343">
    <literal><![CDATA[
      a(x,y,z * ((u * R(w,v5,v6)) * v7)) = a(x,y,z * ((u * L(w,v5,v6)) * v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,17341,a(flip),b,17342,a),flip(a)].">
      <j1 rule="hyper" parents="63 17341 17342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17344">
    <literal><![CDATA[
      a(x,y,z * ((u * L(w,v5,v6)) * (L(u * R(w,v5,v6),v7,v8) \ (u * R(w,v5,v6))))) = a(x,y,L(u * R(w,v5,v6),v7,v8) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5904,a(flip),b,17343,a),flip(a)].">
      <j1 rule="hyper" parents="63 5904 17343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17345">
    <literal><![CDATA[
      a(x,y,z * (((u \ w) * L(v5,v6,v7)) * a(u,u \ w,R(v5,v6,v7)))) = a(x,y,z * (u \ (w * R(v5,v6,v7))))
    ]]></literal>
    <justification jstring="[para(8437(a,1),17343(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="8437 17343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17346">
    <literal><![CDATA[
      a(x,y,z * (((u \ w) * L(v5,v6,v7)) * a(u,u \ w,L(v5,v6,v7)))) = a(x,y,z * (u \ (w * R(v5,v6,v7))))
    ]]></literal>
    <justification jstring="[para(5746(a,1),17345(a,1,3,2,2))].">
      <j1 rule="para" parents="5746 17345"/>
    </justification>
  </clause>

  <clause id="17347">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * R(v5,v6,v7)))) = a(x,y,z * (u \ (w * L(v5,v6,v7))))
    ]]></literal>
    <justification jstring="[para(8437(a,1),17346(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="8437 17346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17348">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * L(w,v5,v5)))) = a(x,y,z * (u \ a(w,v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7784,a(flip),b,17347,a),flip(a)].">
      <j1 rule="hyper" parents="63 7784 17347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17349">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ (w * L(v5,v6,v7)))) = a(x,y,(u \ (w * R(v5,v6,v7))) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6701,a(flip),b,17347,a),flip(a)].">
      <j1 rule="hyper" parents="63 6701 17347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17350">
    <literal><![CDATA[
      a(x,y,z * (u \ a(w,v5,v5))) = a(x,y,z * (u \ a(v5,v5,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11105,a(flip),b,17348,a),flip(a)].">
      <j1 rule="hyper" parents="63 11105 17348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17351">
    <literal><![CDATA[
      a(x,y,(z \ (u * R(w,v5,v6))) * v7) = a(x,y,(z \ (u * L(w,v5,v6))) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,6701,a(flip),b,17349,a),flip(a)].">
      <j1 rule="hyper" parents="63 6701 17349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17352">
    <literal><![CDATA[
      a(x,y,(L((z * u) * w,v5,(z * u) * w) \ ((z * u) * L(w,u,z))) * v6) = a(x,y,a(w,u,z) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,8085,a(flip),b,17351,a),flip(a)].">
      <j1 rule="hyper" parents="63 8085 17351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17353">
    <literal><![CDATA[
      a(x,y,(L((z * u) * w,v5,(z * u) * w) \ (z * (u * w))) * v6) = a(x,y,a(w,u,z) * v6)
    ]]></literal>
    <justification jstring="[para(100(a,1),17352(a,1,3,1,2))].">
      <j1 rule="para" parents="100 17352"/>
    </justification>
  </clause>

  <clause id="17354">
    <literal><![CDATA[
      a(x,y,(((z * u) * w) \ (z * (u * w))) * v5) = a(x,y,a(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,8080,a(flip),b,17353,a)].">
      <j1 rule="hyper" parents="63 8080 17353"/>
    </justification>
  </clause>

  <clause id="17355">
    <literal><![CDATA[
      a(x,y,(z \ (u \ ((u * (z * w)) / w))) * v5) = a(x,y,a(w,z,u) * v5)
    ]]></literal>
    <justification jstring="[para(9351(a,1),17354(a,1,3,1))].">
      <j1 rule="para" parents="9351 17354"/>
    </justification>
  </clause>

  <clause id="17357">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ z,z,w * u) * v5) = a(x,y,a(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,13504,a,b,17355,a)].">
      <j1 rule="hyper" parents="63 13504 17355"/>
    </justification>
  </clause>

  <clause id="17358">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ ((w * (u * v5)) / v5)))) = a(x,y,a(v5,u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,17355,a)].">
      <j1 rule="hyper" parents="63 5469 17355"/>
    </justification>
  </clause>

  <clause id="17359">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,u,z)) * v5) = a(x,y,a(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[para(11885(a,1),17357(a,1,3,1))].">
      <j1 rule="para" parents="11885 17357"/>
    </justification>
  </clause>

  <clause id="17361">
    <literal><![CDATA[
      a(x,y,z * a(u,w,L(v5,w,u))) = a(x,y,a(v5,w,u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,17359,a)].">
      <j1 rule="hyper" parents="63 5469 17359"/>
    </justification>
  </clause>

  <clause id="17362">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * v5) = a(x,y,v5 * a(w,u,z))
    ]]></literal>
    <justification jstring="[para(13635(a,1),17361(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="13635 17361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17364">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,w,v5)) * v6) = a(x,y,v6 * a(u,z,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[para(16797(a,1),17362(a,2,3,2))].">
      <j1 rule="para" parents="16797 17362"/>
    </justification>
  </clause>

  <clause id="17365">
    <literal><![CDATA[
      a(x,y,z * a(u,w,L(w,v5,v6))) = a(x,y,z * a(w,w,L(u,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,17364,a),flip(a)].">
      <j1 rule="hyper" parents="63 5469 17364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17366">
    <literal><![CDATA[
      a(x,y,a(z,z,L(L(u,w,v5),v6,v7)) * v8) = a(x,y,v8 * a(u,z,L(L(z,w,v5),v6,v7)))
    ]]></literal>
    <justification jstring="[para(16817(a,1),17364(a,2,3,2))].">
      <j1 rule="para" parents="16817 17364"/>
    </justification>
  </clause>

  <clause id="17367">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ (((w \ 1) * (u * v5)) / v5)))) = a(x,y,a(v5,u,w \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7780,a(flip),b,17358,a)].">
      <j1 rule="hyper" parents="63 7780 17358"/>
    </justification>
  </clause>

  <clause id="17368">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ (((w \ 1) * (u * v5)) / v5)))) = a(x,y,a(v5,u,w) * z)
    ]]></literal>
    <justification jstring="[para(2534(a,1),17367(a,2,3,1))].">
      <j1 rule="para" parents="2534 17367"/>
    </justification>
  </clause>

  <clause id="17369">
    <literal><![CDATA[
      a(x,y,L(a(z \ 1,u,w),a(z,u,w),u) * v5) = a(x,y,a(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,12366,a,b,17368,a)].">
      <j1 rule="hyper" parents="63 12366 17368"/>
    </justification>
  </clause>

  <clause id="17370">
    <literal><![CDATA[
      a(x,y,a(z \ 1,u,w) * v5) = a(x,y,a(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[para(14492(a,1),17369(a,1,3,1))].">
      <j1 rule="para" parents="14492 17369"/>
    </justification>
  </clause>

  <clause id="17372">
    <literal><![CDATA[
      a(x,y,z * ((u * L(w,v5,v6)) * (L(u * L(w,v5,v6),v7,v8) \ (u * L(w,v5,v6))))) = a(x,y,L(u * R(w,v5,v6),v7,v8) * z)
    ]]></literal>
    <justification jstring="[para(14933(a,1),17344(a,1,3,2,2))].">
      <j1 rule="para" parents="14933 17344"/>
    </justification>
  </clause>

  <clause id="17373">
    <literal><![CDATA[
      a(x,y,L(z * R(u,w,v5),v6,v7) * v8) = a(x,y,L(z * L(u,w,v5),v6,v7) * v8)
    ]]></literal>
    <justification jstring="[hyper(63,a,5904,a(flip),b,17372,a),flip(a)].">
      <j1 rule="hyper" parents="63 5904 17372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17374">
    <literal><![CDATA[
      a(x,y,L(R(z,u,w) \ z,v5,v6) * v7) = a(x,y,L(z * L(z,u,w),v5,v6) * v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,9604,a,b,17373,a)].">
      <j1 rule="hyper" parents="63 9604 17373"/>
    </justification>
  </clause>

  <clause id="17382">
    <literal><![CDATA[
      L((a(x,y,z) \ (u * (w * a(x,y,z)))) \ v5,a(x,y,z) \ (u * (w * a(x,y,z))),a(x,y,z) \ 1) = (u * ((a(x,y,z) \ 1) * w)) \ ((a(x,y,z) \ 1) * v5)
    ]]></literal>
    <justification jstring="[para(7965(a,1),8067(a,1,2))].">
      <j1 rule="para" parents="7965 8067"/>
    </justification>
  </clause>

  <clause id="17383">
    <literal><![CDATA[
      L((a(x,y,z) \ (u * (w * a(x,y,z)))) \ v5,a(x,y,z) \ (u * (w * a(x,y,z))),a(x,y,z)) = (u * ((a(x,y,z) \ 1) * w)) \ ((a(x,y,z) \ 1) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,16973,a(flip),b,17382,a)].">
      <j1 rule="hyper" parents="63 16973 17382"/>
    </justification>
  </clause>

  <clause id="17384">
    <literal><![CDATA[
      (x * ((a(y,z,u) \ 1) * w)) \ ((a(y,z,u) \ 1) * v5) = (x * (w * a(y,z,u))) \ (a(y,z,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,475,a(flip),b,17383,a),flip(a)].">
      <j1 rule="hyper" parents="63 475 17383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17385">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ ((a(y,z,u) \ 1) * v5) = (x * (w * a(y,z,u))) \ (a(y,z,u) * v5)
    ]]></literal>
    <justification jstring="[para(14391(a,1),17384(a,1,1,2))].">
      <j1 rule="para" parents="14391 17384"/>
    </justification>
  </clause>

  <clause id="17386">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ (a(y,z,u) \ v5) = (x * (w * a(y,z,u))) \ (a(y,z,u) * v5)
    ]]></literal>
    <justification jstring="[para(14391(a,1),17385(a,1,2))].">
      <j1 rule="para" parents="14391 17385"/>
    </justification>
  </clause>

  <clause id="17387">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ (a(y,z,u) \ ((v5 * (v6 * a(y,z,u))) / a(y,z,u))) = (x * (w * a(y,z,u))) \ (L(a(y,z,u),v6,v5) * (v5 * v6))
    ]]></literal>
    <justification jstring="[para(4415(a,2),17386(a,2,2))].">
      <j1 rule="para" parents="4415 17386"/>
    </justification>
  </clause>

  <clause id="17388">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ (a(y,z,u) \ (a(y,z,u) \ (v5 * (v6 * a(y,z,u))))) = (x * (w * a(y,z,u))) \ (L(a(y,z,u),v6,v5) * (v5 * v6))
    ]]></literal>
    <justification jstring="[para(2276(a,1),17387(a,1,2,2))].">
      <j1 rule="para" parents="2276 17387"/>
    </justification>
  </clause>

  <clause id="17389">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ (a(y,z,u) \ (a(y,z,u) * (v5 * (a(y,z,u) \ v6)))) = (x * (w * a(y,z,u))) \ (L(a(y,z,u),v6,v5) * (v5 * v6))
    ]]></literal>
    <justification jstring="[para(14825(a,1),17388(a,1,2,2))].">
      <j1 rule="para" parents="14825 17388"/>
    </justification>
  </clause>

  <clause id="17390">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ (L(a(z,u,w),v5,v6) * (v6 * v5)) = (x * (a(z,u,w) \ y)) \ (v6 * (a(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(9(a,1),17389(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 17389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17392">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ (v5 * (a(y,z,u) \ v6)) = (x * (w * a(y,z,u))) \ (v5 * (v6 * a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(2307(a,1),17390(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2307 17390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17393">
    <literal><![CDATA[
      L(L(x,y,z) \ (x * L(x \ L(x,y,z),u,w)),v5 * x,v5 * x) * (v6 * a(w,u,a(L(x,y,z) \ x,L(x,y,z) \ x,u))) = a(w,u,(v5 \ L(x,y,z)) \ (v5 \ x)) \ v6
    ]]></literal>
    <justification jstring="[para(1252(a,1),16737(a,1,1,1))].">
      <j1 rule="para" parents="1252 16737"/>
    </justification>
  </clause>

  <clause id="17394">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),v5 * z,v5 * z)) * (v6 * a(x,y,a(L(z,u,w) \ z,L(z,u,w) \ z,y))) = a(x,y,(v5 \ L(z,u,w)) \ (v5 \ z)) \ v6
    ]]></literal>
    <justification jstring="[para(14957(a,1),17393(a,1,1))].">
      <j1 rule="para" parents="14957 17393"/>
    </justification>
  </clause>

  <clause id="17395">
    <literal><![CDATA[
      a(x,y,z * (u * (L(u,w,v5) \ z))) * (v6 * a(x,y,a(L(u,w,v5) \ u,L(u,w,v5) \ u,y))) = a(x,y,(z \ L(u,w,v5)) \ (z \ u)) \ v6
    ]]></literal>
    <justification jstring="[para(14134(a,1),17394(a,1,1))].">
      <j1 rule="para" parents="14134 17394"/>
    </justification>
  </clause>

  <clause id="17396">
    <literal><![CDATA[
      a(x,y,z * (u * (L(u,w,v5) \ z))) * (v6 * a(x,y,1)) = a(x,y,(z \ L(u,w,v5)) \ (z \ u)) \ v6
    ]]></literal>
    <justification jstring="[para(14504(a,1),17395(a,1,2,2,3))].">
      <j1 rule="para" parents="14504 17395"/>
    </justification>
  </clause>

  <clause id="17397">
    <literal><![CDATA[
      a(x,y,z * (u * (L(u,w,v5) \ z))) * (v6 * 1) = a(x,y,(z \ L(u,w,v5)) \ (z \ u)) \ v6
    ]]></literal>
    <justification jstring="[para(469(a,1),17396(a,1,2,2))].">
      <j1 rule="para" parents="469 17396"/>
    </justification>
  </clause>

  <clause id="17399">
    <literal><![CDATA[
      a(x,y,(z \ L(u,w,v5)) \ (z \ u)) \ v6 = a(x,y,z * (u * (L(u,w,v5) \ z))) * v6
    ]]></literal>
    <justification jstring="[hyper(538,a,17397,a),flip(a)].">
      <j1 rule="hyper" parents="538 17397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17401">
    <literal><![CDATA[
      a(x,y,z * (u * (L(u,w,v5) \ z))) \ v6 = a(x,y,z * (u * (L(u,w,v5) \ z))) * v6
    ]]></literal>
    <justification jstring="[para(16744(a,1),17399(a,1,1))].">
      <j1 rule="para" parents="16744 17399"/>
    </justification>
  </clause>

  <clause id="17402">
    <literal><![CDATA[
      a(L(x \ a(y,z,y),u,w),L(x \ 1,u,w),a(v5,v6,v6)) * L(L(L(x \ a(y,z,y),u,w),v6,v5) \ L(x \ a(y,z,y),u,w),v7,v8) = a(v5,v6,L(L(x,u,w),v7,v8))
    ]]></literal>
    <justification jstring="[para(8060(a,1),15453(a,1,1))].">
      <j1 rule="para" parents="8060 15453"/>
    </justification>
  </clause>

  <clause id="17404">
    <literal><![CDATA[
      a(L(x \ a(y,z,y),u,w),L(x,u,w),a(v5,v6,v6)) * L(L(L(x \ a(y,z,y),u,w),v6,v5) \ L(x \ a(y,z,y),u,w),v7,v8) = a(v5,v6,L(L(x,u,w),v7,v8))
    ]]></literal>
    <justification jstring="[para(15763(a,1),17402(a,1,1))].">
      <j1 rule="para" parents="15763 17402"/>
    </justification>
  </clause>

  <clause id="17405">
    <literal><![CDATA[
      a(L(x \ 1,y,z),L(x,y,z),a(u,w,w)) * L(L(L(x \ a(v5,v6,v5),y,z),w,u) \ L(x \ a(v5,v6,v5),y,z),v7,v8) = a(u,w,L(L(x,y,z),v7,v8))
    ]]></literal>
    <justification jstring="[para(8061(a,1),17404(a,1,1))].">
      <j1 rule="para" parents="8061 17404"/>
    </justification>
  </clause>

  <clause id="17407">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),a(u,w,w)) * L(L(L(x \ a(v5,v6,v5),y,z),w,u) \ L(x \ a(v5,v6,v5),y,z),v7,v8) = a(u,w,L(L(x,y,z),v7,v8))
    ]]></literal>
    <justification jstring="[para(13035(a,1),17405(a,1,1))].">
      <j1 rule="para" parents="13035 17405"/>
    </justification>
  </clause>

  <clause id="17408">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L(L(L(x \ a(u,w,u),v5,v6),z,y) \ L(x \ a(u,w,u),v5,v6),v7,v8) = a(y,z,L(L(x,v5,v6),v7,v8))
    ]]></literal>
    <justification jstring="[para(11923(a,1),17407(a,1,1))].">
      <j1 rule="para" parents="11923 17407"/>
    </justification>
  </clause>

  <clause id="17410">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L(L(L(x \ a(u,w,u),z,y) \ (x \ a(u,w,u)),v5,v6),v7,v8) = a(y,z,L(L(x,v5,v6),v7,v8))
    ]]></literal>
    <justification jstring="[para(13383(a,1),17408(a,1,2,1))].">
      <j1 rule="para" parents="13383 17408"/>
    </justification>
  </clause>

  <clause id="17411">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L(L(a(u,w,u) \ (L(x / a(u,w,u),z,y) \ x),v5,v6),v7,v8) = a(y,z,L(L(x,v5,v6),v7,v8))
    ]]></literal>
    <justification jstring="[para(13906(a,1),17410(a,1,2,1,1))].">
      <j1 rule="para" parents="13906 17410"/>
    </justification>
  </clause>

  <clause id="17412">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L(L(a(u,w,u) \ (L(a(u,w,u) \ x,z,y) \ x),v5,v6),v7,v8) = a(y,z,L(L(x,v5,v6),v7,v8))
    ]]></literal>
    <justification jstring="[para(2276(a,1),17411(a,1,2,1,1,2,1,1))].">
      <j1 rule="para" parents="2276 17411"/>
    </justification>
  </clause>

  <clause id="17413">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L(L(a(u,w,u) \ ((L(x,z,y) \ x) * a(u,w,u)),v5,v6),v7,v8) = a(y,z,L(L(x,v5,v6),v7,v8))
    ]]></literal>
    <justification jstring="[para(6149(a,1),17412(a,1,2,1,1,2))].">
      <j1 rule="para" parents="6149 17412"/>
    </justification>
  </clause>

  <clause id="17414">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L(L(L(x,z,y) \ x,u,w),v5,v6) = a(y,z,L(L(x,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(2275(a,1),17413(a,1,2,1,1))].">
      <j1 rule="para" parents="2275 17413"/>
    </justification>
  </clause>

  <clause id="17416">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),a(u,w,w)) * L(L((y * z) \ (z * (x * y)),w,u) \ ((y * z) \ (z * (x * y))),v5,v6) = a(u,w,L((y * z) \ (z * (x * y)),v5,v6))
    ]]></literal>
    <justification jstring="[para(11323(a,1),15456(a,1,1))].">
      <j1 rule="para" parents="11323 15456"/>
    </justification>
  </clause>

  <clause id="17417">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L(L((u * w) \ (w * (x * u)),z,y) \ ((u * w) \ (w * (x * u))),v5,v6) = a(y,z,L((u * w) \ (w * (x * u)),v5,v6))
    ]]></literal>
    <justification jstring="[para(11923(a,1),17416(a,1,1))].">
      <j1 rule="para" parents="11923 17416"/>
    </justification>
  </clause>

  <clause id="17419">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L((u * (x * w)) \ (L((w * u) / (u * (x * w)),z,y) \ (w * u)),v5,v6) = a(y,z,L((w * u) \ (u * (x * w)),v5,v6))
    ]]></literal>
    <justification jstring="[para(13906(a,1),17417(a,1,2,1))].">
      <j1 rule="para" parents="13906 17417"/>
    </justification>
  </clause>

  <clause id="17420">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L((((x * u) * L((x * u) \ u,z,y)) * w) \ (u * w),v5,v6) = a(y,z,L((u * w) \ (w * (x * u)),v5,v6))
    ]]></literal>
    <justification jstring="[para(9193(a,1),17419(a,1,2,1))].">
      <j1 rule="para" parents="9193 17419"/>
    </justification>
  </clause>

  <clause id="17421">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L(((x * (u * L(u \ (x \ u),z,y))) * w) \ (u * w),v5,v6) = a(y,z,L((u * w) \ (w * (x * u)),v5,v6))
    ]]></literal>
    <justification jstring="[para(879(a,1),17420(a,1,2,1,1,1))].">
      <j1 rule="para" parents="879 17420"/>
    </justification>
  </clause>

  <clause id="17422">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L(((u * (x \ L(x,z,y))) * w) \ (u * w),v5,v6) = a(y,z,L((u * w) \ (w * (x * u)),v5,v6))
    ]]></literal>
    <justification jstring="[para(5105(a,1),17421(a,1,2,1,1,1))].">
      <j1 rule="para" parents="5105 17421"/>
    </justification>
  </clause>

  <clause id="17423">
    <literal><![CDATA[
      a(x,y,L((z * u) \ (u * (w * z)),v5,v6)) = a(w,w,a(x,y,y)) * L(L(L(w,y,x) \ w,z,u),v5,v6)
    ]]></literal>
    <justification jstring="[para(14308(a,1),17422(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14308 17422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17424">
    <literal><![CDATA[
      a(x,y,L((z * u) \ (u * (w * z)),v5,v6)) = a(x,y,L(L(w,z,u),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,17414,a(flip),b,17423,a),flip(a)].">
      <j1 rule="hyper" parents="316 17414 17423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17425">
    <literal><![CDATA[
      a(x,y,L(L(a(z,u,w) * u,z,w),v5,v6)) = a(x,y,L(L(u,w,z),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,14877,a,b,17424,a)].">
      <j1 rule="hyper" parents="63 14877 17424"/>
    </justification>
  </clause>

  <clause id="17426">
    <literal><![CDATA[
      a(x,a(y,z,u) \ z,L(L(z,u,y),w,v5)) = a(x,L(z,u,y),L(a(y,z,u) * z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,14998,a(flip),b,17425,a),flip(a)].">
      <j1 rule="hyper" parents="63 14998 17425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17427">
    <literal><![CDATA[
      a(x,y * a(z,y,u),L(L(y,u,z),w,v5)) = a(x,L(y,u,z),L(a(z,y,u) * y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,14435,a(flip),b,17426,a)].">
      <j1 rule="hyper" parents="63 14435 17426"/>
    </justification>
  </clause>

  <clause id="17428">
    <literal><![CDATA[
      R(x,y * a(z,y,u),y * a(z,y,u)) = x * a(x,L(y,u,z),L(a(z,y,u) * y,z,u))
    ]]></literal>
    <justification jstring="[para(17427(a,1),11905(a,2,2))].">
      <j1 rule="para" parents="17427 11905"/>
    </justification>
  </clause>

  <clause id="17429">
    <literal><![CDATA[
      R(x,y * a(z,y,u),y * a(z,y,u)) = x * a(x,L(y,u,z),L(y,u,z))
    ]]></literal>
    <justification jstring="[para(13881(a,1),17428(a,2,2))].">
      <j1 rule="para" parents="13881 17428"/>
    </justification>
  </clause>

  <clause id="17430">
    <literal><![CDATA[
      R(x,y * a(z,y,u),y * a(z,y,u)) = x * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(13575(a,1),17429(a,2,2))].">
      <j1 rule="para" parents="13575 17429"/>
    </justification>
  </clause>

  <clause id="17431">
    <literal><![CDATA[
      R(x,y * a(z,y,u),y * a(z,y,u)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,2381,a(flip),b,17430,a),flip(a)].">
      <j1 rule="hyper" parents="316 2381 17430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17433">
    <literal><![CDATA[
      R(x,y * a(z,y,u),y * a(u,y,z)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16598,a,b,17431,a)].">
      <j1 rule="hyper" parents="63 16598 17431"/>
    </justification>
  </clause>

  <clause id="17435">
    <literal><![CDATA[
      (x * ((L(y,z,u) * L(y \ 1,z,u)) \ w)) \ v5 = (x * w) \ ((L(y,z,u) * L(y \ 1,z,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,17326,a(flip),b,9833,a)].">
      <j1 rule="hyper" parents="63 17326 9833"/>
    </justification>
  </clause>

  <clause id="17437">
    <literal><![CDATA[
      (x * ((L(y,z,u) * L(y \ 1,z,u)) \ w)) \ v5 = ((x * w) \ v5) * (L(y,z,u) * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,9817,a(flip),b,17435,a),flip(a)].">
      <j1 rule="hyper" parents="316 9817 17435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17439">
    <literal><![CDATA[
      ((x * y) \ z) * (L(u,w,v5) * L(u \ 1,w,v5)) = (x * (y * (L(L(u,w,v5),w,v5) \ u))) \ z
    ]]></literal>
    <justification jstring="[para(10046(a,1),17437(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10046 17437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17440">
    <literal><![CDATA[
      (x * (y * (L(L(z,u,w),u,w) \ z))) \ v5 = ((x * y) \ v5) * (z \ L(L(z,u,w),u,w))
    ]]></literal>
    <justification jstring="[para(9957(a,1),17439(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9957 17439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17441">
    <literal><![CDATA[
      ((x * y) \ (x * (y * (z * (L(L(z,u,w),u,w) \ v5))))) * (z \ L(L(z,u,w),u,w)) = L(L(v5,L(L(z,u,w),u,w) \ z,y),z * (L(L(z,u,w),u,w) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,16673,a(flip),b,17440,a),flip(a)].">
      <j1 rule="hyper" parents="63 16673 17440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17442">
    <literal><![CDATA[
      L(L(x,L(L(y,z,u),z,u) \ y,w),y * (L(L(y,z,u),z,u) \ w),v5) = L(y * (L(L(y,z,u),z,u) \ x),w,v5) * (y \ L(L(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[para(18(a,2),17441(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 17441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17443">
    <literal><![CDATA[
      L(L(x,L(L(y,z,u),z,u) \ y,w),y * (L(L(y,z,u),z,u) \ w),v5) = L((y * (L(L(y,z,u),z,u) \ x)) * (y \ L(L(y,z,u),z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,10077,a,b,17442,a),flip(a)].">
      <j1 rule="hyper" parents="316 10077 17442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17444">
    <literal><![CDATA[
      L(L(x,L(L(y,z,u),z,u) \ y,w),y * (L(L(y,z,u),z,u) \ w),v5) = L(y * ((L(L(y,z,u),z,u) \ x) * (y \ L(L(y,z,u),z,u))),w,v5)
    ]]></literal>
    <justification jstring="[para(10081(a,1),17443(a,2,1))].">
      <j1 rule="para" parents="10081 17443"/>
    </justification>
  </clause>

  <clause id="17445">
    <literal><![CDATA[
      L(L(x,L(L(y,z,u),z,u) \ y,w),y * (L(L(y,z,u),z,u) \ w),v5) = L(y * (y \ x),w,v5)
    ]]></literal>
    <justification jstring="[para(10066(a,1),17444(a,2,1,2))].">
      <j1 rule="para" parents="10066 17444"/>
    </justification>
  </clause>

  <clause id="17446">
    <literal><![CDATA[
      L(L(x,L(L(y,z,u),z,u) \ y,w),y * (L(L(y,z,u),z,u) \ w),v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),17445(a,2,1))].">
      <j1 rule="para" parents="10 17445"/>
    </justification>
  </clause>

  <clause id="17448">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ a(L(L(a(x,y,z),w,v5),v6,v7),a(x,y,z),u))) = L(u,a(x,y,z) \ L(L(a(x,y,z),w,v5),v6,v7),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,101,a(flip),b,14953,a),flip(a)].">
      <j1 rule="hyper" parents="63 101 14953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17469">
    <literal><![CDATA[
      ((((x \ 1) \ ((y \ ((x \ 1) * z)) * y)) / x) \ u) * (((x \ 1) \ ((y \ ((x \ 1) * z)) * y)) / x) = (((y \ (z * (x \ 1))) * y) \ u) * ((y \ (z * (x \ 1))) * y)
    ]]></literal>
    <justification jstring="[para(7254(a,1),7255(a,2,2))].">
      <j1 rule="para" parents="7254 7255"/>
    </justification>
  </clause>

  <clause id="17470">
    <literal><![CDATA[
      ((((x \ 1) \ ((y \ ((x \ 1) * z)) * y)) / x) \ u) * (((x \ 1) \ ((y \ ((x \ 1) * z)) * y)) / x) = (T(z * (x \ 1),y) \ u) * T(z * (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(316,a,13208,a(flip),b,17469,a),flip(a)].">
      <j1 rule="hyper" parents="316 13208 17469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17471">
    <literal><![CDATA[
      ((((1 \ x) * ((y \ ((1 \ x) \ z)) * y)) / x) \ u) * (((x \ 1) \ ((y \ ((x \ 1) * z)) * y)) / x) = (T(z * (x \ 1),y) \ u) * T(z * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(12214(a,1),17470(a,1,1,1,1))].">
      <j1 rule="para" parents="12214 17470"/>
    </justification>
  </clause>

  <clause id="17472">
    <literal><![CDATA[
      (((x * ((y \ ((1 \ x) \ z)) * y)) / x) \ u) * (((x \ 1) \ ((y \ ((x \ 1) * z)) * y)) / x) = (T(z * (x \ 1),y) \ u) * T(z * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(66(a,1),17471(a,1,1,1,1,1))].">
      <j1 rule="para" parents="66 17471"/>
    </justification>
  </clause>

  <clause id="17473">
    <literal><![CDATA[
      (((x * ((y \ (x \ z)) * y)) / x) \ u) * (((x \ 1) \ ((y \ ((x \ 1) * z)) * y)) / x) = (T(z * (x \ 1),y) \ u) * T(z * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(66(a,1),17472(a,1,1,1,1,2,1,2,1))].">
      <j1 rule="para" parents="66 17472"/>
    </justification>
  </clause>

  <clause id="17474">
    <literal><![CDATA[
      (((x \ (y / z)) * x) \ u) * (((z \ 1) \ ((x \ ((z \ 1) * y)) * x)) / z) = (T(y * (z \ 1),x) \ u) * T(y * (z \ 1),x)
    ]]></literal>
    <justification jstring="[para(2716(a,1),17473(a,1,1,1))].">
      <j1 rule="para" parents="2716 17473"/>
    </justification>
  </clause>

  <clause id="17475">
    <literal><![CDATA[
      (((x \ (y / z)) * x) \ u) * (((1 \ z) * ((x \ ((1 \ z) \ y)) * x)) / z) = (T(y * (z \ 1),x) \ u) * T(y * (z \ 1),x)
    ]]></literal>
    <justification jstring="[para(12214(a,1),17474(a,1,2,1))].">
      <j1 rule="para" parents="12214 17474"/>
    </justification>
  </clause>

  <clause id="17476">
    <literal><![CDATA[
      (((x \ (y / z)) * x) \ u) * ((z * ((x \ ((1 \ z) \ y)) * x)) / z) = (T(y * (z \ 1),x) \ u) * T(y * (z \ 1),x)
    ]]></literal>
    <justification jstring="[para(66(a,1),17475(a,1,2,1,1))].">
      <j1 rule="para" parents="66 17475"/>
    </justification>
  </clause>

  <clause id="17477">
    <literal><![CDATA[
      (((x \ (y / z)) * x) \ u) * ((z * ((x \ (z \ y)) * x)) / z) = (T(y * (z \ 1),x) \ u) * T(y * (z \ 1),x)
    ]]></literal>
    <justification jstring="[para(66(a,1),17476(a,1,2,1,2,1,2,1))].">
      <j1 rule="para" parents="66 17476"/>
    </justification>
  </clause>

  <clause id="17478">
    <literal><![CDATA[
      (T(x * (y \ 1),z) \ u) * T(x * (y \ 1),z) = (((z \ (x / y)) * z) \ u) * ((z \ (x / y)) * z)
    ]]></literal>
    <justification jstring="[para(2716(a,1),17477(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2716 17477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17479">
    <literal><![CDATA[
      (T(x * (y \ 1),z) \ u) * T(x * (y \ 1),z) = (T(x / y,z) \ u) * T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,13208,a(flip),b,17478,a),flip(a)].">
      <j1 rule="hyper" parents="316 13208 17478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17491">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ (((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1) * u)) / u = y * a(a(a(x,y,z),y,y),y,u)
    ]]></literal>
    <justification jstring="[para(8766(a,1),8782(a,2,2,2))].">
      <j1 rule="para" parents="8766 8782"/>
    </justification>
  </clause>

  <clause id="17492">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ (((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1) * (u / w))) / (u / w) = y * a(a(a(x,y,z),y,y),y,w \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11830,a,b,17491,a)].">
      <j1 rule="hyper" parents="63 11830 17491"/>
    </justification>
  </clause>

  <clause id="17493">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ (((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1) * (u / (w / v5)))) / (u / (w / v5)) = y * a(a(a(x,y,z),y,y),y,(v5 \ w) \ u)
    ]]></literal>
    <justification jstring="[para(5546(a,1),17492(a,2,2))].">
      <j1 rule="para" parents="5546 17492"/>
    </justification>
  </clause>

  <clause id="17494">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ (((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1) * (u / (w / v5)))) / (u / (w / v5)) = y * a(y,a(a(x,y,z),y,y),(v5 \ w) \ u)
    ]]></literal>
    <justification jstring="[para(7009(a,1),17493(a,2,2))].">
      <j1 rule="para" parents="7009 17493"/>
    </justification>
  </clause>

  <clause id="17495">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ (((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1) * (a(u,y,w) / ((u \ ((u * y) * w)) / w)))) / (a(u,y,w) / ((u \ ((u * y) * w)) / w)) = y * a(y,a(a(x,y,z),y,y),y)
    ]]></literal>
    <justification jstring="[para(8638(a,1),17494(a,2,2))].">
      <j1 rule="para" parents="8638 17494"/>
    </justification>
  </clause>

  <clause id="17496">
    <literal><![CDATA[
      (x * K(y,z)) * ((a(u,w,v5) \ 1) * L((a(u,w,v5) \ 1) \ (K(z,y) * (x \ v6)),x * K(y,z),a(u,w,v5) \ 1)) = (a(u,w,v5) \ 1) * ((x * K(y,z)) * ((x * (a(u,w,v5) \ K(y,z))) \ v6))
    ]]></literal>
    <justification jstring="[para(10176(a,1),11081(a,1,2,2,1,2))].">
      <j1 rule="para" parents="10176 11081"/>
    </justification>
  </clause>

  <clause id="17497">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) * ((x * L(a(y,z,u) \ 1,v5,v6)) \ (L(a(y,z,u) \ 1,v5,v6) * (w * x))) = L(a(L(a(y,z,u) \ 1,v5,v6),w,x) \ w,L(a(y,z,u) \ 1,v5,v6),x)
    ]]></literal>
    <justification jstring="[para(6453(a,1),12906(a,1,1))].">
      <j1 rule="para" parents="6453 12906"/>
    </justification>
  </clause>

  <clause id="17499">
    <literal><![CDATA[
      K(x,y) * ((x * L(a(z,u,w) \ 1,v5,v6)) \ (L(a(z,u,w) \ 1,v5,v6) * (y * x))) = L(a(L(a(z,u,w) \ 1,v5,v6),y,x) \ y,L(a(z,u,w) \ 1,v5,v6),x)
    ]]></literal>
    <justification jstring="[para(5290(a,1),17497(a,1,1))].">
      <j1 rule="para" parents="5290 17497"/>
    </justification>
  </clause>

  <clause id="17501">
    <literal><![CDATA[
      T((x * L(a(y,z,u) \ 1,w,v5)) \ (L(a(y,z,u) \ 1,w,v5) * (x * v6)),K(x,v6)) = L(a(L(a(y,z,u) \ 1,w,v5),v6,x) \ v6,L(a(y,z,u) \ 1,w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11066,a,b,17499,a)].">
      <j1 rule="hyper" parents="63 11066 17499"/>
    </justification>
  </clause>

  <clause id="17502">
    <literal><![CDATA[
      K(x,y) * ((x * L(a(z,u,w) \ 1,v5,v6)) \ ((y * x) * L(a(z,u,w) \ 1,v5,v6))) = L(a(L(a(z,u,w) \ 1,v5,v6),y,x) \ y,L(a(z,u,w) \ 1,v5,v6),x)
    ]]></literal>
    <justification jstring="[para(5005(a,1),17499(a,1,2,2))].">
      <j1 rule="para" parents="5005 17499"/>
    </justification>
  </clause>

  <clause id="17504">
    <literal><![CDATA[
      T(L(K(L(a(x,y,z) \ 1,u,w),v5) * v6,v5,L(a(x,y,z) \ 1,u,w)),K(v5,v6)) = L(a(L(a(x,y,z) \ 1,u,w),v6,v5) \ v6,L(a(x,y,z) \ 1,u,w),v5)
    ]]></literal>
    <justification jstring="[para(3299(a,1),17501(a,1,1))].">
      <j1 rule="para" parents="3299 17501"/>
    </justification>
  </clause>

  <clause id="17505">
    <literal><![CDATA[
      T(L(K(a(x,y,z) \ 1,u) * w,u,L(a(x,y,z) \ 1,v5,v6)),K(u,w)) = L(a(L(a(x,y,z) \ 1,v5,v6),w,u) \ w,L(a(x,y,z) \ 1,v5,v6),u)
    ]]></literal>
    <justification jstring="[para(4279(a,1),17504(a,1,1,1,1))].">
      <j1 rule="para" parents="4279 17504"/>
    </justification>
  </clause>

  <clause id="17507">
    <literal><![CDATA[
      L(a(L(a(x,y,z) \ 1,u,w),v5,v6) \ v5,L(a(x,y,z) \ 1,u,w),v6) = T(L(1 * v5,v6,L(a(x,y,z) \ 1,u,w)),K(v6,v5))
    ]]></literal>
    <justification jstring="[para(4998(a,1),17505(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4998 17505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17508">
    <literal><![CDATA[
      L(a(L(a(x,y,z) \ 1,u,w),v5,v6) \ v5,L(a(x,y,z) \ 1,u,w),v6) = T(L(v5,v6,L(a(x,y,z) \ 1,u,w)),K(v6,v5))
    ]]></literal>
    <justification jstring="[para(7(a,1),17507(a,2,1,1))].">
      <j1 rule="para" parents="7 17507"/>
    </justification>
  </clause>

  <clause id="17510">
    <literal><![CDATA[
      L(a(L(a(x,y,z) \ 1,u,w),v5,v6) \ v5,L(a(x,y,z) \ 1,u,w),v6) = L(T(v5,K(v6,v5)),v6,L(a(x,y,z) \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,25,a,b,17508,a),flip(a)].">
      <j1 rule="hyper" parents="316 25 17508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17511">
    <literal><![CDATA[
      L(a(L(a(x,y,z) \ 1,u,w),v5,v6) \ v5,L(a(x,y,z) \ 1,u,w),v6) = L(v5,v6,L(a(x,y,z) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(1975(a,1),17510(a,2,1))].">
      <j1 rule="para" parents="1975 17510"/>
    </justification>
  </clause>

  <clause id="17512">
    <literal><![CDATA[
      K(x,y) * R(T(y,x * L(a(z,u,w) \ 1,v5,v6)),x,L(a(z,u,w) \ 1,v5,v6)) = L(a(L(a(z,u,w) \ 1,v5,v6),y,x) \ y,L(a(z,u,w) \ 1,v5,v6),x)
    ]]></literal>
    <justification jstring="[para(560(a,1),17502(a,1,2))].">
      <j1 rule="para" parents="560 17502"/>
    </justification>
  </clause>

  <clause id="17514">
    <literal><![CDATA[
      L(a(L(a(x,y,z) \ 1,u,w),v5,v6) \ v5,L(a(x,y,z) \ 1,u,w),v6) = K(v6,v5) * R(T(v5,v6 * (a(x,y,z) \ 1)),v6,L(a(x,y,z) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(6514(a,1),17512(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6514 17512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17515">
    <literal><![CDATA[
      L(a(L(a(x,y,z) \ 1,u,w),v5,v6) \ v5,L(a(x,y,z) \ 1,u,w),v6) = K(v6,v5) * R(T(v5,v6 / a(x,y,z)),v6,L(a(x,y,z) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(2844(a,1),17514(a,2,2,1))].">
      <j1 rule="para" parents="2844 17514"/>
    </justification>
  </clause>

  <clause id="17517">
    <literal><![CDATA[
      L(a(L(a(x,y,z) \ 1,u,w),v5,v6) \ v5,L(a(x,y,z) \ 1,u,w),v6) = K(v6,v5) * R(T(v5,v6),v6,L(a(x,y,z) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(5252(a,1),17515(a,2,2,1))].">
      <j1 rule="para" parents="5252 17515"/>
    </justification>
  </clause>

  <clause id="17518">
    <literal><![CDATA[
      L(a(L(a(x,y,z) \ 1,u,w),v5,v6) \ v5,L(a(x,y,z) \ 1,u,w),v6) = K(v6,v5) * R(T(v5,v6),v6,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(1713(a,1),17517(a,2,2))].">
      <j1 rule="para" parents="1713 17517"/>
    </justification>
  </clause>

  <clause id="17520">
    <literal><![CDATA[
      L(a(L(a(x,y,z) \ 1,u,w),v5,v6) \ v5,L(a(x,y,z) \ 1,u,w),v6) = K(v6,v5) * L(T(v5,v6),v6,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(7812(a,1),17518(a,2,2))].">
      <j1 rule="para" parents="7812 17518"/>
    </justification>
  </clause>

  <clause id="17521">
    <literal><![CDATA[
      L(a(L(a(x,y,z) \ 1,u,w),v5,v6) \ v5,L(a(x,y,z) \ 1,u,w),v6) = L(v5,v6,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,4344,a(flip),b,17520,a),flip(a)].">
      <j1 rule="hyper" parents="316 4344 17520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17523">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w) \ 1,v5,v6)) = L(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,17511,a(flip),b,17521,a)].">
      <j1 rule="hyper" parents="63 17511 17521"/>
    </justification>
  </clause>

  <clause id="17524">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) \ (L(a(x,y,z),u,w) \ (v5 * v6)) = L(v6,v5,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14960,a,b,17523,a)].">
      <j1 rule="hyper" parents="63 14960 17523"/>
    </justification>
  </clause>

  <clause id="17525">
    <literal><![CDATA[
      (L(a(x,y,z) \ 1,u,w) * (v5 * v6)) / (L(a(x,y,z) \ 1,u,w) * v6) = L(v5,v6,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15982,a,b,17524,a)].">
      <j1 rule="hyper" parents="63 15982 17524"/>
    </justification>
  </clause>

  <clause id="17526">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ (v5 * v6)) / (L(a(x,y,z) \ 1,u,w) * v6) = L(v5,v6,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(14662(a,1),17525(a,1,1))].">
      <j1 rule="para" parents="14662 17525"/>
    </justification>
  </clause>

  <clause id="17527">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ (v5 * v6)) / (L(a(x,y,z),u,w) \ v6) = L(v5,v6,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(14662(a,1),17526(a,1,2))].">
      <j1 rule="para" parents="14662 17526"/>
    </justification>
  </clause>

  <clause id="17528">
    <literal><![CDATA[
      R(x * K(y,L(a(z,u,w) \ 1,v5,v6)),y,L(a(z,u,w) \ 1,v5,v6)) = L(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,15175,a,b,17527,a)].">
      <j1 rule="hyper" parents="63 15175 17527"/>
    </justification>
  </clause>

  <clause id="17529">
    <literal><![CDATA[
      R(x * K(y,a(z,u,w) \ 1),y,L(a(z,u,w) \ 1,v5,v6)) = L(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(4291(a,1),17528(a,1,1,2))].">
      <j1 rule="para" parents="4291 17528"/>
    </justification>
  </clause>

  <clause id="17531">
    <literal><![CDATA[
      R(x * 1,y,L(a(z,u,w) \ 1,v5,v6)) = L(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(5003(a,1),17529(a,1,1,2))].">
      <j1 rule="para" parents="5003 17529"/>
    </justification>
  </clause>

  <clause id="17532">
    <literal><![CDATA[
      R(x,y,L(a(z,u,w) \ 1,v5,v6)) = L(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(8(a,1),17531(a,1,1))].">
      <j1 rule="para" parents="8 17531"/>
    </justification>
  </clause>

  <clause id="17534">
    <literal><![CDATA[
      R(x,y,L(a(z,u,w),v5,v6)) = L(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,1713,a(flip),b,17532,a)].">
      <j1 rule="hyper" parents="63 1713 17532"/>
    </justification>
  </clause>

  <clause id="17535">
    <literal><![CDATA[
      L(L(x,y,L(a(z,u,w),y,y)) \ x,x,(1 / y) \ a(z,u,w)) = a(x,y,L(a(z,u,w),y,y)) \ 1
    ]]></literal>
    <justification jstring="[para(17534(a,1),13464(a,1,1,1))].">
      <j1 rule="para" parents="17534 13464"/>
    </justification>
  </clause>

  <clause id="17536">
    <literal><![CDATA[
      L(x \ L(x,y,L(a(z,u,w),y,v5)),x,v5 \ ((v5 * y) * a(z,u,w))) = a(x,y,L(a(z,u,w),y,v5))
    ]]></literal>
    <justification jstring="[para(17534(a,1),13467(a,1,1,2))].">
      <j1 rule="para" parents="17534 13467"/>
    </justification>
  </clause>

  <clause id="17559">
    <literal><![CDATA[
      (x * K(y,z)) * ((a(u,w,v5) \ 1) * L((a(u,w,v5) \ K(y,z)) \ (x \ v6),x * K(y,z),a(u,w,v5) \ 1)) = (a(u,w,v5) \ 1) * ((x * K(y,z)) * ((x * (a(u,w,v5) \ K(y,z))) \ v6))
    ]]></literal>
    <justification jstring="[para(3130(a,1),17496(a,1,2,2,1))].">
      <j1 rule="para" parents="3130 17496"/>
    </justification>
  </clause>

  <clause id="17560">
    <literal><![CDATA[
      (x * K(y,z)) * ((a(u,w,v5) \ 1) * L((a(u,w,v5) \ K(y,z)) \ (x \ v6),x * K(y,z),a(u,w,v5))) = (a(u,w,v5) \ 1) * ((x * K(y,z)) * ((x * (a(u,w,v5) \ K(y,z))) \ v6))
    ]]></literal>
    <justification jstring="[para(16973(a,1),17559(a,1,2,2))].">
      <j1 rule="para" parents="16973 17559"/>
    </justification>
  </clause>

  <clause id="17561">
    <literal><![CDATA[
      (x * K(y,z)) * ((a(u,w,v5) \ 1) * L((a(u,w,v5) \ K(y,z)) \ (x \ v6),x,a(u,w,v5))) = (a(u,w,v5) \ 1) * ((x * K(y,z)) * ((x * (a(u,w,v5) \ K(y,z))) \ v6))
    ]]></literal>
    <justification jstring="[para(10815(a,1),17560(a,1,2,2))].">
      <j1 rule="para" parents="10815 17560"/>
    </justification>
  </clause>

  <clause id="17563">
    <literal><![CDATA[
      (x * K(y,z)) * (a(u,w,v5) * L(K(z,y) * (a(u,w,v5) \ (x \ v6)),x,a(u,w,v5))) = (a(u,w,v5) \ 1) * ((x * K(y,z)) * ((x * (a(u,w,v5) \ K(y,z))) \ v6))
    ]]></literal>
    <justification jstring="[para(11848(a,1),17561(a,1,2))].">
      <j1 rule="para" parents="11848 17561"/>
    </justification>
  </clause>

  <clause id="17564">
    <literal><![CDATA[
      x * (K(y,z) * (a(u,w,v5) * L(K(z,y) * (a(u,w,v5) \ (x \ v6)),x,a(u,w,v5)))) = (a(u,w,v5) \ 1) * ((x * K(y,z)) * ((x * (a(u,w,v5) \ K(y,z))) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,10165,a(flip),b,17563,a)].">
      <j1 rule="hyper" parents="63 10165 17563"/>
    </justification>
  </clause>

  <clause id="17565">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * ((u * K(w,v5)) * ((u * (a(x,y,z) \ K(w,v5))) \ v6)) = u * (T(a(x,y,z),K(v5,w)) * L(a(x,y,z) \ (u \ v6),u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(10439(a,1),17564(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10439 17564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17566">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * ((u * K(w,v5)) * ((u * (a(x,y,z) \ K(w,v5))) \ v6)) = u * (a(x,y,z) * L(a(x,y,z) \ (u \ v6),u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(2286(a,1),17565(a,2,2,1))].">
      <j1 rule="para" parents="2286 17565"/>
    </justification>
  </clause>

  <clause id="17568">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * ((u * K(w,v5)) * ((u * (a(x,y,z) \ K(w,v5))) \ v6)) = a(x,y,z) * (u * ((a(x,y,z) * u) \ v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,6232,a(flip),b,17566,a),flip(a)].">
      <j1 rule="hyper" parents="316 6232 17566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17569">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u * (K(w,v5) * ((u * (a(x,y,z) \ K(w,v5))) \ v6))) = a(x,y,z) * (u * ((a(x,y,z) * u) \ v6))
    ]]></literal>
    <justification jstring="[para(10165(a,1),17568(a,1,2))].">
      <j1 rule="para" parents="10165 17568"/>
    </justification>
  </clause>

  <clause id="17570">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u * ((u * (a(x,y,z) \ 1)) \ w)) = a(x,y,z) * (u * ((a(x,y,z) * u) \ w))
    ]]></literal>
    <justification jstring="[para(10227(a,1),17569(a,1,2,2))].">
      <j1 rule="para" parents="10227 17569"/>
    </justification>
  </clause>

  <clause id="17571">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u * ((a(x,y,z) \ u) \ w)) = a(x,y,z) * (u * ((a(x,y,z) * u) \ w))
    ]]></literal>
    <justification jstring="[para(14393(a,1),17570(a,1,2,2,1))].">
      <j1 rule="para" parents="14393 17570"/>
    </justification>
  </clause>

  <clause id="17572">
    <literal><![CDATA[
      a(x,y,z) \ (u * ((a(x,y,z) \ u) \ w)) = a(x,y,z) * (u * ((a(x,y,z) * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14391,a(flip),b,17571,a)].">
      <j1 rule="hyper" parents="63 14391 17571"/>
    </justification>
  </clause>

  <clause id="17573">
    <literal><![CDATA[
      a(x,y,z) * (z \ (a(x,y,z) * (u * ((a(x,y,z) * u) \ w)))) = z \ (u * ((a(x,y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(17572(a,1),6895(a,1,2,2))].">
      <j1 rule="para" parents="17572 6895"/>
    </justification>
  </clause>

  <clause id="17574">
    <literal><![CDATA[
      a(x,y,z) * ((z \ (u * ((a(x,y,z) * u) \ w))) * a(x,y,z)) = z \ (u * ((a(x,y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(6896(a,1),17573(a,1,2))].">
      <j1 rule="para" parents="6896 17573"/>
    </justification>
  </clause>

  <clause id="17575">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ (u * ((a(z,y,x) * u) \ w)) = x \ (u * ((a(z,y,x) \ u) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14727,a(flip),b,17574,a)].">
      <j1 rule="hyper" parents="63 14727 17574"/>
    </justification>
  </clause>

  <clause id="17577">
    <literal><![CDATA[
      a(x,y,z \ (u * R((T(w / v5,v6) \ v7) * T(w / v5,v6),(w * (v5 \ 1)) \ 1,w * (v5 \ 1)))) = a(x,y,z \ (u * (T(v7 * (1 / (w * (v5 \ 1))),T(w * (v5 \ 1),v6)) * (w * v5))))
    ]]></literal>
    <justification jstring="[para(17479(a,1),11857(a,1,3,2,2,1))].">
      <j1 rule="para" parents="17479 11857"/>
    </justification>
  </clause>

  <clause id="17578">
    <literal><![CDATA[
      a(x,y,z \ (u * R((T(w / v5,v6) \ v7) * T(w / v5,v6),(w * (v5 \ 1)) \ 1,w * v5))) = a(x,y,z \ (u * (T(v7 * (1 / (w * (v5 \ 1))),T(w * (v5 \ 1),v6)) * (w * v5))))
    ]]></literal>
    <justification jstring="[para(1711(a,1),17577(a,1,3,2,2))].">
      <j1 rule="para" parents="1711 17577"/>
    </justification>
  </clause>

  <clause id="17579">
    <literal><![CDATA[
      a(x,y,z \ (u * R((T(w / v5,v6) \ v7) * T(w / v5,v6),w \ v5,w \ v5))) = a(x,y,z \ (u * (T(v7 * (1 / (w * (v5 \ 1))),T(w * (v5 \ 1),v6)) * (w * v5))))
    ]]></literal>
    <justification jstring="[para(13596(a,1),17578(a,1,3,2,2))].">
      <j1 rule="para" parents="13596 17578"/>
    </justification>
  </clause>

  <clause id="17580">
    <literal><![CDATA[
      a(x,y,z \ (u * L((T(w / v5,v6) \ v7) * T(w / v5,v6),w \ v5,w \ v5))) = a(x,y,z \ (u * (T(v7 * (1 / (w * (v5 \ 1))),T(w * (v5 \ 1),v6)) * (w * v5))))
    ]]></literal>
    <justification jstring="[hyper(63,a,12129,a(flip),b,17579,a)].">
      <j1 rule="hyper" parents="63 12129 17579"/>
    </justification>
  </clause>

  <clause id="17581">
    <literal><![CDATA[
      a(x,y,z \ (L((u / w) * (T(u / w,v5) \ v6),u \ w,u \ w) * v7)) = a(x,y,z \ (v7 * (T(v6 * (1 / (u * (w \ 1))),T(u * (w \ 1),v5)) * (u * w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,15684,a(flip),b,17580,a)].">
      <j1 rule="hyper" parents="63 15684 17580"/>
    </justification>
  </clause>

  <clause id="17583">
    <literal><![CDATA[
      a(x,y,z \ (u * (T(w * (1 / (v5 * (v6 \ 1))),T(v5 * (v6 \ 1),v7)) * (v5 * v6)))) = a(x,y,z \ (L(K(v7,v5 / v6) * w,v5 \ v6,v5 \ v6) * u))
    ]]></literal>
    <justification jstring="[para(2949(a,1),17581(a,1,3,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2949 17581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17584">
    <literal><![CDATA[
      a(x,y,z \ (u * (T(w * (1 / (v5 * (v6 \ 1))),T(v5 * (v6 \ 1),v7)) * (v5 * v6)))) = a(x,y,z \ (K(v7,v5 / v6) * (L(w,v5 \ v6,v5 \ v6) * u)))
    ]]></literal>
    <justification jstring="[para(4856(a,1),17583(a,2,3,2))].">
      <j1 rule="para" parents="4856 17583"/>
    </justification>
  </clause>

  <clause id="17585">
    <literal><![CDATA[
      a(x,y,z \ (u * (T(w * (1 / (v5 * (v6 \ 1))),T(v5 * (v6 \ 1),v7)) * (v5 * v6)))) = a(x,y,z \ (L(w,v5 \ v6,v5 \ v6) * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5496,a(flip),b,17584,a),flip(a)].">
      <j1 rule="hyper" parents="316 5496 17584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17587">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * (1 / (v5 * (v6 \ 1)))) * (v5 * v6)))) = a(x,y,z \ (L(w,v5 \ v6,v5 \ v6) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5773,a(flip),b,17585,a)].">
      <j1 rule="hyper" parents="63 5773 17585"/>
    </justification>
  </clause>

  <clause id="17589">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * ((v5 * (v6 \ 1)) \ 1)) * (v5 * v6)))) = a(x,y,z \ (L(w,v5 \ v6,v5 \ v6) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12589,a(flip),b,17587,a)].">
      <j1 rule="hyper" parents="63 12589 17587"/>
    </justification>
  </clause>

  <clause id="17590">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * v5) * (v6 * (w * (v5 \ 1)))))) = a(x,y,z \ (L(v6,w \ v5,w \ v5) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11858,a(flip),b,17589,a)].">
      <j1 rule="hyper" parents="63 11858 17589"/>
    </justification>
  </clause>

  <clause id="17591">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * v5) * (v6 * (w * v5))))) = a(x,y,z \ (L(v6,w \ v5,w \ v5) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9068,a(flip),b,17590,a)].">
      <j1 rule="hyper" parents="63 9068 17590"/>
    </justification>
  </clause>

  <clause id="17592">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w \ v5,w \ v5) * v6)) = a(x,y,z \ (L(u,w * v5,w * v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,6794,a(flip),b,17591,a),flip(a)].">
      <j1 rule="hyper" parents="63 6794 17591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17593">
    <literal><![CDATA[
      (1 / (a(x,y,z) / ((x \ ((x * y) * z)) / z))) * K((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,a(x,y,z) * (z / (x \ ((x * y) * z)))) = L(y * a(z \ (x \ ((x * y) * z)),y,y),y,y)
    ]]></literal>
    <justification jstring="[para(6470(a,1),12743(a,1,2))].">
      <j1 rule="para" parents="6470 12743"/>
    </justification>
  </clause>

  <clause id="17594">
    <literal><![CDATA[
      (1 / (a(x,y,z) / ((x \ ((x * y) * z)) / z))) * K((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,a(x,y,z) * (z * (((x * y) * z) \ x))) = L(y * a(z \ (x \ ((x * y) * z)),y,y),y,y)
    ]]></literal>
    <justification jstring="[para(10550(a,1),17593(a,1,2))].">
      <j1 rule="para" parents="10550 17593"/>
    </justification>
  </clause>

  <clause id="17595">
    <literal><![CDATA[
      L(x * a(y \ (z \ ((z * x) * y)),x,x),x,x) = (1 / (a(z,x,y) / ((z \ ((z * x) * y)) / y))) * K((a(z,x,y) / ((z \ ((z * x) * y)) / y)) \ 1,y * (((z * x) * y) \ z))
    ]]></literal>
    <justification jstring="[para(5289(a,1),17594(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5289 17594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17597">
    <literal><![CDATA[
      L(x * a(y \ (z \ ((z * x) * y)),x,x),x,x) = (1 / (a(z,x,y) / ((z \ ((z * x) * y)) / y))) * K((a(z,x,y) / ((z \ ((z * x) * y)) / y)) \ 1,y * (y \ ((z * x) \ z)))
    ]]></literal>
    <justification jstring="[para(6450(a,1),17595(a,2,2))].">
      <j1 rule="para" parents="6450 17595"/>
    </justification>
  </clause>

  <clause id="17598">
    <literal><![CDATA[
      L(x * a(y \ (z \ ((z * x) * y)),x,x),x,x) = (1 / (a(z,x,y) / ((z \ ((z * x) * y)) / y))) * K((a(z,x,y) / ((z \ ((z * x) * y)) / y)) \ 1,(z * x) \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),17597(a,2,2,2))].">
      <j1 rule="para" parents="10 17597"/>
    </justification>
  </clause>

  <clause id="17600">
    <literal><![CDATA[
      L(x * a(y \ (z \ ((z * x) * y)),x,x),x,x) = (1 / (a(z,x,y) / ((z \ ((z * x) * y)) / y))) * K((a(z,x,y) / ((z \ ((z * x) * y)) / y)) \ 1,x \ 1)
    ]]></literal>
    <justification jstring="[para(3540(a,1),17598(a,2,2))].">
      <j1 rule="para" parents="3540 17598"/>
    </justification>
  </clause>

  <clause id="17601">
    <literal><![CDATA[
      L(x * a(y \ (z \ ((z * x) * y)),x,x),x,x) = (1 / (a(z,x,y) / ((z \ ((z * x) * y)) / y))) * K(((z \ ((z * x) * y)) / y) / a(z,x,y),x \ 1)
    ]]></literal>
    <justification jstring="[para(3192(a,1),17600(a,2,2))].">
      <j1 rule="para" parents="3192 17600"/>
    </justification>
  </clause>

  <clause id="17603">
    <literal><![CDATA[
      L(x * a(y \ (z \ ((z * x) * y)),x,x),x,x) = (1 / (a(z,x,y) / ((z \ ((z * x) * y)) / y))) * K(a(z,x,y) \ ((z \ ((z * x) * y)) / y),x \ 1)
    ]]></literal>
    <justification jstring="[para(2276(a,1),17601(a,2,2,1))].">
      <j1 rule="para" parents="2276 17601"/>
    </justification>
  </clause>

  <clause id="17604">
    <literal><![CDATA[
      L(x * a(y \ (z \ ((z * x) * y)),x,x),x,x) = (1 / (a(z,x,y) / ((z \ ((z * x) * y)) / y))) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(8477(a,1),17603(a,2,2,1))].">
      <j1 rule="para" parents="8477 17603"/>
    </justification>
  </clause>

  <clause id="17605">
    <literal><![CDATA[
      L(x * a(y \ (z \ ((z * x) * y)),x,x),x,x) = K(x,x \ 1) / (a(z,x,y) / ((z \ ((z * x) * y)) / y))
    ]]></literal>
    <justification jstring="[hyper(316,a,2240,a(flip),b,17604,a),flip(a)].">
      <j1 rule="hyper" parents="316 2240 17604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17606">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ (((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1) * (a(u,y,w) / ((u \ ((u * y) * w)) / w)))) / (a(u,y,w) / ((u \ ((u * y) * w)) / w)) = y
    ]]></literal>
    <justification jstring="[hyper(316,a,5324,a(flip),b,17495,a),flip(a)].">
      <j1 rule="hyper" parents="316 5324 17495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17608">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ K((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,a(x,y,z) / ((x \ ((x * y) * z)) / z))) / (a(x,y,z) / ((x \ ((x * y) * z)) / z)) = y
    ]]></literal>
    <justification jstring="[para(272(a,2),17606(a,1,1,2))].">
      <j1 rule="para" parents="272 17606"/>
    </justification>
  </clause>

  <clause id="17609">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ K((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,a(x,y,z) * (z / (x \ ((x * y) * z))))) / (a(x,y,z) / ((x \ ((x * y) * z)) / z)) = y
    ]]></literal>
    <justification jstring="[para(6470(a,1),17608(a,1,1,2))].">
      <j1 rule="para" parents="6470 17608"/>
    </justification>
  </clause>

  <clause id="17610">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ K((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,a(x,y,z) * (z * (((x * y) * z) \ x)))) / (a(x,y,z) / ((x \ ((x * y) * z)) / z)) = y
    ]]></literal>
    <justification jstring="[para(10550(a,1),17609(a,1,1,2))].">
      <j1 rule="para" parents="10550 17609"/>
    </justification>
  </clause>

  <clause id="17611">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ K((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,z * (((x * y) * z) \ x))) / (a(x,y,z) / ((x \ ((x * y) * z)) / z)) = y
    ]]></literal>
    <justification jstring="[para(5289(a,1),17610(a,1,1,2))].">
      <j1 rule="para" parents="5289 17610"/>
    </justification>
  </clause>

  <clause id="17613">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ K((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,z * (z \ ((x * y) \ x)))) / (a(x,y,z) / ((x \ ((x * y) * z)) / z)) = y
    ]]></literal>
    <justification jstring="[para(6450(a,1),17611(a,1,1,2))].">
      <j1 rule="para" parents="6450 17611"/>
    </justification>
  </clause>

  <clause id="17614">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ K((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,(x * y) \ x)) / (a(x,y,z) / ((x \ ((x * y) * z)) / z)) = y
    ]]></literal>
    <justification jstring="[para(10(a,1),17613(a,1,1,2,2))].">
      <j1 rule="para" parents="10 17613"/>
    </justification>
  </clause>

  <clause id="17616">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ K((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,y \ 1)) / (a(x,y,z) / ((x \ ((x * y) * z)) / z)) = y
    ]]></literal>
    <justification jstring="[para(3540(a,1),17614(a,1,1,2))].">
      <j1 rule="para" parents="3540 17614"/>
    </justification>
  </clause>

  <clause id="17617">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ K(((x \ ((x * y) * z)) / z) / a(x,y,z),y \ 1)) / (a(x,y,z) / ((x \ ((x * y) * z)) / z)) = y
    ]]></literal>
    <justification jstring="[para(3192(a,1),17616(a,1,1,2))].">
      <j1 rule="para" parents="3192 17616"/>
    </justification>
  </clause>

  <clause id="17619">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ K(a(x,y,z) \ ((x \ ((x * y) * z)) / z),y \ 1)) / (a(x,y,z) / ((x \ ((x * y) * z)) / z)) = y
    ]]></literal>
    <justification jstring="[para(2276(a,1),17617(a,1,1,2,1))].">
      <j1 rule="para" parents="2276 17617"/>
    </justification>
  </clause>

  <clause id="17620">
    <literal><![CDATA[
      (a(a(x,y,z),y,y) \ K(y,y \ 1)) / (a(x,y,z) / ((x \ ((x * y) * z)) / z)) = y
    ]]></literal>
    <justification jstring="[para(8477(a,1),17619(a,1,1,2,1))].">
      <j1 rule="para" parents="8477 17619"/>
    </justification>
  </clause>

  <clause id="17621">
    <literal><![CDATA[
      (x \ L(T(x,x \ 1),x,a(y,x,z))) / (a(y,x,z) / ((y \ ((y * x) * z)) / z)) = x
    ]]></literal>
    <justification jstring="[para(7380(a,1),17620(a,1,1))].">
      <j1 rule="para" parents="7380 17620"/>
    </justification>
  </clause>

  <clause id="17622">
    <literal><![CDATA[
      (x \ L(x,x,x \ a(y,x,z))) / (a(y,x,z) / ((y \ ((y * x) * z)) / z)) = x
    ]]></literal>
    <justification jstring="[para(15709(a,1),17621(a,1,1,2))].">
      <j1 rule="para" parents="15709 17621"/>
    </justification>
  </clause>

  <clause id="17623">
    <literal><![CDATA[
      K(x,x \ 1) / (a(y,x,z) / ((y \ ((y * x) * z)) / z)) = x
    ]]></literal>
    <justification jstring="[para(15725(a,1),17622(a,1,1))].">
      <j1 rule="para" parents="15725 17622"/>
    </justification>
  </clause>

  <clause id="17627">
    <literal><![CDATA[
      L(a(x,L(y,z,u) \ (L(1 / y,z,u) \ 1),w),L(y,z,u) * L(y \ 1,z,u),L(y,z,u) * L(y \ 1,z,u)) = (L(y,z,u) * L(y \ 1,z,u)) * ((x \ (((L(y,z,u) * L(y \ 1,z,u)) \ (x * 1)) * w)) / w)
    ]]></literal>
    <justification jstring="[para(9822(a,1),9836(a,1,1,2))].">
      <j1 rule="para" parents="9822 9836"/>
    </justification>
  </clause>

  <clause id="17628">
    <literal><![CDATA[
      L(a(x,L(y,z,u) \ (L(y \ 1,z,u) \ 1),w),L(y,z,u) * L(y \ 1,z,u),L(y,z,u) * L(y \ 1,z,u)) = (L(y,z,u) * L(y \ 1,z,u)) * ((x \ (((L(y,z,u) * L(y \ 1,z,u)) \ (x * 1)) * w)) / w)
    ]]></literal>
    <justification jstring="[para(11268(a,1),17627(a,1,1))].">
      <j1 rule="para" parents="11268 17627"/>
    </justification>
  </clause>

  <clause id="17629">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) * ((u \ (((L(x,y,z) * L(x \ 1,y,z)) \ (u * 1)) * w)) / w) = a(u,L(x,y,z) \ (L(x \ 1,y,z) \ 1),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17326,a(flip),b,17628,a),flip(a)].">
      <j1 rule="hyper" parents="63 17326 17628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17631">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) * ((u \ (((L(x,y,z) * L(x \ 1,y,z)) \ u) * w)) / w) = a(u,L(x,y,z) \ (L(x \ 1,y,z) \ 1),w)
    ]]></literal>
    <justification jstring="[para(8(a,1),17629(a,1,2,1,2,1,2))].">
      <j1 rule="para" parents="8 17629"/>
    </justification>
  </clause>

  <clause id="17632">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) * ((u \ (u * ((L(x,y,z) * L(x \ 1,y,z)) \ w))) / w) = a(u,L(x,y,z) \ (L(x \ 1,y,z) \ 1),w)
    ]]></literal>
    <justification jstring="[para(17329(a,1),17631(a,1,2,1,2))].">
      <j1 rule="para" parents="17329 17631"/>
    </justification>
  </clause>

  <clause id="17633">
    <literal><![CDATA[
      a(x,L(y,z,u) \ (L(y \ 1,z,u) \ 1),w) = (L(y,z,u) * L(y \ 1,z,u)) * (((L(y,z,u) * L(y \ 1,z,u)) \ w) / w)
    ]]></literal>
    <justification jstring="[para(9(a,1),17632(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 17632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17635">
    <literal><![CDATA[
      a(x,L(y,z,u) \ (L(y \ 1,z,u) \ 1),w) = (L(y,z,u) * L(y \ 1,z,u)) * (L(y,z,u) \ (L(1 / y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(9828(a,1),17633(a,2,2))].">
      <j1 rule="para" parents="9828 17633"/>
    </justification>
  </clause>

  <clause id="17636">
    <literal><![CDATA[
      a(x,L(y,z,u) \ (L(y \ 1,z,u) \ 1),w) = (L(y,z,u) * L(y \ 1,z,u)) \ (L(y,z,u) * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,9827,a(flip),b,17635,a),flip(a)].">
      <j1 rule="hyper" parents="316 9827 17635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17638">
    <literal><![CDATA[
      a(x,L(y,z,u) \ (L(y \ 1,z,u) \ 1),w) = 1
    ]]></literal>
    <justification jstring="[hyper(316,a,67,a(flip),b,17636,a),flip(a)].">
      <j1 rule="hyper" parents="316 67 17636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17640">
    <literal><![CDATA[
      a(x,y * (L(y,z,u) \ (L(y,z,u) \ y)),w) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,11370,a(flip),b,17638,a)].">
      <j1 rule="hyper" parents="63 11370 17638"/>
    </justification>
  </clause>

  <clause id="17641">
    <literal><![CDATA[
      a(x,L(L(y,z,u),z,u) \ y,w) = 1
    ]]></literal>
    <justification jstring="[para(13856(a,1),17640(a,1,2))].">
      <j1 rule="para" parents="13856 17640"/>
    </justification>
  </clause>

  <clause id="17642">
    <literal><![CDATA[
      L(x,L(L(y,z,u),z,u) \ y,w) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,17641,a)].">
      <j1 rule="hyper" parents="52 17641"/>
    </justification>
  </clause>

  <clause id="17643">
    <literal><![CDATA[
      L(x,y * (L(L(y,z,u),z,u) \ w),v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[para(17642(a,1),17446(a,1,1))].">
      <j1 rule="para" parents="17642 17446"/>
    </justification>
  </clause>

  <clause id="17644">
    <literal><![CDATA[
      L(x,L(L(y,z,u),z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(183(a,1),17643(a,1,2)),flip(a)].">
      <j1 rule="para" parents="183 17643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17645">
    <literal><![CDATA[
      L(x,y * (z \ L(L(z,u,w),u,w)),v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(10063(a,1),17643(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10063 17643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17648">
    <literal><![CDATA[
      L(x,L(y * (z \ 1),z,z),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11111,a(flip),b,17644,a)].">
      <j1 rule="hyper" parents="63 11111 17644"/>
    </justification>
  </clause>

  <clause id="17650">
    <literal><![CDATA[
      L(x,L(y \ z,z \ y,z),u) = L(x,(z \ y) \ 1,u)
    ]]></literal>
    <justification jstring="[para(356(a,1),17644(a,1,2,1))].">
      <j1 rule="para" parents="356 17644"/>
    </justification>
  </clause>

  <clause id="17651">
    <literal><![CDATA[
      L(x,L(y * z,y \ 1,y),u) = L(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(474(a,1),17644(a,1,2,1))].">
      <j1 rule="para" parents="474 17644"/>
    </justification>
  </clause>

  <clause id="17654">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u),w) = L(x,L(y,z,u) \ 1,w)
    ]]></literal>
    <justification jstring="[para(9873(a,1),17644(a,1,2,1))].">
      <j1 rule="para" parents="9873 17644"/>
    </justification>
  </clause>

  <clause id="17655">
    <literal><![CDATA[
      a(x,y,z * (L(u * (w \ 1),w,w) * L(v5,w \ u,L(u * (w \ 1),w,w)))) = a(x,y,(L(u * (w \ 1),w,w) \ v5) * z)
    ]]></literal>
    <justification jstring="[para(17648(a,1),8684(a,1,3,2,2))].">
      <j1 rule="para" parents="17648 8684"/>
    </justification>
  </clause>

  <clause id="17656">
    <literal><![CDATA[
      L(x,y * (z * (u \ L(L(u,w,v5),w,v5))),v6) = L(x,y * z,v6)
    ]]></literal>
    <justification jstring="[para(10081(a,1),17645(a,1,2))].">
      <j1 rule="para" parents="10081 17645"/>
    </justification>
  </clause>

  <clause id="17657">
    <literal><![CDATA[
      L(x,y \ (a(z,u,w) \ v5),v6) = L(x,y \ (a(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(14444(a,1),17645(a,1,2))].">
      <j1 rule="para" parents="14444 17645"/>
    </justification>
  </clause>

  <clause id="17658">
    <literal><![CDATA[
      L(x,L((y \ z) \ 1,y,z \ u),L((y \ z) \ 1,y,z \ u)) = L(x,u \ ((z \ u) * y),u \ ((z \ u) * y))
    ]]></literal>
    <justification jstring="[hyper(316,a,17024,a(flip),b,17654,a),flip(a)].">
      <j1 rule="hyper" parents="316 17024 17654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17659">
    <literal><![CDATA[
      L(x,L(((y \ R(z,u,w)) \ 1) \ 1,v5,v6),v7) = L(x,L((y \ L(z,u,w)) \ 1,v5,v6) \ 1,v7)
    ]]></literal>
    <justification jstring="[hyper(316,a,16637,a(flip),b,17654,a),flip(a)].">
      <j1 rule="hyper" parents="316 16637 17654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17660">
    <literal><![CDATA[
      L(x,y \ (((y \ z) \ 1) \ y),u) = L(x,(z \ y) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11442,a(flip),b,17650,a)].">
      <j1 rule="hyper" parents="63 11442 17650"/>
    </justification>
  </clause>

  <clause id="17661">
    <literal><![CDATA[
      L(x,L(y * z,y,y),u) = L(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11033,a(flip),b,17651,a)].">
      <j1 rule="hyper" parents="63 11033 17651"/>
    </justification>
  </clause>

  <clause id="17663">
    <literal><![CDATA[
      L(x,L(y * z,z,z),u) = L(x,(z \ 1) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10857,a,b,17661,a)].">
      <j1 rule="hyper" parents="63 10857 17661"/>
    </justification>
  </clause>

  <clause id="17664">
    <literal><![CDATA[
      a(x,y * z,y \ z) \ (y * z) = L(y * z,(y \ 1) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10020,a(flip),b,17661,a)].">
      <j1 rule="hyper" parents="63 10020 17661"/>
    </justification>
  </clause>

  <clause id="17665">
    <literal><![CDATA[
      L(a(L(x * y,y,y),z,u),(y \ 1) \ x,u * z) = L(x * y,y,y) \ R(L(x * y,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13447,a(flip),b,17663,a),flip(a)].">
      <j1 rule="hyper" parents="63 13447 17663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17666">
    <literal><![CDATA[
      L(x,L(y \ z,y \ z,y),u) = L(x,(z \ y) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10894,a,b,17660,a)].">
      <j1 rule="hyper" parents="63 10894 17660"/>
    </justification>
  </clause>

  <clause id="17667">
    <literal><![CDATA[
      L(x,(y \ z) \ 1,(y \ z) \ 1) = L(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,17032,a(flip),b,17666,a),flip(a)].">
      <j1 rule="hyper" parents="63 17032 17666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17669">
    <literal><![CDATA[
      L(x,a(y,z,u) \ w,v5) = L(x,a(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(14420(a,1),17656(a,1,2))].">
      <j1 rule="para" parents="14420 17656"/>
    </justification>
  </clause>

  <clause id="17671">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ a(L(L(a(x,y,z),w,v5),v6,v7),a(x,y,z),u))) = L(u,a(x,y,z) * L(L(a(x,y,z),w,v5),v6,v7),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17448,a,b,17669,a)].">
      <j1 rule="hyper" parents="63 17448 17669"/>
    </justification>
  </clause>

  <clause id="17673">
    <literal><![CDATA[
      L(x,y \ (a(z,u,w) \ v5),v6) = L(x,y \ (v5 * a(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,10862,a,b,17657,a),flip(a)].">
      <j1 rule="hyper" parents="316 10862 17657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17674">
    <literal><![CDATA[
      L(x * y,L(x * y,x,y),z) = L(x * y,(x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10021,a(flip),b,17664,a)].">
      <j1 rule="hyper" parents="63 10021 17664"/>
    </justification>
  </clause>

  <clause id="17675">
    <literal><![CDATA[
      L(x * y,x * y,L(z,x,y)) = L(x * y,(x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,16803,a(flip),b,17674,a)].">
      <j1 rule="hyper" parents="63 16803 17674"/>
    </justification>
  </clause>

  <clause id="17676">
    <literal><![CDATA[
      L(x,y,L(z * u,u * z,L(w,u,z))) = L(x,y,L(u * z,(u \ 1) \ z,w))
    ]]></literal>
    <justification jstring="[para(17675(a,1),1671(a,1,3)),flip(a)].">
      <j1 rule="para" parents="17675 1671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17677">
    <literal><![CDATA[
      L(x,y \ (a(z,u,w) * u),v5) = L(x,y \ (u * a(w,u,z)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,14621,a(flip),b,17673,a)].">
      <j1 rule="hyper" parents="63 14621 17673"/>
    </justification>
  </clause>

  <clause id="17678">
    <literal><![CDATA[
      L(x,(y * z) \ (z * a(y,z,u)),(y * z) \ (z * a(y,z,u))) = L(x,L(y,z,u) \ 1,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,17083,a(flip),b,17677,a),flip(a)].">
      <j1 rule="hyper" parents="63 17083 17677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17681">
    <literal><![CDATA[
      L(x,y,L(z * u,u * z,L(w,u,z))) = L(x,y,L(u * z,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,16919,a(flip),b,17676,a),flip(a)].">
      <j1 rule="hyper" parents="316 16919 17676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17682">
    <literal><![CDATA[
      L(a(x,y,z),u,L(w \ v5,v5,v5)) = L(a(x,y,z),u,L(w * v5,w \ v5,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14935,a(flip),b,17681,a)].">
      <j1 rule="hyper" parents="63 14935 17681"/>
    </justification>
  </clause>

  <clause id="17683">
    <literal><![CDATA[
      L(x,L((y \ L(z,u,w)) \ 1,v5,v6) \ 1,v7) = L(x,L(y \ R(z,u,w),v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,10837,a(flip),b,17659,a),flip(a)].">
      <j1 rule="hyper" parents="63 10837 17659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17685">
    <literal><![CDATA[
      L(x,L(((y \ L(z,u,w)) \ 1) \ 1,v5,v6),v7) = L(x,L(y \ R(z,u,w),v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,17654,a,b,17683,a)].">
      <j1 rule="hyper" parents="63 17654 17683"/>
    </justification>
  </clause>

  <clause id="17686">
    <literal><![CDATA[
      L(x,L(y \ R(z,u,w),v5,v6),v7) = L(x,L(y \ L(z,u,w),v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,10837,a(flip),b,17685,a),flip(a)].">
      <j1 rule="hyper" parents="63 10837 17685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17688">
    <literal><![CDATA[
      L(x,y,a(a(z,u,u) * L(u,w,v5),z,y)) = L(x,L(u \ L(u,z,y),w,v5),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16829,a,b,17686,a)].">
      <j1 rule="hyper" parents="63 16829 17686"/>
    </justification>
  </clause>

  <clause id="17689">
    <literal><![CDATA[
      a(x,y,L(((z \ u) / z) * L(z,w,L(v5,v5,w)),L(v5 \ L(v5,w,z),z,w),z)) = a(x,y,L(v5 \ R(v5,w,z),z,w) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(17686(a,1),14786(a,1,3))].">
      <j1 rule="para" parents="17686 14786"/>
    </justification>
  </clause>

  <clause id="17690">
    <literal><![CDATA[
      L(x,L(y \ L(y,z,u),w,v5),u) = L(x,u,L(y \ R(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(16827(a,1),17688(a,1,3)),flip(a)].">
      <j1 rule="para" parents="16827 17688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17691">
    <literal><![CDATA[
      L(x,L(y \ L(y,z,u),w,v5),u) = L(x,u,L(y \ L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,16792,a(flip),b,17690,a),flip(a)].">
      <j1 rule="hyper" parents="316 16792 17690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17692">
    <literal><![CDATA[
      L(a(L(x * y,y,y),z,u),(y \ 1) \ x,u * z) = L(x * y,y,y) \ L(R(x * y,z,u),y,y)
    ]]></literal>
    <justification jstring="[para(29(a,1),17665(a,2,2))].">
      <j1 rule="para" parents="29 17665"/>
    </justification>
  </clause>

  <clause id="17693">
    <literal><![CDATA[
      L(a((x \ 1) \ y,z,u),(x \ 1) \ y,u * z) = L(y * x,x,x) \ L(R(y * x,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(13109(a,1),17692(a,1,1))].">
      <j1 rule="para" parents="13109 17692"/>
    </justification>
  </clause>

  <clause id="17694">
    <literal><![CDATA[
      L(x * y,y,y) \ L(R(x * y,z,u),y,y) = ((y \ 1) \ x) \ R((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13447,a(flip),b,17693,a),flip(a)].">
      <j1 rule="hyper" parents="63 13447 17693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17695">
    <literal><![CDATA[
      L((x * y) \ R(x * y,z,u),y,y) = ((y \ 1) \ x) \ R((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16782,a(flip),b,17694,a)].">
      <j1 rule="hyper" parents="63 16782 17694"/>
    </justification>
  </clause>

  <clause id="17696">
    <literal><![CDATA[
      ((x \ 1) \ y) \ R((x \ 1) \ y,z,u) = x \ (y \ R(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15568,a(flip),b,17695,a),flip(a)].">
      <j1 rule="hyper" parents="63 15568 17695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17697">
    <literal><![CDATA[
      L(x,(y * z) \ (z * a(y,z,u)),(y * z) \ (z * a(y,z,u))) = L(x,L(y,z,u) \ 1,L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,16981,a,b,17678,a),flip(a)].">
      <j1 rule="hyper" parents="316 16981 17678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17698">
    <literal><![CDATA[
      L(x,(y * z) \ (z * a(y,z,u)),(y * z) \ (z * a(y,z,u))) = L(x,L(y \ 1,z,u),L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,17654,a,b,17697,a),flip(a)].">
      <j1 rule="hyper" parents="316 17654 17697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17699">
    <literal><![CDATA[
      L(x,(y * z) \ (z * a(y,z,u)),(y * z) \ (z * a(y,z,u))) = L(x,y \ 1,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,14208,a(flip),b,17698,a),flip(a)].">
      <j1 rule="hyper" parents="316 14208 17698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17701">
    <literal><![CDATA[
      L(x,y \ (z \ (y * a(z,y,u))),y \ (z \ (y * a(z,y,u)))) = L(x,z \ 1,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,14229,a(flip),b,17699,a)].">
      <j1 rule="hyper" parents="63 14229 17699"/>
    </justification>
  </clause>

  <clause id="17702">
    <literal><![CDATA[
      L(x,y \ ((z \ y) * a(z,y,u)),y \ (z \ (y * a(z,y,u)))) = L(x,z \ 1,z \ 1)
    ]]></literal>
    <justification jstring="[para(8420(a,1),17701(a,1,2,2))].">
      <j1 rule="para" parents="8420 17701"/>
    </justification>
  </clause>

  <clause id="17703">
    <literal><![CDATA[
      L(x,y \ ((z \ y) * a(z,y,u)),y \ ((z \ y) * a(z,y,u))) = L(x,z \ 1,z \ 1)
    ]]></literal>
    <justification jstring="[para(8420(a,1),17702(a,1,3,2))].">
      <j1 rule="para" parents="8420 17702"/>
    </justification>
  </clause>

  <clause id="17704">
    <literal><![CDATA[
      L(x,y \ ((z \ y) * u),y \ ((z \ y) * u)) = L(x,(u \ z) \ 1,(u \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,14208,a(flip),b,17658,a),flip(a)].">
      <j1 rule="hyper" parents="63 14208 17658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17706">
    <literal><![CDATA[
      L(x,y \ ((z \ y) * u),y \ ((z \ y) * u)) = L(x,z \ u,z \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,17667,a(flip),b,17704,a),flip(a)].">
      <j1 rule="hyper" parents="316 17667 17704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17707">
    <literal><![CDATA[
      L(x,y \ a(y,z,u),y \ a(y,z,u)) = L(x,y \ 1,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,17703,a(flip),b,17706,a),flip(a)].">
      <j1 rule="hyper" parents="63 17703 17706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17709">
    <literal><![CDATA[
      a(x,y,z * (L(u * (w \ 1),w,w) * L(v5,w \ u,w \ u))) = a(x,y,(L(u * (w \ 1),w,w) \ v5) * z)
    ]]></literal>
    <justification jstring="[para(17030(a,1),17655(a,1,3,2,2))].">
      <j1 rule="para" parents="17030 17655"/>
    </justification>
  </clause>

  <clause id="17710">
    <literal><![CDATA[
      a(x,y,z * (L(u,w \ v5,w \ v5) * (w \ v5))) = a(x,y,(L(v5 * (w \ 1),w,w) \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12346,a(flip),b,17709,a)].">
      <j1 rule="hyper" parents="63 12346 17709"/>
    </justification>
  </clause>

  <clause id="17711">
    <literal><![CDATA[
      a(x,y,(L(z * (u \ 1),u,u) \ w) * v5) = a(x,y,((u \ z) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,8686,a(flip),b,17710,a),flip(a)].">
      <j1 rule="hyper" parents="63 8686 17710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17712">
    <literal><![CDATA[
      a(x,y,(L(z * u,z,z) \ w) * v5) = a(x,y,((z \ u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,17304,a(flip),b,17711,a)].">
      <j1 rule="hyper" parents="63 17304 17711"/>
    </justification>
  </clause>

  <clause id="17713">
    <literal><![CDATA[
      a(x,y,((z \ a(u,z,w)) \ v5) * v6) = a(x,y,((z * a(u,z,w)) \ v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,15126,a(flip),b,17712,a),flip(a)].">
      <j1 rule="hyper" parents="63 15126 17712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17714">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ a(L(a(x,y,z),w,v5),a(z,y,x),L(u,v6,v7)))) = L(u,a(x,y,z) * L(L(a(x,y,z),w,v5),v6,v7),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(16252(a,1),17671(a,1,2,2,2))].">
      <j1 rule="para" parents="16252 17671"/>
    </justification>
  </clause>

  <clause id="17715">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ a(a(x,y,z),a(x,y,z),L(L(u,w,v5),v6,v7)))) = L(u,a(x,y,z) * L(L(a(x,y,z),v6,v7),w,v5),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(16252(a,1),17714(a,1,2,2,2))].">
      <j1 rule="para" parents="16252 17714"/>
    </justification>
  </clause>

  <clause id="17716">
    <literal><![CDATA[
      L(x,a(y,z,u) * L(L(a(y,z,u),w,v5),v6,v7),a(y,z,u)) = a(y,z,u) * (x * (a(y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(14385(a,1),17715(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14385 17715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17718">
    <literal><![CDATA[
      L(x,a(y,z,u) * L(L(a(y,z,u),w,v5),v6,v7),a(y,z,u)) = a(y,z,u) * (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(14393(a,1),17716(a,2,2))].">
      <j1 rule="para" parents="14393 17716"/>
    </justification>
  </clause>

  <clause id="17719">
    <literal><![CDATA[
      L(x,a(y,z,u) * L(L(a(y,z,u),w,v5),v6,v7),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,10,a(flip),b,17718,a),flip(a)].">
      <j1 rule="hyper" parents="316 10 17718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17721">
    <literal><![CDATA[
      L(x,L(L(a(y,z,u),w,v5),v6,v7),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,17099,a(flip),b,17719,a)].">
      <j1 rule="hyper" parents="63 17099 17719"/>
    </justification>
  </clause>

  <clause id="17722">
    <literal><![CDATA[
      L(x,L(L(a(y,z,u),w,v5),v6,v7),a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,16986,a,b,17721,a)].">
      <j1 rule="hyper" parents="63 16986 17721"/>
    </justification>
  </clause>

  <clause id="17723">
    <literal><![CDATA[
      L(x,a(y,a(z,u,w),v5),a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,17154,a(flip),b,17722,a)].">
      <j1 rule="hyper" parents="63 17154 17722"/>
    </justification>
  </clause>

  <clause id="17725">
    <literal><![CDATA[
      (a(x,a(y,z,u),w) * (a(y,z,u) \ 1)) \ v5 = (a(y,z,u) * v5) * a(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,16107,a(flip),b,17723,a)].">
      <j1 rule="hyper" parents="63 16107 17723"/>
    </justification>
  </clause>

  <clause id="17727">
    <literal><![CDATA[
      (a(x,y,z) \ a(u,a(x,y,z),w)) \ v5 = (a(x,y,z) * v5) * a(w,a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(14393(a,1),17725(a,1,1))].">
      <j1 rule="para" parents="14393 17725"/>
    </justification>
  </clause>

  <clause id="17728">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * L(L(a(x,y,z) \ 1,u,w) * a(v5,L(a(x,y,z),u,w),L(a(x,y,z),u,w)),v6,v7) = L(L(a(x,y,z),u,w) \ L(L(a(x,y,z),u,w),v6,v7),L(a(x,y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(16820(a,1),14683(a,1,1))].">
      <j1 rule="para" parents="16820 14683"/>
    </justification>
  </clause>

  <clause id="17729">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w) \ L(L(a(x,y,z),u,w),v5,v6),L(a(x,y,z),u,w),v7) = L(a(x,y,z),u,w) * L(L(a(x,y,z) \ 1,u,w) * a(v7,a(x,y,z),a(x,y,z)),v5,v6)
    ]]></literal>
    <justification jstring="[para(13575(a,1),17728(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="13575 17728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17732">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w) \ L(L(a(x,y,z),u,w),v5,v6),L(a(x,y,z),u,w),v7) = L(a(x,y,z),u,w) * L(L(a(x,y,z) \ 1,u,w) * 1,v5,v6)
    ]]></literal>
    <justification jstring="[para(14416(a,1),17729(a,2,2,1,2))].">
      <j1 rule="para" parents="14416 17729"/>
    </justification>
  </clause>

  <clause id="17733">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w) \ L(L(a(x,y,z),u,w),v5,v6),L(a(x,y,z),u,w),v7) = L(a(x,y,z),u,w) * L(L(a(x,y,z) \ 1,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(8(a,1),17732(a,2,2,1))].">
      <j1 rule="para" parents="8 17732"/>
    </justification>
  </clause>

  <clause id="17735">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w) \ L(L(a(x,y,z),u,w),v5,v6),L(a(x,y,z),u,w),v7) = L(a(v6,v5,a(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,14889,a(flip),b,17733,a),flip(a)].">
      <j1 rule="hyper" parents="316 14889 17733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17736">
    <literal><![CDATA[
      L(L(a(x,y,z) \ L(a(x,y,z),u,w),v5,v6),L(a(x,y,z),v5,v6),v7) = L(a(w,u,a(x,y,z)),v5,v6)
    ]]></literal>
    <justification jstring="[para(2136(a,1),17735(a,1,1))].">
      <j1 rule="para" parents="2136 17735"/>
    </justification>
  </clause>

  <clause id="17737">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) = L(a(v6,v5,a(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15012,a(flip),b,17736,a)].">
      <j1 rule="hyper" parents="63 15012 17736"/>
    </justification>
  </clause>

  <clause id="17738">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) = L(a(x,y,a(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,13501,a(flip),b,17736,a)].">
      <j1 rule="hyper" parents="63 13501 17736"/>
    </justification>
  </clause>

  <clause id="17739">
    <literal><![CDATA[
      L(L(a(x,y,a(z,u,w)),v5,v6),L(a(z,u,w),v5,v6),v7) = L(a(x,y,a(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(14577(a,1),17736(a,1,1,1))].">
      <j1 rule="para" parents="14577 17736"/>
    </justification>
  </clause>

  <clause id="17741">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * a(a(y,a(z,u,y),x),w,v5) = a(L(a(z,u,y),w,v5),y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,14604,a,b,17737,a)].">
      <j1 rule="hyper" parents="316 14604 17737"/>
    </justification>
  </clause>

  <clause id="17742">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) = L(a(a(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,14065,a,b,17737,a),flip(a)].">
      <j1 rule="hyper" parents="316 14065 17737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17743">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),z,v5) = a(v5,L(z,u,w),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,13747,a,b,17737,a),flip(a)].">
      <j1 rule="hyper" parents="316 13747 17737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17744">
    <literal><![CDATA[
      a(L(a(x,y,z),u,u \ a(w,v5,a(x,y,z))),v5,w) = u * ((a(w,v5,a(x,y,z)) \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(316,a,14743,a(flip),b,17737,a),flip(a)].">
      <j1 rule="hyper" parents="316 14743 17737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17746">
    <literal><![CDATA[
      x \ a(L(a(y,z,u),x,x),w,v5) = a(v5,w,a(y,z,u)) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,17737,a,b,2459,a)].">
      <j1 rule="hyper" parents="133 17737 2459"/>
    </justification>
  </clause>

  <clause id="17747">
    <literal><![CDATA[
      x \ (L(x,y,a(z,u,y)) * L(L(x,y,a(z,u,y)) \ x,w,v5)) = a(x,y,a(z,u,y)) \ a(L(a(z,u,y),w,v5),y,x)
    ]]></literal>
    <justification jstring="[para(17737(a,2),12727(a,2,2))].">
      <j1 rule="para" parents="17737 12727"/>
    </justification>
  </clause>

  <clause id="17748">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) = L(a(v6,v5,a(z,y,x)),u,w)
    ]]></literal>
    <justification jstring="[para(13660(a,1),17737(a,2,1))].">
      <j1 rule="para" parents="13660 17737"/>
    </justification>
  </clause>

  <clause id="17749">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) \ v7 = L(a(v6,v5,a(x,y,z)),u,w) * v7
    ]]></literal>
    <justification jstring="[para(17737(a,2),14663(a,1,1))].">
      <j1 rule="para" parents="17737 14663"/>
    </justification>
  </clause>

  <clause id="17750">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) * a(L(a(x,y,z),u,w),v6,v7) = v5 * L(L(a(x,y,z) \ 1,u,w),v6,v7)
    ]]></literal>
    <justification jstring="[para(17737(a,2),14965(a,1,2))].">
      <j1 rule="para" parents="17737 14965"/>
    </justification>
  </clause>

  <clause id="17751">
    <literal><![CDATA[
      x * L(a(L(a(y,z,u),w,v5),v6,v7),L(a(y,z,u),w,v5),x) = L(a(y,z,u),w,v5) * (L(L(a(y,z,u),w,v5),v6,v7) \ x)
    ]]></literal>
    <justification jstring="[para(17737(a,2),14589(a,1,2,1))].">
      <j1 rule="para" parents="17737 14589"/>
    </justification>
  </clause>

  <clause id="17752">
    <literal><![CDATA[
      (x * (a(x,y,a(z,u,y)) \ a(L(a(z,u,y),w,v5),y,x))) * a(x,y,a(z,u,y)) = (a(x,y,a(z,u,y)) \ L(a(x,y,a(z,u,y)),w,v5)) * L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(17737(a,2),11695(a,1,1,2,2))].">
      <j1 rule="para" parents="17737 11695"/>
    </justification>
  </clause>

  <clause id="17755">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) = L(a(a(z,u,w),y,x),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,14065,a,b,17738,a),flip(a)].">
      <j1 rule="hyper" parents="316 14065 17738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17756">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,y)) = a(x,y,L(a(w,v5,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,13747,a,b,17738,a)].">
      <j1 rule="hyper" parents="316 13747 17738"/>
    </justification>
  </clause>

  <clause id="17761">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) * v7 = v7 * L(a(a(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,17742,a(flip),b,2295,a),flip(a)].">
      <j1 rule="hyper" parents="139 17742 2295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17762">
    <literal><![CDATA[
      L(((x * a(y,z,u)) \ (a(y,z,u) * (w * x))) \ T(w,x),v5,v6) = L(a(L(a(y,z,u),v5,v6),x,w),T(w,x),x)
    ]]></literal>
    <justification jstring="[para(17742(a,2),14294(a,2,1))].">
      <j1 rule="para" parents="17742 14294"/>
    </justification>
  </clause>

  <clause id="17763">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),z,v5) = a(z,a(x,y,z),L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,16264,a(flip),b,17743,a),flip(a)].">
      <j1 rule="hyper" parents="316 16264 17743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17764">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) = a(v6,v5,L(a(z,y,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,17738,a,b,17748,a),flip(a)].">
      <j1 rule="hyper" parents="316 17738 17748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17766">
    <literal><![CDATA[
      a(x,a(y,z,u),L(y,w,v5)) = a(x,y,L(a(u,z,y),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,13672,a(flip),b,17756,a)].">
      <j1 rule="hyper" parents="63 13672 17756"/>
    </justification>
  </clause>

  <clause id="17771">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * v5) \ ((L(a(x,y,z),u,w) * z) * T(v5,z)) = L(z * a(z,a(x,y,z),L(v5,u,w)),v5,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(17763(a,1),8578(a,2,1,2))].">
      <j1 rule="para" parents="17763 8578"/>
    </justification>
  </clause>

  <clause id="17772">
    <literal><![CDATA[
      a(x,a(L(y,y,z),z,x),L(u,w,v5)) = a(L(y \ R(y,z,x),w,v5),x,u)
    ]]></literal>
    <justification jstring="[para(14759(a,1),17763(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14759 17763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17773">
    <literal><![CDATA[
      L(x,y,L(a(z,u,y),w,v5)) * a(x,x,a(y,a(z,u,y),L(y,w,v5))) = a(L(a(z,u,y),w,v5),y,x) \ x
    ]]></literal>
    <justification jstring="[para(17763(a,1),15363(a,1,2,3))].">
      <j1 rule="para" parents="17763 15363"/>
    </justification>
  </clause>

  <clause id="17776">
    <literal><![CDATA[
      a(x,a(y,z,u),L(y,w,u)) = a(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(8510(a,1),17766(a,2,3))].">
      <j1 rule="para" parents="8510 17766"/>
    </justification>
  </clause>

  <clause id="17779">
    <literal><![CDATA[
      L(x,y,z) * a(u,x,a(z,w,x)) = L(L(x,y,z),a(z,w,x),u)
    ]]></literal>
    <justification jstring="[para(17776(a,1),16198(a,1,2))].">
      <j1 rule="para" parents="17776 16198"/>
    </justification>
  </clause>

  <clause id="17780">
    <literal><![CDATA[
      L(x,y,z) * a(x,a(z,u,x),w) = L(L(x,y,z),a(z,u,x),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,13474,a,b,17779,a)].">
      <j1 rule="hyper" parents="63 13474 17779"/>
    </justification>
  </clause>

  <clause id="17781">
    <literal><![CDATA[
      L(x,y,z) * a(x,a(z,u,x),w) = L(L(x,a(z,u,x),w),y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,30,a,b,17780,a),flip(a)].">
      <j1 rule="hyper" parents="316 30 17780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17782">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) \ v7 = a(L(a(x,y,z),u,w),v5,v6) * v7
    ]]></literal>
    <justification jstring="[para(17737(a,2),17749(a,2,1))].">
      <j1 rule="para" parents="17737 17749"/>
    </justification>
  </clause>

  <clause id="17783">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w),v5,v6)) \ x = x \ L(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(38,a,13490,a,b,17782,a)].">
      <j1 rule="hyper" parents="38 13490 17782"/>
    </justification>
  </clause>

  <clause id="17784">
    <literal><![CDATA[
      a(L(x \ R(x,y,z),u,w),z,v5) = a(z,x \ L(x,y,z),L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14573,a(flip),b,17772,a),flip(a)].">
      <j1 rule="hyper" parents="63 14573 17772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17785">
    <literal><![CDATA[
      a(L(x \ R(x,y,z),u,w),z,v5) = a(a(L(v5,u,w),z,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,17245,a(flip),b,17784,a),flip(a)].">
      <j1 rule="hyper" parents="316 17245 17784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17786">
    <literal><![CDATA[
      a(x,y,L(z * L(z,x,u),w,v5)) = a(a(L(u,w,v5),x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,16946,a(flip),b,17785,a)].">
      <j1 rule="hyper" parents="63 16946 17785"/>
    </justification>
  </clause>

  <clause id="17787">
    <literal><![CDATA[
      a(a(L(x,y,z),u,w),v5,u) = a(u,v5,L(a(x,u,w),y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15523,a(flip),b,17786,a),flip(a)].">
      <j1 rule="hyper" parents="63 15523 17786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17788">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),x,v5)) = a(x,y,L(a(z,x,v5),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14010,a(flip),b,17787,a)].">
      <j1 rule="hyper" parents="63 14010 17787"/>
    </justification>
  </clause>

  <clause id="17789">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,y) = a(y,v5,a(L(z,u,w),y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,17764,a,b,17788,a)].">
      <j1 rule="hyper" parents="316 17764 17788"/>
    </justification>
  </clause>

  <clause id="17790">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),x,v5)) = L(a(a(z,x,v5),y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,17755,a(flip),b,17788,a),flip(a)].">
      <j1 rule="hyper" parents="316 17755 17788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17791">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * a(a(y,a(z,u,y),x),w,v5) = a(y,a(z,u,y),L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,17763,a(flip),b,17741,a),flip(a)].">
      <j1 rule="hyper" parents="316 17763 17741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17792">
    <literal><![CDATA[
      L(a(L(a(x,y,z),u,w),v5,v6),L(a(x,y,z),u,w),v7) = L(a(v6,v5,a(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(17737(a,2),17739(a,1,1))].">
      <j1 rule="para" parents="17737 17739"/>
    </justification>
  </clause>

  <clause id="17793">
    <literal><![CDATA[
      L(a(L(a(x,y,z),u,w),v5,v6),L(a(x,y,z),u,w),v7) = a(L(a(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,17737,a,b,17792,a),flip(a)].">
      <j1 rule="hyper" parents="316 17737 17792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17795">
    <literal><![CDATA[
      a(L(a(x,y,z),u,u \ a(w,v5,a(x,y,z))),v5,w) = u * ((u * a(w,v5,a(x,y,z))) \ 1)
    ]]></literal>
    <justification jstring="[para(14470(a,1),17744(a,2,2,1))].">
      <j1 rule="para" parents="14470 17744"/>
    </justification>
  </clause>

  <clause id="17796">
    <literal><![CDATA[
      x * ((x * a(y,z,a(u,w,v5))) \ 1) = a(L(a(u,w,v5),x,x),z,y)
    ]]></literal>
    <justification jstring="[para(14864(a,1),17795(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14864 17795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17797">
    <literal><![CDATA[
      x \ a(L(a(y,z,u),x,x),w,v5) = (x * a(v5,w,a(y,z,u))) \ 1
    ]]></literal>
    <justification jstring="[hyper(144,a,17796,a)].">
      <j1 rule="hyper" parents="144 17796"/>
    </justification>
  </clause>

  <clause id="17799">
    <literal><![CDATA[
      (x * a(y,z,a(u,w,v5))) \ 1 = a(y,z,a(u,w,v5)) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,17746,a(flip),b,17797,a),flip(a)].">
      <j1 rule="hyper" parents="63 17746 17797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17800">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ 1 = a(x,y,a(z,u,w)) * (v5 \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2324,a,b,17799,a)].">
      <j1 rule="hyper" parents="63 2324 17799"/>
    </justification>
  </clause>

  <clause id="17801">
    <literal><![CDATA[
      (a(x,y,a(z,x,y)) * (u \ 1)) * (L(y,x,z) \ y) = (a(z,x,y) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(17800(a,1),17167(a,1,1))].">
      <j1 rule="para" parents="17800 17167"/>
    </justification>
  </clause>

  <clause id="17802">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * ((u \ 1) * (L(y,x,z) \ y)) = (a(z,x,y) \ u) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,13548,a(flip),b,17801,a)].">
      <j1 rule="hyper" parents="63 13548 17801"/>
    </justification>
  </clause>

  <clause id="17803">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ 1 = a(x,y,z) * (u \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,15193,a(flip),b,17802,a),flip(a)].">
      <j1 rule="hyper" parents="63 15193 17802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17805">
    <literal><![CDATA[
      (a(x,y,z) * (u \ 1)) \ (u \ a(x,y,z)) = (a(x,y,z) \ u) * (u \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(17803(a,1),1483(a,1,1))].">
      <j1 rule="para" parents="17803 1483"/>
    </justification>
  </clause>

  <clause id="17807">
    <literal><![CDATA[
      L(a(x,y,z),u,u * a(x,y,z)) = u * (a(x,y,z) * (u \ 1))
    ]]></literal>
    <justification jstring="[para(17803(a,1),16100(a,2,2))].">
      <j1 rule="para" parents="17803 16100"/>
    </justification>
  </clause>

  <clause id="17808">
    <literal><![CDATA[
      L(a(x,y,z),u,u * a(x,y,z)) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,2459,a(flip),b,17807,a),flip(a)].">
      <j1 rule="hyper" parents="316 2459 17807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17809">
    <literal><![CDATA[
      L(a(x,y,z),u,u * a(x,y,z)) = a(u,u,a(x,y,z)) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,14579,a,b,17808,a),flip(a)].">
      <j1 rule="hyper" parents="316 14579 17808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17810">
    <literal><![CDATA[
      L(a(x,y,z),u \ w,(u \ w) * a(x,y,z)) = a(u * w,u * w,a(x,y,z)) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(15769(a,1),17809(a,2,1))].">
      <j1 rule="para" parents="15769 17809"/>
    </justification>
  </clause>

  <clause id="17811">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (u \ a(x,y,z)) = u * (a(x,y,z) \ (u \ a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7697,a(flip),b,17805,a),flip(a)].">
      <j1 rule="hyper" parents="63 7697 17805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17812">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (u \ a(x,y,z)) = a(u,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,7413,a(flip),b,17811,a),flip(a)].">
      <j1 rule="hyper" parents="316 7413 17811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17813">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (u \ a(x,y,z)) = L(a(x,y,z),u,u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,14522,a,b,17812,a),flip(a)].">
      <j1 rule="hyper" parents="316 14522 17812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17814">
    <literal><![CDATA[
      (a(x,y,z) \ (u \ w)) * ((u \ w) \ a(x,y,z)) = a(u * w,u * w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,15769,a(flip),b,17812,a),flip(a)].">
      <j1 rule="hyper" parents="316 15769 17812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17815">
    <literal><![CDATA[
      (a(x,y,z) \ (u / w)) * ((u / w) \ a(x,y,z)) = L(a(x,y,z),w \ u,w \ u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10484,a,b,17813,a)].">
      <j1 rule="hyper" parents="63 10484 17813"/>
    </justification>
  </clause>

  <clause id="17816">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ a(x,y,z)) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(39,a,14742,a,b,17813,a(flip))].">
      <j1 rule="hyper" parents="39 14742 17813"/>
    </justification>
  </clause>

  <clause id="17817">
    <literal><![CDATA[
      (a(x,y,z) \ (u / w)) * ((u / w) \ a(x,y,z)) = L(a(x,y,z),w * u,w * u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(15778(a,1),17815(a,2,1))].">
      <j1 rule="para" parents="15778 17815"/>
    </justification>
  </clause>

  <clause id="17818">
    <literal><![CDATA[
      L(x,y,L(a(z,u,y),w,v5)) * a(x,x,a(y,a(z,u,y),y)) = a(L(a(z,u,y),w,v5),y,x) \ x
    ]]></literal>
    <justification jstring="[para(7508(a,1),17773(a,1,2,3))].">
      <j1 rule="para" parents="7508 17773"/>
    </justification>
  </clause>

  <clause id="17819">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),z,v5) \ v5 = L(v5,z,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5411,a(flip),b,17818,a),flip(a)].">
      <j1 rule="hyper" parents="63 5411 17818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17822">
    <literal><![CDATA[
      a(x,a(y,z,x),L(u,w,v5)) \ u = L(u,x,L(a(y,z,x),w,v5))
    ]]></literal>
    <justification jstring="[para(17763(a,1),17819(a,1,1))].">
      <j1 rule="para" parents="17763 17819"/>
    </justification>
  </clause>

  <clause id="17823">
    <literal><![CDATA[
      L(x,a(y,z,u),L(y,w,v5)) = L(x,y,L(a(u,z,y),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16263,a(flip),b,17822,a)].">
      <j1 rule="hyper" parents="63 16263 17822"/>
    </justification>
  </clause>

  <clause id="17825">
    <literal><![CDATA[
      L(x,a(y,z,u),L(u,w,v5)) = L(x,u,L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16124,a,b,17823,a)].">
      <j1 rule="hyper" parents="63 16124 17823"/>
    </justification>
  </clause>

  <clause id="17827">
    <literal><![CDATA[
      L(x,L(y,z,u),a(w,v5,y)) = L(x,y,L(a(w,v5,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10635,a,b,17825,a)].">
      <j1 rule="hyper" parents="63 10635 17825"/>
    </justification>
  </clause>

  <clause id="17828">
    <literal><![CDATA[
      L(x,a(y,z,u),L(u,w,y)) = L(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(8510(a,1),17825(a,2,3))].">
      <j1 rule="para" parents="8510 17825"/>
    </justification>
  </clause>

  <clause id="17830">
    <literal><![CDATA[
      L(x,L(y,z,u),a(u,w,y)) = L(x,y,a(u,w,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10635,a,b,17828,a)].">
      <j1 rule="hyper" parents="63 10635 17828"/>
    </justification>
  </clause>

  <clause id="17831">
    <literal><![CDATA[
      L(x,L(y,z,u),a(y,w,u)) = L(x,y,a(u,w,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16986,a,b,17830,a)].">
      <j1 rule="hyper" parents="63 16986 17830"/>
    </justification>
  </clause>

  <clause id="17832">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) * L(y,y,a(u,u,z)) = a(z,u,y) * (x * L(y,u,z))
    ]]></literal>
    <justification jstring="[para(17830(a,1),15398(a,1,1))].">
      <j1 rule="para" parents="17830 15398"/>
    </justification>
  </clause>

  <clause id="17833">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) * L(y,y,a(u,u,z)) = (a(y,u,z) \ x) * R(y,u,z)
    ]]></literal>
    <justification jstring="[para(17831(a,1),17202(a,1,1))].">
      <j1 rule="para" parents="17831 17202"/>
    </justification>
  </clause>

  <clause id="17835">
    <literal><![CDATA[
      L(a(x,y,z) \ (L(z,u,w) \ v5),z,L(a(x,y,z),u,w)) = (a(x,y,z) * L(z,u,w)) \ v5
    ]]></literal>
    <justification jstring="[hyper(63,a,7002,a(flip),b,17827,a),flip(a)].">
      <j1 rule="hyper" parents="63 7002 17827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17840">
    <literal><![CDATA[
      (a(x,y,z) \ u) * R(x,y,z) = a(z,y,x) * (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17832,a(flip),b,17833,a),flip(a)].">
      <j1 rule="hyper" parents="63 17832 17833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17843">
    <literal><![CDATA[
      L(((x * a(y,z,u)) \ (a(y,z,u) * (w * x))) \ T(w,x),v5,v6) = L(a(L(a(y,z,u),v5,v6),x,w),w,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,10796,a(flip),b,17762,a),flip(a)].">
      <j1 rule="hyper" parents="316 10796 17762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17845">
    <literal><![CDATA[
      L(((x * a(y,z,u)) \ (a(y,z,u) * (w * x))) \ T(w,x),v5,v6) = L(w,x,L(a(y,z,u),v5,v6)) \ w
    ]]></literal>
    <justification jstring="[hyper(316,a,13403,a(flip),b,17843,a),flip(a)].">
      <j1 rule="hyper" parents="316 13403 17843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17846">
    <literal><![CDATA[
      L(L(T(x,y),y,a(z,u,w)) \ T(x,y),v5,v6) = L(x,y,L(a(z,u,w),v5,v6)) \ x
    ]]></literal>
    <justification jstring="[para(2355(a,1),17845(a,1,1,1))].">
      <j1 rule="para" parents="2355 17845"/>
    </justification>
  </clause>

  <clause id="17847">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)) \ x,v5,v6) = L(x,y,L(a(z,u,w),v5,v6)) \ x
    ]]></literal>
    <justification jstring="[para(4348(a,1),17846(a,1,1))].">
      <j1 rule="para" parents="4348 17846"/>
    </justification>
  </clause>

  <clause id="17848">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)) \ x,v5,v6) = x \ L(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,17783,a(flip),b,17847,a),flip(a)].">
      <j1 rule="hyper" parents="316 17783 17847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17850">
    <literal><![CDATA[
      x * L(x \ L(x,y,a(z,u,w)),v5,v6) = L(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(39,a,14713,a,b,17847,a(flip))].">
      <j1 rule="hyper" parents="39 14713 17847"/>
    </justification>
  </clause>

  <clause id="17851">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),v5,v6) = L(x,y,L(a(z,u,w),v5,v6)) \ x
    ]]></literal>
    <justification jstring="[para(14060(a,1),17847(a,1,1))].">
      <j1 rule="para" parents="14060 17847"/>
    </justification>
  </clause>

  <clause id="17852">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),v5,v6) = x \ L(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(14060(a,1),17848(a,1,1))].">
      <j1 rule="para" parents="14060 17848"/>
    </justification>
  </clause>

  <clause id="17853">
    <literal><![CDATA[
      x * L(x \ L(x,y,a(z,z,u)),w,v5) = L(x,y,a(z,z,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(11868(a,2),17850(a,2,3))].">
      <j1 rule="para" parents="11868 17850"/>
    </justification>
  </clause>

  <clause id="17854">
    <literal><![CDATA[
      L(L(x \ L(x,y,a(z,u,w)),y,y),x,(1 / y) \ a(z,u,w)) = a(x,y,L(a(z,u,w),y,y)) \ 1
    ]]></literal>
    <justification jstring="[para(17851(a,2),17535(a,1,1))].">
      <j1 rule="para" parents="17851 17535"/>
    </justification>
  </clause>

  <clause id="17855">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),a(z,u,w),v5) = x \ L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14418(a,1),17852(a,2,2,3))].">
      <j1 rule="para" parents="14418 17852"/>
    </justification>
  </clause>

  <clause id="17856">
    <literal><![CDATA[
      L(L(x \ L(x,y,a(z,u,w)),y,v5),x,v5 \ ((v5 * y) * a(z,u,w))) = a(x,y,L(a(z,u,w),y,v5))
    ]]></literal>
    <justification jstring="[para(17852(a,2),17536(a,1,1))].">
      <j1 rule="para" parents="17852 17536"/>
    </justification>
  </clause>

  <clause id="17857">
    <literal><![CDATA[
      a(x,a(y,z,u),w \ L(w,v5,a(u,z,y))) = 1
    ]]></literal>
    <justification jstring="[hyper(132,a,17855,a,b,16214,a),flip(a)].">
      <j1 rule="hyper" parents="132 17855 16214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17859">
    <literal><![CDATA[
      (x * a(y,x,a(z,u,w))) * (x \ L(x,y,a(w,u,z))) = L(x,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[para(17855(a,1),15015(a,1,2))].">
      <j1 rule="para" parents="17855 15015"/>
    </justification>
  </clause>

  <clause id="17860">
    <literal><![CDATA[
      a(x,a(y,z,u),w * L(w,v5,a(u,z,y))) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,8934,a(flip),b,17857,a)].">
      <j1 rule="hyper" parents="63 8934 17857"/>
    </justification>
  </clause>

  <clause id="17861">
    <literal><![CDATA[
      a(a(x,y,z),u,a(w,a(x,y,z),v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,16243,a(flip),b,17860,a)].">
      <j1 rule="hyper" parents="63 16243 17860"/>
    </justification>
  </clause>

  <clause id="17862">
    <literal><![CDATA[
      L(a(x,a(y,z,u),w),v5,a(y,z,u)) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(52,a,17861,a)].">
      <j1 rule="hyper" parents="52 17861"/>
    </justification>
  </clause>

  <clause id="17864">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(w,a(x,y,z),v5) = a(x,y,z) * (u * a(w,a(x,y,z),v5))
    ]]></literal>
    <justification jstring="[hyper(139,a,17862,a(flip),b,7635,a(flip))].">
      <j1 rule="hyper" parents="139 17862 7635"/>
    </justification>
  </clause>

  <clause id="17865">
    <literal><![CDATA[
      x * (a(y,x,a(z,u,w)) * (x \ L(x,y,a(w,u,z)))) = L(x,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5132,a(flip),b,17859,a)].">
      <j1 rule="hyper" parents="63 5132 17859"/>
    </justification>
  </clause>

  <clause id="17867">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (y \ L(y,x,a(w,u,z))) = a(x,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(34,a,16197,a,b,17865,a),flip(a)].">
      <j1 rule="hyper" parents="34 16197 17865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17868">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * a(x,w,a(u,z,y)) = w \ L(w,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(34,a,14565,a,b,17867,a)].">
      <j1 rule="hyper" parents="34 14565 17867"/>
    </justification>
  </clause>

  <clause id="17869">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(y,a(z,u,w),x) = y \ L(y,x,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14126,a(flip),b,17868,a)].">
      <j1 rule="hyper" parents="63 14126 17868"/>
    </justification>
  </clause>

  <clause id="17870">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * a(u,a(z,y,x),w) = u \ L(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14034,a,b,17869,a)].">
      <j1 rule="hyper" parents="63 14034 17869"/>
    </justification>
  </clause>

  <clause id="17871">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) * a(z,a(u,w,v5),y * x) = z \ L(z,y * x,a(v5,w,u))
    ]]></literal>
    <justification jstring="[para(2771(a,1),17869(a,1,1))].">
      <j1 rule="para" parents="2771 17869"/>
    </justification>
  </clause>

  <clause id="17872">
    <literal><![CDATA[
      a(x,y,a(z,u * w,v5)) * a(y,a(z,w * u,v5),x) = y \ L(y,x,a(v5,w * u,z))
    ]]></literal>
    <justification jstring="[para(11190(a,1),17869(a,1,1,3))].">
      <j1 rule="para" parents="11190 17869"/>
    </justification>
  </clause>

  <clause id="17873">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(w,a(z,y,x),v5) = a(x,y,z) * (u * a(w,a(x,y,z),v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,13677,a,b,17864,a)].">
      <j1 rule="hyper" parents="63 13677 17864"/>
    </justification>
  </clause>

  <clause id="17874">
    <literal><![CDATA[
      (a(x,y,z) \ a(u,a(x,y,z),w)) \ v5 = a(x,y,z) * (v5 * a(w,a(x,y,z),u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17727,a,b,17873,a)].">
      <j1 rule="hyper" parents="63 17727 17873"/>
    </justification>
  </clause>

  <clause id="17875">
    <literal><![CDATA[
      a(x,y,a(z,u * w,v5)) = a(x,y,a(z,w * u,v5))
    ]]></literal>
    <justification jstring="[hyper(35,a,17869,a,b,17872,a)].">
      <j1 rule="hyper" parents="35 17869 17872"/>
    </justification>
  </clause>

  <clause id="17876">
    <literal><![CDATA[
      L(L(x \ L(x,y,a(z,u,w)),y,y),x,(y \ 1) \ a(z,u,w)) = a(x,y,L(a(z,u,w),y,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,3218,a(flip),b,17854,a)].">
      <j1 rule="hyper" parents="63 3218 17854"/>
    </justification>
  </clause>

  <clause id="17877">
    <literal><![CDATA[
      L(L(x \ L(x,((1 / y) * z) * u,a(w,v5,v6)),((1 / y) * z) * u,K(v7,v8)),x,K(v7,v8) \ ((((K(v7,v8) / y) * z) * u) * a(w,v5,v6))) = a(x,((1 / y) * z) * u,L(a(w,v5,v6),((1 / y) * z) * u,K(v7,v8)))
    ]]></literal>
    <justification jstring="[para(761(a,1),17856(a,1,3,2,1))].">
      <j1 rule="para" parents="761 17856"/>
    </justification>
  </clause>

  <clause id="17878">
    <literal><![CDATA[
      x \ (L(x,y,a(z,u,y)) * L(L(x,y,a(z,u,y)) \ x,w,v5)) = a(x,y,a(z,u,y)) \ a(y,a(z,u,y),L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(17763(a,1),17747(a,2,2))].">
      <j1 rule="para" parents="17763 17747"/>
    </justification>
  </clause>

  <clause id="17879">
    <literal><![CDATA[
      x \ (L(x,y,a(z,u,y)) * L(L(x,y,a(z,u,y)) \ x,w,v5)) = a(y,a(z,u,y),L(x,w,v5)) * a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,14470,a(flip),b,17878,a),flip(a)].">
      <j1 rule="hyper" parents="316 14470 17878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17880">
    <literal><![CDATA[
      x \ (L(x,y,a(z,u,y)) * L(x \ L(x,y,a(z,u,y)),w,v5)) = a(y,a(z,u,y),L(x,w,v5)) * a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(14060(a,1),17879(a,1,2,2,1))].">
      <j1 rule="para" parents="14060 17879"/>
    </justification>
  </clause>

  <clause id="17881">
    <literal><![CDATA[
      x \ (L(x,y,a(z,u,y)) * L(a(x,y,a(z,u,y)),w,v5)) = a(y,a(z,u,y),L(x,w,v5)) * a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(11689(a,1),17880(a,1,2,2,1))].">
      <j1 rule="para" parents="11689 17880"/>
    </justification>
  </clause>

  <clause id="17882">
    <literal><![CDATA[
      x \ (L(x,y,a(z,u,y)) * a(L(a(z,u,y),w,v5),y,x)) = a(y,a(z,u,y),L(x,w,v5)) * a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(17737(a,2),17881(a,1,2,2))].">
      <j1 rule="para" parents="17737 17881"/>
    </justification>
  </clause>

  <clause id="17883">
    <literal><![CDATA[
      x \ (L(x,y,a(z,u,y)) * a(y,a(z,u,y),L(x,w,v5))) = a(y,a(z,u,y),L(x,w,v5)) * a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(17763(a,1),17882(a,1,2,2))].">
      <j1 rule="para" parents="17763 17882"/>
    </justification>
  </clause>

  <clause id="17884">
    <literal><![CDATA[
      x \ (x * a(a(x,y,a(z,u,y)),w,v5)) = a(y,a(z,u,y),L(x,w,v5)) * a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(16382(a,1),17883(a,1,2))].">
      <j1 rule="para" parents="16382 17883"/>
    </justification>
  </clause>

  <clause id="17885">
    <literal><![CDATA[
      a(x,a(y,z,x),L(u,w,v5)) * a(u,x,a(y,z,x)) = a(a(u,x,a(y,z,x)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(322,a,17884,a),flip(a)].">
      <j1 rule="hyper" parents="322 17884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17887">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (L(L(a(x,y,z),u,w),v5,v6) \ v7) = v7 * a(L(a(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(17793(a,1),17751(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17793 17751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17888">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) * a(L(a(x,y,z),u,w),v6,v7) = L(L(a(x,y,z),u,w),v6,v7) \ v5
    ]]></literal>
    <justification jstring="[hyper(63,a,1130,a(flip),b,17887,a),flip(a)].">
      <j1 rule="hyper" parents="63 1130 17887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17890">
    <literal><![CDATA[
      x * L(L(a(y,z,u) \ 1,w,v5),v6,v7) = L(L(a(y,z,u),w,v5),v6,v7) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,17750,a(flip),b,17888,a)].">
      <j1 rule="hyper" parents="63 17750 17888"/>
    </justification>
  </clause>

  <clause id="17891">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ 1,v5,v6) * L(L(a(z,u,w) \ 1,v5,v6),v7,v8)) * v9 = a(v8,v7,L(L(a(z,u,w),v5,v6),y,x) \ L(a(z,u,w) \ 1,v5,v6)) * v9
    ]]></literal>
    <justification jstring="[para(17890(a,1),15304(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="17890 15304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17892">
    <literal><![CDATA[
      L(x * a(x,a(y,z,x),L(u,w,v5)),u,L(a(y,z,x),w,v5)) = (L(a(y,z,x),w,v5) * u) \ (u * (x * L(a(y,z,x),w,v5)))
    ]]></literal>
    <justification jstring="[para(13230(a,1),17771(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13230 17771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17893">
    <literal><![CDATA[
      L(x * a(x,a(y,z,x),L(u,w,v5)),u,L(a(y,z,x),w,v5)) = L(x,L(a(y,z,x),w,v5),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,2676,a(flip),b,17892,a),flip(a)].">
      <j1 rule="hyper" parents="316 2676 17892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17894">
    <literal><![CDATA[
      L(L(x,a(y,z,x),L(u,w,v5)),u,L(a(y,z,x),w,v5)) = L(x,L(a(y,z,x),w,v5),u)
    ]]></literal>
    <justification jstring="[para(9466(a,1),17893(a,1,1))].">
      <j1 rule="para" parents="9466 17893"/>
    </justification>
  </clause>

  <clause id="17895">
    <literal><![CDATA[
      L(x,a(y,z,x),L(z,u,w)) = L(x,x,a(z,z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(41,a,16376,a,b,17894,a),flip(a)].">
      <j1 rule="hyper" parents="41 16376 17894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17896">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ 1,v5,v6) * L(L(a(z,u,w) \ 1,v5,v6),v7,v8)) * v9 = a(v8,v7,L(L(a(z,u,w),v5,v6),y,x) \ L(a(z,u,w),v5,v6)) * v9
    ]]></literal>
    <justification jstring="[para(5818(a,1),17891(a,2,1))].">
      <j1 rule="para" parents="5818 17891"/>
    </justification>
  </clause>

  <clause id="17897">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ 1,v5,v6) * L(L(a(z,u,w) \ 1,v5,v6),v7,v8)) * v9 = a(v8,v7,L(L(a(z,u,w),y,x) \ a(z,u,w),v5,v6)) * v9
    ]]></literal>
    <justification jstring="[para(13383(a,1),17896(a,2,1,3))].">
      <j1 rule="para" parents="13383 17896"/>
    </justification>
  </clause>

  <clause id="17898">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ 1,v5,v6) * L(L(a(z,u,w) \ 1,v5,v6),v7,v8)) * v9 = a(v8,v7,L(a(x,y,a(z,u,w)),v5,v6)) * v9
    ]]></literal>
    <justification jstring="[para(14522(a,1),17897(a,2,1,3,1))].">
      <j1 rule="para" parents="14522 17897"/>
    </justification>
  </clause>

  <clause id="17899">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ 1,x,y) * L(L(a(z,u,w) \ 1,x,y),v5,v6)) * v7 = a(v6,v5,x \ R(x,y,a(z,u,w))) * v7
    ]]></literal>
    <justification jstring="[para(14606(a,1),17898(a,2,1,3))].">
      <j1 rule="para" parents="14606 17898"/>
    </justification>
  </clause>

  <clause id="17900">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ 1,x,y) * L(L(a(z,u,w) \ 1,x,y),v5,v6)) * v7 = a(v6,v5,x \ L(x,y,a(z,u,w))) * v7
    ]]></literal>
    <justification jstring="[para(5371(a,1),17899(a,2,1,3,2))].">
      <j1 rule="para" parents="5371 17899"/>
    </justification>
  </clause>

  <clause id="17901">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ 1,x,y) * L(L(a(z,u,w) \ 1,x,y),v5,v6)) * v7 = a(v6,v5,x * L(x,y,a(z,u,w))) * v7
    ]]></literal>
    <justification jstring="[para(5566(a,1),17900(a,2,1))].">
      <j1 rule="para" parents="5566 17900"/>
    </justification>
  </clause>

  <clause id="17902">
    <literal><![CDATA[
      a(x,y,L(L(a(z,u,w),x,y),v5,v6) \ L(a(z,u,w) \ 1,x,y)) * v7 = a(v6,v5,x * L(x,y,a(z,u,w))) * v7
    ]]></literal>
    <justification jstring="[para(17890(a,1),17901(a,1,1,3))].">
      <j1 rule="para" parents="17890 17901"/>
    </justification>
  </clause>

  <clause id="17903">
    <literal><![CDATA[
      a(x,y,L(L(a(z,u,w),x,y),v5,v6) \ L(a(z,u,w),x,y)) * v7 = a(v6,v5,x * L(x,y,a(z,u,w))) * v7
    ]]></literal>
    <justification jstring="[para(5818(a,1),17902(a,1,1))].">
      <j1 rule="para" parents="5818 17902"/>
    </justification>
  </clause>

  <clause id="17904">
    <literal><![CDATA[
      a(x,y,L(L(a(z,u,w),v5,v6) \ a(z,u,w),x,y)) * v7 = a(v6,v5,x * L(x,y,a(z,u,w))) * v7
    ]]></literal>
    <justification jstring="[para(13383(a,1),17903(a,1,1,3))].">
      <j1 rule="para" parents="13383 17903"/>
    </justification>
  </clause>

  <clause id="17905">
    <literal><![CDATA[
      a(x,y,L(a(z,u,a(w,v5,v6)),x,y)) * v7 = a(z,u,x * L(x,y,a(w,v5,v6))) * v7
    ]]></literal>
    <justification jstring="[para(14522(a,1),17904(a,1,1,3,1))].">
      <j1 rule="para" parents="14522 17904"/>
    </justification>
  </clause>

  <clause id="17906">
    <literal><![CDATA[
      a(x,y,z * L(z,u,a(w,v5,v6))) * v7 = (z \ L(z,u,a(x,y,a(w,v5,v6)))) * v7
    ]]></literal>
    <justification jstring="[para(16304(a,1),17905(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16304 17905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17907">
    <literal><![CDATA[
      a(x,y,z * L(z,u,a(w,v5,v6))) = z \ L(z,u,a(x,y,a(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(135,a,17906,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="135 17906 8"/>
    </justification>
  </clause>

  <clause id="17908">
    <literal><![CDATA[
      a(x,y,z * L(z,u,a(w,v5,v6))) = z \ L(z,u,a(a(w,v5,v6),y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,17006,a,b,17907,a),flip(a)].">
      <j1 rule="hyper" parents="316 17006 17907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17909">
    <literal><![CDATA[
      L(a(x,y,z * L(z,u,a(w,v5,v6))),z,u) = a(z,u * a(a(w,v5,v6),y,x),a(a(w,v5,v6),y,x))
    ]]></literal>
    <justification jstring="[para(17908(a,2),17100(a,1,1))].">
      <j1 rule="para" parents="17908 17100"/>
    </justification>
  </clause>

  <clause id="17910">
    <literal><![CDATA[
      a(x,y * a(a(z,u,w),v5,v6),a(a(z,u,w),v5,v6)) = a(v6,v5,L(x * L(x,y,a(z,u,w)),x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15231,a,b,17909,a),flip(a)].">
      <j1 rule="hyper" parents="63 15231 17909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17911">
    <literal><![CDATA[
      a(x,y * a(a(z,u,w),v5,v6),a(a(z,u,w),v5,v6)) = a(v6,v5,a(a(z,u,w),y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,10007,a(flip),b,17910,a),flip(a)].">
      <j1 rule="hyper" parents="316 10007 17910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17912">
    <literal><![CDATA[
      a(a(a(x,y,z),u,w),v5,v6) = a(w,u,a(a(x,y,z),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,14834,a(flip),b,17911,a)].">
      <j1 rule="hyper" parents="63 14834 17911"/>
    </justification>
  </clause>

  <clause id="17913">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)),v5,v6) = a(x,y,a(a(w,u,z),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,14043,a(flip),b,17912,a)].">
      <j1 rule="hyper" parents="63 14043 17912"/>
    </justification>
  </clause>

  <clause id="17914">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w),v5,v6)) = a(v6,v5,a(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14012,a(flip),b,17912,a),flip(a)].">
      <j1 rule="hyper" parents="63 14012 17912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17916">
    <literal><![CDATA[
      a(L(a(x,y,z),u,u \ a(x,y,z)) \ a(x,y,z),w,v5) = a(u \ a(x,y,z),u,a(a(z,y,x),w,v5))
    ]]></literal>
    <justification jstring="[para(6955(a,2),17913(a,1,1))].">
      <j1 rule="para" parents="6955 17913"/>
    </justification>
  </clause>

  <clause id="17919">
    <literal><![CDATA[
      ((x \ a(y,z,a(a(u,w,v5),v5,x))) \ 1) * a(x \ 1,x,x) = L(x,v5,a(y,z,a(v5,w,u)))
    ]]></literal>
    <justification jstring="[para(17913(a,1),16516(a,1,1,1,2))].">
      <j1 rule="para" parents="17913 16516"/>
    </justification>
  </clause>

  <clause id="17920">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(z,u,a(x,y,a(v6,v5,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13702,a(flip),b,17914,a)].">
      <j1 rule="hyper" parents="63 13702 17914"/>
    </justification>
  </clause>

  <clause id="17924">
    <literal><![CDATA[
      ((x \ a(y,z,a(u,a(w,v5,u),x))) \ 1) * a(x \ 1,x,x) = L(x,u,a(y,z,a(u,v5,w)))
    ]]></literal>
    <justification jstring="[para(7009(a,1),17919(a,1,1,1,2,3))].">
      <j1 rule="para" parents="7009 17919"/>
    </justification>
  </clause>

  <clause id="17925">
    <literal><![CDATA[
      a(L(a(x,y,z),u,u) \ a(x,y,z),w,v5) = a(u \ a(x,y,z),u,a(a(z,y,x),w,v5))
    ]]></literal>
    <justification jstring="[para(17816(a,1),17916(a,1,1,1))].">
      <j1 rule="para" parents="17816 17916"/>
    </justification>
  </clause>

  <clause id="17926">
    <literal><![CDATA[
      a(x \ a(y,z,u),x,a(a(u,z,y),w,v5)) = a(a(x,x,a(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(4952(a,1),17925(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4952 17925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17927">
    <literal><![CDATA[
      (x * (a(x,y,a(z,u,y)) \ a(y,a(z,u,y),L(x,w,v5)))) * a(x,y,a(z,u,y)) = (a(x,y,a(z,u,y)) \ L(a(x,y,a(z,u,y)),w,v5)) * L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(17763(a,1),17752(a,1,1,2,2))].">
      <j1 rule="para" parents="17763 17752"/>
    </justification>
  </clause>

  <clause id="17928">
    <literal><![CDATA[
      (x * (a(y,a(z,u,y),L(x,w,v5)) * a(x,y,a(z,u,y)))) * a(x,y,a(z,u,y)) = (a(x,y,a(z,u,y)) \ L(a(x,y,a(z,u,y)),w,v5)) * L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(14470(a,1),17927(a,1,1,2))].">
      <j1 rule="para" parents="14470 17927"/>
    </justification>
  </clause>

  <clause id="17929">
    <literal><![CDATA[
      L(L(x \ L(x,((y \ 1) * z) * u,a(w,v5,v6)),((1 / y) * z) * u,K(v7,v8)),x,K(v7,v8) \ ((((K(v7,v8) / y) * z) * u) * a(w,v5,v6))) = a(x,((1 / y) * z) * u,L(a(w,v5,v6),((1 / y) * z) * u,K(v7,v8)))
    ]]></literal>
    <justification jstring="[para(10812(a,1),17877(a,1,1,1,2))].">
      <j1 rule="para" parents="10812 17877"/>
    </justification>
  </clause>

  <clause id="17930">
    <literal><![CDATA[
      L(L(x \ L(x,y * (z * u),a(w,v5,v6)),((1 / u) * z) * y,K(v7,v8)),x,K(v7,v8) \ ((((K(v7,v8) / u) * z) * y) * a(w,v5,v6))) = a(x,((1 / u) * z) * y,L(a(w,v5,v6),((1 / u) * z) * y,K(v7,v8)))
    ]]></literal>
    <justification jstring="[para(15735(a,1),17929(a,1,1,1,2))].">
      <j1 rule="para" parents="15735 17929"/>
    </justification>
  </clause>

  <clause id="17931">
    <literal><![CDATA[
      L(x \ L(x,y * (z * u),a(w,v5,v6)),x,K(v7,v8) \ ((((K(v7,v8) / u) * z) * y) * a(w,v5,v6))) = a(x,((1 / u) * z) * y,L(a(w,v5,v6),((1 / u) * z) * y,K(v7,v8)))
    ]]></literal>
    <justification jstring="[para(155(a,1),17930(a,1,1))].">
      <j1 rule="para" parents="155 17930"/>
    </justification>
  </clause>

  <clause id="17933">
    <literal><![CDATA[
      L(x \ L(x,y * (z * u),a(w,v5,v6)),x,(((1 / u) * z) * y) * a(w,v5,v6)) = a(x,((1 / u) * z) * y,L(a(w,v5,v6),((1 / u) * z) * y,K(v7,v8)))
    ]]></literal>
    <justification jstring="[para(1966(a,1),17931(a,1,3))].">
      <j1 rule="para" parents="1966 17931"/>
    </justification>
  </clause>

  <clause id="17934">
    <literal><![CDATA[
      L(x \ L(x,y * (z * u),a(w,v5,v6)),x,(((u \ 1) * z) * y) * a(w,v5,v6)) = a(x,((1 / u) * z) * y,L(a(w,v5,v6),((1 / u) * z) * y,K(v7,v8)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3353,a(flip),b,17933,a)].">
      <j1 rule="hyper" parents="63 3353 17933"/>
    </justification>
  </clause>

  <clause id="17936">
    <literal><![CDATA[
      L(x \ L(x,y * (z * u),a(w,v5,v6)),x,(y * (z * u)) * a(w,v5,v6)) = a(x,((1 / u) * z) * y,L(a(w,v5,v6),((1 / u) * z) * y,K(v7,v8)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15630,a(flip),b,17934,a)].">
      <j1 rule="hyper" parents="63 15630 17934"/>
    </justification>
  </clause>

  <clause id="17937">
    <literal><![CDATA[
      a(x,((1 / y) * z) * u,L(a(w,v5,v6),((1 / y) * z) * u,K(v7,v8))) = a(x,u * (z * y),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5385,a(flip),b,17936,a),flip(a)].">
      <j1 rule="hyper" parents="63 5385 17936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17938">
    <literal><![CDATA[
      a(x,((1 / y) * z) * u,a(w,v5,v6)) = a(x,u * (z * y),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5526,a(flip),b,17937,a)].">
      <j1 rule="hyper" parents="63 5526 17937"/>
    </justification>
  </clause>

  <clause id="17940">
    <literal><![CDATA[
      a(x,((y \ 1) * z) * u,a(w,v5,v6)) = a(x,u * (z * y),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,11243,a(flip),b,17938,a)].">
      <j1 rule="hyper" parents="63 11243 17938"/>
    </justification>
  </clause>

  <clause id="17941">
    <literal><![CDATA[
      a(x,L(((y \ 1) * z) \ u,z * y,z * y),a(w,v5,v6)) = a(x,u * (z * y),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,15792,a,b,17940,a)].">
      <j1 rule="hyper" parents="63 15792 17940"/>
    </justification>
  </clause>

  <clause id="17942">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),L(x \ L(x,u,w),v5,v6) \ (L(x \ L(x,u,w),v5,v6) \ v7)) \ v7) = ((L(x \ L(x,u,w),v5,v6) \ (v7 * L(L(x,u,w) \ x,v5,v6))) * a(x,y,z)) * L(x \ L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(14736(a,1),9532(a,2,1,1,2))].">
      <j1 rule="para" parents="14736 9532"/>
    </justification>
  </clause>

  <clause id="17943">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),L(x \ L(x,u,w),v5,v6) \ (L(x \ L(x,u,w),v5,v6) \ v7)) \ v7) = (((v7 * L(L(x,u,w) \ x,v5,v6)) * L(L(x,u,w) \ x,v5,v6)) * a(x,y,z)) * L(x \ L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(14736(a,1),17942(a,2,1,1))].">
      <j1 rule="para" parents="14736 17942"/>
    </justification>
  </clause>

  <clause id="17944">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),L(x \ L(x,u,w),v5,v6) \ (L(x \ L(x,u,w),v5,v6) \ v7)) \ v7) = (((v7 * (L(x,u,w) \ x)) * L(L(L(x,u,w) \ x,v5,v6),v5,v6)) * a(x,y,z)) * L(x \ L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(13890(a,1),17943(a,2,1,1))].">
      <j1 rule="para" parents="13890 17943"/>
    </justification>
  </clause>

  <clause id="17945">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),L(x \ L(x,u,w),v5,v6) \ (L(x \ L(x,u,w),v5,v6) \ v7)) \ v7) = (((v7 * (L(x,u,w) \ x)) * (L(x,u,w) \ x)) * a(x,y,z)) * L(x \ L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(13399(a,1),17944(a,2,1,1,2))].">
      <j1 rule="para" parents="13399 17944"/>
    </justification>
  </clause>

  <clause id="17947">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),L(x \ L(x,u,w),v5,v6) \ (L(x \ L(x,u,w),v5,v6) \ v7)) \ v7) = ((v7 * (a(w,u,x) * a(w,u,x))) * a(x,y,z)) * L(x \ L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(14772(a,1),17945(a,2,1,1))].">
      <j1 rule="para" parents="14772 17945"/>
    </justification>
  </clause>

  <clause id="17948">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),L(x \ L(x,u,w),v5,v6) \ (L(x \ L(x,u,w),v5,v6) \ v7)) \ v7) = (v7 * ((a(w,u,x) * a(w,u,x)) * a(x,y,z))) * L(x \ L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(2620(a,1),17947(a,2,1))].">
      <j1 rule="para" parents="2620 17947"/>
    </justification>
  </clause>

  <clause id="17949">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),L(x \ L(x,u,w),v5,v6) \ (L(x \ L(x,u,w),v5,v6) \ v7)) \ v7) = (v7 * (x * (L(L(x,u,w),u,w) \ a(x,y,z)))) * L(x \ L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(14046(a,1),17948(a,2,1,2))].">
      <j1 rule="para" parents="14046 17948"/>
    </justification>
  </clause>

  <clause id="17950">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),L(x \ L(x,u,w),v5,v6) \ (L(x \ L(x,u,w),v5,v6) \ v7)) \ v7) = (v7 * a(x,y,z)) * (L(x \ L(x,u,w),v5,v6) * (a(w,u,x) * a(w,u,x)))
    ]]></literal>
    <justification jstring="[hyper(316,a,17337,a(flip),b,17949,a),flip(a)].">
      <j1 rule="hyper" parents="316 17337 17949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17951">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),L(x \ L(x,u,w),v5,v6) \ (L(x \ L(x,u,w),v5,v6) \ v7)) \ v7) = (v7 * a(x,y,z)) * L((x \ L(x,u,w)) * (a(w,u,x) * a(w,u,x)),v5,v6)
    ]]></literal>
    <justification jstring="[para(1058(a,2),17950(a,2,2))].">
      <j1 rule="para" parents="1058 17950"/>
    </justification>
  </clause>

  <clause id="17952">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),L(x \ L(x,u,w),v5,v6) \ (L(x \ L(x,u,w),v5,v6) \ v7)) \ v7) = (v7 * a(x,y,z)) * L(L(L(x,u,w),u,w) \ L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(14087(a,1),17951(a,2,2,1))].">
      <j1 rule="para" parents="14087 17951"/>
    </justification>
  </clause>

  <clause id="17953">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),L(x \ L(x,u,w),v5,v6) \ (L(x \ L(x,u,w),v5,v6) \ v7)) \ v7) = (v7 * a(x,y,z)) * L(L(L(x,u,w) \ x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(13382(a,1),17952(a,2,2,1))].">
      <j1 rule="para" parents="13382 17952"/>
    </justification>
  </clause>

  <clause id="17954">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),L(x \ L(x,u,w),v5,v6) \ (L(x \ L(x,u,w),v5,v6) \ v7)) \ v7) = (v7 * a(x,y,z)) * L(L(x,u,w) \ x,v5,v6)
    ]]></literal>
    <justification jstring="[para(9861(a,1),17953(a,2,2,1))].">
      <j1 rule="para" parents="9861 17953"/>
    </justification>
  </clause>

  <clause id="17956">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),L(x \ L(x,u,w),v5,v6) \ (v7 * L(L(x,u,w) \ x,v5,v6))) \ v7) = (v7 * a(x,y,z)) * L(L(x,u,w) \ x,v5,v6)
    ]]></literal>
    <justification jstring="[para(14736(a,1),17954(a,1,2,1,2,2))].">
      <j1 rule="para" parents="14736 17954"/>
    </justification>
  </clause>

  <clause id="17957">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),(v7 * L(L(x,u,w) \ x,v5,v6)) * L(L(x,u,w) \ x,v5,v6)) \ v7) = (v7 * a(x,y,z)) * L(L(x,u,w) \ x,v5,v6)
    ]]></literal>
    <justification jstring="[para(14736(a,1),17956(a,1,2,1,2))].">
      <j1 rule="para" parents="14736 17956"/>
    </justification>
  </clause>

  <clause id="17958">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),(v7 * (L(x,u,w) \ x)) * L(L(L(x,u,w) \ x,v5,v6),v5,v6)) \ v7) = (v7 * a(x,y,z)) * L(L(x,u,w) \ x,v5,v6)
    ]]></literal>
    <justification jstring="[para(13890(a,1),17957(a,1,2,1,2))].">
      <j1 rule="para" parents="13890 17957"/>
    </justification>
  </clause>

  <clause id="17959">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),(v7 * (L(x,u,w) \ x)) * (L(x,u,w) \ x)) \ v7) = (v7 * a(x,y,z)) * L(L(x,u,w) \ x,v5,v6)
    ]]></literal>
    <justification jstring="[para(13399(a,1),17958(a,1,2,1,2,2))].">
      <j1 rule="para" parents="13399 17958"/>
    </justification>
  </clause>

  <clause id="17961">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),v7 * (a(w,u,x) * a(w,u,x))) \ v7) = (v7 * a(x,y,z)) * L(L(x,u,w) \ x,v5,v6)
    ]]></literal>
    <justification jstring="[para(14772(a,1),17959(a,1,2,1,2))].">
      <j1 rule="para" parents="14772 17959"/>
    </justification>
  </clause>

  <clause id="17962">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),v7 * a(w,u,x)) \ v7) = (v7 * a(x,y,z)) * L(L(x,u,w) \ x,v5,v6)
    ]]></literal>
    <justification jstring="[para(5242(a,1),17961(a,1,2,1))].">
      <j1 rule="para" parents="5242 17961"/>
    </justification>
  </clause>

  <clause id="17963">
    <literal><![CDATA[
      a(x,y,z) * (T(L(x \ L(x,u,w),v5,v6),v7) \ v7) = (v7 * a(x,y,z)) * L(L(x,u,w) \ x,v5,v6)
    ]]></literal>
    <justification jstring="[para(5243(a,1),17962(a,1,2,1))].">
      <j1 rule="para" parents="5243 17962"/>
    </justification>
  </clause>

  <clause id="17966">
    <literal><![CDATA[
      a(x,y,z) * (L(T(x \ L(x,u,w),v5),v6,v7) \ v5) = (v5 * a(x,y,z)) * L(L(x,u,w) \ x,v6,v7)
    ]]></literal>
    <justification jstring="[para(25(a,2),17963(a,1,2,1))].">
      <j1 rule="para" parents="25 17963"/>
    </justification>
  </clause>

  <clause id="17968">
    <literal><![CDATA[
      (x * a(y,z,u)) * L(L(y,w,v5) \ y,v6,v7) = a(y,z,u) * (L(y \ L(y,w,v5),v6,v7) \ x)
    ]]></literal>
    <justification jstring="[para(5017(a,1),17966(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5017 17966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17970">
    <literal><![CDATA[
      (x * a(y,z,u)) * L(L(y,w,v5) \ y,v6,v7) = a(y,z,u) * (x * L(L(y,w,v5) \ y,v6,v7))
    ]]></literal>
    <justification jstring="[para(14736(a,1),17968(a,2,2))].">
      <j1 rule="para" parents="14736 17968"/>
    </justification>
  </clause>

  <clause id="17974">
    <literal><![CDATA[
      ((((x \ 1) * (x * y)) \ 1) \ ((y \ 1) * 1)) * T(z,(y \ 1) \ ((y * (((x \ 1) * (x * y)) \ 1)) \ (y \ 1))) = T(z * ((((x \ 1) * (x * y)) \ 1) \ (y \ 1)),K(y * (((x \ 1) * (x * y)) \ 1),y \ 1))
    ]]></literal>
    <justification jstring="[para(8315(a,1),10771(a,1,1))].">
      <j1 rule="para" parents="8315 10771"/>
    </justification>
  </clause>

  <clause id="17975">
    <literal><![CDATA[
      ((((x \ 1) * (x * y)) \ 1) \ (y \ 1)) * T(z,(y \ 1) \ ((y * (((x \ 1) * (x * y)) \ 1)) \ (y \ 1))) = T(z * ((((x \ 1) * (x * y)) \ 1) \ (y \ 1)),K(y * (((x \ 1) * (x * y)) \ 1),y \ 1))
    ]]></literal>
    <justification jstring="[para(8(a,1),17974(a,1,1,2))].">
      <j1 rule="para" parents="8 17974"/>
    </justification>
  </clause>

  <clause id="17976">
    <literal><![CDATA[
      ((((x \ 1) * (x * y)) \ 1) \ (y \ 1)) * T(z,(y \ 1) \ ((((x \ 1) * (x * y)) \ 1) \ (y \ (y \ 1)))) = T(z * ((((x \ 1) * (x * y)) \ 1) \ (y \ 1)),K(y * (((x \ 1) * (x * y)) \ 1),y \ 1))
    ]]></literal>
    <justification jstring="[para(6564(a,1),17975(a,1,2))].">
      <j1 rule="para" parents="6564 17975"/>
    </justification>
  </clause>

  <clause id="17977">
    <literal><![CDATA[
      ((((x \ 1) * (x * y)) \ 1) \ (y \ 1)) * T(z,T(((((x \ 1) * (x * y)) \ 1) \ 1) / y,y \ 1)) = T(z * ((((x \ 1) * (x * y)) \ 1) \ (y \ 1)),K(y * (((x \ 1) * (x * y)) \ 1),y \ 1))
    ]]></literal>
    <justification jstring="[para(685(a,1),17976(a,1,2,2))].">
      <j1 rule="para" parents="685 17976"/>
    </justification>
  </clause>

  <clause id="17978">
    <literal><![CDATA[
      ((((x \ 1) * (x * y)) \ 1) \ (y \ 1)) * T(z,T(((x \ 1) * (x * ((y \ 1) \ 1))) / y,y \ 1)) = T(z * ((((x \ 1) * (x * y)) \ 1) \ (y \ 1)),K(y * (((x \ 1) * (x * y)) \ 1),y \ 1))
    ]]></literal>
    <justification jstring="[para(8346(a,1),17977(a,1,2,2,1,1))].">
      <j1 rule="para" parents="8346 17977"/>
    </justification>
  </clause>

  <clause id="17979">
    <literal><![CDATA[
      T(x * ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)),K(z * (((y \ 1) * (y * z)) \ 1),z \ 1)) = ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)) * T(x,T(((y \ 1) * (y * ((z \ 1) \ 1))) / z,z))
    ]]></literal>
    <justification jstring="[para(6427(a,1),17978(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6427 17978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17980">
    <literal><![CDATA[
      T(x * ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)),K(z * (((y \ 1) * (y * z)) \ 1),z \ 1)) = ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)) * T(x,z \ ((y \ 1) * (y * ((z \ 1) \ 1))))
    ]]></literal>
    <justification jstring="[para(116(a,1),17979(a,2,2,2))].">
      <j1 rule="para" parents="116 17979"/>
    </justification>
  </clause>

  <clause id="17981">
    <literal><![CDATA[
      T(x * ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)),K(z * (((y \ 1) * (y * z)) \ 1),z \ 1)) = ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)) * T(x,(z \ (y \ 1)) * (y * ((z \ 1) \ 1)))
    ]]></literal>
    <justification jstring="[para(3512(a,1),17980(a,2,2))].">
      <j1 rule="para" parents="3512 17980"/>
    </justification>
  </clause>

  <clause id="17982">
    <literal><![CDATA[
      T(x * ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)),K(z * (((y \ 1) * (y * z)) \ 1),z \ 1)) = ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)) * T(x,(z \ (y \ 1)) * (y / (z \ 1)))
    ]]></literal>
    <justification jstring="[para(3486(a,1),17981(a,2,2))].">
      <j1 rule="para" parents="3486 17981"/>
    </justification>
  </clause>

  <clause id="17983">
    <literal><![CDATA[
      T(x * ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)),K(z * (((y \ 1) * (y * z)) \ 1),z \ 1)) = ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)) * T(x,(z \ (y \ 1)) * (y * z))
    ]]></literal>
    <justification jstring="[para(4570(a,1),17982(a,2,2))].">
      <j1 rule="para" parents="4570 17982"/>
    </justification>
  </clause>

  <clause id="17984">
    <literal><![CDATA[
      T(x * ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)),K(z * (((y \ 1) * (y * z)) \ 1),z \ 1)) = ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)) * T(x,T((y \ 1) * y,z))
    ]]></literal>
    <justification jstring="[para(10604(a,1),17983(a,2,2))].">
      <j1 rule="para" parents="10604 17983"/>
    </justification>
  </clause>

  <clause id="17985">
    <literal><![CDATA[
      T(x * ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)),K(z * (((y \ 1) * (y * z)) \ 1),z \ 1)) = ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)) * T(x,K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(2224(a,1),17984(a,2,2,2))].">
      <j1 rule="para" parents="2224 17984"/>
    </justification>
  </clause>

  <clause id="17986">
    <literal><![CDATA[
      T(x * ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)),K(z * (((y \ 1) * (y * z)) \ 1),z \ 1)) = ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)) * x
    ]]></literal>
    <justification jstring="[para(2206(a,1),17985(a,2,2))].">
      <j1 rule="para" parents="2206 17985"/>
    </justification>
  </clause>

  <clause id="17988">
    <literal><![CDATA[
      T(x * ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)),K(z / ((y \ 1) * (y * z)),z \ 1)) = ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)) * x
    ]]></literal>
    <justification jstring="[para(3392(a,1),17986(a,1,2))].">
      <j1 rule="para" parents="3392 17986"/>
    </justification>
  </clause>

  <clause id="17989">
    <literal><![CDATA[
      T(x * ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)),K(y * (z / (y * z)),z \ 1)) = ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)) * x
    ]]></literal>
    <justification jstring="[para(11166(a,1),17988(a,1,2,1))].">
      <j1 rule="para" parents="11166 17988"/>
    </justification>
  </clause>

  <clause id="17990">
    <literal><![CDATA[
      T(x * ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)),1) = ((((y \ 1) * (y * z)) \ 1) \ (z \ 1)) * x
    ]]></literal>
    <justification jstring="[para(2265(a,1),17989(a,1,2))].">
      <j1 rule="para" parents="2265 17989"/>
    </justification>
  </clause>

  <clause id="17991">
    <literal><![CDATA[
      ((((x \ 1) * (x * y)) \ 1) \ (y \ 1)) * z = z * ((((x \ 1) * (x * y)) \ 1) \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(214,a,17990,a),flip(a)].">
      <j1 rule="hyper" parents="214 17990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17993">
    <literal><![CDATA[
      ((x \ ((x \ 1) \ (y \ 1))) \ (y \ 1)) * z = z * ((((x \ 1) * (x * y)) \ 1) \ (y \ 1))
    ]]></literal>
    <justification jstring="[para(12178(a,1),17991(a,1,1,1))].">
      <j1 rule="para" parents="12178 17991"/>
    </justification>
  </clause>

  <clause id="17994">
    <literal><![CDATA[
      ((x \ ((x \ 1) \ (y \ 1))) \ (y \ 1)) * z = z * ((x \ ((x \ 1) \ (y \ 1))) \ (y \ 1))
    ]]></literal>
    <justification jstring="[para(12178(a,1),17993(a,2,2,1))].">
      <j1 rule="para" parents="12178 17993"/>
    </justification>
  </clause>

  <clause id="17995">
    <literal><![CDATA[
      x * ((y \ ((y \ 1) \ (z \ 1))) \ (z \ 1)) = (z \ ((y \ 1) * (y * z))) * x
    ]]></literal>
    <justification jstring="[para(15846(a,1),17994(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15846 17994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17996">
    <literal><![CDATA[
      x * ((y \ ((y \ 1) \ (z \ 1))) \ (z \ 1)) = (y * (z / (y * z))) \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,14389,a(flip),b,17995,a),flip(a)].">
      <j1 rule="hyper" parents="316 14389 17995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17997">
    <literal><![CDATA[
      x * (y \ ((z \ 1) * (z * y))) = (z * (y / (z * y))) \ x
    ]]></literal>
    <justification jstring="[para(15846(a,1),17996(a,1,2))].">
      <j1 rule="para" parents="15846 17996"/>
    </justification>
  </clause>

  <clause id="17998">
    <literal><![CDATA[
      a(x,y,L(((z * (u / (z * u))) \ w) \ v5,v6,v7)) = a(x,y,L(((z * (u / (z * u))) * w) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(17997(a,1),12708(a,1,3,1,1))].">
      <j1 rule="para" parents="17997 12708"/>
    </justification>
  </clause>

  <clause id="17999">
    <literal><![CDATA[
      a(x,y,L(((z * (u / (z * u))) * w) \ v5,a(u,z,z),w)) = a(x,y,(z * (u / (z * u))) * (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,15009,a(flip),b,17998,a),flip(a)].">
      <j1 rule="hyper" parents="63 15009 17998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18000">
    <literal><![CDATA[
      a(x,y,L(((z * (u / (z * u))) * w) \ v5,a(u,z,z),w)) = a(x,y,(z * ((z * u) \ u)) * (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,5689,a(flip),b,17999,a),flip(a)].">
      <j1 rule="hyper" parents="316 5689 17999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18001">
    <literal><![CDATA[
      a(x,y,L(((z * (u / (z * u))) * w) \ v5,a(u,z,z),w)) = a(x,y,a(u,z,z) * (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,7399,a(flip),b,18000,a),flip(a)].">
      <j1 rule="hyper" parents="316 7399 18000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18003">
    <literal><![CDATA[
      ((((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1) * (a(a(x,y,z),y,y) \ ((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1))) / ((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1)) * a(a(x,y,z),y,y) = T((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2276(a,1),8781(a,1,1,1,2))].">
      <j1 rule="para" parents="2276 8781"/>
    </justification>
  </clause>

  <clause id="18004">
    <literal><![CDATA[
      ((((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1) * y) / ((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1)) * a(a(x,y,z),y,y) = T((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(8766(a,1),18003(a,1,1,1,2))].">
      <j1 rule="para" parents="8766 18003"/>
    </justification>
  </clause>

  <clause id="18005">
    <literal><![CDATA[
      (x * K((a(y,x,z) / ((y \ ((y * x) * z)) / z)) \ 1,x)) * a(a(y,x,z),x,x) = T((a(y,x,z) / ((y \ ((y * x) * z)) / z)) \ 1,x)
    ]]></literal>
    <justification jstring="[para(2722(a,1),18004(a,1,1))].">
      <j1 rule="para" parents="2722 18004"/>
    </justification>
  </clause>

  <clause id="18006">
    <literal><![CDATA[
      (x * K(((y \ ((y * x) * z)) / z) / a(y,x,z),x)) * a(a(y,x,z),x,x) = T((a(y,x,z) / ((y \ ((y * x) * z)) / z)) \ 1,x)
    ]]></literal>
    <justification jstring="[para(3192(a,1),18005(a,1,1,2))].">
      <j1 rule="para" parents="3192 18005"/>
    </justification>
  </clause>

  <clause id="18007">
    <literal><![CDATA[
      (x * K(a(y,x,z) \ ((y \ ((y * x) * z)) / z),x)) * a(a(y,x,z),x,x) = T((a(y,x,z) / ((y \ ((y * x) * z)) / z)) \ 1,x)
    ]]></literal>
    <justification jstring="[para(2276(a,1),18006(a,1,1,2,1))].">
      <j1 rule="para" parents="2276 18006"/>
    </justification>
  </clause>

  <clause id="18008">
    <literal><![CDATA[
      T((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,y) = (y * K(y,y)) * a(a(x,y,z),y,y)
    ]]></literal>
    <justification jstring="[para(8477(a,1),18007(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8477 18007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18009">
    <literal><![CDATA[
      T((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,y) = y * a(a(x,y,z),y,y)
    ]]></literal>
    <justification jstring="[para(194(a,1),18008(a,2,1))].">
      <j1 rule="para" parents="194 18008"/>
    </justification>
  </clause>

  <clause id="18010">
    <literal><![CDATA[
      T((a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1,y) = L(1 / y,y,a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,7299,a,b,18009,a),flip(a)].">
      <j1 rule="hyper" parents="316 7299 18009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18011">
    <literal><![CDATA[
      L(x * a(y \ (z \ ((z * x) * y)),x,x),x,x) = L(1 / x,x,a(z,x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,15986,a(flip),b,18010,a)].">
      <j1 rule="hyper" parents="63 15986 18010"/>
    </justification>
  </clause>

  <clause id="18012">
    <literal><![CDATA[
      K(x,x \ 1) / (a(y,x,z) / ((y \ ((y * x) * z)) / z)) = L(1 / x,x,a(y,x,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,17605,a(flip),b,18011,a)].">
      <j1 rule="hyper" parents="63 17605 18011"/>
    </justification>
  </clause>

  <clause id="18013">
    <literal><![CDATA[
      K(x,x \ 1) / (a(y,x,z) / ((y \ ((y * x) * z)) / z)) = L(x,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,14063,a(flip),b,18012,a),flip(a)].">
      <j1 rule="hyper" parents="316 14063 18012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18014">
    <literal><![CDATA[
      L(x,x,a(y,x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,17623,a(flip),b,18013,a),flip(a)].">
      <j1 rule="hyper" parents="63 17623 18013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18016">
    <literal><![CDATA[
      a(a(x,y,z),y,y) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,18014,a,b,7298,a),flip(a)].">
      <j1 rule="hyper" parents="134 18014 7298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18017">
    <literal><![CDATA[
      (a(x,y,z) / ((x \ ((x * y) * z)) / z)) \ 1 = y
    ]]></literal>
    <justification jstring="[hyper(63,a,14096,a(flip),b,18014,a)].">
      <j1 rule="hyper" parents="63 14096 18014"/>
    </justification>
  </clause>

  <clause id="18018">
    <literal><![CDATA[
      a(x,x,a(y,x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,18014,a(flip),b,7339,a),flip(a)].">
      <j1 rule="hyper" parents="134 18014 7339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18019">
    <literal><![CDATA[
      a(x,y,z \ a(u,z,w)) = a(x,y,z * a(u,z,w))
    ]]></literal>
    <justification jstring="[para(18014(a,1),5821(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="18014 5821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18020">
    <literal><![CDATA[
      a(x,y,z) * (y \ 1) = y \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(18014(a,1),11606(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18014 11606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18021">
    <literal><![CDATA[
      a(x,y,z) \ (y \ 1) = y \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(18014(a,1),14451(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18014 14451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18022">
    <literal><![CDATA[
      (x \ 1) * a(y,x,z) = x \ a(y,x,z)
    ]]></literal>
    <justification jstring="[para(18014(a,1),17033(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18014 17033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18023">
    <literal><![CDATA[
      L(x,y \ a(z,y,u),a(z,y,u)) = L(x,y,a(z,y,u))
    ]]></literal>
    <justification jstring="[para(18014(a,1),17106(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18014 17106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18024">
    <literal><![CDATA[
      a(x \ L(x,y,z),y,y) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,17240,a,b,18016,a)].">
      <j1 rule="hyper" parents="63 17240 18016"/>
    </justification>
  </clause>

  <clause id="18026">
    <literal><![CDATA[
      a(x,y,z) \ (y \ a(x,y,z)) = y \ 1
    ]]></literal>
    <justification jstring="[para(18016(a,1),14035(a,2,2))].">
      <j1 rule="para" parents="18016 14035"/>
    </justification>
  </clause>

  <clause id="18027">
    <literal><![CDATA[
      a(L(x,y,z) \ x,y,y) = 1
    ]]></literal>
    <justification jstring="[para(14509(a,1),18016(a,1,1))].">
      <j1 rule="para" parents="14509 18016"/>
    </justification>
  </clause>

  <clause id="18028">
    <literal><![CDATA[
      (a(x,y,z) \ y) * (y \ a(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,17812,a,b,18018,a)].">
      <j1 rule="hyper" parents="63 17812 18018"/>
    </justification>
  </clause>

  <clause id="18029">
    <literal><![CDATA[
      L(a(x,y,z),y,y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(52,a,18018,a)].">
      <j1 rule="hyper" parents="52 18018"/>
    </justification>
  </clause>

  <clause id="18030">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ 1 = y \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,18018,a(flip),b,17812,a)].">
      <j1 rule="hyper" parents="133 18018 17812"/>
    </justification>
  </clause>

  <clause id="18031">
    <literal><![CDATA[
      L(x,x,y \ L(y,x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,18024,a)].">
      <j1 rule="hyper" parents="52 18024"/>
    </justification>
  </clause>

  <clause id="18032">
    <literal><![CDATA[
      a(x,y,a(z,y,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,15308,a(flip),b,18027,a)].">
      <j1 rule="hyper" parents="63 15308 18027"/>
    </justification>
  </clause>

  <clause id="18033">
    <literal><![CDATA[
      a(x,y,a(z,y,y)) = u \ u
    ]]></literal>
    <justification jstring="[hyper(316,a,67,a,b,18032,a),flip(a)].">
      <j1 rule="hyper" parents="316 67 18032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18034">
    <literal><![CDATA[
      a(x,a(y,x,x),z) = 1
    ]]></literal>
    <justification jstring="[hyper(132,a,18032,a,b,9449,a),flip(a)].">
      <j1 rule="hyper" parents="132 18032 9449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18036">
    <literal><![CDATA[
      a(x,y,a(y,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,13660,a,b,18032,a)].">
      <j1 rule="hyper" parents="63 13660 18032"/>
    </justification>
  </clause>

  <clause id="18037">
    <literal><![CDATA[
      a(x,y,a(z,y,L(y,u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,13597,a(flip),b,18032,a)].">
      <j1 rule="hyper" parents="63 13597 18032"/>
    </justification>
  </clause>

  <clause id="18038">
    <literal><![CDATA[
      L(a(x,y,y),y,z) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(52,a,18032,a)].">
      <j1 rule="hyper" parents="52 18032"/>
    </justification>
  </clause>

  <clause id="18040">
    <literal><![CDATA[
      L(x,a(y,z,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,18034,a)].">
      <j1 rule="hyper" parents="52 18034"/>
    </justification>
  </clause>

  <clause id="18042">
    <literal><![CDATA[
      a(x,y,a(y,y,z)) = u \ u
    ]]></literal>
    <justification jstring="[hyper(316,a,67,a,b,18036,a),flip(a)].">
      <j1 rule="hyper" parents="316 67 18036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18043">
    <literal><![CDATA[
      L(x,y,a(z,y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,6997,a(flip),b,18040,a)].">
      <j1 rule="hyper" parents="63 6997 18040"/>
    </justification>
  </clause>

  <clause id="18044">
    <literal><![CDATA[
      (x * a(y,x,x)) * z = x * (a(y,x,x) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,18040,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="139 18040 18"/>
    </justification>
  </clause>

  <clause id="18045">
    <literal><![CDATA[
      a(x * (a(y,x,x) * z),u,w) = a(z * (x * a(y,x,x)),u,w)
    ]]></literal>
    <justification jstring="[para(18040(a,1),2790(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="18040 2790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18046">
    <literal><![CDATA[
      L(x,a(y,z,z),L(z,u,w)) = x
    ]]></literal>
    <justification jstring="[para(13575(a,1),18040(a,1,2))].">
      <j1 rule="para" parents="13575 18040"/>
    </justification>
  </clause>

  <clause id="18047">
    <literal><![CDATA[
      (a(x,x,y) \ z) * x = z * (a(x,x,y) \ x)
    ]]></literal>
    <justification jstring="[para(18040(a,1),16153(a,1,1,2))].">
      <j1 rule="para" parents="18040 16153"/>
    </justification>
  </clause>

  <clause id="18048">
    <literal><![CDATA[
      L(x,y,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,16986,a,b,18043,a)].">
      <j1 rule="hyper" parents="63 16986 18043"/>
    </justification>
  </clause>

  <clause id="18049">
    <literal><![CDATA[
      (x * a(y,x,x)) \ z = x \ (a(y,x,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14059,a(flip),b,18043,a),flip(a)].">
      <j1 rule="hyper" parents="63 14059 18043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18050">
    <literal><![CDATA[
      L(x,y,a(a(z,y,y),u,w)) = x
    ]]></literal>
    <justification jstring="[para(15280(a,1),18043(a,1,3))].">
      <j1 rule="para" parents="15280 18043"/>
    </justification>
  </clause>

  <clause id="18052">
    <literal><![CDATA[
      L(x,y \ (z \ y),z) = L(x,z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14179,a(flip),b,18048,a),flip(a)].">
      <j1 rule="hyper" parents="63 14179 18048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18053">
    <literal><![CDATA[
      R(x,x,y) * (x \ z) = a(x,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(34,a,16025,a(flip),b,18048,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 16025 18048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18054">
    <literal><![CDATA[
      a(x,y,y) * (z * L(y,y,x)) = z * y
    ]]></literal>
    <justification jstring="[para(18048(a,1),13875(a,2,1))].">
      <j1 rule="para" parents="18048 13875"/>
    </justification>
  </clause>

  <clause id="18055">
    <literal><![CDATA[
      a(x \ y,x,x) \ (z * (1 / (y \ (y / x)))) = z * x
    ]]></literal>
    <justification jstring="[para(18048(a,1),14893(a,2,1))].">
      <j1 rule="para" parents="18048 14893"/>
    </justification>
  </clause>

  <clause id="18056">
    <literal><![CDATA[
      (x / y) \ L(x,y,z) = y * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(18031(a,1),9756(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18031 9756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18057">
    <literal><![CDATA[
      a(x,y,L(y,y,z)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,14586,a,b,18033,a(flip))].">
      <j1 rule="hyper" parents="39 14586 18033"/>
    </justification>
  </clause>

  <clause id="18058">
    <literal><![CDATA[
      x * (L(x,x,y) \ z) = z * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,13794,a,b,18033,a(flip))].">
      <j1 rule="hyper" parents="39 13794 18033"/>
    </justification>
  </clause>

  <clause id="18059">
    <literal><![CDATA[
      L(x,a(y,x,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(39,a,9472,a,b,18033,a(flip))].">
      <j1 rule="hyper" parents="39 9472 18033"/>
    </justification>
  </clause>

  <clause id="18061">
    <literal><![CDATA[
      x * (y * a(x,x,z)) = R(x,x,z) * y
    ]]></literal>
    <justification jstring="[para(18059(a,1),16141(a,1,1))].">
      <j1 rule="para" parents="18059 16141"/>
    </justification>
  </clause>

  <clause id="18062">
    <literal><![CDATA[
      a(x,x,L(y,x,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,14578,a,b,18042,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 14578 18042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18063">
    <literal><![CDATA[
      a(x,x,y) \ (R(x,x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(39,a,9158,a,b,18042,a(flip))].">
      <j1 rule="hyper" parents="39 9158 18042"/>
    </justification>
  </clause>

  <clause id="18064">
    <literal><![CDATA[
      a(x,y,L(z,y,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,16295,a,b,18029,a)].">
      <j1 rule="hyper" parents="63 16295 18029"/>
    </justification>
  </clause>

  <clause id="18065">
    <literal><![CDATA[
      a(x,y,y \ z) = a(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15967,a(flip),b,18029,a),flip(a)].">
      <j1 rule="hyper" parents="63 15967 18029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18066">
    <literal><![CDATA[
      a(x,y,(z \ y) * y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(41,a,15968,a,b,18029,a),flip(a)].">
      <j1 rule="hyper" parents="41 15968 18029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18068">
    <literal><![CDATA[
      L(a(x,y,L(y,z,u)),y,w) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(52,a,18037,a)].">
      <j1 rule="hyper" parents="52 18037"/>
    </justification>
  </clause>

  <clause id="18069">
    <literal><![CDATA[
      a(L(x,y,z),y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16796,a,b,18038,a)].">
      <j1 rule="hyper" parents="63 16796 18038"/>
    </justification>
  </clause>

  <clause id="18072">
    <literal><![CDATA[
      a(x,y,y) * (y \ z) = L(y,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(133,a,18046,a(flip),b,10653,a),flip(a)].">
      <j1 rule="hyper" parents="133 18046 10653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18073">
    <literal><![CDATA[
      (x / y) * L(y,y,z) = a(z,y,y) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,18046,a(flip),b,10643,a),flip(a)].">
      <j1 rule="hyper" parents="133 18046 10643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18074">
    <literal><![CDATA[
      a(a(x,y,y),z,u) * (w * y) = w * (a(a(x,y,y),z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(138,a,18050,a(flip),b,5343,a),flip(a)].">
      <j1 rule="hyper" parents="138 18050 5343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18075">
    <literal><![CDATA[
      L(x,L(x,x,y),z) = a(z,x,x) \ x
    ]]></literal>
    <justification jstring="[para(18057(a,1),10018(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18057 10018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18077">
    <literal><![CDATA[
      a(x,a(y,z,u) * w,L(a(y,z,u) * w,w,a(y,z,u))) = a(x,a(y,z,u) * w,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[para(17099(a,1),18057(a,1,3))].">
      <j1 rule="para" parents="17099 18057"/>
    </justification>
  </clause>

  <clause id="18078">
    <literal><![CDATA[
      a(x,x,a(y,y,L(z,x,u))) = a(x,x,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5178,a,b,18062,a)].">
      <j1 rule="hyper" parents="63 5178 18062"/>
    </justification>
  </clause>

  <clause id="18084">
    <literal><![CDATA[
      a(L(x,y,y),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,16882,a,b,18064,a)].">
      <j1 rule="hyper" parents="63 16882 18064"/>
    </justification>
  </clause>

  <clause id="18087">
    <literal><![CDATA[
      a(x,y,y \ z) = a(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8605,a(flip),b,18064,a)].">
      <j1 rule="hyper" parents="63 8605 18064"/>
    </justification>
  </clause>

  <clause id="18088">
    <literal><![CDATA[
      a(x,y,z) * L(x,x,a(y,y,z)) = R(x,y,L(z,y,y))
    ]]></literal>
    <justification jstring="[para(18064(a,1),15390(a,1,1))].">
      <j1 rule="para" parents="18064 15390"/>
    </justification>
  </clause>

  <clause id="18089">
    <literal><![CDATA[
      L(L(x \ L(x,y,a(z,u,w)),y,y),x,(y \ 1) \ a(z,u,w)) = a(x,y,a(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[para(18064(a,1),17876(a,2,1))].">
      <j1 rule="para" parents="18064 17876"/>
    </justification>
  </clause>

  <clause id="18093">
    <literal><![CDATA[
      a(L(x,y,y),L(y,z,u),w) = a(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,13873,a(flip),b,18084,a)].">
      <j1 rule="hyper" parents="63 13873 18084"/>
    </justification>
  </clause>

  <clause id="18094">
    <literal><![CDATA[
      a(x * (y \ 1),y,z) = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13115,a(flip),b,18084,a),flip(a)].">
      <j1 rule="hyper" parents="63 13115 18084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18096">
    <literal><![CDATA[
      a(x,y,a(L(z \ u,w,v5),z,v6)) = a(x,y,a(L(z * u,w,v5),z,v6))
    ]]></literal>
    <justification jstring="[para(18084(a,1),12311(a,1,3))].">
      <j1 rule="para" parents="18084 12311"/>
    </justification>
  </clause>

  <clause id="18099">
    <literal><![CDATA[
      (x * y) \ (L(z / (x * y),y,x) \ z) = a(x,y,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13724,a,b,18065,a)].">
      <j1 rule="hyper" parents="63 13724 18065"/>
    </justification>
  </clause>

  <clause id="18100">
    <literal><![CDATA[
      a(x,y \ z,z * (y \ z)) = a(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5479,a(flip),b,18065,a),flip(a)].">
      <j1 rule="hyper" parents="63 5479 18065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18101">
    <literal><![CDATA[
      x \ ((x * y) * (y \ z)) = z * a(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,18065,a(flip),b,8451,a),flip(a)].">
      <j1 rule="hyper" parents="139 18065 8451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18102">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,w),z,y)) = a(x,y,((y / z) * L(z,u,w)) * y)
    ]]></literal>
    <justification jstring="[para(7101(a,2),18065(a,1,3))].">
      <j1 rule="para" parents="7101 18065"/>
    </justification>
  </clause>

  <clause id="18103">
    <literal><![CDATA[
      a(x,y * z,y \ ((y / z) * L(z,u,w))) = a(x,y * z,(y * L(z,u,w)) * (y * z))
    ]]></literal>
    <justification jstring="[para(7109(a,1),18065(a,1,3))].">
      <j1 rule="para" parents="7109 18065"/>
    </justification>
  </clause>

  <clause id="18108">
    <literal><![CDATA[
      L(x,y,z) = a(z,y,(x \ y) * y) \ x
    ]]></literal>
    <justification jstring="[para(18065(a,1),14511(a,2,1))].">
      <j1 rule="para" parents="18065 14511"/>
    </justification>
  </clause>

  <clause id="18109">
    <literal><![CDATA[
      a(a(x,y,z),u,w * u) \ v5 = a(u \ w,u,a(x,y,z)) * v5
    ]]></literal>
    <justification jstring="[para(18065(a,1),14440(a,1,1))].">
      <j1 rule="para" parents="18065 14440"/>
    </justification>
  </clause>

  <clause id="18110">
    <literal><![CDATA[
      ((x / y) * (y * a(z,u,w))) / x = a(z,u,w) * a(a(z,u,w),y,x * y)
    ]]></literal>
    <justification jstring="[para(18065(a,1),14655(a,2,2))].">
      <j1 rule="para" parents="18065 14655"/>
    </justification>
  </clause>

  <clause id="18115">
    <literal><![CDATA[
      a(x,y * z,L(z \ u,z,y)) = a(x,y * z,(y * z) * (u * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,5612,a,b,18087,a)].">
      <j1 rule="hyper" parents="63 5612 18087"/>
    </justification>
  </clause>

  <clause id="18116">
    <literal><![CDATA[
      a(x,y,y * (z \ y)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,14509,a(flip),b,18087,a),flip(a)].">
      <j1 rule="hyper" parents="63 14509 18087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18118">
    <literal><![CDATA[
      a(x,y,y * (z * (L(z,u,w) \ y))) \ 1 = a(y \ (z * (L(z,u,w) \ y)),y,x)
    ]]></literal>
    <justification jstring="[para(18087(a,1),15092(a,1,1))].">
      <j1 rule="para" parents="18087 15092"/>
    </justification>
  </clause>

  <clause id="18120">
    <literal><![CDATA[
      L(x,L(x,x,y),z) = L(x,x,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,7297,a(flip),b,18075,a),flip(a)].">
      <j1 rule="hyper" parents="316 7297 18075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18121">
    <literal><![CDATA[
      L(x,x,L(y,x,z)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16803,a(flip),b,18120,a)].">
      <j1 rule="hyper" parents="63 16803 18120"/>
    </justification>
  </clause>

  <clause id="18122">
    <literal><![CDATA[
      L(L(x,y,z),L(x,x,u),w) = L(L(x,x,w),y,z)
    ]]></literal>
    <justification jstring="[para(18120(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18120 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18125">
    <literal><![CDATA[
      L(L(x,y,z),x,L(u,x,w)) = L(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(18121(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18121 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18128">
    <literal><![CDATA[
      a(x,L(y,z,u),L(z,z,y)) = L(z,L(y,z,u),x) \ z
    ]]></literal>
    <justification jstring="[para(18121(a,1),14510(a,1,3))].">
      <j1 rule="para" parents="18121 14510"/>
    </justification>
  </clause>

  <clause id="18129">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (L(x,y,z) * (x \ a(u,x,w))) = L(a(u,x,w),x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(18022(a,1),974(a,1,2,2))].">
      <j1 rule="para" parents="18022 974"/>
    </justification>
  </clause>

  <clause id="18130">
    <literal><![CDATA[
      x * (a(y,x,z) * L(x \ 1,u,w)) = a(y,x,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(18026(a,1),5105(a,1,2,2,1))].">
      <j1 rule="para" parents="18026 5105"/>
    </justification>
  </clause>

  <clause id="18131">
    <literal><![CDATA[
      1 / (a(x,y,z) \ y) = a(x,y,z) / y
    ]]></literal>
    <justification jstring="[hyper(136,a,18028,a(flip),b,5354,a(flip))].">
      <j1 rule="hyper" parents="136 18028 5354"/>
    </justification>
  </clause>

  <clause id="18132">
    <literal><![CDATA[
      (L(x \ 1,y,z) * y) \ R(x \ 1,y * a(x,y,z),y * a(z,y,x)) = y \ a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,16599,a,b,18030,a)].">
      <j1 rule="hyper" parents="63 16599 18030"/>
    </justification>
  </clause>

  <clause id="18142">
    <literal><![CDATA[
      (x * y) * (L(x * y,x \ 1,x) \ z) = (z / (x * y)) * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(18052(a,1),14270(a,1,2,1))].">
      <j1 rule="para" parents="18052 14270"/>
    </justification>
  </clause>

  <clause id="18144">
    <literal><![CDATA[
      x * (R(x,x,y) \ z) = a(x,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(133,a,75,a(flip),b,18053,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 75 18053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18148">
    <literal><![CDATA[
      x * (L(x,x,a(y,z,z)) \ L(x \ L(x,z,y),u,w)) = a(y,z,L(x,u,w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,15535,a(flip),b,18058,a),flip(a)].">
      <j1 rule="hyper" parents="316 15535 18058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18149">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (L(x \ 1,z,u) * w) = (L(x,z,u) * (x \ w)) * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9090,a,b,18058,a)].">
      <j1 rule="hyper" parents="63 9090 18058"/>
    </justification>
  </clause>

  <clause id="18150">
    <literal><![CDATA[
      (x / y) * a(z,y,y) = x / L(y,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4400,a(flip),b,18058,a),flip(a)].">
      <j1 rule="hyper" parents="63 4400 18058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18152">
    <literal><![CDATA[
      (L(1 / x,x,y) \ 1) * z = x * (z * a(y,x,x))
    ]]></literal>
    <justification jstring="[para(18058(a,1),13802(a,2,2))].">
      <j1 rule="para" parents="18058 13802"/>
    </justification>
  </clause>

  <clause id="18155">
    <literal><![CDATA[
      R(x,x,x * y) * y = (x * x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8553,a(flip),b,18061,a),flip(a)].">
      <j1 rule="hyper" parents="63 8553 18061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18157">
    <literal><![CDATA[
      a(x,y,((z \ u) \ y) * y) = u \ (L(z / u,y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,13906,a(flip),b,18066,a),flip(a)].">
      <j1 rule="hyper" parents="316 13906 18066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18158">
    <literal><![CDATA[
      x * a(y,z,(x \ z) * z) = L(1 / x,z,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,18066,a,b,6591,a)].">
      <j1 rule="hyper" parents="139 18066 6591"/>
    </justification>
  </clause>

  <clause id="18159">
    <literal><![CDATA[
      a(x,y,(z \ y) * y) * u = u * (L(z,y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,18066,a(flip),b,2295,a),flip(a)].">
      <j1 rule="hyper" parents="139 18066 2295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18160">
    <literal><![CDATA[
      a(x,y,a(z,u,(w \ u) * u)) = a(x,y,w * L(w,u,z))
    ]]></literal>
    <justification jstring="[para(18066(a,2),2652(a,1,3))].">
      <j1 rule="para" parents="18066 2652"/>
    </justification>
  </clause>

  <clause id="18161">
    <literal><![CDATA[
      L(x,x,a(y,z,(u \ z) * z)) = L(x,x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[para(18066(a,2),8823(a,1,3))].">
      <j1 rule="para" parents="18066 8823"/>
    </justification>
  </clause>

  <clause id="18162">
    <literal><![CDATA[
      L(x,y,a(z,u,(w \ u) * u)) = L(x,y,w \ L(w,u,z))
    ]]></literal>
    <justification jstring="[para(18066(a,2),9212(a,1,3))].">
      <j1 rule="para" parents="18066 9212"/>
    </justification>
  </clause>

  <clause id="18163">
    <literal><![CDATA[
      L(x,a(y,z,(u \ z) * z),w) = L(x,u \ L(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(18066(a,2),12400(a,1,2))].">
      <j1 rule="para" parents="18066 12400"/>
    </justification>
  </clause>

  <clause id="18167">
    <literal><![CDATA[
      a(x,y,(z \ y) * y) \ u = u * (z \ L(z,y,x))
    ]]></literal>
    <justification jstring="[para(18066(a,2),14358(a,1,1))].">
      <j1 rule="para" parents="18066 14358"/>
    </justification>
  </clause>

  <clause id="18169">
    <literal><![CDATA[
      L(x,x,y \ L(y,z,u)) \ w = a(a(y,x,x),z,u) * (x \ w)
    ]]></literal>
    <justification jstring="[para(15280(a,1),18072(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15280 18072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18170">
    <literal><![CDATA[
      L(L(L(x,x,y) \ x,z / x,u),x,L(u * (z / x),z / x,u)) = (u * (a(y,x,x) \ z)) \ (u * ((z / x) * x))
    ]]></literal>
    <justification jstring="[para(18073(a,1),16493(a,2,1,2))].">
      <j1 rule="para" parents="18073 16493"/>
    </justification>
  </clause>

  <clause id="18174">
    <literal><![CDATA[
      a(x,y,a(z,u,u * (w \ u))) = a(x,y,w * L(w,u,z))
    ]]></literal>
    <justification jstring="[para(18116(a,2),2652(a,1,3))].">
      <j1 rule="para" parents="18116 2652"/>
    </justification>
  </clause>

  <clause id="18175">
    <literal><![CDATA[
      a(x,y,y * (z \ y)) \ u = u * (z \ L(z,y,x))
    ]]></literal>
    <justification jstring="[para(18116(a,2),14358(a,1,1))].">
      <j1 rule="para" parents="18116 14358"/>
    </justification>
  </clause>

  <clause id="18176">
    <literal><![CDATA[
      a(x,y,z) \ (1 / (1 / y)) = 1 / (a(x,y,z) / y)
    ]]></literal>
    <justification jstring="[hyper(209,a,18131,a(flip),b,7503,a),flip(a)].">
      <j1 rule="hyper" parents="209 18131 7503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18177">
    <literal><![CDATA[
      a(x,x,y) \ (a(z,u,x) * y) = L(a(z,u,x) * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7474,a(flip),b,18144,a),flip(a)].">
      <j1 rule="hyper" parents="63 7474 18144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18179">
    <literal><![CDATA[
      ((x * (y * z)) / L(z,z,y)) \ ((a(y,z,z) * x) * y) = a(a(y,z,z) * x,y,z)
    ]]></literal>
    <justification jstring="[para(18150(a,1),9248(a,1,1))].">
      <j1 rule="para" parents="18150 9248"/>
    </justification>
  </clause>

  <clause id="18180">
    <literal><![CDATA[
      a(x,y,R(z,z,z * (((u * (w / v5)) * v6) * v7)) * (((u * (v5 \ w)) * v6) * v7)) = a(x,y,(z * z) * (z \ (((u * (w / v5)) * v6) * v7)))
    ]]></literal>
    <justification jstring="[para(18155(a,1),9550(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18155 9550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18181">
    <literal><![CDATA[
      x \ (a(x \ y,x,x) \ ((y / x) \ (y * (1 / (y \ (y / x)))))) = 1 / (y \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,12847,a(flip),b,18049,a),flip(a)].">
      <j1 rule="hyper" parents="63 12847 18049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18182">
    <literal><![CDATA[
      L(x \ L(x,y,z),y,y) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,12512,a,b,18056,a(flip))].">
      <j1 rule="hyper" parents="34 12512 18056"/>
    </justification>
  </clause>

  <clause id="18184">
    <literal><![CDATA[
      ((x \ ((x * y) * z)) / z) \ a(x,y,z) = y \ 1
    ]]></literal>
    <justification jstring="[para(18017(a,1),5272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18017 5272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18185">
    <literal><![CDATA[
      a(x,y,L(L(y,z,u),y,w)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13557,a,b,18068,a)].">
      <j1 rule="hyper" parents="63 13557 18068"/>
    </justification>
  </clause>

  <clause id="18186">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (R(y,z,z) * z)) = a(y,z,L(z,L(y,z,z),x))
    ]]></literal>
    <justification jstring="[hyper(63,a,16497,a(flip),b,18068,a)].">
      <j1 rule="hyper" parents="63 16497 18068"/>
    </justification>
  </clause>

  <clause id="18187">
    <literal><![CDATA[
      a(x,y,a(L(z,y,u),x,y)) = a(y,y,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15345,a,b,18078,a)].">
      <j1 rule="hyper" parents="63 15345 18078"/>
    </justification>
  </clause>

  <clause id="18188">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) * a(y \ x,y \ x,a(z,z,u)) = L(a(u,z,y \ x) \ 1,y \ x,y)
    ]]></literal>
    <justification jstring="[para(18078(a,1),16428(a,1,2))].">
      <j1 rule="para" parents="18078 16428"/>
    </justification>
  </clause>

  <clause id="18189">
    <literal><![CDATA[
      (x * y) / ((L(x,y,y) * (R(y,y,x) * z)) / z) = a(x,L(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12633,a,b,18093,a)].">
      <j1 rule="hyper" parents="63 12633 18093"/>
    </justification>
  </clause>

  <clause id="18190">
    <literal><![CDATA[
      x \ ((x * ((y / z) \ 1)) * T(y / z,y \ z)) = 1 * a(x,(y / z) \ 1,1 * ((y / z) \ 1))
    ]]></literal>
    <justification jstring="[para(2446(a,2),18101(a,1,2,2))].">
      <j1 rule="para" parents="2446 18101"/>
    </justification>
  </clause>

  <clause id="18191">
    <literal><![CDATA[
      x \ ((x * (y \ z)) * ((y \ z) \ u)) = u * a(x,z / y,u * (z / y))
    ]]></literal>
    <justification jstring="[para(10657(a,1),18101(a,1,2))].">
      <j1 rule="para" parents="10657 18101"/>
    </justification>
  </clause>

  <clause id="18192">
    <literal><![CDATA[
      a(x,y,L(L(z,z,y),z,u)) = L(L(z,y,x) \ z,z,u)
    ]]></literal>
    <justification jstring="[para(18122(a,1),14895(a,1,3))].">
      <j1 rule="para" parents="18122 14895"/>
    </justification>
  </clause>

  <clause id="18193">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(x,u,w) \ v5) = a(z,y,L(L(x,x,y),x,x \ v5))
    ]]></literal>
    <justification jstring="[para(18125(a,1),16849(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18125 16849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18195">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ (((x \ ((x * y) * z)) / z) \ a(x,y,z)),u,w) = (y \ 1) * (((x \ ((x * y) * z)) / z) \ L((x \ ((x * y) * z)) / z,u,w))
    ]]></literal>
    <justification jstring="[para(18184(a,1),5107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18184 5107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18196">
    <literal><![CDATA[
      a(x,y,(y \ z) * z) = a(x,y,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6703,a(flip),b,18185,a)].">
      <j1 rule="hyper" parents="63 6703 18185"/>
    </justification>
  </clause>

  <clause id="18197">
    <literal><![CDATA[
      a(x,y,(y \ z) * z) * x = R(x,y,L(y,z,z))
    ]]></literal>
    <justification jstring="[para(18196(a,2),7940(a,1,1))].">
      <j1 rule="para" parents="18196 7940"/>
    </justification>
  </clause>

  <clause id="18198">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) * L(L(x,y,z) \ x,x,u) = L(a(z,y,x),x,u)
    ]]></literal>
    <justification jstring="[para(18187(a,1),16290(a,1,1))].">
      <j1 rule="para" parents="18187 16290"/>
    </justification>
  </clause>

  <clause id="18203">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * L(1 / v5,v5,v6)))) = a(x,y,z \ (u \ (v5 * (w * a(v6,v5,v5)))))
    ]]></literal>
    <justification jstring="[para(18152(a,1),7736(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="18152 7736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18204">
    <literal><![CDATA[
      L(a(x,y,(z \ y) * y) \ u,a(x,y,(z \ y) * y),w) = (w * (L(z,y,x) \ z)) \ (w * u)
    ]]></literal>
    <justification jstring="[para(18159(a,1),2334(a,2,1))].">
      <j1 rule="para" parents="18159 2334"/>
    </justification>
  </clause>

  <clause id="18205">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ y) * y) \ v5 = v5 * L(z \ L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(2136(a,1),18167(a,2,2))].">
      <j1 rule="para" parents="2136 18167"/>
    </justification>
  </clause>

  <clause id="18206">
    <literal><![CDATA[
      a(x,y,y * (z \ y)) \ a(u,z \ L(z,y,x),w) = (u \ ((u * (z \ L(z,y,x))) * w)) / w
    ]]></literal>
    <justification jstring="[hyper(316,a,8461,a,b,18175,a),flip(a)].">
      <j1 rule="hyper" parents="316 8461 18175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18207">
    <literal><![CDATA[
      a(x,y,y * (z \ y)) \ L(z,u,a(w,v5,v6)) = z * (L(z,u,a(w,v5,v6)) \ L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,14062,a(flip),b,18175,a),flip(a)].">
      <j1 rule="hyper" parents="316 14062 18175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18208">
    <literal><![CDATA[
      a(x * (y \ x),x,a(z,u,w)) = y \ L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(38,a,14440,a,b,18175,a),flip(a)].">
      <j1 rule="hyper" parents="38 14440 18175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18209">
    <literal><![CDATA[
      L((a(x,y,y * ((z \ u) \ y)) \ w) / w,z \ u,z) = (w * (u \ (z * L(z \ u,y,x)))) / w
    ]]></literal>
    <justification jstring="[para(18175(a,2),769(a,1,1,1))].">
      <j1 rule="para" parents="18175 769"/>
    </justification>
  </clause>

  <clause id="18211">
    <literal><![CDATA[
      x * L((x \ 1) * L(x,x,y),z,u) = 1 / (a(y,x,L(x,z,u)) / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,14265,a(flip),b,18176,a)].">
      <j1 rule="hyper" parents="63 14265 18176"/>
    </justification>
  </clause>

  <clause id="18212">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),L(T(1 / (1 / y),x),z,u),w) = T(1 / (a(w,y,L(y,z,u)) / y),x)
    ]]></literal>
    <justification jstring="[para(18176(a,1),13152(a,2,1))].">
      <j1 rule="para" parents="18176 13152"/>
    </justification>
  </clause>

  <clause id="18215">
    <literal><![CDATA[
      R(x,y,L(z,y,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,15386,a,b,18088,a),flip(a)].">
      <j1 rule="hyper" parents="63 15386 18088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18216">
    <literal><![CDATA[
      R(x,y,y \ z) = R(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,11676,a(flip),b,18215,a)].">
      <j1 rule="hyper" parents="63 11676 18215"/>
    </justification>
  </clause>

  <clause id="18217">
    <literal><![CDATA[
      L(x \ R(x,y,z),y,y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(18215(a,1),16316(a,2,2))].">
      <j1 rule="para" parents="18215 16316"/>
    </justification>
  </clause>

  <clause id="18218">
    <literal><![CDATA[
      R(x \ R(x,y,z),u,w * u) = L(x \ R(x,y,z),u,u \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15885,a(flip),b,18216,a),flip(a)].">
      <j1 rule="hyper" parents="63 15885 18216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18219">
    <literal><![CDATA[
      a(x,y,R(z,u,w * u)) = a(x,y,L(z,u,u \ w))
    ]]></literal>
    <justification jstring="[para(18216(a,1),5746(a,1,3))].">
      <j1 rule="para" parents="18216 5746"/>
    </justification>
  </clause>

  <clause id="18220">
    <literal><![CDATA[
      L(a(x,y,z),y * x,y * x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,16890,a,b,18217,a)].">
      <j1 rule="hyper" parents="63 16890 18217"/>
    </justification>
  </clause>

  <clause id="18221">
    <literal><![CDATA[
      a(x,y,L(z,u,u \ w)) = a(x,y,L(z,u,w * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5746,a(flip),b,18219,a),flip(a)].">
      <j1 rule="hyper" parents="63 5746 18219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18222">
    <literal><![CDATA[
      a(x,y,L(z * a(u,z,u * w),u,w * u)) = a(x,y,L(z,u \ w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15522,a(flip),b,18221,a),flip(a)].">
      <j1 rule="hyper" parents="63 15522 18221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18228">
    <literal><![CDATA[
      a(x,y,a(z * (u \ z),z,w)) = a(x,y,u * L(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,13687,a,b,18160,a)].">
      <j1 rule="hyper" parents="63 13687 18160"/>
    </justification>
  </clause>

  <clause id="18229">
    <literal><![CDATA[
      a(a(x,y,(z \ y) * y),u,u) = L(u,u,z \ L(z,y,x)) \ u
    ]]></literal>
    <justification jstring="[para(18161(a,1),7290(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18161 7290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18230">
    <literal><![CDATA[
      L(x,a(y,z,u),a(w,v5,(v6 \ v5) * v5)) = L(x,a(u,z,y),v6 \ L(v6,v5,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,16124,a,b,18162,a),flip(a)].">
      <j1 rule="hyper" parents="316 16124 18162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18231">
    <literal><![CDATA[
      a(x,y,L(z,a(u,w,(v5 \ w) * w),v6)) = a(x,y,L(z,v5 * L(v5,w,u),v6))
    ]]></literal>
    <justification jstring="[para(18163(a,2),10969(a,1,3))].">
      <j1 rule="para" parents="18163 10969"/>
    </justification>
  </clause>

  <clause id="18234">
    <literal><![CDATA[
      a(x,y,a(y,z,z * (u \ z))) = a(a(x,y,u),z,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,17241,a(flip),b,18174,a),flip(a)].">
      <j1 rule="hyper" parents="316 17241 18174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18235">
    <literal><![CDATA[
      a(x,a(x,y,y * (z \ y)),u) = a(a(u,x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13710,a,b,18234,a)].">
      <j1 rule="hyper" parents="63 13710 18234"/>
    </justification>
  </clause>

  <clause id="18236">
    <literal><![CDATA[
      a(x,a(y * (z \ y),y,x),u) = a(a(u,x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13681,a,b,18234,a)].">
      <j1 rule="hyper" parents="63 13681 18234"/>
    </justification>
  </clause>

  <clause id="18238">
    <literal><![CDATA[
      a(x,x,a(y,z,x) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(39,a,4950,a,b,18177,a)].">
      <j1 rule="hyper" parents="39 4950 18177"/>
    </justification>
  </clause>

  <clause id="18239">
    <literal><![CDATA[
      a(x,x,a(x,y,z) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17370,a(flip),b,18238,a)].">
      <j1 rule="hyper" parents="63 17370 18238"/>
    </justification>
  </clause>

  <clause id="18242">
    <literal><![CDATA[
      (1 / x) \ a(y * (x \ y),y,a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(133,a,18208,a,b,1458,a)].">
      <j1 rule="hyper" parents="133 18208 1458"/>
    </justification>
  </clause>

  <clause id="18243">
    <literal><![CDATA[
      a(x * (a(y,x,x) * (z \ (x * a(y,x,x)))),x * a(y,x,x),a(u,w,v5)) = z \ L(z,x * a(y,x,x),a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(18044(a,1),18208(a,1,1))].">
      <j1 rule="para" parents="18044 18208"/>
    </justification>
  </clause>

  <clause id="18244">
    <literal><![CDATA[
      a(x,y,a(L(z,z,u) * ((L(z,z,u) \ w) \ L(z,z,u)),L(z,z,u),u)) = a(x,y,(L(z,z,u) \ w) * ((u / (z \ 1)) \ (u * w)))
    ]]></literal>
    <justification jstring="[para(1449(a,1),18228(a,2,3,2))].">
      <j1 rule="para" parents="1449 18228"/>
    </justification>
  </clause>

  <clause id="18245">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(z \ u,u,w)) = a(x,y,a(z * u,u,w))
    ]]></literal>
    <justification jstring="[para(3146(a,1),18228(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3146 18228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18248">
    <literal><![CDATA[
      a(x * (a(y,x,x) * z),u,w) = a(z * L(x,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,14085,a(flip),b,18045,a),flip(a)].">
      <j1 rule="hyper" parents="316 14085 18045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18249">
    <literal><![CDATA[
      a(a(x,y,y),z,u) * (w * y) = w * L(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(15409(a,2),18074(a,2,2))].">
      <j1 rule="para" parents="15409 18074"/>
    </justification>
  </clause>

  <clause id="18250">
    <literal><![CDATA[
      a(x,y,((z \ (x * y)) \ y) * y) = a(x,y,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,18157,a,b,18099,a)].">
      <j1 rule="hyper" parents="63 18157 18099"/>
    </justification>
  </clause>

  <clause id="18251">
    <literal><![CDATA[
      a(x \ y,x,a(z,u,w)) * v5 = a(y * x,x,a(z,u,w)) * v5
    ]]></literal>
    <justification jstring="[hyper(63,a,14440,a(flip),b,18109,a),flip(a)].">
      <j1 rule="hyper" parents="63 14440 18109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18252">
    <literal><![CDATA[
      a(x \ y,x,a(z,u,w)) = a(y * x,x,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(38,a,14560,a,b,18109,a)].">
      <j1 rule="hyper" parents="38 14560 18109"/>
    </justification>
  </clause>

  <clause id="18253">
    <literal><![CDATA[
      (a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w)))) \ u = a(u * (z \ w),z \ w,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,14841,a,b,18252,a)].">
      <j1 rule="hyper" parents="63 14841 18252"/>
    </justification>
  </clause>

  <clause id="18254">
    <literal><![CDATA[
      (a(x,y,z) * ((u / (w * z)) * ((a(x,y,z) \ w) * z))) \ u = a(u * (w * z),w * z,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,14840,a,b,18252,a)].">
      <j1 rule="hyper" parents="63 14840 18252"/>
    </justification>
  </clause>

  <clause id="18258">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,u \ w) = L(x \ R(x,y,z),u,w * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15885,a(flip),b,18218,a),flip(a)].">
      <j1 rule="hyper" parents="63 15885 18218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18259">
    <literal><![CDATA[
      (1 / x) \ a(y * (x \ y),y,a(z,z,a(u,w,w))) = L(x,y,a(w,w,a(u,z,z)))
    ]]></literal>
    <justification jstring="[para(15286(a,1),18242(a,1,2,3))].">
      <j1 rule="para" parents="15286 18242"/>
    </justification>
  </clause>

  <clause id="18260">
    <literal><![CDATA[
      a(x,y,a(z \ u,z,w)) = a(x,y,a(u * z,z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,13990,a(flip),b,18245,a)].">
      <j1 rule="hyper" parents="63 13990 18245"/>
    </justification>
  </clause>

  <clause id="18261">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((z \ (u \ w)) \ w)) = a(x,y,a((u \ w) * z,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8772,a,b,18260,a)].">
      <j1 rule="hyper" parents="63 8772 18260"/>
    </justification>
  </clause>

  <clause id="18262">
    <literal><![CDATA[
      a(x * y,y,a(z,u,w)) * a(y,a(z,u,w),y \ x) = y \ L(y,y \ x,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17869,a(flip),b,18251,a),flip(a)].">
      <j1 rule="hyper" parents="63 17869 18251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18263">
    <literal><![CDATA[
      a(x * y,y,a(z,u,w)) * x = a(z,u,w) * ((x / y) * (a(z,u,w) \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14827,a(flip),b,18251,a),flip(a)].">
      <j1 rule="hyper" parents="63 14827 18251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18264">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,(x \ 1) * u) = (1 / (u * x)) * (u * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16785,a(flip),b,18258,a),flip(a)].">
      <j1 rule="hyper" parents="63 16785 18258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18265">
    <literal><![CDATA[
      a(x,y * z,L(z \ L(z,u,w),z,y)) = a(x,y * z,L(z * L(z,u,w),y,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,11991,a(flip),b,18115,a),flip(a)].">
      <j1 rule="hyper" parents="316 11991 18115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18266">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((R(u,w,w) \ w) \ (z * L(w,w,u)))) = a(x,y,a(L(u * w,w,w),u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12295,a,b,18096,a)].">
      <j1 rule="hyper" parents="63 12295 18096"/>
    </justification>
  </clause>

  <clause id="18267">
    <literal><![CDATA[
      L(a(x,y,z),y,L(y,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,12287,a,b,18130,a(flip))].">
      <j1 rule="hyper" parents="35 12287 18130"/>
    </justification>
  </clause>

  <clause id="18268">
    <literal><![CDATA[
      L(a(x,y,z),y \ 1,L(y,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8806,a,b,18267,a)].">
      <j1 rule="hyper" parents="63 8806 18267"/>
    </justification>
  </clause>

  <clause id="18271">
    <literal><![CDATA[
      a(x,y,L(y,L(x,y,y),z)) = L(a(x,y,y),x * y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14876,a(flip),b,18186,a),flip(a)].">
      <j1 rule="hyper" parents="63 14876 18186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18272">
    <literal><![CDATA[
      a(x,y,L(y,L(x,y,y),z)) = a(x,y,L(y,x * y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,13562,a,b,18271,a),flip(a)].">
      <j1 rule="hyper" parents="316 13562 18271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18273">
    <literal><![CDATA[
      a(x,y,y) \ a(x,y,L(y,x * y,z)) = a(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(18272(a,1),14784(a,1,2))].">
      <j1 rule="para" parents="18272 14784"/>
    </justification>
  </clause>

  <clause id="18274">
    <literal><![CDATA[
      a(x \ L(x,x,y),y * x,z) = a(z,y,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,17252,a(flip),b,18273,a)].">
      <j1 rule="hyper" parents="63 17252 18273"/>
    </justification>
  </clause>

  <clause id="18275">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) = L(a(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15457,a(flip),b,18198,a)].">
      <j1 rule="hyper" parents="63 15457 18198"/>
    </justification>
  </clause>

  <clause id="18276">
    <literal><![CDATA[
      a(x,y,z) * a(z,a(x,y,z),u) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,11611,a,b,18275,a)].">
      <j1 rule="hyper" parents="316 11611 18275"/>
    </justification>
  </clause>

  <clause id="18278">
    <literal><![CDATA[
      L(a(x,y,z \ u),u * z,u) = a(x,y,L(z \ u,z \ u,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,16356,a(flip),b,18275,a)].">
      <j1 rule="hyper" parents="316 16356 18275"/>
    </justification>
  </clause>

  <clause id="18279">
    <literal><![CDATA[
      a(x,y,L(z,z,x * y)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(316,a,13719,a(flip),b,18275,a),flip(a)].">
      <j1 rule="hyper" parents="316 13719 18275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18280">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,z,u) = a(x,y,L(z,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(18275(a,2),13442(a,2,1))].">
      <j1 rule="para" parents="18275 13442"/>
    </justification>
  </clause>

  <clause id="18282">
    <literal><![CDATA[
      a(x,y,L(z * (x * y),(x * y) * z,x * y)) = L(z * (x * y),y,x) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[para(3462(a,1),18279(a,1,3))].">
      <j1 rule="para" parents="3462 18279"/>
    </justification>
  </clause>

  <clause id="18284">
    <literal><![CDATA[
      L(a(x,y,z \ u) \ 1,z \ u,z) = a(x,y,u \ z) \ 1
    ]]></literal>
    <justification jstring="[para(2657(a,1),18280(a,2,1))].">
      <j1 rule="para" parents="2657 18280"/>
    </justification>
  </clause>

  <clause id="18285">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) = a(y,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(34,a,17254,a,b,18276,a)].">
      <j1 rule="hyper" parents="34 17254 18276"/>
    </justification>
  </clause>

  <clause id="18286">
    <literal><![CDATA[
      a(x \ L(x,y,z),x,u) = a(x,a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(34,a,17253,a,b,18276,a)].">
      <j1 rule="hyper" parents="34 17253 18276"/>
    </justification>
  </clause>

  <clause id="18290">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) \ a(x,y,y) = a(y,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,17234,a,b,18285,a)].">
      <j1 rule="hyper" parents="63 17234 18285"/>
    </justification>
  </clause>

  <clause id="18291">
    <literal><![CDATA[
      a(x \ L(x,x,y),z,u) = a(x,a(u,z,x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15295,a,b,18285,a)].">
      <j1 rule="hyper" parents="63 15295 18285"/>
    </justification>
  </clause>

  <clause id="18292">
    <literal><![CDATA[
      a(a(x,y,y),z,u) = a(y,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,15309,a(flip),b,18285,a)].">
      <j1 rule="hyper" parents="63 15309 18285"/>
    </justification>
  </clause>

  <clause id="18293">
    <literal><![CDATA[
      L(x,y,y \ L(y,z,u)) = x * a(y,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(139,a,18285,a(flip),b,8241,a),flip(a)].">
      <j1 rule="hyper" parents="139 18285 8241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18294">
    <literal><![CDATA[
      L(x \ y,y,y \ L(y,z,u)) = a(y,a(u,z,y),x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(18285(a,1),8244(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18285 8244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18295">
    <literal><![CDATA[
      L(x,y,z) * a(x,a(z,y,x),u) = x * L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(18285(a,1),13923(a,1,2))].">
      <j1 rule="para" parents="18285 13923"/>
    </justification>
  </clause>

  <clause id="18299">
    <literal><![CDATA[
      a(a(x,y,y),z,u) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,13681,a(flip),b,18292,a),flip(a)].">
      <j1 rule="hyper" parents="316 13681 18292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18301">
    <literal><![CDATA[
      a(x,x,y * L(y,z,u)) = a(x,a(u,z,x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15282,a,b,18292,a)].">
      <j1 rule="hyper" parents="63 15282 18292"/>
    </justification>
  </clause>

  <clause id="18302">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,u) = a(u,a(z,y,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,15280,a,b,18292,a)].">
      <j1 rule="hyper" parents="63 15280 18292"/>
    </justification>
  </clause>

  <clause id="18303">
    <literal><![CDATA[
      a(a(x,x,y),z,u) = a(x,a(u,z,x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14029,a,b,18292,a)].">
      <j1 rule="hyper" parents="63 14029 18292"/>
    </justification>
  </clause>

  <clause id="18304">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(y,z,a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14012,a(flip),b,18292,a),flip(a)].">
      <j1 rule="hyper" parents="63 14012 18292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18305">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(y,z,a(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,14010,a(flip),b,18292,a),flip(a)].">
      <j1 rule="hyper" parents="63 14010 18292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18307">
    <literal><![CDATA[
      x * a(y,a(z,u,y),w) = x * a(z,u,a(y,y,w))
    ]]></literal>
    <justification jstring="[para(18292(a,1),13707(a,1,2))].">
      <j1 rule="para" parents="18292 13707"/>
    </justification>
  </clause>

  <clause id="18309">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * a(y,y,a(u,z,a(x,x,z))) = L(y,z,a(u,x,x)) \ y
    ]]></literal>
    <justification jstring="[para(18292(a,1),15418(a,1,1))].">
      <j1 rule="para" parents="18292 15418"/>
    </justification>
  </clause>

  <clause id="18310">
    <literal><![CDATA[
      L(x,y,a(y,a(z,u,y),w)) = x
    ]]></literal>
    <justification jstring="[para(18292(a,1),18050(a,1,3))].">
      <j1 rule="para" parents="18292 18050"/>
    </justification>
  </clause>

  <clause id="18311">
    <literal><![CDATA[
      L(x,x,y \ L(y,z,u)) \ w = a(x,a(u,z,x),y) * (x \ w)
    ]]></literal>
    <justification jstring="[para(18292(a,1),18169(a,2,1))].">
      <j1 rule="para" parents="18292 18169"/>
    </justification>
  </clause>

  <clause id="18312">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * (w * x) = w * L(x,x \ L(x,z,y),u)
    ]]></literal>
    <justification jstring="[para(18292(a,1),18249(a,1,1))].">
      <j1 rule="para" parents="18292 18249"/>
    </justification>
  </clause>

  <clause id="18313">
    <literal><![CDATA[
      x * (L(x,a(y,z,x),u) \ w) = w * a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,17275,a(flip),b,18310,a)].">
      <j1 rule="hyper" parents="63 17275 18310"/>
    </justification>
  </clause>

  <clause id="18315">
    <literal><![CDATA[
      a(x,x,L(y,z,u) \ y) = a(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15281,a,b,18299,a)].">
      <j1 rule="hyper" parents="63 15281 18299"/>
    </justification>
  </clause>

  <clause id="18316">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) = a(u,z,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,14012,a(flip),b,18299,a)].">
      <j1 rule="hyper" parents="63 14012 18299"/>
    </justification>
  </clause>

  <clause id="18317">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) = a(z,u,a(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,14010,a(flip),b,18299,a)].">
      <j1 rule="hyper" parents="63 14010 18299"/>
    </justification>
  </clause>

  <clause id="18320">
    <literal><![CDATA[
      a(x \ a(y,z,u),x,a(a(u,z,y),w,v5)) = a(x,a(v5,w,x),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17926,a,b,18303,a)].">
      <j1 rule="hyper" parents="63 17926 18303"/>
    </justification>
  </clause>

  <clause id="18321">
    <literal><![CDATA[
      x * a(x,y,a(z,a(y,u,z),w)) = L(x,y,a(a(z,z,w),u,y))
    ]]></literal>
    <justification jstring="[para(18303(a,1),11690(a,1,2,3))].">
      <j1 rule="para" parents="18303 11690"/>
    </justification>
  </clause>

  <clause id="18322">
    <literal><![CDATA[
      a(x,a(y,z,x),a(u,w,v5)) = a(x,x,a(y,z,a(v5,w,u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,17920,a,b,18304,a),flip(a)].">
      <j1 rule="hyper" parents="316 17920 18304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18326">
    <literal><![CDATA[
      a(x * (y \ x),x,a(z,z,u)) = a(a(u,z,y),x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,18236,a(flip),b,18304,a),flip(a)].">
      <j1 rule="hyper" parents="63 18236 18304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18327">
    <literal><![CDATA[
      x * a(y,z,a(u,u,x)) = L(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(18304(a,1),13472(a,1,2))].">
      <j1 rule="para" parents="18304 13472"/>
    </justification>
  </clause>

  <clause id="18329">
    <literal><![CDATA[
      x * a(y,z,a(u,u,x)) = L(x,u,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(18304(a,1),13712(a,1,2))].">
      <j1 rule="para" parents="18304 13712"/>
    </justification>
  </clause>

  <clause id="18332">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) = a(z,u,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13469,a(flip),b,18305,a),flip(a)].">
      <j1 rule="hyper" parents="63 13469 18305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18336">
    <literal><![CDATA[
      a(x,a(y,z,x),L(u,x,w)) = a(y,z,a(u,x,x))
    ]]></literal>
    <justification jstring="[para(18069(a,1),18305(a,2,3))].">
      <j1 rule="para" parents="18069 18305"/>
    </justification>
  </clause>

  <clause id="18337">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * a(u,y,x) = L(a(u,y,x),u,z)
    ]]></literal>
    <justification jstring="[para(18317(a,2),14597(a,1,1))].">
      <j1 rule="para" parents="18317 14597"/>
    </justification>
  </clause>

  <clause id="18338">
    <literal><![CDATA[
      x * a(y,z,a(x \ L(x,u,w),v5,v5)) = x * a(w,u,x * L(x,v5,a(v5,z,y)))
    ]]></literal>
    <justification jstring="[para(18317(a,2),15293(a,1,2))].">
      <j1 rule="para" parents="18317 15293"/>
    </justification>
  </clause>

  <clause id="18339">
    <literal><![CDATA[
      a(x,x \ y,a(z,y,y)) = a(z,y,a(x,y * x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,13963,a(flip),b,18332,a),flip(a)].">
      <j1 rule="hyper" parents="316 13963 18332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18341">
    <literal><![CDATA[
      a(x,y \ z,a(u,w,y \ z)) = a(u,w,a(x,y * z,y * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13961,a(flip),b,18332,a),flip(a)].">
      <j1 rule="hyper" parents="63 13961 18332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18344">
    <literal><![CDATA[
      L(L(x,x \ L(x,y,z),u),y,z) = L(x,y,z) * a(x,a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(18286(a,1),15551(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18286 15551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18345">
    <literal><![CDATA[
      a(x,a(y,z * x,x),z) = a(y,z,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18274,a(flip),b,18291,a),flip(a)].">
      <j1 rule="hyper" parents="63 18274 18291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18347">
    <literal><![CDATA[
      a(x,x,a(y,z,(u \ z) * z)) = a(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18160,a,b,18301,a)].">
      <j1 rule="hyper" parents="63 18160 18301"/>
    </justification>
  </clause>

  <clause id="18352">
    <literal><![CDATA[
      a(x,y * z,a(y,z,z)) = a(x,y,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,18305,a(flip),b,18345,a)].">
      <j1 rule="hyper" parents="63 18305 18345"/>
    </justification>
  </clause>

  <clause id="18353">
    <literal><![CDATA[
      a(x,y * z,a(z,z,y)) = a(x,y,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,18304,a(flip),b,18345,a)].">
      <j1 rule="hyper" parents="63 18304 18345"/>
    </justification>
  </clause>

  <clause id="18354">
    <literal><![CDATA[
      a(x,y,a(z,y \ x,y)) = a(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,17079,a(flip),b,18352,a)].">
      <j1 rule="hyper" parents="63 17079 18352"/>
    </justification>
  </clause>

  <clause id="18355">
    <literal><![CDATA[
      L(x,y * z,a(z,z,y)) = x * a(x,y,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,18352,a(flip),b,9235,a),flip(a)].">
      <j1 rule="hyper" parents="139 18352 9235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18356">
    <literal><![CDATA[
      a(x,a(x,x \ y,z),y) = a(z,y,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16405,a,b,18353,a)].">
      <j1 rule="hyper" parents="63 16405 18353"/>
    </justification>
  </clause>

  <clause id="18357">
    <literal><![CDATA[
      a(x,y \ z,a(y,z,z)) = a(x,y,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16415,a,b,18354,a)].">
      <j1 rule="hyper" parents="63 16415 18354"/>
    </justification>
  </clause>

  <clause id="18358">
    <literal><![CDATA[
      a(x,y,a(z,y * z,y)) = a(x,z,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15774,a(flip),b,18354,a)].">
      <j1 rule="hyper" parents="63 15774 18354"/>
    </justification>
  </clause>

  <clause id="18359">
    <literal><![CDATA[
      a(x,x,a(x \ y,x \ y,z)) = a(z,y,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16407,a,b,18356,a)].">
      <j1 rule="hyper" parents="63 16407 18356"/>
    </justification>
  </clause>

  <clause id="18360">
    <literal><![CDATA[
      (x \ y) * a(z,x,a(y,y,x)) = L(x \ y,a(x,y,y),z)
    ]]></literal>
    <justification jstring="[para(18357(a,1),16161(a,1,2))].">
      <j1 rule="para" parents="18357 16161"/>
    </justification>
  </clause>

  <clause id="18361">
    <literal><![CDATA[
      a(x,L(y,y,z),a(u,w,y)) = a(u,w,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16264,a,b,18336,a)].">
      <j1 rule="hyper" parents="63 16264 18336"/>
    </justification>
  </clause>

  <clause id="18362">
    <literal><![CDATA[
      a(x,L(y,y,z),a(y,u,y * w)) = a(y \ w,u,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15521,a(flip),b,18361,a)].">
      <j1 rule="hyper" parents="63 15521 18361"/>
    </justification>
  </clause>

  <clause id="18364">
    <literal><![CDATA[
      L(x,y,y \ L(y,z,u)) = L(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,13472,a(flip),b,18293,a),flip(a)].">
      <j1 rule="hyper" parents="316 13472 18293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18366">
    <literal><![CDATA[
      L(x,y,a(z,u,(y \ u) * u)) = L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,18162,a,b,18364,a)].">
      <j1 rule="hyper" parents="63 18162 18364"/>
    </justification>
  </clause>

  <clause id="18367">
    <literal><![CDATA[
      L(a(x,y,z),u * L(u,w,v5),L(u,w,v5)) = L(a(x,y,z),u,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15865,a,b,18364,a)].">
      <j1 rule="hyper" parents="63 15865 18364"/>
    </justification>
  </clause>

  <clause id="18368">
    <literal><![CDATA[
      (x * L(y,z,u)) * (L(y,z,u) \ y) = L(x * y,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14748,a(flip),b,18364,a)].">
      <j1 rule="hyper" parents="63 14748 18364"/>
    </justification>
  </clause>

  <clause id="18369">
    <literal><![CDATA[
      R(x,x \ y,a(z,a(u,w,z),v5)) \ (y * a(u,w,a(z,z,v5))) = (x \ y) * a(z,a(u,w,z),v5)
    ]]></literal>
    <justification jstring="[para(18307(a,1),492(a,1,2))].">
      <j1 rule="para" parents="18307 492"/>
    </justification>
  </clause>

  <clause id="18371">
    <literal><![CDATA[
      a(x * (y \ x),x,a(L(z \ 1,u,w),L(z \ 1,u,w),v5)) = a(a(v5,L(z \ 1,u,w),y),x,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,2655,a(flip),b,18326,a),flip(a)].">
      <j1 rule="hyper" parents="316 2655 18326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18372">
    <literal><![CDATA[
      x \ L(x,y,a(z,z,u)) = a(a(u,z,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,18208,a(flip),b,18326,a)].">
      <j1 rule="hyper" parents="63 18208 18326"/>
    </justification>
  </clause>

  <clause id="18374">
    <literal><![CDATA[
      a(x,y \ L(y,z,x),u) = y \ L(y,z,a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,17245,a,b,18372,a)].">
      <j1 rule="hyper" parents="316 17245 18372"/>
    </justification>
  </clause>

  <clause id="18375">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,u)) = a(a(z,u,x),y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17006,a,b,18372,a)].">
      <j1 rule="hyper" parents="63 17006 18372"/>
    </justification>
  </clause>

  <clause id="18376">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,u)),w,v5) = a(a(z,u,L(x,w,v5)),y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9223,a(flip),b,18372,a)].">
      <j1 rule="hyper" parents="63 9223 18372"/>
    </justification>
  </clause>

  <clause id="18377">
    <literal><![CDATA[
      x * L(y \ L(y,z,a(u,u,w)),v5,v6) = a(L(a(w,u,y),v5,v6),z,u) * x
    ]]></literal>
    <justification jstring="[para(18372(a,2),17761(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="18372 17761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18378">
    <literal><![CDATA[
      a(x,x \ y,a(z,y,y)) = a(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,18358,a(flip),b,18339,a),flip(a)].">
      <j1 rule="hyper" parents="316 18358 18339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18379">
    <literal><![CDATA[
      L(x,y * z,a(z,z,y)) = L(x,y,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,11690,a(flip),b,18355,a),flip(a)].">
      <j1 rule="hyper" parents="316 11690 18355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18380">
    <literal><![CDATA[
      L(x * a(y,z,z * y),y,a(z,z,y)) = (y * z) * (L(y * z,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,17156,a(flip),b,18379,a),flip(a)].">
      <j1 rule="hyper" parents="63 17156 18379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18381">
    <literal><![CDATA[
      a(x \ y,x \ y,a(z,x,x)) = a(z,y,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15285,a,b,18359,a)].">
      <j1 rule="hyper" parents="63 15285 18359"/>
    </justification>
  </clause>

  <clause id="18384">
    <literal><![CDATA[
      (x \ y) * a(z,x,a(u,w,x)) = L(x,a(u,w,x),z) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,1130,a(flip),b,18313,a),flip(a)].">
      <j1 rule="hyper" parents="63 1130 18313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18388">
    <literal><![CDATA[
      L(x \ y,a(x,y,y),z) = L(x,a(y,y,x),z) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,18360,a(flip),b,18384,a)].">
      <j1 rule="hyper" parents="63 18360 18384"/>
    </justification>
  </clause>

  <clause id="18389">
    <literal><![CDATA[
      L(x \ y,a(x,y,y),z) = L(x,y,a(z,x,y)) \ y
    ]]></literal>
    <justification jstring="[para(15373(a,1),18388(a,2,1))].">
      <j1 rule="para" parents="15373 18388"/>
    </justification>
  </clause>

  <clause id="18390">
    <literal><![CDATA[
      L(a(x,y,z \ u),u * z,u) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,2657,a(flip),b,18278,a),flip(a)].">
      <j1 rule="hyper" parents="316 2657 18278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18391">
    <literal><![CDATA[
      a(x,y,z \ u) \ (z \ u) = z \ (a(x,y,u \ z) \ u)
    ]]></literal>
    <justification jstring="[para(18390(a,1),16357(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18390 16357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18392">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * (u \ x) = L(u \ x,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,18364,a(flip),b,18294,a),flip(a)].">
      <j1 rule="hyper" parents="63 18364 18294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18393">
    <literal><![CDATA[
      L(x \ y,y,a(z,u,y)) = L(x,a(z,u,y),y) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,13819,a(flip),b,18392,a),flip(a)].">
      <j1 rule="hyper" parents="63 13819 18392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18394">
    <literal><![CDATA[
      L(x \ y,y,a(z,u,y)) = L(x,y,a(z,u,y)) \ y
    ]]></literal>
    <justification jstring="[para(6997(a,1),18393(a,2,1))].">
      <j1 rule="para" parents="6997 18393"/>
    </justification>
  </clause>

  <clause id="18395">
    <literal><![CDATA[
      L(x \ y,a(x,y,y),z) = L(x \ y,y,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,18389,a,b,18394,a)].">
      <j1 rule="hyper" parents="316 18389 18394"/>
    </justification>
  </clause>

  <clause id="18397">
    <literal><![CDATA[
      L(x,x,y \ L(y,z,u)) = L(x,a(u,z,x),y)
    ]]></literal>
    <justification jstring="[hyper(39,a,13479,a(flip),b,18311,a),flip(a)].">
      <j1 rule="hyper" parents="39 13479 18311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18399">
    <literal><![CDATA[
      L(x,x,a(y,z,(u \ z) * z)) = L(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18162,a,b,18397,a)].">
      <j1 rule="hyper" parents="63 18162 18397"/>
    </justification>
  </clause>

  <clause id="18401">
    <literal><![CDATA[
      L(x,a(y \ L(y,y,z),u,x),w) = L(x,x,w \ L(w,u,a(y,y,z)))
    ]]></literal>
    <justification jstring="[para(7488(a,1),18397(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="7488 18397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18403">
    <literal><![CDATA[
      a(a(x,y,(z \ y) * y),u,u) = L(u,a(x,y,u),z) \ u
    ]]></literal>
    <justification jstring="[para(18397(a,1),18229(a,2,1))].">
      <j1 rule="para" parents="18397 18229"/>
    </justification>
  </clause>

  <clause id="18405">
    <literal><![CDATA[
      a(a(x,y,(z \ y) * y),u,u) = a(z,u,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,9472,a(flip),b,18403,a),flip(a)].">
      <j1 rule="hyper" parents="316 9472 18403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18406">
    <literal><![CDATA[
      x * a(x,y,a(z,a(y,u,z),w)) = L(x,y,a(z,a(y,u,z),w))
    ]]></literal>
    <justification jstring="[para(18303(a,1),18321(a,2,3))].">
      <j1 rule="para" parents="18303 18321"/>
    </justification>
  </clause>

  <clause id="18407">
    <literal><![CDATA[
      a(x,y \ z,a(u,w,y \ z)) = a(x,y * z,a(u,w,y * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,18332,a(flip),b,18341,a),flip(a)].">
      <j1 rule="hyper" parents="316 18332 18341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18410">
    <literal><![CDATA[
      a(a(x,y,L(z,u,w)),v5,y) = L(a(a(x,y,z),v5,y),u,w)
    ]]></literal>
    <justification jstring="[para(18375(a,1),18376(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18375 18376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18411">
    <literal><![CDATA[
      a(a(x,y,L(z,u,w)),v5,y) = a(y,v5,a(L(x,u,w),y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,17790,a,b,18410,a),flip(a)].">
      <j1 rule="hyper" parents="316 17790 18410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18412">
    <literal><![CDATA[
      L(x,y,L(z \ L(z,u,y),w,v5)) = a(y,u,a(L(x,w,v5),y,z)) * x
    ]]></literal>
    <justification jstring="[para(18411(a,1),17246(a,2,1))].">
      <j1 rule="para" parents="18411 17246"/>
    </justification>
  </clause>

  <clause id="18414">
    <literal><![CDATA[
      a(x \ y,z,u) * a(y,x * y,a(u,z,x * y)) = L(a(x \ y,z,u),x \ y,x)
    ]]></literal>
    <justification jstring="[para(18407(a,1),14694(a,1,2))].">
      <j1 rule="para" parents="18407 14694"/>
    </justification>
  </clause>

  <clause id="18416">
    <literal><![CDATA[
      L(L(x,y,z),a(z,y,x),u) = x * L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17780,a(flip),b,18295,a)].">
      <j1 rule="hyper" parents="63 17780 18295"/>
    </justification>
  </clause>

  <clause id="18426">
    <literal><![CDATA[
      L(x,x \ 1,L(x * y,z,u)) = 1 / (a(y,x,L(x,z,u)) / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,16836,a(flip),b,18211,a)].">
      <j1 rule="hyper" parents="63 16836 18211"/>
    </justification>
  </clause>

  <clause id="18428">
    <literal><![CDATA[
      L(x,x \ L(x,y,z),u) = L(x,a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(41,a,17781,a(flip),b,18344,a),flip(a)].">
      <j1 rule="hyper" parents="41 17781 18344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18429">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * L(x,a(z,y,x),u)) = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(18428(a,1),12820(a,1,2,2))].">
      <j1 rule="para" parents="18428 12820"/>
    </justification>
  </clause>

  <clause id="18431">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * (w * x) = w * L(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[para(18428(a,1),18312(a,2,2))].">
      <j1 rule="para" parents="18428 18312"/>
    </justification>
  </clause>

  <clause id="18432">
    <literal><![CDATA[
      a(x \ y,a(x,y,x * y),z) * (u * (x \ y)) = u * L(x \ y,a(x,y,x \ y),z)
    ]]></literal>
    <justification jstring="[para(13369(a,1),18431(a,1,1,2))].">
      <j1 rule="para" parents="13369 18431"/>
    </justification>
  </clause>

  <clause id="18434">
    <literal><![CDATA[
      ((R(x,y,z) \ u) \ L(R(x,y,z) \ u,w,v5)) * (R(v6,v7,v8) * L(R(x,y,z) \ u,a(v5,w,R(x,y,z) \ u),R(v6,v7,v8))) = L(R(x,y,z) \ u,w,v5) * R(T(v6,x \ u),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(316,a,4576,a,b,18429,a),flip(a)].">
      <j1 rule="hyper" parents="316 4576 18429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18435">
    <literal><![CDATA[
      (x * L(y,a(z,u,y),x)) * (y \ L(y,u,z)) = x * L(y,u,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5023,a(flip),b,18429,a)].">
      <j1 rule="hyper" parents="63 5023 18429"/>
    </justification>
  </clause>

  <clause id="18436">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) * (w * L(x \ y,a(u,z,x \ y),w)) = w * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1252(a,1),18429(a,1,1))].">
      <j1 rule="para" parents="1252 18429"/>
    </justification>
  </clause>

  <clause id="18437">
    <literal><![CDATA[
      (x \ L(x,y,a(z,z,u))) * (w * L(x,a(z \ L(z,z,u),y,x),w)) = w * L(x,y,z \ L(z,z,u))
    ]]></literal>
    <justification jstring="[para(7488(a,1),18429(a,1,1,2))].">
      <j1 rule="para" parents="7488 18429"/>
    </justification>
  </clause>

  <clause id="18438">
    <literal><![CDATA[
      L(x,a(y \ L(y,y,z),u,x),w) = L(x,x,a(y,w \ L(w,u,y),z))
    ]]></literal>
    <justification jstring="[para(18374(a,2),18401(a,2,3))].">
      <j1 rule="para" parents="18374 18401"/>
    </justification>
  </clause>

  <clause id="18439">
    <literal><![CDATA[
      L(x,x,a(y,z \ L(z,u,y),w)) = L(x,a(y,a(x,u,y),w),z)
    ]]></literal>
    <justification jstring="[para(18291(a,1),18438(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18291 18438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18440">
    <literal><![CDATA[
      L(x,a(y,a(x,z,y),u),w) = L(x,x,a(a(u,y,w),z,y))
    ]]></literal>
    <justification jstring="[para(17245(a,1),18439(a,1,3)),flip(a)].">
      <j1 rule="para" parents="17245 18439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18441">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),z,y)) = a(x,y,((y / z) * L(z,u,w)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5893,a(flip),b,18102,a)].">
      <j1 rule="hyper" parents="63 5893 18102"/>
    </justification>
  </clause>

  <clause id="18442">
    <literal><![CDATA[
      (x * y) * (L(x * y,y \ 1,y) \ z) = (z / (y * x)) * ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12940,a,b,18142,a)].">
      <j1 rule="hyper" parents="63 12940 18142"/>
    </justification>
  </clause>

  <clause id="18444">
    <literal><![CDATA[
      a(x,y,L(z,u \ w,u)) = a(x,y,L(z,u * w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13879,a(flip),b,18222,a),flip(a)].">
      <j1 rule="hyper" parents="63 13879 18222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18446">
    <literal><![CDATA[
      a(x,y,z) * a(a(x,y,z),u,L(w,v5 * v6,v5)) = L(a(x,y,z),u,L(w,v5 \ v6,v5))
    ]]></literal>
    <justification jstring="[hyper(139,a,18444,a(flip),b,14590,a)].">
      <j1 rule="hyper" parents="139 18444 14590"/>
    </justification>
  </clause>

  <clause id="18450">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((z \ (u \ w)) \ w)) = a(x,y,a(u,z,(u \ w) * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,13660,a,b,18261,a),flip(a)].">
      <j1 rule="hyper" parents="316 13660 18261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18451">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,u * x) = (1 / (u * x)) * (u * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15898,a(flip),b,18264,a)].">
      <j1 rule="hyper" parents="63 15898 18264"/>
    </justification>
  </clause>

  <clause id="18452">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,u * x) = L(x \ R(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,16889,a(flip),b,18451,a),flip(a)].">
      <j1 rule="hyper" parents="316 16889 18451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18454">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,u),x,z * y) = L(a(x,y,z),u,u * x)
    ]]></literal>
    <justification jstring="[para(18452(a,1),3431(a,1,1))].">
      <j1 rule="para" parents="18452 3431"/>
    </justification>
  </clause>

  <clause id="18455">
    <literal><![CDATA[
      L(a(x,y,z),u,u * x) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3431,a(flip),b,18454,a),flip(a)].">
      <j1 rule="hyper" parents="63 3431 18454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18456">
    <literal><![CDATA[
      a(x \ a(y,z,u),x,a(a(u,z,y),w,v5)) = a(x,x,a(v5,w,a(u,z,y)))
    ]]></literal>
    <justification jstring="[hyper(316,a,18322,a(flip),b,18320,a),flip(a)].">
      <j1 rule="hyper" parents="316 18322 18320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18457">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * (((L(x,y,z) \ 1) \ x) * a(u,w,v5)) = L(a(u,w,v5),x,a(z,y,x)) * x
    ]]></literal>
    <justification jstring="[para(18367(a,1),12477(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18367 12477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18458">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),z,y)) = a(x,y,y * ((y / z) * L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,18441,a),flip(a)].">
      <j1 rule="hyper" parents="316 5469 18441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18460">
    <literal><![CDATA[
      a(a(x,y,z) * u,u,a(w,v5,a(z,y,x))) = a(u,u,a(w,v5,a(z,y,x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18252,a(flip),b,18456,a)].">
      <j1 rule="hyper" parents="63 18252 18456"/>
    </justification>
  </clause>

  <clause id="18461">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),z,y)) = a(x,y,y * ((z \ y) * L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5642,a(flip),b,18458,a),flip(a)].">
      <j1 rule="hyper" parents="316 5642 18458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18469">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),z,y)) = a(x,y,y * (z * (L(z,u,w) \ y)))
    ]]></literal>
    <justification jstring="[hyper(316,a,13626,a(flip),b,18461,a),flip(a)].">
      <j1 rule="hyper" parents="316 13626 18461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18470">
    <literal><![CDATA[
      ((x / y) * (y * a(z,u,w))) / x = L(a(z,u,w),y,x * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,14592,a(flip),b,18110,a),flip(a)].">
      <j1 rule="hyper" parents="316 14592 18110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18471">
    <literal><![CDATA[
      L(a(x,y,z),u,w * u) * w = (w / u) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(138,a,14592,a(flip),b,18110,a)].">
      <j1 rule="hyper" parents="138 14592 18110"/>
    </justification>
  </clause>

  <clause id="18472">
    <literal><![CDATA[
      L(a(x,y,z),u,u * w) * w = (w / u) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(138,a,1668,a,b,18470,a)].">
      <j1 rule="hyper" parents="138 1668 18470"/>
    </justification>
  </clause>

  <clause id="18473">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ w) = L(a(x,y,z),u,w * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2437,a(flip),b,18470,a)].">
      <j1 rule="hyper" parents="63 2437 18470"/>
    </justification>
  </clause>

  <clause id="18474">
    <literal><![CDATA[
      L(a(x,y,z),u,(w \ 1) * u) * (a(w,v5,v6) \ (a(w,v5,v6) / w)) = (((a(w,v5,v6) / w) / a(w,v5,v6)) / u) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(18473(a,1),12805(a,1,1))].">
      <j1 rule="para" parents="18473 12805"/>
    </justification>
  </clause>

  <clause id="18475">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z) * u,w * (a(x,y,z) * u)) * w = (w / (a(x,y,z) * u)) * ((u * a(x,y,z)) * T(a(x,y,z),u))
    ]]></literal>
    <justification jstring="[para(922(a,2),18471(a,2,2))].">
      <j1 rule="para" parents="922 18471"/>
    </justification>
  </clause>

  <clause id="18476">
    <literal><![CDATA[
      L(a(x,y,z),(u \ 1) \ w,(u \ w) * v5) * v5 = (v5 / ((u \ 1) \ w)) * (((u \ 1) \ w) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(12050(a,1),18472(a,1,1))].">
      <j1 rule="para" parents="12050 18472"/>
    </justification>
  </clause>

  <clause id="18477">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(x,u,w) \ v5) = a(z,y,L(L(x,x,y),x,v5 * x))
    ]]></literal>
    <justification jstring="[hyper(316,a,18221,a(flip),b,18193,a),flip(a)].">
      <j1 rule="hyper" parents="316 18221 18193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18479">
    <literal><![CDATA[
      L(x,a(y,z,u),a(w,v5,(v6 \ v5) * v5)) = L(x,a(u,z,y),v6 * L(v6,v5,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,10633,a(flip),b,18230,a),flip(a)].">
      <j1 rule="hyper" parents="316 10633 18230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18481">
    <literal><![CDATA[
      a(x * y,x,a(z,u,w)) * y = a(z,u,w) * ((y / x) * (a(z,u,w) \ x))
    ]]></literal>
    <justification jstring="[para(2771(a,1),18263(a,1,1))].">
      <j1 rule="para" parents="2771 18263"/>
    </justification>
  </clause>

  <clause id="18486">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,y) * z = L(z,v5,a(y,y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17853,a(flip),b,18377,a),flip(a)].">
      <j1 rule="hyper" parents="63 17853 18377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18487">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),x,v5)) * z = L(z,y,a(x,x,L(v5,u,w)))
    ]]></literal>
    <justification jstring="[para(17789(a,1),18486(a,1,1))].">
      <j1 rule="para" parents="17789 18486"/>
    </justification>
  </clause>

  <clause id="18488">
    <literal><![CDATA[
      L(x,y,L(z \ L(z,u,y),w,v5)) = L(x,u,a(y,y,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18412,a,b,18487,a)].">
      <j1 rule="hyper" parents="63 18412 18487"/>
    </justification>
  </clause>

  <clause id="18489">
    <literal><![CDATA[
      L(x,L(y \ L(y,z,u),w,v5),u) = L(x,z,a(u,u,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17691,a,b,18488,a)].">
      <j1 rule="hyper" parents="63 17691 18488"/>
    </justification>
  </clause>

  <clause id="18490">
    <literal><![CDATA[
      a(x,y,L(((z \ u) / z) * L(z,w,L(v5,v5,w)),w,a(z,z,L(v5,z,w)))) = a(x,y,L(v5 \ R(v5,w,z),z,w) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(18489(a,1),17689(a,1,3))].">
      <j1 rule="para" parents="18489 17689"/>
    </justification>
  </clause>

  <clause id="18491">
    <literal><![CDATA[
      (x * y) * (L(x * y,y,x) \ z) = (z / x) * R(x,y,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,17143,a(flip),b,18380,a),flip(a)].">
      <j1 rule="hyper" parents="63 17143 18380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18492">
    <literal><![CDATA[
      a(x,y,z \ ((u / w) * R(w,v5,v5 * w))) = a(x,y,z \ (((w * v5) \ u) * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(18491(a,1),14250(a,1,3,2))].">
      <j1 rule="para" parents="18491 14250"/>
    </justification>
  </clause>

  <clause id="18493">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(x,u,w) \ v5) = L(L(x,y,z) \ x,x,v5 * x)
    ]]></literal>
    <justification jstring="[hyper(316,a,18192,a(flip),b,18477,a),flip(a)].">
      <j1 rule="hyper" parents="316 18192 18477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18494">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(x,u,w) \ v5) = L(L(x,y,z) \ x,x,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,9096,a(flip),b,18493,a),flip(a)].">
      <j1 rule="hyper" parents="316 9096 18493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18496">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,L(x,u,w) * v5) = L(L(x,y,z) \ x,x,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,17125,a(flip),b,18494,a)].">
      <j1 rule="hyper" parents="63 17125 18494"/>
    </justification>
  </clause>

  <clause id="18499">
    <literal><![CDATA[
      (L(x,y,z) * u) * L(L(x,w,v5) \ x,x,u) = x * ((L(x,y,z) * u) / L(T(x,u),w,v5))
    ]]></literal>
    <justification jstring="[para(18496(a,1),13788(a,1,2))].">
      <j1 rule="para" parents="18496 13788"/>
    </justification>
  </clause>

  <clause id="18501">
    <literal><![CDATA[
      L(a(x,y,z),u,u * w) \ w = (w / u) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(34,a,14792,a,b,18481,a(flip))].">
      <j1 rule="hyper" parents="34 14792 18481"/>
    </justification>
  </clause>

  <clause id="18502">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * a(y,y,a(u,z,a(x,x,z))) = y \ L(y,z,a(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,14060,a(flip),b,18309,a),flip(a)].">
      <j1 rule="hyper" parents="316 14060 18309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18503">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * a(y,y,a(u,z,a(x,x,z))) = a(a(u,x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,18375,a(flip),b,18502,a),flip(a)].">
      <j1 rule="hyper" parents="316 18375 18502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18504">
    <literal><![CDATA[
      a(x,y,y * (z * (L(z,u,w) \ y))) * 1 = a(y \ (z * (L(z,u,w) \ y)),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,17401,a(flip),b,18118,a)].">
      <j1 rule="hyper" parents="63 17401 18118"/>
    </justification>
  </clause>

  <clause id="18505">
    <literal><![CDATA[
      L(x,x,a(y,z,z)) \ (x * L(x \ L(x,z,y),u,w)) = a(y,z,L(x,u,w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1129,a,b,18148,a)].">
      <j1 rule="hyper" parents="63 1129 18148"/>
    </justification>
  </clause>

  <clause id="18506">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (L(x \ 1,z,u) * w) = L(x,z,u) * (a(y,x,x) * (x \ w))
    ]]></literal>
    <justification jstring="[hyper(316,a,6886,a(flip),b,18149,a),flip(a)].">
      <j1 rule="hyper" parents="316 6886 18149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18507">
    <literal><![CDATA[
      ((x * (y * z)) / L(z,z,y)) \ (a(y,z,z) * (x * y)) = a(a(y,z,z) * x,y,z)
    ]]></literal>
    <justification jstring="[para(8402(a,1),18179(a,1,2))].">
      <j1 rule="para" parents="8402 18179"/>
    </justification>
  </clause>

  <clause id="18508">
    <literal><![CDATA[
      (1 / x) \ a(a(a(y,z,z),u,x),w,u) = L(x,w,a(z,z,a(y,u,u)))
    ]]></literal>
    <justification jstring="[para(18326(a,1),18259(a,1,2))].">
      <j1 rule="para" parents="18326 18259"/>
    </justification>
  </clause>

  <clause id="18509">
    <literal><![CDATA[
      (1 / x) \ a(a(y,a(x,z,y),u),w,z) = L(x,w,a(y,y,a(u,z,z)))
    ]]></literal>
    <justification jstring="[para(18292(a,1),18508(a,1,2,1))].">
      <j1 rule="para" parents="18292 18508"/>
    </justification>
  </clause>

  <clause id="18510">
    <literal><![CDATA[
      a(x,y * z,L(z * L(z,u,w),z,y)) = a(x,y * z,L(z * L(z,u,w),y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,5893,a(flip),b,18265,a)].">
      <j1 rule="hyper" parents="63 5893 18265"/>
    </justification>
  </clause>

  <clause id="18511">
    <literal><![CDATA[
      x * a(y,z,x * L(x,u,a(u,w,v5))) = x * a(v5,w,a(u,a(y,z,u),x))
    ]]></literal>
    <justification jstring="[para(18302(a,1),18338(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="18302 18338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18512">
    <literal><![CDATA[
      x * a(y,z,a(u,a(w,v5,u),x)) = x * a(w,v5,a(x,u,a(u,z,y)))
    ]]></literal>
    <justification jstring="[para(11775(a,1),18511(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11775 18511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18514">
    <literal><![CDATA[
      a(a(x,y,a(y,z,u)),w,v5) = a(u,z,a(y,a(v5,w,y),x))
    ]]></literal>
    <justification jstring="[hyper(34,a,14019,a,b,18512,a)].">
      <j1 rule="hyper" parents="34 14019 18512"/>
    </justification>
  </clause>

  <clause id="18516">
    <literal><![CDATA[
      a(a(x,y,a(z,u,y)),w,v5) = a(z,u,a(y,a(v5,w,y),x))
    ]]></literal>
    <justification jstring="[para(13660(a,1),18514(a,1,1))].">
      <j1 rule="para" parents="13660 18514"/>
    </justification>
  </clause>

  <clause id="18517">
    <literal><![CDATA[
      a(a(x,a(y,z,x),u),w,v5) = a(y,z,a(x,a(v5,w,x),u))
    ]]></literal>
    <justification jstring="[para(13681(a,2),18514(a,1,1))].">
      <j1 rule="para" parents="13681 18514"/>
    </justification>
  </clause>

  <clause id="18519">
    <literal><![CDATA[
      a(x,a(y,z,x),L(u,w,v5)) * a(u,x,a(y,z,x)) = a(y,z,a(x,a(v5,w,x),u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17885,a,b,18516,a)].">
      <j1 rule="hyper" parents="63 17885 18516"/>
    </justification>
  </clause>

  <clause id="18521">
    <literal><![CDATA[
      R(x,a(y,z,u),y * L(y,w,v5)) = x * a(u,z,a(y,a(v5,w,y),x))
    ]]></literal>
    <justification jstring="[para(18516(a,1),16294(a,2,2))].">
      <j1 rule="para" parents="18516 16294"/>
    </justification>
  </clause>

  <clause id="18522">
    <literal><![CDATA[
      L(x,a(y,z,u),y * L(y,w,v5)) = ((x \ a(u,z,a(y,a(v5,w,y),x))) \ 1) * a(x \ 1,x,x)
    ]]></literal>
    <justification jstring="[para(18517(a,1),16517(a,2,1,1,2))].">
      <j1 rule="para" parents="18517 16517"/>
    </justification>
  </clause>

  <clause id="18523">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * a(z,u,a(y,a(w,v5,y),x)) = a(y,a(z,u,y),L(x,v5,w))
    ]]></literal>
    <justification jstring="[para(18517(a,1),17791(a,1,2))].">
      <j1 rule="para" parents="18517 17791"/>
    </justification>
  </clause>

  <clause id="18524">
    <literal><![CDATA[
      (1 / x) \ a(x,y,a(z,a(y,u,z),w)) = L(x,u,a(z,z,a(w,y,y)))
    ]]></literal>
    <justification jstring="[para(18517(a,1),18509(a,1,2))].">
      <j1 rule="para" parents="18517 18509"/>
    </justification>
  </clause>

  <clause id="18525">
    <literal><![CDATA[
      L(x,a(y,z,u),y * L(y,w,v5)) = x * a(u,z,a(y,a(v5,w,y),x))
    ]]></literal>
    <justification jstring="[hyper(63,a,10628,a(flip),b,18521,a)].">
      <j1 rule="hyper" parents="63 10628 18521"/>
    </justification>
  </clause>

  <clause id="18526">
    <literal><![CDATA[
      x * a(x,y,a(z,a(y,u,z),w)) = L(x,u,a(z,z,a(w,y,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,2501,a(flip),b,18524,a)].">
      <j1 rule="hyper" parents="63 2501 18524"/>
    </justification>
  </clause>

  <clause id="18527">
    <literal><![CDATA[
      L(x,y,a(z,a(y,u,z),w)) = L(x,u,a(z,z,a(w,y,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18406,a(flip),b,18526,a)].">
      <j1 rule="hyper" parents="63 18406 18526"/>
    </justification>
  </clause>

  <clause id="18528">
    <literal><![CDATA[
      a(x,y,z \ (u * (L(u,z,w) \ z))) = a(w,z,z * (u * (L(u,y,x) \ z)))
    ]]></literal>
    <justification jstring="[hyper(135,a,18504,a,b,15665,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="135 18504 15665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18529">
    <literal><![CDATA[
      a(x,y,y * (z * (L(z,u,w) \ y))) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(13633(a,2),18528(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13633 18528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18530">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),z,y)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18469,a,b,18529,a)].">
      <j1 rule="hyper" parents="63 18469 18529"/>
    </justification>
  </clause>

  <clause id="18531">
    <literal><![CDATA[
      a(x,y * z,L(z * R(z \ 1,u,w),z,y)) = a(w,u,a(x,y * z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16419,a,b,18530,a)].">
      <j1 rule="hyper" parents="63 16419 18530"/>
    </justification>
  </clause>

  <clause id="18532">
    <literal><![CDATA[
      a(x,y * z,L(z * L(z \ 1,u,w),z,y)) = a(w,u,a(x,y * z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15874,a(flip),b,18531,a)].">
      <j1 rule="hyper" parents="63 15874 18531"/>
    </justification>
  </clause>

  <clause id="18533">
    <literal><![CDATA[
      a(x,y * z,L(z * L(z,u,w),z,y)) = a(w,u,a(x,y * z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9067,a(flip),b,18532,a)].">
      <j1 rule="hyper" parents="63 9067 18532"/>
    </justification>
  </clause>

  <clause id="18534">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ L(z,z,a(x,y,y)) = z * L(z \ L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(38,a,14399,a,b,18505,a)].">
      <j1 rule="hyper" parents="38 14399 18505"/>
    </justification>
  </clause>

  <clause id="18535">
    <literal><![CDATA[
      L(x,T(y,z),L(u,z,y)) = x * L(x \ L(x,y,u),z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16904,a,b,18534,a)].">
      <j1 rule="hyper" parents="63 16904 18534"/>
    </justification>
  </clause>

  <clause id="18536">
    <literal><![CDATA[
      x * L(x \ L(x,y,z),u,y) = L(x,y,L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(10874,a,18535,a),flip(a)].">
      <j1 rule="hyper" parents="10874 18535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18538">
    <literal><![CDATA[
      L(L(x,y,z),a(z,y,x),y) = L(x,y,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,18416,a,b,18536,a)].">
      <j1 rule="hyper" parents="63 18416 18536"/>
    </justification>
  </clause>

  <clause id="18539">
    <literal><![CDATA[
      L(x,y,L(z,x,y)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,14705,a(flip),b,18538,a),flip(a)].">
      <j1 rule="hyper" parents="63 14705 18538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18540">
    <literal><![CDATA[
      L((a(x,y,z) \ z) \ z,z * u,z * u) = (u \ L(z,y,L(x,z,y))) \ (u \ z)
    ]]></literal>
    <justification jstring="[para(18539(a,1),16735(a,1,1,1))].">
      <j1 rule="para" parents="18539 16735"/>
    </justification>
  </clause>

  <clause id="18541">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (L(x \ 1,z,u) * w) = L(x,z,u) * (L(x,x,y) \ w)
    ]]></literal>
    <justification jstring="[para(18072(a,1),18506(a,2,2))].">
      <j1 rule="para" parents="18072 18506"/>
    </justification>
  </clause>

  <clause id="18542">
    <literal><![CDATA[
      L(x,x,y) \ (L(x,z,u) * w) = L(x,z,u) * (L(x,x,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9091,a(flip),b,18541,a)].">
      <j1 rule="hyper" parents="63 9091 18541"/>
    </justification>
  </clause>

  <clause id="18543">
    <literal><![CDATA[
      L(x,y,a(z,x,y)) \ (L(x,u,w) * v5) = L(x,u,w) * (L(x,x,a(z,y,y)) \ v5)
    ]]></literal>
    <justification jstring="[para(16998(a,2),18542(a,1,1))].">
      <j1 rule="para" parents="16998 18542"/>
    </justification>
  </clause>

  <clause id="18544">
    <literal><![CDATA[
      ((x * (y * z)) / L(z,z,y)) \ (a(y,z,z) * (x * y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,16897,a(flip),b,18507,a),flip(a)].">
      <j1 rule="hyper" parents="316 16897 18507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18545">
    <literal><![CDATA[
      a(x,y * z,L(z * L(z,u,w),y,y)) = a(w,u,a(x,y * z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18533,a(flip),b,18510,a),flip(a)].">
      <j1 rule="hyper" parents="63 18533 18510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18546">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) \ L(a(x,y,a(z,u,y)),w,v5)) * L(x,y,a(z,u,y)) = (x * a(z,u,a(y,a(v5,w,y),x))) * a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(18519(a,1),17928(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="18519 17928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18547">
    <literal><![CDATA[
      (x \ L(y,z,L(u,y,z))) \ (x \ y) = L(a(u,z,y),y * x,y * x)
    ]]></literal>
    <justification jstring="[para(2301(a,1),18540(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2301 18540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18549">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ u)) \ (x \ u) = L(a(y,z,u),u * x,u * x)
    ]]></literal>
    <justification jstring="[para(18539(a,1),18547(a,1,1,2))].">
      <j1 rule="para" parents="18539 18547"/>
    </justification>
  </clause>

  <clause id="18550">
    <literal><![CDATA[
      L(x,y,y) * (L(x,x,a(z,y,y)) \ z) = a(y,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,16143,a(flip),b,18543,a),flip(a)].">
      <j1 rule="hyper" parents="63 16143 18543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18551">
    <literal><![CDATA[
      x \ ((y / x) \ (a(x \ y,x,x) \ (y * (1 / (y \ (y / x)))))) = 1 / (y \ (y / x))
    ]]></literal>
    <justification jstring="[para(11768(a,1),18181(a,1,2))].">
      <j1 rule="para" parents="11768 18181"/>
    </justification>
  </clause>

  <clause id="18552">
    <literal><![CDATA[
      L(a(x,y,z),u,L(w,v5 \ v6,v5)) = L(a(x,y,z),u,L(w,v5 * v6,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,14592,a(flip),b,18446,a),flip(a)].">
      <j1 rule="hyper" parents="63 14592 18446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18553">
    <literal><![CDATA[
      L(a(x,y,z),u,L(w \ v5,v5,v5)) = L(a(x,y,z),u,L(w * v5,w * v5,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17682,a,b,18552,a)].">
      <j1 rule="hyper" parents="63 17682 18552"/>
    </justification>
  </clause>

  <clause id="18554">
    <literal><![CDATA[
      a(x,y,z \ ((u / w) * L(w,v5,v5 * w))) = a(x,y,z \ (((w * v5) \ u) * (v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12129,a(flip),b,18492,a)].">
      <j1 rule="hyper" parents="63 12129 18492"/>
    </justification>
  </clause>

  <clause id="18555">
    <literal><![CDATA[
      x \ ((y / x) \ (y * x)) = 1 / (y \ (y / x))
    ]]></literal>
    <justification jstring="[para(18055(a,1),18551(a,1,2,2))].">
      <j1 rule="para" parents="18055 18551"/>
    </justification>
  </clause>

  <clause id="18556">
    <literal><![CDATA[
      a(x,1 / (y \ (y / z)),a(u,w,v5)) = a(x,y \ ((z \ 1) \ y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(18555(a,1),15800(a,1,2))].">
      <j1 rule="para" parents="18555 15800"/>
    </justification>
  </clause>

  <clause id="18558">
    <literal><![CDATA[
      a(x,y \ ((z \ 1) \ y),a(u,w,v5)) = a(x,y \ (y / z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,15744,a(flip),b,18556,a),flip(a)].">
      <j1 rule="hyper" parents="63 15744 18556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18559">
    <literal><![CDATA[
      a(x,y \ ((z \ 1) \ y),a(u,w,v5)) = a(x,y \ (z \ y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,11209,a(flip),b,18558,a),flip(a)].">
      <j1 rule="hyper" parents="316 11209 18558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18560">
    <literal><![CDATA[
      a(x,y,z \ (((u * w) \ v5) * (w \ u))) = a(x,y,z \ (L(u,w,w) * (v5 / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12143,a(flip),b,18554,a),flip(a)].">
      <j1 rule="hyper" parents="63 12143 18554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18561">
    <literal><![CDATA[
      a(x,y,z \ (((u * w) \ v5) * (w \ u))) = a(x,y,z \ (u * (L(u,w,w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,14161,a(flip),b,18560,a),flip(a)].">
      <j1 rule="hyper" parents="316 14161 18560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18562">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * (L(u * w,w \ 1,w) \ v5))) = a(x,y,z \ (u * (L(u,w,w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14167,a,b,18561,a)].">
      <j1 rule="hyper" parents="63 14167 18561"/>
    </justification>
  </clause>

  <clause id="18563">
    <literal><![CDATA[
      a(x,y * z,y \ (z * (L(z,u,w) \ y))) = a(x,y * z,(y * L(z,u,w)) * (y * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14162,a(flip),b,18103,a)].">
      <j1 rule="hyper" parents="63 14162 18103"/>
    </justification>
  </clause>

  <clause id="18564">
    <literal><![CDATA[
      (L(x,y,z) * (x \ a(u,x,w))) * (L(x,y,z) \ x) = L(a(u,x,w),x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14351,a(flip),b,18129,a)].">
      <j1 rule="hyper" parents="63 14351 18129"/>
    </justification>
  </clause>

  <clause id="18565">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * (v5 * a(v6,w,w))))) = a(x,y,z \ (u \ (v5 * L(w,w,v6))))
    ]]></literal>
    <justification jstring="[hyper(63,a,14227,a(flip),b,18203,a),flip(a)].">
      <j1 rule="hyper" parents="63 14227 18203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18566">
    <literal><![CDATA[
      a(x * y,y,a(z,u,w)) * a(y,a(z,u,w),y * x) = y \ L(y,y \ x,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(15485(a,1),18262(a,1,2))].">
      <j1 rule="para" parents="15485 18262"/>
    </justification>
  </clause>

  <clause id="18567">
    <literal><![CDATA[
      a(x \ y,a(x,y,y),z) * (u * (x \ y)) = u * L(x \ y,a(x,y,x \ y),z)
    ]]></literal>
    <justification jstring="[para(16235(a,1),18432(a,1,1))].">
      <j1 rule="para" parents="16235 18432"/>
    </justification>
  </clause>

  <clause id="18568">
    <literal><![CDATA[
      a(x \ y,a(x,y,y),z) * (u * (x \ y)) = u * L(x \ y,a(x,y,x * y),z)
    ]]></literal>
    <justification jstring="[para(13369(a,1),18567(a,2,2,2))].">
      <j1 rule="para" parents="13369 18567"/>
    </justification>
  </clause>

  <clause id="18569">
    <literal><![CDATA[
      a(x \ y,a(x,y,y),z) * (u * (x \ y)) = u * L(x \ y,a(x,y,y),z)
    ]]></literal>
    <justification jstring="[para(16160(a,1),18568(a,2,2))].">
      <j1 rule="para" parents="16160 18568"/>
    </justification>
  </clause>

  <clause id="18570">
    <literal><![CDATA[
      a(x,y,a(z,y \ x,y)) * (u * (x \ y)) = u * L(x \ y,a(x,y,y),z)
    ]]></literal>
    <justification jstring="[para(16414(a,1),18569(a,1,1))].">
      <j1 rule="para" parents="16414 18569"/>
    </justification>
  </clause>

  <clause id="18571">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) * (u * (y \ z)) = u * L(y \ z,a(y,z,z),x)
    ]]></literal>
    <justification jstring="[para(18354(a,1),18570(a,1,1))].">
      <j1 rule="para" parents="18354 18570"/>
    </justification>
  </clause>

  <clause id="18572">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) * (u * (y \ z)) = u * L(y \ z,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(18395(a,1),18571(a,2,2))].">
      <j1 rule="para" parents="18395 18571"/>
    </justification>
  </clause>

  <clause id="18574">
    <literal><![CDATA[
      a(x,y * z,y \ (z * (L(z,u,w) \ y))) = a(x,y * z,(y * z) * (y * L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,18563,a),flip(a)].">
      <j1 rule="hyper" parents="316 5469 18563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18575">
    <literal><![CDATA[
      L(x,y,z) * ((x \ a(u,x,w)) * (L(x,y,z) \ x)) = L(a(u,x,w),x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5153,a(flip),b,18564,a)].">
      <j1 rule="hyper" parents="63 5153 18564"/>
    </justification>
  </clause>

  <clause id="18577">
    <literal><![CDATA[
      L(x,x \ y,a(z,u,w)) = L(x,x * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(38,a,17871,a(flip),b,18566,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 17871 18566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18579">
    <literal><![CDATA[
      R(x,x \ y,a(z,u,w)) = L(x,x * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5371,a,b,18577,a)].">
      <j1 rule="hyper" parents="63 5371 18577"/>
    </justification>
  </clause>

  <clause id="18580">
    <literal><![CDATA[
      L(x \ L(x,x * y,a(z,u,w)),x,x \ y) = a(x,x \ y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(18577(a,1),13746(a,1,1,2))].">
      <j1 rule="para" parents="18577 13746"/>
    </justification>
  </clause>

  <clause id="18581">
    <literal><![CDATA[
      L(x \ L(x,x * y,a(z,u,w)),x,y) = a(x,x \ y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7105,a(flip),b,18580,a)].">
      <j1 rule="hyper" parents="63 7105 18580"/>
    </justification>
  </clause>

  <clause id="18582">
    <literal><![CDATA[
      a(a(x,y,z),u * w,u) \ 1 = a(u,u \ w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13364,a(flip),b,18581,a)].">
      <j1 rule="hyper" parents="63 13364 18581"/>
    </justification>
  </clause>

  <clause id="18583">
    <literal><![CDATA[
      a(x,x \ y,a(z,u,w)) = a(x,x * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,13734,a(flip),b,18582,a),flip(a)].">
      <j1 rule="hyper" parents="63 13734 18582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18584">
    <literal><![CDATA[
      a(a(x,y,z),u \ w,u) = a(a(x,y,z),u * w,u)
    ]]></literal>
    <justification jstring="[hyper(39,a,13734,a,b,18582,a)].">
      <j1 rule="hyper" parents="39 13734 18582"/>
    </justification>
  </clause>

  <clause id="18585">
    <literal><![CDATA[
      a(x,x \ (y * ((z * a(u,w,v5)) / z)),a(u,w,v5)) = a(x,x * y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16487,a,b,18583,a)].">
      <j1 rule="hyper" parents="63 16487 18583"/>
    </justification>
  </clause>

  <clause id="18586">
    <literal><![CDATA[
      x / (y * (a(z,u,w) * (y \ (a(z,u,w) \ x)))) = a(y,y * x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14851,a,b,18583,a)].">
      <j1 rule="hyper" parents="63 14851 18583"/>
    </justification>
  </clause>

  <clause id="18587">
    <literal><![CDATA[
      (a(x,y,z) * (u \ w)) \ (u \ (w * a(x,y,z))) = a(u,u * w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7147,a,b,18583,a)].">
      <j1 rule="hyper" parents="63 7147 18583"/>
    </justification>
  </clause>

  <clause id="18588">
    <literal><![CDATA[
      a(x,x * y,a(z,y,y)) = a(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,18378,a(flip),b,18583,a),flip(a)].">
      <j1 rule="hyper" parents="63 18378 18583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18589">
    <literal><![CDATA[
      a(x,y,z) * a(u,u * w,a(x,y,z)) = L(a(x,y,z),u \ w,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,18583,a(flip),b,14577,a)].">
      <j1 rule="hyper" parents="139 18583 14577"/>
    </justification>
  </clause>

  <clause id="18590">
    <literal><![CDATA[
      a(x,y,z) \ a(u,u * w,a(z,y,x)) = L(a(x,y,z) \ 1,u \ w,u)
    ]]></literal>
    <justification jstring="[para(18583(a,1),14697(a,1,2))].">
      <j1 rule="para" parents="18583 14697"/>
    </justification>
  </clause>

  <clause id="18591">
    <literal><![CDATA[
      L(a(x,y,z),u \ w,u) = L(a(x,y,z),u * w,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14582,a(flip),b,18589,a),flip(a)].">
      <j1 rule="hyper" parents="63 14582 18589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18592">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ w)) \ (x \ w) = L(a(y,z,u),x * w,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,14740,a,b,18591,a)].">
      <j1 rule="hyper" parents="63 14740 18591"/>
    </justification>
  </clause>

  <clause id="18593">
    <literal><![CDATA[
      L(a(x,y,z),z * u,z * u) = L(a(x,y,z),u * z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18549,a(flip),b,18592,a)].">
      <j1 rule="hyper" parents="63 18549 18592"/>
    </justification>
  </clause>

  <clause id="18594">
    <literal><![CDATA[
      (a(x,y,z) \ (u / z)) * ((u / z) \ a(x,y,z)) = L(a(x,y,z),u * z,u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(18593(a,1),17817(a,2,1))].">
      <j1 rule="para" parents="18593 17817"/>
    </justification>
  </clause>

  <clause id="18595">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u \ w,u) = L(a(x,y,z) \ 1,u * w,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14697,a(flip),b,18590,a),flip(a)].">
      <j1 rule="hyper" parents="63 14697 18590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18596">
    <literal><![CDATA[
      a(x,x \ (L(R(y,z,z) \ y,u,w) \ v5),L(R(y,z,z) \ y,u,w)) = a(x,x * v5,a(y,z,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17261,a,b,18586,a)].">
      <j1 rule="hyper" parents="63 17261 18586"/>
    </justification>
  </clause>

  <clause id="18597">
    <literal><![CDATA[
      a(x,x * y,a(z,u,w)) * (a(z,u,w) * (x \ y)) = x \ (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(38,a,2295,a,b,18587,a)].">
      <j1 rule="hyper" parents="38 2295 18587"/>
    </justification>
  </clause>

  <clause id="18598">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) * (a(x,z,z) * (y \ z)) = y \ (z * a(x,z,z))
    ]]></literal>
    <justification jstring="[para(18588(a,1),18597(a,1,1))].">
      <j1 rule="para" parents="18588 18597"/>
    </justification>
  </clause>

  <clause id="18599">
    <literal><![CDATA[
      a(x,y,y) * L(z \ y,y,a(x,z,y)) = z \ (y * a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,18572,a(flip),b,18598,a)].">
      <j1 rule="hyper" parents="63 18572 18598"/>
    </justification>
  </clause>

  <clause id="18600">
    <literal><![CDATA[
      a(x,x \ (y * a(z,u,w)),a(z,u,w)) = a(x,x * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(11(a,1),18585(a,1,2,2,2))].">
      <j1 rule="para" parents="11 18585"/>
    </justification>
  </clause>

  <clause id="18601">
    <literal><![CDATA[
      a(x,x * (y * a(z,u,w)),a(z,u,w)) = a(x,x * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18583,a(flip),b,18600,a)].">
      <j1 rule="hyper" parents="63 18583 18600"/>
    </justification>
  </clause>

  <clause id="18602">
    <literal><![CDATA[
      a(x,y * z,y \ (z * (L(z,u,w) \ y))) = a(x,y * z,L(z * L(z,u,w),y,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,11990,a(flip),b,18574,a),flip(a)].">
      <j1 rule="hyper" parents="316 11990 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18603">
    <literal><![CDATA[
      a(x,y * z,y \ (z * (L(z,u,w) \ y))) = a(w,u,a(x,y * z,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,18545,a(flip),b,18602,a),flip(a)].">
      <j1 rule="hyper" parents="316 18545 18602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18604">
    <literal><![CDATA[
      ((x * (y * z)) \ (x * (y * R(z,u,w)))) \ (y \ ((y / z) * R(z,u,w))) = a(w,u,a(x,y * z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15001,a,b,18603,a)].">
      <j1 rule="hyper" parents="63 15001 18603"/>
    </justification>
  </clause>

  <clause id="18605">
    <literal><![CDATA[
      (x \ a(y,x,z)) * (L(x,u,w) \ x) = L(x,u,w) \ a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,18268,a(flip),b,18575,a),flip(a)].">
      <j1 rule="hyper" parents="133 18268 18575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18606">
    <literal><![CDATA[
      (L(x,y,z) \ x) * a(u,x,w) = x * (L(x,y,z) \ a(u,x,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,18605,a(flip),b,6551,a),flip(a)].">
      <j1 rule="hyper" parents="139 18605 6551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18608">
    <literal><![CDATA[
      L(L(x \ L(x,y,a(z,u,w)),y,y),x,(y \ 1) \ a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,14009,a(flip),b,18089,a),flip(a)].">
      <j1 rule="hyper" parents="316 14009 18089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18609">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,(y \ 1) \ a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(18182(a,1),18608(a,1,1))].">
      <j1 rule="para" parents="18182 18608"/>
    </justification>
  </clause>

  <clause id="18610">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,y \ a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8710,a(flip),b,18609,a)].">
      <j1 rule="hyper" parents="63 8710 18609"/>
    </justification>
  </clause>

  <clause id="18611">
    <literal><![CDATA[
      a(x,L(1 / y,y,a(z,u,w)),a(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17187,a(flip),b,18610,a)].">
      <j1 rule="hyper" parents="63 17187 18610"/>
    </justification>
  </clause>

  <clause id="18613">
    <literal><![CDATA[
      a(x,L(y \ 1,y,a(z,u,w)),a(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11217,a(flip),b,18611,a)].">
      <j1 rule="hyper" parents="63 11217 18611"/>
    </justification>
  </clause>

  <clause id="18615">
    <literal><![CDATA[
      a(x,L(y,y,a(z,u,w)),a(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15763,a(flip),b,18613,a)].">
      <j1 rule="hyper" parents="63 15763 18613"/>
    </justification>
  </clause>

  <clause id="18617">
    <literal><![CDATA[
      a(x \ y,z,a(u,x,x)) = a(u,x,a(x * y,z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,18362,a(flip),b,18615,a)].">
      <j1 rule="hyper" parents="63 18362 18615"/>
    </justification>
  </clause>

  <clause id="18618">
    <literal><![CDATA[
      a(x,y,a(y * z,y \ z,y)) = a(x,z,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18381,a(flip),b,18617,a),flip(a)].">
      <j1 rule="hyper" parents="63 18381 18617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18619">
    <literal><![CDATA[
      a(a(x,y,y),y \ z,u) * a(u,u,a(x,y,a(y * z,y \ z,y))) = L(u,y \ z,a(x,y,y)) \ u
    ]]></literal>
    <justification jstring="[para(18617(a,1),15352(a,1,2,3))].">
      <j1 rule="para" parents="18617 15352"/>
    </justification>
  </clause>

  <clause id="18622">
    <literal><![CDATA[
      (L(x \ 1,y,z) * y) \ R(x \ 1,y,y) = y \ a(z,y,x)
    ]]></literal>
    <justification jstring="[para(17433(a,1),18132(a,1,2))].">
      <j1 rule="para" parents="17433 18132"/>
    </justification>
  </clause>

  <clause id="18623">
    <literal><![CDATA[
      (x \ 1) * (L(y \ 1,x,z) \ (y \ 1)) = x \ a(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13491,a(flip),b,18622,a)].">
      <j1 rule="hyper" parents="63 13491 18622"/>
    </justification>
  </clause>

  <clause id="18625">
    <literal><![CDATA[
      (x \ 1) * (L(y,x,z) \ y) = x \ a(z,x,y)
    ]]></literal>
    <justification jstring="[para(7090(a,1),18623(a,1,2))].">
      <j1 rule="para" parents="7090 18623"/>
    </justification>
  </clause>

  <clause id="18626">
    <literal><![CDATA[
      a(x,y,z) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(34,a,18022,a,b,18625,a)].">
      <j1 rule="hyper" parents="34 18022 18625"/>
    </justification>
  </clause>

  <clause id="18627">
    <literal><![CDATA[
      a(x,L(y,z,u),L(z,z,y)) = a(x,L(y,z,u),z)
    ]]></literal>
    <justification jstring="[hyper(316,a,18128,a,b,18626,a)].">
      <j1 rule="hyper" parents="316 18128 18626"/>
    </justification>
  </clause>

  <clause id="18628">
    <literal><![CDATA[
      a(x,y,y * (z \ y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,18116,a,b,18626,a)].">
      <j1 rule="hyper" parents="316 18116 18626"/>
    </justification>
  </clause>

  <clause id="18629">
    <literal><![CDATA[
      a(x,y,(z \ y) * y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,18066,a,b,18626,a)].">
      <j1 rule="hyper" parents="316 18066 18626"/>
    </justification>
  </clause>

  <clause id="18630">
    <literal><![CDATA[
      ((x * (y * z)) / L(z,z,y)) \ (x * R(y,z,z)) = a(x,L(y,z,z),z)
    ]]></literal>
    <justification jstring="[hyper(316,a,14572,a,b,18626,a)].">
      <j1 rule="hyper" parents="316 14572 18626"/>
    </justification>
  </clause>

  <clause id="18632">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w)) = a(a(w,u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,17008,a(flip),b,18626,a)].">
      <j1 rule="hyper" parents="316 17008 18626"/>
    </justification>
  </clause>

  <clause id="18634">
    <literal><![CDATA[
      x \ (L(y / x,z,u) \ y) = a(u,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(316,a,13906,a(flip),b,18626,a)].">
      <j1 rule="hyper" parents="316 13906 18626"/>
    </justification>
  </clause>

  <clause id="18635">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) = a(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,13383,a(flip),b,18626,a)].">
      <j1 rule="hyper" parents="316 13383 18626"/>
    </justification>
  </clause>

  <clause id="18637">
    <literal><![CDATA[
      L(x,y,z) = x / a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(209,a,18626,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="209 18626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18638">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ u = u * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,18626,a,b,14355,a),flip(a)].">
      <j1 rule="hyper" parents="139 18626 14355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18644">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,18626,a,b,xx)].">
      <j1 rule="hyper" parents="139 18626"/>
    </justification>
  </clause>

  <clause id="18645">
    <literal><![CDATA[
      a(x,y,z) * L(z,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(138,a,18626,a,b,1378,a)].">
      <j1 rule="hyper" parents="138 18626 1378"/>
    </justification>
  </clause>

  <clause id="18646">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,18626,a,b,9921,a),flip(a)].">
      <j1 rule="hyper" parents="134 18626 9921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18649">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(132,a,18626,a,b,15352,a),flip(a)].">
      <j1 rule="hyper" parents="132 18626 15352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18660">
    <literal><![CDATA[
      x * (L(y,z,u) \ y) = a(u,z,y) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,18626,a(flip),b,2295,a)].">
      <j1 rule="hyper" parents="139 18626 2295"/>
    </justification>
  </clause>

  <clause id="18662">
    <literal><![CDATA[
      L(x,y,z) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(39,a,2301,a,b,18626,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 2301 18626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18663">
    <literal><![CDATA[
      L(x,x,a(y,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,15629,a,b,18626,a(flip))].">
      <j1 rule="hyper" parents="38 15629 18626"/>
    </justification>
  </clause>

  <clause id="18664">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,15406,a,b,18626,a(flip))].">
      <j1 rule="hyper" parents="38 15406 18626"/>
    </justification>
  </clause>

  <clause id="18668">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(18626(a,2),2652(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18626 2652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18674">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(u,w,v5))) = a(x,y,z \ a(v5,w,u))
    ]]></literal>
    <justification jstring="[para(18626(a,2),5819(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="18626 5819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18677">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = a(z,y,x) * x
    ]]></literal>
    <justification jstring="[para(18626(a,2),6592(a,2,1))].">
      <j1 rule="para" parents="18626 6592"/>
    </justification>
  </clause>

  <clause id="18680">
    <literal><![CDATA[
      x * (L(x,y,z) \ L(x,u,w)) = a(z,y,x) * L(x,u,w)
    ]]></literal>
    <justification jstring="[para(18626(a,2),6542(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18626 6542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18687">
    <literal><![CDATA[
      L(x,y,z \ L(z,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(18626(a,2),9212(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18626 9212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18695">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(18626(a,2),12828(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18626 12828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18703">
    <literal><![CDATA[
      ((x \ y) / x) * L(x,z,u) = (x * a(u,z,x)) \ y
    ]]></literal>
    <justification jstring="[para(18626(a,2),13850(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="18626 13850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18708">
    <literal><![CDATA[
      (x \ L(x,y,z)) * u = a(z,y,x) \ u
    ]]></literal>
    <justification jstring="[para(18626(a,2),14352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18626 14352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18709">
    <literal><![CDATA[
      x * (y \ L(y,z,u)) = a(u,z,y) \ x
    ]]></literal>
    <justification jstring="[para(18626(a,2),14358(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18626 14358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18712">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(18626(a,2),15299(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18626 15299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18718">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) = a(y,y,a(u,z,x))
    ]]></literal>
    <justification jstring="[para(18626(a,2),18315(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18626 18315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18719">
    <literal><![CDATA[
      L(x * y,y,a(z,u,y)) = (x * L(y,u,z)) * a(z,u,y)
    ]]></literal>
    <justification jstring="[para(18626(a,2),18368(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18626 18368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18720">
    <literal><![CDATA[
      x * (L(x,y,z) \ a(u,x,w)) = a(z,y,x) * a(u,x,w)
    ]]></literal>
    <justification jstring="[para(18626(a,2),18606(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18626 18606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18721">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,15360,a(flip),b,18646,a)].">
      <j1 rule="hyper" parents="63 15360 18646"/>
    </justification>
  </clause>

  <clause id="18723">
    <literal><![CDATA[
      R(x,y,z) \ x = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(18646(a,1),13946(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18646 13946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18726">
    <literal><![CDATA[
      a(x,x,y) \ (z \ a(x,x,y)) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,18649,a(flip),b,7413,a),flip(a)].">
      <j1 rule="hyper" parents="133 18649 7413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18727">
    <literal><![CDATA[
      L(x,y,a(z,x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,16998,a,b,18663,a)].">
      <j1 rule="hyper" parents="63 16998 18663"/>
    </justification>
  </clause>

  <clause id="18728">
    <literal><![CDATA[
      L(x \ 1,x,a(y,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,16993,a(flip),b,18663,a)].">
      <j1 rule="hyper" parents="63 16993 18663"/>
    </justification>
  </clause>

  <clause id="18729">
    <literal><![CDATA[
      a(x,y,y) * (z \ 1) = z \ a(x,y,y)
    ]]></literal>
    <justification jstring="[para(18663(a,1),11606(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18663 11606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18730">
    <literal><![CDATA[
      a(x,x,y) * (z \ 1) = z \ a(x,x,y)
    ]]></literal>
    <justification jstring="[para(18663(a,1),11620(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18663 11620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18731">
    <literal><![CDATA[
      R(x,y,z) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[para(18663(a,1),15379(a,2,2))].">
      <j1 rule="para" parents="18663 15379"/>
    </justification>
  </clause>

  <clause id="18732">
    <literal><![CDATA[
      R(x,y,z) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(18663(a,1),15382(a,2,1))].">
      <j1 rule="para" parents="18663 15382"/>
    </justification>
  </clause>

  <clause id="18733">
    <literal><![CDATA[
      a(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(18663(a,1),15383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18663 15383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18734">
    <literal><![CDATA[
      (x \ 1) * a(y,y,z) = x \ a(y,y,z)
    ]]></literal>
    <justification jstring="[para(18663(a,1),17033(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18663 17033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18735">
    <literal><![CDATA[
      (1 / x) \ a(y,y,z) = a(y,y,z) * x
    ]]></literal>
    <justification jstring="[para(18663(a,1),17081(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18663 17081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18737">
    <literal><![CDATA[
      L(x,y,y) * (x \ z) = a(y,y,x) \ z
    ]]></literal>
    <justification jstring="[para(18663(a,1),18550(a,1,2,1))].">
      <j1 rule="para" parents="18663 18550"/>
    </justification>
  </clause>

  <clause id="18739">
    <literal><![CDATA[
      (x \ 1) * a(y,z,z) = x \ a(y,z,z)
    ]]></literal>
    <justification jstring="[para(18664(a,1),11622(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18664 11622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18741">
    <literal><![CDATA[
      (x * a(y,y,x)) * z = x * (a(y,y,x) * z)
    ]]></literal>
    <justification jstring="[para(18664(a,1),15446(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18664 15446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18742">
    <literal><![CDATA[
      (x * y) * a(z,z,y) = x * (y * a(z,z,y))
    ]]></literal>
    <justification jstring="[para(18664(a,1),15525(a,1,1,2))].">
      <j1 rule="para" parents="18664 15525"/>
    </justification>
  </clause>

  <clause id="18743">
    <literal><![CDATA[
      a(x,y,y) * (z * x) = z * R(x,y,y)
    ]]></literal>
    <justification jstring="[para(18664(a,1),15541(a,1,2,2))].">
      <j1 rule="para" parents="18664 15541"/>
    </justification>
  </clause>

  <clause id="18745">
    <literal><![CDATA[
      L(x,y,L(y,x,z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(18664(a,1),16876(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18664 16876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18749">
    <literal><![CDATA[
      L(x,y,a(z,z,a(u,w,w))) = x
    ]]></literal>
    <justification jstring="[para(18721(a,2),227(a,1,3))].">
      <j1 rule="para" parents="18721 227"/>
    </justification>
  </clause>

  <clause id="18753">
    <literal><![CDATA[
      L(x \ y,y,a(z,x,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(18727(a,1),18394(a,2,1))].">
      <j1 rule="para" parents="18727 18394"/>
    </justification>
  </clause>

  <clause id="18755">
    <literal><![CDATA[
      L(x,y,z) \ x != u
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(18637(a,2),324(a,1,1)),flip(b)].">
      <j1 rule="para" parents="18637 324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18761">
    <literal><![CDATA[
      a(x,y,z) \ 1 = L(z,y,x) / z
    ]]></literal>
    <justification jstring="[hyper(209,a,18644,a(flip),b,14394,a),flip(a)].">
      <j1 rule="hyper" parents="209 18644 14394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18782">
    <literal><![CDATA[
      x \ (a(y,z,u \ x) \ u) = L(x \ u,z,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,18391,a(flip),b,18662,a)].">
      <j1 rule="hyper" parents="316 18391 18662"/>
    </justification>
  </clause>

  <clause id="18787">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(133,a,18662,a,b,14467,a(flip))].">
      <j1 rule="hyper" parents="133 18662 14467"/>
    </justification>
  </clause>

  <clause id="18810">
    <literal><![CDATA[
      a(x,(y * a(z,u,y)) \ w,v5) = a(x,L(y,u,z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(18662(a,2),16090(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18662 16090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18812">
    <literal><![CDATA[
      a(x,y,z) \ L(z,u,a(w,v5,x)) = L(L(z,u,a(w,v5,x)),y,x)
    ]]></literal>
    <justification jstring="[para(17043(a,1),18662(a,2,1)),flip(a)].">
      <j1 rule="para" parents="17043 18662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18815">
    <literal><![CDATA[
      a(x,y,z) * (x * L(z,y,x)) = L(x,y,z) * R(z,y,x)
    ]]></literal>
    <justification jstring="[para(18662(a,2),17840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18662 17840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18818">
    <literal><![CDATA[
      R(x,y,(y \ z) * z) = R(x,y,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,18197,a(flip),b,18731,a),flip(a)].">
      <j1 rule="hyper" parents="316 18197 18731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18821">
    <literal><![CDATA[
      a(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(136,a,18731,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="136 18731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18837">
    <literal><![CDATA[
      x \ (y \ R(y * x,z,u)) = L(a(y * x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(18731(a,2),13465(a,1,2,2))].">
      <j1 rule="para" parents="18731 13465"/>
    </justification>
  </clause>

  <clause id="18841">
    <literal><![CDATA[
      x * (L(x,y,z) * a(x,u,w)) = L(x,y,z) * R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,18732,a,b,1125,a),flip(a)].">
      <j1 rule="hyper" parents="139 18732 1125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18860">
    <literal><![CDATA[
      a(x,y,L(z,x,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,16303,a(flip),b,18732,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 16303 18732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18868">
    <literal><![CDATA[
      x \ (y \ R(y * x,z,u)) = a((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,17696,a(flip),b,18733,a)].">
      <j1 rule="hyper" parents="316 17696 18733"/>
    </justification>
  </clause>

  <clause id="18885">
    <literal><![CDATA[
      x \ ((x / y) * R(y,z,u)) = L(a(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(18733(a,2),14720(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18733 14720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18886">
    <literal><![CDATA[
      x \ (L(R(y,z,u),w,v5) * (L(y,w,v5) \ x)) = L(L(a(y,z,u),w,v5),y,L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(18733(a,2),16937(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="18733 16937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18888">
    <literal><![CDATA[
      (x \ y) * a(z,z,x) = L(x,z,z) \ y
    ]]></literal>
    <justification jstring="[para(18745(a,1),16871(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18745 16871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18890">
    <literal><![CDATA[
      a(x,y,z \ y) = a(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5584,a(flip),b,18628,a),flip(a)].">
      <j1 rule="hyper" parents="63 5584 18628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18891">
    <literal><![CDATA[
      a(a(x,y,z),u,y) = a(y,a(y,u,z),x)
    ]]></literal>
    <justification jstring="[para(18628(a,1),18235(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18628 18235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18892">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ L(x,v5,v6)) = a(v6,v5,x) \ L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(18628(a,1),18207(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18628 18207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18893">
    <literal><![CDATA[
      a(x,y,z \ (x * y)) = a(x,y,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,18250,a(flip),b,18629,a),flip(a)].">
      <j1 rule="hyper" parents="63 18250 18629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18894">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(18629(a,1),18347(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18629 18347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18895">
    <literal><![CDATA[
      L(x,a(y,z,x),u) = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(18629(a,1),18399(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18629 18399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18896">
    <literal><![CDATA[
      a(a(x,y,z),u,u) = a(z,u,a(x,y,u))
    ]]></literal>
    <justification jstring="[para(18629(a,1),18405(a,1,1))].">
      <j1 rule="para" parents="18629 18405"/>
    </justification>
  </clause>

  <clause id="18897">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),w,v5) = a(u,z,L(y,w,v5)) \ x
    ]]></literal>
    <justification jstring="[para(18629(a,1),18205(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18629 18205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18898">
    <literal><![CDATA[
      a(x,y,L(z,u * L(u,w,v5),v6)) = a(x,y,L(z,a(v5,w,u),v6))
    ]]></literal>
    <justification jstring="[para(18629(a,1),18231(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="18629 18231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18899">
    <literal><![CDATA[
      L(x,a(y,z,u),w * L(w,v5,v6)) = L(x,a(u,z,y),a(v6,v5,w))
    ]]></literal>
    <justification jstring="[para(18629(a,1),18479(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18629 18479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18903">
    <literal><![CDATA[
      x \ (y * a(z,y,y)) = a(z,y,y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(18753(a,1),18599(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18753 18599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18904">
    <literal><![CDATA[
      L(x,y,z) = (R(z,y,x) \ z) * x
    ]]></literal>
    <justification jstring="[hyper(138,a,18723,a,b,18761,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="138 18723 18761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18911">
    <literal><![CDATA[
      R(x,y,z) \ x = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1273,a,b,18904,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 1273 18904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18925">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * w = L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14063,a(flip),b,18677,a),flip(a)].">
      <j1 rule="hyper" parents="63 14063 18677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18937">
    <literal><![CDATA[
      L(x,y,z) * (x \ a(x,u,w)) = a(z,y,x) \ a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8516,a(flip),b,18708,a)].">
      <j1 rule="hyper" parents="63 8516 18708"/>
    </justification>
  </clause>

  <clause id="18945">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) = a(z,z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18316,a,b,18718,a)].">
      <j1 rule="hyper" parents="63 18316 18718"/>
    </justification>
  </clause>

  <clause id="18946">
    <literal><![CDATA[
      a(x,a(x,y,z),u) = a(x,x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13710,a,b,18718,a)].">
      <j1 rule="hyper" parents="63 13710 18718"/>
    </justification>
  </clause>

  <clause id="18949">
    <literal><![CDATA[
      (x \ a(y,y,a(z,u,x))) * L(w,x,a(x,y,a(y,u,z))) = (x \ 1) * (a(x,y,a(y,u,z)) * w)
    ]]></literal>
    <justification jstring="[para(18718(a,1),10681(a,1,1,2))].">
      <j1 rule="para" parents="18718 10681"/>
    </justification>
  </clause>

  <clause id="18953">
    <literal><![CDATA[
      a(x,y,y) * (z \ K(u,z)) = T(z,u) \ a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2985,a(flip),b,18729,a)].">
      <j1 rule="hyper" parents="63 2985 18729"/>
    </justification>
  </clause>

  <clause id="18955">
    <literal><![CDATA[
      a(x,x,L(y,z,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,11872,a(flip),b,18730,a),flip(a)].">
      <j1 rule="hyper" parents="35 11872 18730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18964">
    <literal><![CDATA[
      (x / (y \ a(z,z,u))) * (y \ 1) = y * ((a(z,z,u) * y) \ x)
    ]]></literal>
    <justification jstring="[para(18734(a,1),11957(a,1,1,2))].">
      <j1 rule="para" parents="18734 11957"/>
    </justification>
  </clause>

  <clause id="18965">
    <literal><![CDATA[
      a((x \ 1) \ (a(y,y,z) \ u),x \ 1,a(y,y,z)) * (a(y,y,z) \ u) = T((u / (x \ a(y,y,z))) * (x \ 1),a(y,y,z))
    ]]></literal>
    <justification jstring="[para(18734(a,1),14791(a,2,1,1,2))].">
      <j1 rule="para" parents="18734 14791"/>
    </justification>
  </clause>

  <clause id="18966">
    <literal><![CDATA[
      (1 / (((x / y) * (y * a(z,z,u))) / a(z,z,u))) \ a(z,z,u) = L(a(z,z,u),y,y \ x) * x
    ]]></literal>
    <justification jstring="[hyper(316,a,4494,a,b,18735,a),flip(a)].">
      <j1 rule="hyper" parents="316 4494 18735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18968">
    <literal><![CDATA[
      a(x,x,y) * (y \ z) = L(y,x,x) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,1131,a(flip),b,18737,a(flip))].">
      <j1 rule="hyper" parents="139 1131 18737"/>
    </justification>
  </clause>

  <clause id="18969">
    <literal><![CDATA[
      a(x,x,y) * (L(y,x,x) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(139,a,161,a(flip),b,18737,a(flip))].">
      <j1 rule="hyper" parents="139 161 18737"/>
    </justification>
  </clause>

  <clause id="18970">
    <literal><![CDATA[
      x * (L(x,y,y) \ z) = a(y,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,75,a(flip),b,18737,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 75 18737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18971">
    <literal><![CDATA[
      x * (a(y,y,x) \ z) = L(x,y,y) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,18737,a(flip),b,1126,a)].">
      <j1 rule="hyper" parents="139 18737 1126"/>
    </justification>
  </clause>

  <clause id="18972">
    <literal><![CDATA[
      a(x,y,z * (u \ a(w,v5,v5))) = a(x,y,z * (u * a(w,v5,v5)))
    ]]></literal>
    <justification jstring="[para(18739(a,1),5907(a,1,3,2))].">
      <j1 rule="para" parents="18739 5907"/>
    </justification>
  </clause>

  <clause id="18974">
    <literal><![CDATA[
      a(x,y,z) = ((x * (y * z)) / L(z,z,y)) \ (x * R(y,z,z))
    ]]></literal>
    <justification jstring="[para(18743(a,1),18544(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18743 18544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18980">
    <literal><![CDATA[
      L(x,y,a(z,z,a(u,w,w))) = L(x,w,a(z,z,a(w,y,u)))
    ]]></literal>
    <justification jstring="[para(18894(a,1),18527(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18894 18527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18982">
    <literal><![CDATA[
      L(x,a(x,y,z),u) = L(x,x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16124,a,b,18895,a)].">
      <j1 rule="hyper" parents="63 16124 18895"/>
    </justification>
  </clause>

  <clause id="18987">
    <literal><![CDATA[
      (x * L(y,y,a(z,u,x))) * (y \ L(y,u,z)) = x * L(y,u,z)
    ]]></literal>
    <justification jstring="[para(18895(a,1),18435(a,1,1,2))].">
      <j1 rule="para" parents="18895 18435"/>
    </justification>
  </clause>

  <clause id="18988">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) = a(y,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14012,a(flip),b,18896,a),flip(a)].">
      <j1 rule="hyper" parents="63 14012 18896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18998">
    <literal><![CDATA[
      a(a(x,y,z),u,y) = a(y,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,18891,a,b,18946,a)].">
      <j1 rule="hyper" parents="63 18891 18946"/>
    </justification>
  </clause>

  <clause id="18999">
    <literal><![CDATA[
      a(x,x,y) * (L(y,x,x) / z) = y * L(z \ 1,z,z \ L(y,x,x))
    ]]></literal>
    <justification jstring="[para(1607(a,1),18969(a,1,2))].">
      <j1 rule="para" parents="1607 18969"/>
    </justification>
  </clause>

  <clause id="19000">
    <literal><![CDATA[
      (x * (y * z)) \ ((a(u,u,x) * (L(x,u,u) * y)) * L(z,y,L(x,u,u))) = a(a(u,u,x),L(x,u,u) * y,L(z,y,L(x,u,u)))
    ]]></literal>
    <justification jstring="[para(18969(a,1),457(a,1,1))].">
      <j1 rule="para" parents="18969 457"/>
    </justification>
  </clause>

  <clause id="19002">
    <literal><![CDATA[
      a(x,x,y) * (a(z,z,L(y,x,x)) * u) = y * (L(L(y,x,x),z,z) \ u)
    ]]></literal>
    <justification jstring="[para(18970(a,1),18969(a,1,2))].">
      <j1 rule="para" parents="18970 18969"/>
    </justification>
  </clause>

  <clause id="19003">
    <literal><![CDATA[
      L(x,y,y) * (R(y,y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(18063(a,1),18971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18063 18971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19005">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) = a(x,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,18945,a,b,18988,a),flip(a)].">
      <j1 rule="hyper" parents="316 18945 18988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19012">
    <literal><![CDATA[
      a(x,y,a(z,x * (u * a(y,y,z)),y)) = a(x,x * u,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,18601,a(flip),b,19005,a),flip(a)].">
      <j1 rule="hyper" parents="316 18601 19005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19014">
    <literal><![CDATA[
      R(x,y \ z,L(y \ z,(y \ z) / (1 / y),(y \ z) / (1 / y))) = R(x,y \ z,L(y,y \ 1,z) * ((y \ z) / (1 / y)))
    ]]></literal>
    <justification jstring="[para(7527(a,1),18818(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="7527 18818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19017">
    <literal><![CDATA[
      T(x * (y * L(y \ (x \ z),u,w)),v5) \ T(z,v5) = a(w,u,z \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,12579,a,b,18634,a)].">
      <j1 rule="hyper" parents="63 12579 18634"/>
    </justification>
  </clause>

  <clause id="19018">
    <literal><![CDATA[
      (x \ (y * L(y \ (z * x),u,w))) \ T(z,x) = a(w,u,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,12569,a,b,18634,a)].">
      <j1 rule="hyper" parents="63 12569 18634"/>
    </justification>
  </clause>

  <clause id="19019">
    <literal><![CDATA[
      a(x,y,a(x,y,y) \ z) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,14949,a(flip),b,18634,a),flip(a)].">
      <j1 rule="hyper" parents="63 14949 18634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19020">
    <literal><![CDATA[
      a(x,y,a(x,y,y) * z) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,14403,a(flip),b,19019,a)].">
      <j1 rule="hyper" parents="63 14403 19019"/>
    </justification>
  </clause>

  <clause id="19021">
    <literal><![CDATA[
      a(x,y,a(x,y,y) * z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,18626,a,b,19020,a),flip(a)].">
      <j1 rule="hyper" parents="316 18626 19020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19022">
    <literal><![CDATA[
      a(x,y,z * L(y,y,x)) = a(x,y,z * y)
    ]]></literal>
    <justification jstring="[para(18054(a,1),19021(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18054 19021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19023">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),z,y) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,13408,a,b,18635,a)].">
      <j1 rule="hyper" parents="63 13408 18635"/>
    </justification>
  </clause>

  <clause id="19028">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),v5,v6) * v7) = a(x,y,a(w,u,L(z,v5,v6)) * v7)
    ]]></literal>
    <justification jstring="[para(18635(a,1),7951(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="18635 7951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19031">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) \ u = (u / z) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(18635(a,1),13831(a,1,1))].">
      <j1 rule="para" parents="18635 13831"/>
    </justification>
  </clause>

  <clause id="19033">
    <literal><![CDATA[
      a(x,y,z) * (u * L(L(x,w,v5) \ x,v6,v7)) = (u * a(x,y,z)) * a(v5,w,L(x,v6,v7))
    ]]></literal>
    <justification jstring="[para(18635(a,1),17970(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18635 17970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19034">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(18626(a,2),18635(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18626 18635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19036">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,u,z) = a(w,u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,14605,a,b,19034,a)].">
      <j1 rule="hyper" parents="316 14605 19034"/>
    </justification>
  </clause>

  <clause id="19037">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(z,y,x)) = a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,14593,a,b,19034,a)].">
      <j1 rule="hyper" parents="316 14593 19034"/>
    </justification>
  </clause>

  <clause id="19043">
    <literal><![CDATA[
      L(a(x,y,z),u,L(w * v5,w * v5,w)) = a(x,y,L(z,u,L(w \ v5,v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,18553,a(flip),b,19034,a)].">
      <j1 rule="hyper" parents="316 18553 19034"/>
    </justification>
  </clause>

  <clause id="19044">
    <literal><![CDATA[
      a(x,y,L(z,L(u,w,a(x,y,z)) * w,v5)) = L(a(x,y,z),(a(x,y,z) * w) * u,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,14975,a(flip),b,19034,a),flip(a)].">
      <j1 rule="hyper" parents="316 14975 19034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19047">
    <literal><![CDATA[
      (x * y) * a(z,u,L(w,y,x)) = x * (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,19034,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="139 19034 18"/>
    </justification>
  </clause>

  <clause id="19050">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,L(z,u,w)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,19034,a,b,14582,a)].">
      <j1 rule="hyper" parents="133 19034 14582"/>
    </justification>
  </clause>

  <clause id="19068">
    <literal><![CDATA[
      (a(x,y,a(z,x,L(y,u,w))) \ y) * L(a(z,x,y) \ 1,u,w) = y * L(y \ L(y,x,z),u,w)
    ]]></literal>
    <justification jstring="[para(19034(a,2),14203(a,1,1,1,3))].">
      <j1 rule="para" parents="19034 14203"/>
    </justification>
  </clause>

  <clause id="19072">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(z,u,w) \ v5) = a(z,u,L(w,y,x)) \ v5
    ]]></literal>
    <justification jstring="[para(19034(a,2),14789(a,2,1))].">
      <j1 rule="para" parents="19034 14789"/>
    </justification>
  </clause>

  <clause id="19075">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,x))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(19034(a,2),15465(a,1,3))].">
      <j1 rule="para" parents="19034 15465"/>
    </justification>
  </clause>

  <clause id="19077">
    <literal><![CDATA[
      (a(x,y,L(z,u,w)) \ w) * (u \ L(u,w,a(x,y,z))) = u \ ((a(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(19034(a,2),16317(a,1,1,1))].">
      <j1 rule="para" parents="19034 16317"/>
    </justification>
  </clause>

  <clause id="19078">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,a(x,v6,v7)))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(19034(a,2),17044(a,1,3))].">
      <j1 rule="para" parents="19034 17044"/>
    </justification>
  </clause>

  <clause id="19079">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) = L(a(x,y,a(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(19034(a,2),17738(a,1,3))].">
      <j1 rule="para" parents="19034 17738"/>
    </justification>
  </clause>

  <clause id="19083">
    <literal><![CDATA[
      a(x,a(y,z,u),L(y,w,v5)) = a(x,y,a(u,z,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(19034(a,2),17766(a,2,3))].">
      <j1 rule="para" parents="19034 17766"/>
    </justification>
  </clause>

  <clause id="19084">
    <literal><![CDATA[
      L(x,a(y,z,u),L(u,w,v5)) = L(x,u,a(y,z,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(19034(a,2),17825(a,2,3))].">
      <j1 rule="para" parents="19034 17825"/>
    </justification>
  </clause>

  <clause id="19085">
    <literal><![CDATA[
      L(a(x,y,z) \ (L(z,u,w) \ v5),z,a(x,y,L(z,u,w))) = (a(x,y,z) * L(z,u,w)) \ v5
    ]]></literal>
    <justification jstring="[para(19034(a,2),17835(a,1,3))].">
      <j1 rule="para" parents="19034 17835"/>
    </justification>
  </clause>

  <clause id="19089">
    <literal><![CDATA[
      a(x,y,L(z,u,u * w)) \ w = (w / u) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(19034(a,2),18501(a,1,1))].">
      <j1 rule="para" parents="19034 18501"/>
    </justification>
  </clause>

  <clause id="19101">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,L(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17251,a,b,18668,a)].">
      <j1 rule="hyper" parents="63 17251 18668"/>
    </justification>
  </clause>

  <clause id="19102">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,z) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17234,a,b,18668,a)].">
      <j1 rule="hyper" parents="63 17234 18668"/>
    </justification>
  </clause>

  <clause id="19110">
    <literal><![CDATA[
      a(x,y,z) \ a(u,w,a(x,y,z)) = a(x,y,L(z,w,u)) \ 1
    ]]></literal>
    <justification jstring="[para(18668(a,1),15635(a,1,2))].">
      <j1 rule="para" parents="18668 15635"/>
    </justification>
  </clause>

  <clause id="19111">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,y,x) = a(L(w,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(18668(a,1),16842(a,1,1))].">
      <j1 rule="para" parents="18668 16842"/>
    </justification>
  </clause>

  <clause id="19112">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * (L(w,y,x) \ w)) = v5 * L(L(w,y,x) \ w,u,z)
    ]]></literal>
    <justification jstring="[para(18668(a,1),17231(a,1,1))].">
      <j1 rule="para" parents="18668 17231"/>
    </justification>
  </clause>

  <clause id="19113">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,w) = a(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[para(18668(a,1),17250(a,1,1))].">
      <j1 rule="para" parents="18668 17250"/>
    </justification>
  </clause>

  <clause id="19114">
    <literal><![CDATA[
      a(x,y,z) * (u * a(w,v5,a(x,y,z))) = u * a(x,y,L(z,v5,w))
    ]]></literal>
    <justification jstring="[para(18668(a,1),17255(a,1,2,2))].">
      <j1 rule="para" parents="18668 17255"/>
    </justification>
  </clause>

  <clause id="19117">
    <literal><![CDATA[
      L(x \ y,x,z \ L(z,u,w)) = (a(w,u,z) * x) \ (y * a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,2299,a(flip),b,18687,a),flip(a)].">
      <j1 rule="hyper" parents="316 2299 18687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19120">
    <literal><![CDATA[
      (a(x,y,L(z,u,w)) \ v5) * (u \ L(u,w,a(x,y,z))) = a(x,y,L(L(z,u,w),w,u)) \ v5
    ]]></literal>
    <justification jstring="[para(18687(a,1),16421(a,1,2,2))].">
      <j1 rule="para" parents="18687 16421"/>
    </justification>
  </clause>

  <clause id="19126">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w \ u)) = a(a(x,y,z),u,w * u)
    ]]></literal>
    <justification jstring="[hyper(316,a,18890,a(flip),b,18712,a),flip(a)].">
      <j1 rule="hyper" parents="316 18890 18712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19127">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,14012,a(flip),b,18712,a),flip(a)].">
      <j1 rule="hyper" parents="316 14012 18712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19132">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18668,a(flip),b,18712,a),flip(a)].">
      <j1 rule="hyper" parents="63 18668 18712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19134">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,13660,a,b,19132,a),flip(a)].">
      <j1 rule="hyper" parents="316 13660 19132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19135">
    <literal><![CDATA[
      x \ L(L(x,a(y,z,u),w),w,a(y,z,u)) = a(y,z,a(w,x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17054,a,b,19132,a)].">
      <j1 rule="hyper" parents="63 17054 19132"/>
    </justification>
  </clause>

  <clause id="19137">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,14029,a,b,19132,a)].">
      <j1 rule="hyper" parents="63 14029 19132"/>
    </justification>
  </clause>

  <clause id="19139">
    <literal><![CDATA[
      a(x,y,a(z,a(x,y,u) * w,u)) = a(z,w,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14835,a(flip),b,19132,a),flip(a)].">
      <j1 rule="hyper" parents="63 14835 19132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19140">
    <literal><![CDATA[
      a(x,y * (z * (u \ 1)),a(w,v5,v6)) = a(w,v5,a(v6,y * (z * u),x))
    ]]></literal>
    <justification jstring="[hyper(63,a,14031,a(flip),b,19132,a),flip(a)].">
      <j1 rule="hyper" parents="63 14031 19132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19141">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14012,a(flip),b,19132,a)].">
      <j1 rule="hyper" parents="63 14012 19132"/>
    </justification>
  </clause>

  <clause id="19142">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14010,a(flip),b,19132,a)].">
      <j1 rule="hyper" parents="63 14010 19132"/>
    </justification>
  </clause>

  <clause id="19144">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(19132(a,2),13689(a,2,2))].">
      <j1 rule="para" parents="19132 13689"/>
    </justification>
  </clause>

  <clause id="19145">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(19132(a,1),14018(a,2,2))].">
      <j1 rule="para" parents="19132 14018"/>
    </justification>
  </clause>

  <clause id="19148">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(19132(a,1),14024(a,2,2))].">
      <j1 rule="para" parents="19132 14024"/>
    </justification>
  </clause>

  <clause id="19149">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(u,a(w,y,x),z) = u \ L(u,z,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(19132(a,1),17870(a,1,1))].">
      <j1 rule="para" parents="19132 17870"/>
    </justification>
  </clause>

  <clause id="19150">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(w,v5,a(x,y,a(z,u,v6)))
    ]]></literal>
    <justification jstring="[para(19132(a,1),17914(a,1,3))].">
      <j1 rule="para" parents="19132 17914"/>
    </justification>
  </clause>

  <clause id="19154">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,14012,a(flip),b,19134,a)].">
      <j1 rule="hyper" parents="63 14012 19134"/>
    </justification>
  </clause>

  <clause id="19155">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x)) = L(x,w,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,19134,a(flip),b,18632,a)].">
      <j1 rule="hyper" parents="139 19134 18632"/>
    </justification>
  </clause>

  <clause id="19156">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w),v5,v6)) = a(x,y,a(w,u,a(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(19134(a,1),13820(a,1,3)),flip(a)].">
      <j1 rule="para" parents="19134 13820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19159">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = a(w,u,a(z,y,x)) * v5
    ]]></literal>
    <justification jstring="[para(19134(a,1),14034(a,1,1))].">
      <j1 rule="para" parents="19134 14034"/>
    </justification>
  </clause>

  <clause id="19163">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19134,a(flip),b,19137,a),flip(a)].">
      <j1 rule="hyper" parents="63 19134 19137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19164">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,19132,a(flip),b,19137,a)].">
      <j1 rule="hyper" parents="63 19132 19137"/>
    </justification>
  </clause>

  <clause id="19168">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(w,v5,a(x,y,a(v6,u,z)))
    ]]></literal>
    <justification jstring="[para(19137(a,1),17914(a,1,3))].">
      <j1 rule="para" parents="19137 17914"/>
    </justification>
  </clause>

  <clause id="19176">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),a(z,u,w),y) = x * a(z,u,a(y,x,w))
    ]]></literal>
    <justification jstring="[para(19141(a,1),14080(a,2,2))].">
      <j1 rule="para" parents="19141 14080"/>
    </justification>
  </clause>

  <clause id="19179">
    <literal><![CDATA[
      a(x,x,a(a(x,y,z) * u,w,v5)) = a(v5,w,a(x,x,u))
    ]]></literal>
    <justification jstring="[para(18239(a,1),19141(a,2,3))].">
      <j1 rule="para" parents="18239 19141"/>
    </justification>
  </clause>

  <clause id="19183">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,x))) = a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(15465(a,1),19142(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15465 19142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19184">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(z,y,a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,19141,a,b,19154,a)].">
      <j1 rule="hyper" parents="316 19141 19154"/>
    </justification>
  </clause>

  <clause id="19185">
    <literal><![CDATA[
      a(x,y * z,a(u,w,v5)) = a(v5,w,a(u,z * y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,17875,a,b,19154,a),flip(a)].">
      <j1 rule="hyper" parents="316 17875 19154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19187">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,19142,a,b,19163,a)].">
      <j1 rule="hyper" parents="316 19142 19163"/>
    </justification>
  </clause>

  <clause id="19188">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,19141,a,b,19163,a)].">
      <j1 rule="hyper" parents="316 19141 19163"/>
    </justification>
  </clause>

  <clause id="19190">
    <literal><![CDATA[
      a(x,y * z,a(u,w,v5)) = a(v5,z * y,a(x,w,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,11190,a,b,19163,a),flip(a)].">
      <j1 rule="hyper" parents="316 11190 19163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19191">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,y,a(w,u,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(139,a,19163,a,b,14009,a)].">
      <j1 rule="hyper" parents="139 19163 14009"/>
    </justification>
  </clause>

  <clause id="19193">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(u,z,a(y * x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,13687,a,b,19163,a),flip(a)].">
      <j1 rule="hyper" parents="63 13687 19163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19198">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) = x * a(v5,z,a(u,w,y))
    ]]></literal>
    <justification jstring="[para(19163(a,2),13690(a,1,2))].">
      <j1 rule="para" parents="19163 13690"/>
    </justification>
  </clause>

  <clause id="19201">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(w,y,a(x,v5,a(v6,u,z)))
    ]]></literal>
    <justification jstring="[para(19137(a,1),19163(a,1,3))].">
      <j1 rule="para" parents="19137 19163"/>
    </justification>
  </clause>

  <clause id="19207">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),z,a(w,u,y)) = L(x,a(w,u,y),z)
    ]]></literal>
    <justification jstring="[para(19184(a,1),14038(a,1,1,2))].">
      <j1 rule="para" parents="19184 14038"/>
    </justification>
  </clause>

  <clause id="19209">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(y * x,w,a(v5,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,2771,a,b,19187,a)].">
      <j1 rule="hyper" parents="316 2771 19187"/>
    </justification>
  </clause>

  <clause id="19214">
    <literal><![CDATA[
      L(x,y,a(z,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,5383,a,b,18742,a(flip))].">
      <j1 rule="hyper" parents="35 5383 18742"/>
    </justification>
  </clause>

  <clause id="19215">
    <literal><![CDATA[
      (a(x,x,y) * y) \ z = y \ (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,17037,a(flip),b,19214,a),flip(a)].">
      <j1 rule="hyper" parents="63 17037 19214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19216">
    <literal><![CDATA[
      a(x,y,y) * (R(x,y,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,9222,a(flip),b,19214,a)].">
      <j1 rule="hyper" parents="63 9222 19214"/>
    </justification>
  </clause>

  <clause id="19220">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * (L(L(a(z,u,u),w,v5),v6,v7) * (R(z,u,u) \ v8))) = a(x,y,(z \ v8) * L(L(a(z,u,u),w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(19216(a,1),5533(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="19216 5533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19223">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x)) = L(x,z,a(u,w,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,19164,a,b,18787,a)].">
      <j1 rule="hyper" parents="139 19164 18787"/>
    </justification>
  </clause>

  <clause id="19225">
    <literal><![CDATA[
      a(x * (y \ x),x,a(z,u,w)) = a(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18208,a,b,18787,a)].">
      <j1 rule="hyper" parents="63 18208 18787"/>
    </justification>
  </clause>

  <clause id="19231">
    <literal><![CDATA[
      a(x,y,z) * (u * a(w,u * w,a(x,y,z))) = ((u * w) * a(x,y,z)) * ((u * w) \ u)
    ]]></literal>
    <justification jstring="[para(18787(a,1),15152(a,1,2,2))].">
      <j1 rule="para" parents="18787 15152"/>
    </justification>
  </clause>

  <clause id="19232">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) \ (z \ (u \ w))) = a(x,y,a(u,z,(u \ w) * z))
    ]]></literal>
    <justification jstring="[para(18893(a,1),14130(a,2,3))].">
      <j1 rule="para" parents="18893 14130"/>
    </justification>
  </clause>

  <clause id="19235">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * z = L(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(19132(a,1),18925(a,1,1))].">
      <j1 rule="para" parents="19132 18925"/>
    </justification>
  </clause>

  <clause id="19236">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * w = L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(19134(a,1),18925(a,1,1))].">
      <j1 rule="para" parents="19134 18925"/>
    </justification>
  </clause>

  <clause id="19238">
    <literal><![CDATA[
      (x * y) / ((x * (y * z)) / z) = a(x,L(y,y,x),z)
    ]]></literal>
    <justification jstring="[para(19003(a,1),18189(a,1,2,1))].">
      <j1 rule="para" parents="19003 18189"/>
    </justification>
  </clause>

  <clause id="19239">
    <literal><![CDATA[
      a(x,y,z) \ a(L(x,u,w),y,z) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16843,a,b,19127,a)].">
      <j1 rule="hyper" parents="63 16843 19127"/>
    </justification>
  </clause>

  <clause id="19242">
    <literal><![CDATA[
      a(x,y,z) * a(x,y,a(z,u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(19127(a,1),17254(a,1,2))].">
      <j1 rule="para" parents="19127 17254"/>
    </justification>
  </clause>

  <clause id="19244">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (a(w,w,u) \ v5)) \ v6)) = a(x,y,z \ ((R(u,w,w) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(19215(a,1),13274(a,1,3,2,1))].">
      <j1 rule="para" parents="19215 13274"/>
    </justification>
  </clause>

  <clause id="19247">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19155,a(flip),b,19223,a)].">
      <j1 rule="hyper" parents="63 19155 19223"/>
    </justification>
  </clause>

  <clause id="19248">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) = L(x,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18327,a(flip),b,19223,a)].">
      <j1 rule="hyper" parents="63 18327 19223"/>
    </justification>
  </clause>

  <clause id="19253">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),v5,v6) = L(L(x,v5,v6),u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,16994,a,b,19247,a)].">
      <j1 rule="hyper" parents="316 16994 19247"/>
    </justification>
  </clause>

  <clause id="19254">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,16986,a,b,19247,a)].">
      <j1 rule="hyper" parents="316 16986 19247"/>
    </justification>
  </clause>

  <clause id="19256">
    <literal><![CDATA[
      x * L(y,z,a(u,w,v5)) = x * L(y,w,a(u,z,v5))
    ]]></literal>
    <justification jstring="[hyper(139,a,19247,a,b,9,a)].">
      <j1 rule="hyper" parents="139 19247 9"/>
    </justification>
  </clause>

  <clause id="19259">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6))) = L(x,v5,a(z,y,a(w,u,v6)))
    ]]></literal>
    <justification jstring="[para(19188(a,1),19247(a,1,3))].">
      <j1 rule="para" parents="19188 19247"/>
    </justification>
  </clause>

  <clause id="19263">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(w,y,z) * u) = a(w,y,z) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(138,a,19254,a,b,5343,a)].">
      <j1 rule="hyper" parents="138 19254 5343"/>
    </justification>
  </clause>

  <clause id="19266">
    <literal><![CDATA[
      x \ ((x / y) * R(y,z,u)) = a(y,z,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,19034,a,b,18885,a),flip(a)].">
      <j1 rule="hyper" parents="316 19034 18885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19267">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),z,y) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(19034(a,2),19023(a,1,1))].">
      <j1 rule="para" parents="19034 19023"/>
    </justification>
  </clause>

  <clause id="19268">
    <literal><![CDATA[
      a(x,y,L(L(z,u,u \ (z \ w)),L(z,u,u \ (z \ w)),w)) \ w = ((w / (u * z)) * u) * L(L(z,u,u \ (z \ w)),y,x)
    ]]></literal>
    <justification jstring="[para(14644(a,1),19031(a,2,1))].">
      <j1 rule="para" parents="14644 19031"/>
    </justification>
  </clause>

  <clause id="19273">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * L(z,u,w) = a(w,u,L(z,y,x)) \ z
    ]]></literal>
    <justification jstring="[para(19267(a,1),16887(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19267 16887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19274">
    <literal><![CDATA[
      x \ ((y / x) * L(x,z,u)) = (x * a(u,z,x)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,4421,a,b,18703,a)].">
      <j1 rule="hyper" parents="63 4421 18703"/>
    </justification>
  </clause>

  <clause id="19278">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) * v7 = v7 * a(v6,v5,a(w,u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(19154(a,1),19144(a,2,2))].">
      <j1 rule="para" parents="19154 19144"/>
    </justification>
  </clause>

  <clause id="19279">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) * L(v6,a(z,u,a(x,y,w)),v5) = v5 * (a(z,u,a(x,y,w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(138,a,19145,a,b,202,a)].">
      <j1 rule="hyper" parents="138 19145 202"/>
    </justification>
  </clause>

  <clause id="19281">
    <literal><![CDATA[
      a(x,T(y,z) * (u * (K(z,y) / y)),a(w,v5,v6)) = a(w,R(u,y \ 1,y),a(v6,v5,x))
    ]]></literal>
    <justification jstring="[para(10762(a,1),19190(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10762 19190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19282">
    <literal><![CDATA[
      a(x * (y \ x),z,a(u,x,w)) = a(y,x,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19187,a,b,19225,a)].">
      <j1 rule="hyper" parents="63 19187 19225"/>
    </justification>
  </clause>

  <clause id="19283">
    <literal><![CDATA[
      a(x,L(y,y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6923,a,b,19238,a),flip(a)].">
      <j1 rule="hyper" parents="63 6923 19238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19284">
    <literal><![CDATA[
      a(x,L(y,y,x),z * L(y,y,x)) = a(x,y,z \ L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,18890,a(flip),b,19283,a)].">
      <j1 rule="hyper" parents="63 18890 19283"/>
    </justification>
  </clause>

  <clause id="19286">
    <literal><![CDATA[
      a(x,y,(z * (L(u,w,a(v5,v6,v7)) * v8)) * v9) = a(x,y,v9 * (z * (v8 * L(u,v6,a(v5,w,v7)))))
    ]]></literal>
    <justification jstring="[para(19256(a,1),5666(a,2,3,2,2))].">
      <j1 rule="para" parents="19256 5666"/>
    </justification>
  </clause>

  <clause id="19293">
    <literal><![CDATA[
      x \ (y \ R(y * x,z,u)) = a(y * x,z,L(u,x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,19034,a,b,18837,a),flip(a)].">
      <j1 rule="hyper" parents="316 19034 18837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19296">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,u,z) = a(x,u,L(z,y,w))
    ]]></literal>
    <justification jstring="[para(19164(a,1),19036(a,1,1))].">
      <j1 rule="para" parents="19164 19036"/>
    </justification>
  </clause>

  <clause id="19297">
    <literal><![CDATA[
      a(x,y,z) * a(z,y,a(x,u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(19141(a,2),19037(a,1,2))].">
      <j1 rule="para" parents="19141 19037"/>
    </justification>
  </clause>

  <clause id="19298">
    <literal><![CDATA[
      a(x,y,z) * a(x,u,a(w,y,z)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(19163(a,1),19037(a,1,2))].">
      <j1 rule="para" parents="19163 19037"/>
    </justification>
  </clause>

  <clause id="19299">
    <literal><![CDATA[
      a(x,y,z) * a(z,u,a(w,y,x)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(19184(a,1),19037(a,1,2))].">
      <j1 rule="para" parents="19184 19037"/>
    </justification>
  </clause>

  <clause id="19300">
    <literal><![CDATA[
      (a(x * a(y,z,u),w,v5) * x) * a(y,z,L(u,x,a(x * a(y,z,u),w,v5))) = R(x * a(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,18731,a,b,19047,a),flip(a)].">
      <j1 rule="hyper" parents="316 18731 19047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19301">
    <literal><![CDATA[
      a(L(x,x,y),z,u) = L(a(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,18337,a(flip),b,19111,a),flip(a)].">
      <j1 rule="hyper" parents="63 18337 19111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19302">
    <literal><![CDATA[
      a(L(x,x,y),z,u) = a(x,z,L(u,x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,19034,a,b,19301,a),flip(a)].">
      <j1 rule="hyper" parents="316 19034 19301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19303">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,L(z,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,14564,a,b,19113,a)].">
      <j1 rule="hyper" parents="34 14564 19113"/>
    </justification>
  </clause>

  <clause id="19304">
    <literal><![CDATA[
      a(x,x,a(a(x,y,z) * u,w,v5)) = a(x,x,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,19141,a,b,19179,a),flip(a)].">
      <j1 rule="hyper" parents="316 19141 19179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19305">
    <literal><![CDATA[
      a(L(x,y,z),u,w) = a(x,u,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(38,a,19050,a,b,19239,a),flip(a)].">
      <j1 rule="hyper" parents="38 19050 19239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19309">
    <literal><![CDATA[
      a((x * y) \ z,u,L(w,y,x)) = a(y \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14007,a(flip),b,19305,a),flip(a)].">
      <j1 rule="hyper" parents="63 14007 19305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19310">
    <literal><![CDATA[
      a(x * y,z,L(u,x,x)) = a((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13108,a(flip),b,19305,a),flip(a)].">
      <j1 rule="hyper" parents="63 13108 19305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19311">
    <literal><![CDATA[
      a(a(x,y,z) * y,u,L(w,z,x)) = a(L(y,x,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8756,a(flip),b,19305,a),flip(a)].">
      <j1 rule="hyper" parents="63 8756 19305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19313">
    <literal><![CDATA[
      a((x \ y) \ z,u,L(w,x \ y,x)) = a(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(475(a,1),19305(a,1,1)),flip(a)].">
      <j1 rule="para" parents="475 19305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19317">
    <literal><![CDATA[
      a(a(x,y,L(z,u,w)),v5,v6) = a(v6,v5,a(z,y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(19305(a,1),14012(a,1,1))].">
      <j1 rule="para" parents="19305 14012"/>
    </justification>
  </clause>

  <clause id="19321">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ z = L(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(19305(a,1),18662(a,2,1)),flip(a)].">
      <j1 rule="para" parents="19305 18662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19323">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,v6)) = a(x,u,a(w,v5,L(v6,y,z)))
    ]]></literal>
    <justification jstring="[para(19034(a,2),19305(a,2,3))].">
      <j1 rule="para" parents="19034 19305"/>
    </justification>
  </clause>

  <clause id="19324">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) = a(w,u,a(x,y,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(19305(a,1),19141(a,1,3))].">
      <j1 rule="para" parents="19305 19141"/>
    </justification>
  </clause>

  <clause id="19327">
    <literal><![CDATA[
      a(x * y,z,L(a(u,w,v5),x,x)) = a((x \ 1) \ y,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,13660,a,b,19310,a),flip(a)].">
      <j1 rule="hyper" parents="316 13660 19310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19328">
    <literal><![CDATA[
      a(x * y,z,(x * x) \ (u * x)) = a((x \ 1) \ y,z,x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5614,a,b,19310,a)].">
      <j1 rule="hyper" parents="63 5614 19310"/>
    </justification>
  </clause>

  <clause id="19329">
    <literal><![CDATA[
      a(x * y,z,L(u,y,x)) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18868,a(flip),b,19293,a),flip(a)].">
      <j1 rule="hyper" parents="63 18868 19293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19330">
    <literal><![CDATA[
      a(L(x * y,y,x),z,u) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19305,a,b,19329,a)].">
      <j1 rule="hyper" parents="63 19305 19329"/>
    </justification>
  </clause>

  <clause id="19331">
    <literal><![CDATA[
      a(x * y,z,u) * a(x * y,z,a(u,y,x)) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19242,a,b,19329,a)].">
      <j1 rule="hyper" parents="63 19242 19329"/>
    </justification>
  </clause>

  <clause id="19332">
    <literal><![CDATA[
      a(((x \ y) \ 1) \ x,z,(x \ y) \ u) = a(x * (x \ y),z,y \ (x * u))
    ]]></literal>
    <justification jstring="[para(475(a,1),19329(a,1,3)),flip(a)].">
      <j1 rule="para" parents="475 19329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19333">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ u) \ L(x,x,a(y,y,z \ u)) = a(L(u * z,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,15404,a,b,19330,a)].">
      <j1 rule="hyper" parents="316 15404 19330"/>
    </justification>
  </clause>

  <clause id="19334">
    <literal><![CDATA[
      a(x,y,a(z,u,w) \ v5) * a(x,v5,a(a(z,u,w),y,a(z,u,w) \ v5)) = a(x,y,(a(z,u,w) / v5) \ 1)
    ]]></literal>
    <justification jstring="[para(17089(a,1),19298(a,2,3))].">
      <j1 rule="para" parents="17089 19298"/>
    </justification>
  </clause>

  <clause id="19335">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * a(w,v5,a(x,u,a(z,y,v6))) = a(a(x,y,z),u,L(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(19163(a,2),19299(a,1,2,3))].">
      <j1 rule="para" parents="19163 19299"/>
    </justification>
  </clause>

  <clause id="19336">
    <literal><![CDATA[
      a(x,a(y,z,x),a(u,w,v5)) * a(x,a(y,z,x),L(u,w,v5)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,18894,a(flip),b,19303,a),flip(a)].">
      <j1 rule="hyper" parents="316 18894 19303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19337">
    <literal><![CDATA[
      a(x,y,z) * L(u,a(x,y,L(z,w,v5)),a(x,y,a(z,w,v5))) = a(x,y,a(z,w,v5)) * (a(x,y,L(z,w,v5)) * u)
    ]]></literal>
    <justification jstring="[hyper(138,a,19303,a(flip),b,202,a)].">
      <j1 rule="hyper" parents="138 19303 202"/>
    </justification>
  </clause>

  <clause id="19339">
    <literal><![CDATA[
      a((x * y) \ z,u,a(x,w,v5)) = a(x,w,a(y \ (x \ z),u,v5))
    ]]></literal>
    <justification jstring="[para(19309(a,1),19183(a,1,3)),flip(a)].">
      <j1 rule="para" parents="19309 19183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19340">
    <literal><![CDATA[
      a(a(x,y,z) * y,u,L(w,z,x)) = a(y,u,L(w,x,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,19305,a(flip),b,19311,a),flip(a)].">
      <j1 rule="hyper" parents="316 19305 19311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19342">
    <literal><![CDATA[
      a(x * a(y,x,z),u,L(w,y,z)) = a(x,u,L(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,17062,a(flip),b,19340,a)].">
      <j1 rule="hyper" parents="63 17062 19340"/>
    </justification>
  </clause>

  <clause id="19344">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * a(u,w,a(x,y,z)) = a(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,16384,a(flip),b,18720,a),flip(a)].">
      <j1 rule="hyper" parents="63 16384 18720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19345">
    <literal><![CDATA[
      x * (a(x,y,z) * L(z,y,x)) = L(x,y,z) * R(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8403,a(flip),b,18815,a)].">
      <j1 rule="hyper" parents="63 8403 18815"/>
    </justification>
  </clause>

  <clause id="19356">
    <literal><![CDATA[
      a(x,y,z) * (a(u,w,L(x,a(x,y,z),v5)) \ v5) = v5 * (a(x,y,z) * (x \ L(x,w,u)))
    ]]></literal>
    <justification jstring="[para(18897(a,1),8715(a,1,2))].">
      <j1 rule="para" parents="18897 8715"/>
    </justification>
  </clause>

  <clause id="19360">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ a(w,v5,v6),w \ a(w,v5,v6),w \ a(w,v5,v6))) = a(x,y,(w \ a(w,v5,v6)) \ L(w,u,z))
    ]]></literal>
    <justification jstring="[para(18937(a,1),8606(a,1,3,1))].">
      <j1 rule="para" parents="18937 8606"/>
    </justification>
  </clause>

  <clause id="19361">
    <literal><![CDATA[
      L(x,y,a(z,z,a(y,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,18749,a(flip),b,18980,a),flip(a)].">
      <j1 rule="hyper" parents="63 18749 18980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19363">
    <literal><![CDATA[
      L(x,y,a(y,z,a(z,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,19247,a,b,19361,a)].">
      <j1 rule="hyper" parents="63 19247 19361"/>
    </justification>
  </clause>

  <clause id="19364">
    <literal><![CDATA[
      L(x,y,a(y,z,a(u,w,z))) = x
    ]]></literal>
    <justification jstring="[para(18988(a,2),19361(a,1,3))].">
      <j1 rule="para" parents="18988 19361"/>
    </justification>
  </clause>

  <clause id="19365">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * (w * x) = w * L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(19364(a,1),11694(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19364 11694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19369">
    <literal><![CDATA[
      a(x,y,a(z,u,L(y,w,v5))) * L(y,w,v5) = L(L(y,w,v5),a(y,u,z),x)
    ]]></literal>
    <justification jstring="[para(19083(a,1),16218(a,1,1))].">
      <j1 rule="para" parents="19083 16218"/>
    </justification>
  </clause>

  <clause id="19370">
    <literal><![CDATA[
      a(x,y,a(z,u,L(y,w,v5))) \ y = L(y,a(z,u,y),L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(19083(a,1),16263(a,1,1))].">
      <j1 rule="para" parents="19083 16263"/>
    </justification>
  </clause>

  <clause id="19373">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w \ u)) = a(x,y,a(w * u,u,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,19132,a(flip),b,19126,a),flip(a)].">
      <j1 rule="hyper" parents="316 19132 19126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19374">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(v6,v5,a(z,u,a(x,y,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17920,a,b,19150,a)].">
      <j1 rule="hyper" parents="63 17920 19150"/>
    </justification>
  </clause>

  <clause id="19375">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(x,y,a(v6,u,a(z,v5,w)))
    ]]></literal>
    <justification jstring="[para(19132(a,1),19156(a,1,3))].">
      <j1 rule="para" parents="19132 19156"/>
    </justification>
  </clause>

  <clause id="19376">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(z,y,a(v5,v6,x))) = a(x,y,L(z,v6,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(19168(a,1),19297(a,1,2))].">
      <j1 rule="para" parents="19168 19297"/>
    </justification>
  </clause>

  <clause id="19377">
    <literal><![CDATA[
      a(x,y,a(z,u,a(a(z,u,w) * y,v5,w))) = a(y,y,a(x,v5,a(w,u,z)))
    ]]></literal>
    <justification jstring="[hyper(316,a,18460,a(flip),b,19201,a),flip(a)].">
      <j1 rule="hyper" parents="316 18460 19201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19378">
    <literal><![CDATA[
      L((a(x,y,a(z,u,w)) * v5) \ v6,u,a(x,v5,a(z,y,w))) = v5 \ (a(x,y,a(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,14058,a(flip),b,19259,a),flip(a)].">
      <j1 rule="hyper" parents="63 14058 19259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19380">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),v5,v6)) = a(x,y,a(z,v5,L(v6,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14012,a(flip),b,19317,a)].">
      <j1 rule="hyper" parents="63 14012 19317"/>
    </justification>
  </clause>

  <clause id="19381">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) = a(w,u,a(z,y,L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19154,a,b,19323,a)].">
      <j1 rule="hyper" parents="63 19154 19323"/>
    </justification>
  </clause>

  <clause id="19383">
    <literal><![CDATA[
      a(x,y,a(z,a(u,y,L(x,w,v5)) * v6,L(u,w,v5))) = a(a(u,y,L(x,w,v5)),v6,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14837,a(flip),b,19324,a),flip(a)].">
      <j1 rule="hyper" parents="63 14837 19324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19384">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,a(v6,v7,a(x,v8,v9))))) = a(z,u,a(w,y,x))
    ]]></literal>
    <justification jstring="[para(15246(a,1),19324(a,1,3,3)),flip(a)].">
      <j1 rule="para" parents="15246 19324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19385">
    <literal><![CDATA[
      L(x,y,z) * R(z,y,x) = x * z
    ]]></literal>
    <justification jstring="[para(18645(a,1),19345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18645 19345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19389">
    <literal><![CDATA[
      a(L(x,y,z),L(z,y,x),y) = ((x * (z * y)) / y) \ (x * z)
    ]]></literal>
    <justification jstring="[para(19385(a,1),14806(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19385 14806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19391">
    <literal><![CDATA[
      a(x,y,(z * (((u \ 1) * w) * a(u,v5,a(v6,v7,v5)))) * v8) = a(x,y,(z * (w * L(u,v5,a(v6,v7,v5)))) * v8)
    ]]></literal>
    <justification jstring="[para(19365(a,1),7581(a,2,3,1,2))].">
      <j1 rule="para" parents="19365 7581"/>
    </justification>
  </clause>

  <clause id="19392">
    <literal><![CDATA[
      a(x,y,a(z \ u,u,w)) = a(x,y,a(z * u,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18668,a(flip),b,19373,a)].">
      <j1 rule="hyper" parents="63 18668 19373"/>
    </justification>
  </clause>

  <clause id="19400">
    <literal><![CDATA[
      a(x,y,L(z,u,w * u)) \ w = (w / u) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(1668(a,1),19089(a,1,1,3))].">
      <j1 rule="para" parents="1668 19089"/>
    </justification>
  </clause>

  <clause id="19401">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * L(z,u,w) = L(z,u,L(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,19321,a(flip),b,19273,a),flip(a)].">
      <j1 rule="hyper" parents="316 19321 19273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19402">
    <literal><![CDATA[
      a(x,y,a(z,L(u,u,z),w * L(u,u,z))) = a(x,y,a(w \ L(u,u,z),u,z))
    ]]></literal>
    <justification jstring="[para(19284(a,2),13660(a,1,3))].">
      <j1 rule="para" parents="19284 13660"/>
    </justification>
  </clause>

  <clause id="19403">
    <literal><![CDATA[
      a(x,y,a((x \ z) \ u,w,v5)) = a(x,y,a(z \ (x * u),w,v5))
    ]]></literal>
    <justification jstring="[para(19313(a,1),19075(a,1,3)),flip(a)].">
      <j1 rule="para" parents="19313 19075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19404">
    <literal><![CDATA[
      a(L(x,y,z),L(z,y,x),y) = a(x,z,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,6925,a,b,19389,a),flip(a)].">
      <j1 rule="hyper" parents="316 6925 19389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19406">
    <literal><![CDATA[
      a(x,L(y,z,x),L(z,z,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,19305,a(flip),b,19404,a)].">
      <j1 rule="hyper" parents="63 19305 19404"/>
    </justification>
  </clause>

  <clause id="19407">
    <literal><![CDATA[
      a(x,L(y,z,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,18627,a(flip),b,19406,a)].">
      <j1 rule="hyper" parents="63 18627 19406"/>
    </justification>
  </clause>

  <clause id="19408">
    <literal><![CDATA[
      a(x,y,(z * L(u,z,w)) \ (L(u,w,z) * z)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(19407(a,1),12333(a,2,3))].">
      <j1 rule="para" parents="19407 12333"/>
    </justification>
  </clause>

  <clause id="19409">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ (v5 \ (w \ v5))))) = a(x,y,z * (u * a(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12207,a,b,18972,a)].">
      <j1 rule="hyper" parents="63 12207 18972"/>
    </justification>
  </clause>

  <clause id="19410">
    <literal><![CDATA[
      a(x,y,z * (u \ a(w,w,v5))) = a(x,y,z * (u * a(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17350,a(flip),b,18972,a)].">
      <j1 rule="hyper" parents="63 17350 18972"/>
    </justification>
  </clause>

  <clause id="19411">
    <literal><![CDATA[
      a(x,y,z) \ (u * L(z,z,a(x,y,u))) = u * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,18709,a(flip),b,18987,a)].">
      <j1 rule="hyper" parents="63 18709 18987"/>
    </justification>
  </clause>

  <clause id="19412">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(z,z,a(x,y,u)) = u * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6884,a(flip),b,19411,a)].">
      <j1 rule="hyper" parents="63 6884 19411"/>
    </justification>
  </clause>

  <clause id="19413">
    <literal><![CDATA[
      x \ L(L(x,y,a(z,u,w)),a(w,y,z),u) = a(w,y,a(u,x,z))
    ]]></literal>
    <justification jstring="[para(19253(a,2),19135(a,1,2))].">
      <j1 rule="para" parents="19253 19135"/>
    </justification>
  </clause>

  <clause id="19414">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),a(z,y,w),u) = x * a(z,y,a(u,x,w))
    ]]></literal>
    <justification jstring="[para(19247(a,1),19176(a,1,1))].">
      <j1 rule="para" parents="19247 19176"/>
    </justification>
  </clause>

  <clause id="19415">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),u,a(w,z,y)) = L(x,a(w,u,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,19247,a,b,19207,a)].">
      <j1 rule="hyper" parents="63 19247 19207"/>
    </justification>
  </clause>

  <clause id="19417">
    <literal><![CDATA[
      a((x \ 1) \ y,z,x \ u) = a(x * y,z,u * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5802,a(flip),b,19328,a),flip(a)].">
      <j1 rule="hyper" parents="63 5802 19328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19419">
    <literal><![CDATA[
      a((x * y) \ z,u,a(y,w,v5)) = a(y,w,a(x \ (y \ z),u,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,4176,a,b,19339,a)].">
      <j1 rule="hyper" parents="63 4176 19339"/>
    </justification>
  </clause>

  <clause id="19420">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(u,z,a(x,y,w)) = a(u,a(x,y,w),z)
    ]]></literal>
    <justification jstring="[para(19132(a,1),19344(a,1,1))].">
      <j1 rule="para" parents="19132 19344"/>
    </justification>
  </clause>

  <clause id="19421">
    <literal><![CDATA[
      L(x \ L(L(x,y,a(z,u,w)),a(w,y,z),u),v5,v6) = a(w,y,a(u,L(x,v5,v6),z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2171,a(flip),b,19413,a)].">
      <j1 rule="hyper" parents="63 2171 19413"/>
    </justification>
  </clause>

  <clause id="19422">
    <literal><![CDATA[
      L(L(a(x,y,z),u,a(u,w,v5)),a(u,u,v5),w) = a(x,y,z) * a(v5,a(x,y,z),a(u,u,w))
    ]]></literal>
    <justification jstring="[para(17249(a,2),19414(a,2,2))].">
      <j1 rule="para" parents="17249 19414"/>
    </justification>
  </clause>

  <clause id="19424">
    <literal><![CDATA[
      L(x * a(a(y,y,z),x,a(u,w,v5)),w,a(v5,y,a(z,u,y))) = L(x,a(v5,w,a(y,y,z)),u)
    ]]></literal>
    <justification jstring="[para(19005(a,2),19415(a,1,3))].">
      <j1 rule="para" parents="19005 19415"/>
    </justification>
  </clause>

  <clause id="19427">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,u,a(w,x,y)) = a(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13689,a(flip),b,19420,a)].">
      <j1 rule="hyper" parents="63 13689 19420"/>
    </justification>
  </clause>

  <clause id="19429">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,y,a(z,x,u)) = a(x,a(w,y,z),u)
    ]]></literal>
    <justification jstring="[para(19187(a,1),19427(a,1,1))].">
      <j1 rule="para" parents="19187 19427"/>
    </justification>
  </clause>

  <clause id="19430">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(u,y,a(z,x,w)) = a(x,a(w,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19198,a,b,19429,a)].">
      <j1 rule="hyper" parents="63 19198 19429"/>
    </justification>
  </clause>

  <clause id="19431">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,v5),v6)) * a(z,x,a(u,y,L(v6,w,v5))) = a(x,a(v6,y,z),L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(19324(a,2),19429(a,1,2))].">
      <j1 rule="para" parents="19324 19429"/>
    </justification>
  </clause>

  <clause id="19432">
    <literal><![CDATA[
      (x * a(y,z,a(u,w,x))) * a(w,z,a(u,y,x)) = x * a(y,a(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(19430(a,1),15248(a,2,2))].">
      <j1 rule="para" parents="19430 15248"/>
    </justification>
  </clause>

  <clause id="19433">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(x,y,w) \ v5) = a(x,y,L(w,u,z)) \ v5
    ]]></literal>
    <justification jstring="[para(19142(a,1),19072(a,1,1))].">
      <j1 rule="para" parents="19142 19072"/>
    </justification>
  </clause>

  <clause id="19435">
    <literal><![CDATA[
      a(x,L(y,z,z),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,18974,a,b,18630,a),flip(a)].">
      <j1 rule="hyper" parents="63 18974 18630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19436">
    <literal><![CDATA[
      a(x,y,a(z,u \ w,u)) = a(x,y,a(z,u * w,u))
    ]]></literal>
    <justification jstring="[para(19435(a,1),12004(a,1,3))].">
      <j1 rule="para" parents="19435 12004"/>
    </justification>
  </clause>

  <clause id="19437">
    <literal><![CDATA[
      a(x,L(y,z,z),a(u,w,z)) = a(a(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[para(19435(a,1),19132(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19435 19132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19438">
    <literal><![CDATA[
      a(x,L(y,z,z),a(u,w,z)) = a(x,y,a(u,w,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,19132,a(flip),b,19437,a),flip(a)].">
      <j1 rule="hyper" parents="316 19132 19437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19440">
    <literal><![CDATA[
      a(x,y,(z * ((u \ z) * w)) \ (u * L(w,u \ z,u \ z))) = a(x,y,a((u \ z) * w,u * z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12369,a,b,19436,a)].">
      <j1 rule="hyper" parents="63 12369 19436"/>
    </justification>
  </clause>

  <clause id="19441">
    <literal><![CDATA[
      a(x,y,a(z,u \ ((w / u) * L(u,v5,v6)),u)) = a(x,y,a(z,L(u,v5,v6) * w,u))
    ]]></literal>
    <justification jstring="[para(4385(a,1),19436(a,2,3,2))].">
      <j1 rule="para" parents="4385 19436"/>
    </justification>
  </clause>

  <clause id="19443">
    <literal><![CDATA[
      L(x \ y,x,z \ L(z,u,x)) = R(x,u,z) \ (y * a(x,u,z))
    ]]></literal>
    <justification jstring="[para(18731(a,2),19117(a,2,1))].">
      <j1 rule="para" parents="18731 19117"/>
    </justification>
  </clause>

  <clause id="19444">
    <literal><![CDATA[
      L(x \ y,x,z \ L(z,u,x)) = a(x,u,z) * (R(x,u,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(316,a,8655,a(flip),b,19443,a),flip(a)].">
      <j1 rule="hyper" parents="316 8655 19443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19445">
    <literal><![CDATA[
      L(x \ y,x,a(x,z,u)) = a(x,z,u) * (R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,18687,a(flip),b,19444,a)].">
      <j1 rule="hyper" parents="63 18687 19444"/>
    </justification>
  </clause>

  <clause id="19447">
    <literal><![CDATA[
      a(x,L(y \ z,y,a(y,u,w)),v5) = a(x,a(y,u,w) * (L(y,u,w) \ z),v5)
    ]]></literal>
    <justification jstring="[para(19445(a,2),12651(a,1,2))].">
      <j1 rule="para" parents="19445 12651"/>
    </justification>
  </clause>

  <clause id="19448">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(u,a(w,y,x),z) = a(u,z,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,18787,a(flip),b,19149,a),flip(a)].">
      <j1 rule="hyper" parents="316 18787 19149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19451">
    <literal><![CDATA[
      a(x,x,y) * (a(z,z,y) * u) = y * (L(L(y,x,x),z,z) \ u)
    ]]></literal>
    <justification jstring="[para(18955(a,1),19002(a,1,2,1))].">
      <j1 rule="para" parents="18955 19002"/>
    </justification>
  </clause>

  <clause id="19454">
    <literal><![CDATA[
      L(L(x,y,z),a(x,u,w),v5) = L(L(x,y,z),u,a(v5,x,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19236,a(flip),b,19369,a),flip(a)].">
      <j1 rule="hyper" parents="63 19236 19369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19455">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(z,y,a(x,v5,v6))) = a(x,y,L(z,w,a(v6,v5,u)))
    ]]></literal>
    <justification jstring="[para(19374(a,2),19376(a,1,2))].">
      <j1 rule="para" parents="19374 19376"/>
    </justification>
  </clause>

  <clause id="19457">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * ((z \ (u \ (z \ u))) \ (w * (v5 \ (z \ (u \ (z \ u))))))) = a(x,y,(v5 * T(v5 \ w,z \ (u \ (z \ u)))) * (v5 * a(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12800,a,b,19409,a)].">
      <j1 rule="hyper" parents="63 12800 19409"/>
    </justification>
  </clause>

  <clause id="19458">
    <literal><![CDATA[
      R(x,x,a(y,z,a(u,w,v5))) * a(u,z,y) = x * a(u,z,L(y,x,a(v5,w,x)))
    ]]></literal>
    <justification jstring="[para(19455(a,1),18061(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19455 18061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19463">
    <literal><![CDATA[
      a(x,y,z) \ L(z,u,a(w,v5,v6)) = a(a(w,v5,v6),u,z) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,18680,a(flip),b,18892,a),flip(a)].">
      <j1 rule="hyper" parents="63 18680 18892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19464">
    <literal><![CDATA[
      a(x,y,z) \ L(z,u,a(w,v5,v6)) = a(w,v5,a(z,u,v6)) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(19132(a,1),19463(a,2,1))].">
      <j1 rule="para" parents="19132 19463"/>
    </justification>
  </clause>

  <clause id="19465">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * L(z,v5,w) = L(L(z,u,a(x,y,w)),v5,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18812,a(flip),b,19464,a),flip(a)].">
      <j1 rule="hyper" parents="63 18812 19464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19466">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,w) = L(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19401,a(flip),b,19465,a),flip(a)].">
      <j1 rule="hyper" parents="63 19401 19465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19467">
    <literal><![CDATA[
      L(L(x,y,z),u,a(z,y,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19253,a(flip),b,19466,a)].">
      <j1 rule="hyper" parents="63 19253 19466"/>
    </justification>
  </clause>

  <clause id="19468">
    <literal><![CDATA[
      (x * y) * L(z,y,L(x,u,w)) = x * (y * L(z,y,a(w,u,x)))
    ]]></literal>
    <justification jstring="[hyper(139,a,19466,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="139 19466 18"/>
    </justification>
  </clause>

  <clause id="19473">
    <literal><![CDATA[
      L(x,x,L(y,y,z)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[para(18663(a,1),19466(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18663 19466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19474">
    <literal><![CDATA[
      L(x,x,L(y,z,z)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[para(18664(a,1),19466(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18664 19466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19475">
    <literal><![CDATA[
      L(x \ 1,x,L(y,z,z)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(18728(a,1),19466(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18728 19466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19479">
    <literal><![CDATA[
      a(x,y,L(z,x,L(u,u,w))) = a(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(19473(a,1),19302(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19473 19302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19486">
    <literal><![CDATA[
      a(x,y,L(z,x,L(u,w,w))) = a(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(19474(a,1),19302(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19474 19302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19488">
    <literal><![CDATA[
      a(x,y,L(z,x,L(u,u,w))) = a(x,y,L(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,19305,a(flip),b,19479,a),flip(a)].">
      <j1 rule="hyper" parents="316 19305 19479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19490">
    <literal><![CDATA[
      a(x,y,L(z,x,L(u,w,w))) = a(x,y,L(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,19305,a(flip),b,19486,a),flip(a)].">
      <j1 rule="hyper" parents="316 19305 19486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19495">
    <literal><![CDATA[
      a(x,y,L(z,u,L(w \ v5,v5,v5))) = a(x,y,L(z,u,L(w * v5,w * v5,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19034,a,b,19043,a),flip(a)].">
      <j1 rule="hyper" parents="63 19034 19043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19496">
    <literal><![CDATA[
      a(((x \ y) \ 1) \ x,z,(x \ y) \ u) = a(y,z,y \ (x * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),19332(a,2,1))].">
      <j1 rule="para" parents="10 19332"/>
    </justification>
  </clause>

  <clause id="19497">
    <literal><![CDATA[
      a(((x \ y) \ 1) \ x,z,(x \ y) \ u) = a(y,z,y * (x * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,15485,a(flip),b,19496,a),flip(a)].">
      <j1 rule="hyper" parents="316 15485 19496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19498">
    <literal><![CDATA[
      a((x \ y) * x,z,u * (x \ y)) = a(y,z,y * (x * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19417,a(flip),b,19497,a)].">
      <j1 rule="hyper" parents="63 19417 19497"/>
    </justification>
  </clause>

  <clause id="19499">
    <literal><![CDATA[
      a(x,y,z * (u \ x)) = a(x,y,x * (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2783,a(flip),b,19498,a)].">
      <j1 rule="hyper" parents="63 2783 19498"/>
    </justification>
  </clause>

  <clause id="19500">
    <literal><![CDATA[
      a(a(x,x,y),z,(u * w) * a(x,x,x * y)) = a(a(x,x,y),z,w * (u \ a(x,x,y)))
    ]]></literal>
    <justification jstring="[hyper(316,a,11730,a,b,19499,a)].">
      <j1 rule="hyper" parents="316 11730 19499"/>
    </justification>
  </clause>

  <clause id="19501">
    <literal><![CDATA[
      a(x,y,x * ((z * T(u,w)) * v5)) = a(x,y,v5 * ((z * u) \ x))
    ]]></literal>
    <justification jstring="[hyper(316,a,5644,a,b,19499,a)].">
      <j1 rule="hyper" parents="316 5644 19499"/>
    </justification>
  </clause>

  <clause id="19502">
    <literal><![CDATA[
      a(x,y,(z * u) * x) = a(x,y,u * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,19499,a)].">
      <j1 rule="hyper" parents="316 5469 19499"/>
    </justification>
  </clause>

  <clause id="19504">
    <literal><![CDATA[
      a(x,y,x * ((z * T(x,u)) * w)) = a(x,y,w * (x \ (z \ x)))
    ]]></literal>
    <justification jstring="[hyper(316,a,7781,a(flip),b,19501,a),flip(a)].">
      <j1 rule="hyper" parents="316 7781 19501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19505">
    <literal><![CDATA[
      a(x,y,(z * (u * x)) * x) = a(x,y,z * (x \ (u \ x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6055,a(flip),b,19504,a)].">
      <j1 rule="hyper" parents="63 6055 19504"/>
    </justification>
  </clause>

  <clause id="19506">
    <literal><![CDATA[
      a(x,y,(z * x) * (u \ x)) = a(x,y,u * (x \ (z \ x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19502,a(flip),b,19505,a)].">
      <j1 rule="hyper" parents="63 19502 19505"/>
    </justification>
  </clause>

  <clause id="19507">
    <literal><![CDATA[
      a(a(x,x,y),z,(u * a(x,x,y)) * (w * a(y,x,x))) = a(a(x,x,y),z,w * (a(x,x,y) \ (u \ a(x,x,y))))
    ]]></literal>
    <justification jstring="[hyper(63,a,19410,a(flip),b,19506,a)].">
      <j1 rule="hyper" parents="63 19410 19506"/>
    </justification>
  </clause>

  <clause id="19508">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * a(u,y,a(z,w,x)) = x * a(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(19223(a,1),19432(a,1,1))].">
      <j1 rule="para" parents="19223 19432"/>
    </justification>
  </clause>

  <clause id="19510">
    <literal><![CDATA[
      a(x,y,a(z,L(x \ u,x,a(x,y,w)),w)) = a(z,L(x,y,w) \ u,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(19447(a,2),19139(a,1,3))].">
      <j1 rule="para" parents="19447 19139"/>
    </justification>
  </clause>

  <clause id="19511">
    <literal><![CDATA[
      a(x,y,L(z,x,L(u * w,u * w,u))) = a(x,y,L(z,x,u \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19490,a(flip),b,19495,a),flip(a)].">
      <j1 rule="hyper" parents="63 19490 19495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19512">
    <literal><![CDATA[
      a(x,y,L(z,x,u \ w)) = a(x,y,L(z,x,u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19488,a(flip),b,19511,a),flip(a)].">
      <j1 rule="hyper" parents="63 19488 19511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19514">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(x,y,w) * v5) = v5 * L(L(w,y,x) \ w,u,z)
    ]]></literal>
    <justification jstring="[para(18660(a,1),19112(a,1,2))].">
      <j1 rule="para" parents="18660 19112"/>
    </justification>
  </clause>

  <clause id="19515">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(x,y,w) * v5) = v5 * a(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[para(18635(a,1),19514(a,2,2))].">
      <j1 rule="para" parents="18635 19514"/>
    </justification>
  </clause>

  <clause id="19516">
    <literal><![CDATA[
      L(x,y,L(z * u,u,z)) = L(x,y,(u \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(39,a,15405,a,b,19333,a)].">
      <j1 rule="hyper" parents="39 15405 19333"/>
    </justification>
  </clause>

  <clause id="19517">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),x,(u \ 1) \ w),u,w) = (w * (u * x)) \ ((w * u) * R(L(x,u,w),y,z))
    ]]></literal>
    <justification jstring="[para(19516(a,1),16922(a,1,1))].">
      <j1 rule="para" parents="19516 16922"/>
    </justification>
  </clause>

  <clause id="19518">
    <literal><![CDATA[
      a(x,y,a(z \ L(u,u,w),u,w)) = a(x,y,a(w,u,z * L(u,u,w)))
    ]]></literal>
    <justification jstring="[para(19283(a,1),19402(a,1,3)),flip(a)].">
      <j1 rule="para" parents="19283 19402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19519">
    <literal><![CDATA[
      a(x,y,z \ (((u \ w) * a(v5,v5,u)) \ v6)) = a(x,y,z \ ((R(u,v5,v5) \ w) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,14776,a(flip),b,19244,a)].">
      <j1 rule="hyper" parents="63 14776 19244"/>
    </justification>
  </clause>

  <clause id="19520">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,v5,a(x,u,a(w,y,v6))) = a(a(x,y,w),u,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(19132(a,1),19335(a,1,1))].">
      <j1 rule="para" parents="19132 19335"/>
    </justification>
  </clause>

  <clause id="19521">
    <literal><![CDATA[
      a(x,x,a(y,z,a(u,w,v5))) * a(x,a(y,z,x),L(u,w,v5)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(18894(a,1),19336(a,1,1))].">
      <j1 rule="para" parents="18894 19336"/>
    </justification>
  </clause>

  <clause id="19522">
    <literal><![CDATA[
      a(x,y,a(z,a(u,y,L(x,w,v5)) * v6,L(u,w,v5))) = a(u,y,a(z,v6,L(x,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,19132,a(flip),b,19383,a),flip(a)].">
      <j1 rule="hyper" parents="316 19132 19383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19523">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,v5),v6)) = L(a(x,y,a(z,u,v6)),w,v5)
    ]]></literal>
    <justification jstring="[para(19413(a,1),19421(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19413 19421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19524">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,v5),v6)) = a(x,y,a(z,u,L(v6,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,19079,a,b,19523,a),flip(a)].">
      <j1 rule="hyper" parents="316 19079 19523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19526">
    <literal><![CDATA[
      a(x,y,a(z,x \ u,L(w,x,a(x,y,w)))) = a(z,L(x,y,w) \ u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19510,a(flip),b,19524,a),flip(a)].">
      <j1 rule="hyper" parents="63 19510 19524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19527">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,u))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(8044(a,1),19524(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8044 19524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19531">
    <literal><![CDATA[
      a(x,L(y,z,u) \ w,a(y,z,u)) = a(y,z,a(x,y \ w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19078,a(flip),b,19526,a),flip(a)].">
      <j1 rule="hyper" parents="63 19078 19526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19533">
    <literal><![CDATA[
      a(x,y,a(z,(u * a(w,v5,u)) \ v6,u)) = a(x,y,a(z,L(u,v5,w) * v6,u))
    ]]></literal>
    <justification jstring="[para(19274(a,1),19441(a,1,3,2))].">
      <j1 rule="para" parents="19274 19441"/>
    </justification>
  </clause>

  <clause id="19534">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,v5) \ v6,u)) = a(x,y,a(z,L(u,w,v5) * v6,u))
    ]]></literal>
    <justification jstring="[para(18810(a,1),19533(a,1,3))].">
      <j1 rule="para" parents="18810 19533"/>
    </justification>
  </clause>

  <clause id="19535">
    <literal><![CDATA[
      a(x,L(y,z,u) \ w,a(y,v5,v6)) = a(v6,v5,a(x,L(y,z,u) * w,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,19141,a,b,19534,a)].">
      <j1 rule="hyper" parents="63 19141 19534"/>
    </justification>
  </clause>

  <clause id="19536">
    <literal><![CDATA[
      a(x,y,z \ ((R(u,w,w) \ v5) \ v6)) = a(x,y,z \ ((L(u,w,w) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(18888(a,1),19519(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="18888 19519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19537">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,v5,a(x,u,a(w,y,v6))) = a(x,y,a(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,19132,a(flip),b,19520,a),flip(a)].">
      <j1 rule="hyper" parents="316 19132 19520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19538">
    <literal><![CDATA[
      a(x,x,a(y,z,a(u,w,v5))) * a(x,x,a(y,z,L(u,w,v5))) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(18894(a,1),19521(a,1,2))].">
      <j1 rule="para" parents="18894 19521"/>
    </justification>
  </clause>

  <clause id="19539">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,v5,a(x,u,a(w,y,v6))) = a(x,y,a(z,u,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(316,a,19380,a(flip),b,19537,a),flip(a)].">
      <j1 rule="hyper" parents="316 19380 19537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19540">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(132,a,19527,a(flip),b,19539,a),flip(a)].">
      <j1 rule="hyper" parents="132 19527 19539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19541">
    <literal><![CDATA[
      a(a(x,y,a(z,u,y)),w,v5) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,19540,a,b,13738,a),flip(a)].">
      <j1 rule="hyper" parents="134 19540 13738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19542">
    <literal><![CDATA[
      a(x,y,a(z,z,a(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,19375,a(flip),b,19540,a)].">
      <j1 rule="hyper" parents="63 19375 19540"/>
    </justification>
  </clause>

  <clause id="19544">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,u))) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,19541,a)].">
      <j1 rule="hyper" parents="52 19541"/>
    </justification>
  </clause>

  <clause id="19545">
    <literal><![CDATA[
      a(x,x,a(y,z,a(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,19168,a,b,19542,a)].">
      <j1 rule="hyper" parents="63 19168 19542"/>
    </justification>
  </clause>

  <clause id="19546">
    <literal><![CDATA[
      L(a(x,y,z),u,a(u,w,v5)) = a(x,y,z) * 1
    ]]></literal>
    <justification jstring="[para(19542(a,1),18329(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19542 18329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19551">
    <literal><![CDATA[
      L(x,y,a(z,u,a(u,w,v5))) = x
    ]]></literal>
    <justification jstring="[para(13660(a,1),19544(a,1,3))].">
      <j1 rule="para" parents="13660 19544"/>
    </justification>
  </clause>

  <clause id="19552">
    <literal><![CDATA[
      L(x,y,a(z,z,a(u,w,v5))) = x
    ]]></literal>
    <justification jstring="[para(18988(a,1),19544(a,1,3))].">
      <j1 rule="para" parents="18988 19544"/>
    </justification>
  </clause>

  <clause id="19553">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,w,v5))) = x
    ]]></literal>
    <justification jstring="[para(19005(a,1),19544(a,1,3))].">
      <j1 rule="para" parents="19005 19544"/>
    </justification>
  </clause>

  <clause id="19558">
    <literal><![CDATA[
      1 * a(x,x,a(y,z,L(u,w,v5))) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(19545(a,1),19538(a,1,1))].">
      <j1 rule="para" parents="19545 19538"/>
    </justification>
  </clause>

  <clause id="19559">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,z,v5))) = a(x,y,a(z,u,w)) * 1
    ]]></literal>
    <justification jstring="[para(19545(a,1),19539(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19545 19539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19560">
    <literal><![CDATA[
      L(x,y,a(z,u,a(y,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,19259,a,b,19551,a)].">
      <j1 rule="hyper" parents="63 19259 19551"/>
    </justification>
  </clause>

  <clause id="19565">
    <literal><![CDATA[
      (x * a(y,z,a(u,u,w))) * v5 = (x * v5) * a(y,z,a(u,u,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,19553,a(flip),b,2494,a)].">
      <j1 rule="hyper" parents="139 19553 2494"/>
    </justification>
  </clause>

  <clause id="19566">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * (w * v5) = w * (a(x,y,a(z,z,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(138,a,19553,a(flip),b,5343,a),flip(a)].">
      <j1 rule="hyper" parents="138 19553 5343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19567">
    <literal><![CDATA[
      (x * y) * a(z,u,a(w,w,v5)) = x * (y * a(z,u,a(w,w,v5)))
    ]]></literal>
    <justification jstring="[para(19553(a,1),5383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19553 5383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19569">
    <literal><![CDATA[
      L(a(x,y,z),u,a(u,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,8,a(flip),b,19546,a),flip(a)].">
      <j1 rule="hyper" parents="316 8 19546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19572">
    <literal><![CDATA[
      a(x,y,z) * (a(u,w,w) * v5) = a(u,w,w) * (a(x,y,z) * v5)
    ]]></literal>
    <justification jstring="[para(19569(a,1),19263(a,1,1))].">
      <j1 rule="para" parents="19569 19263"/>
    </justification>
  </clause>

  <clause id="19575">
    <literal><![CDATA[
      a(x,x,a(y,z,L(u,w,v5))) = a(u,z,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(131,a,19558,a,b,19154,a)].">
      <j1 rule="hyper" parents="131 19558 19154"/>
    </justification>
  </clause>

  <clause id="19578">
    <literal><![CDATA[
      a(x,y,a(z,u,L(u,w,v5))) = a(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19381,a,b,19575,a)].">
      <j1 rule="hyper" parents="63 19381 19575"/>
    </justification>
  </clause>

  <clause id="19581">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,z,v5))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,8,a(flip),b,19559,a),flip(a)].">
      <j1 rule="hyper" parents="316 8 19559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19583">
    <literal><![CDATA[
      a(x,y,a(z,u,T(z,w) \ (v5 \ v6))) = a(x,y,a(z,u,(v5 * z) \ v6))
    ]]></literal>
    <justification jstring="[para(11880(a,1),19581(a,1,3))].">
      <j1 rule="para" parents="11880 19581"/>
    </justification>
  </clause>

  <clause id="19590">
    <literal><![CDATA[
      a(x,y,(z * (((u \ 1) * a(w,v5,a(v6,v6,v7))) * v8)) * v9) = a(x,y,(z * (a(w,v5,a(v6,v6,v7)) * (v8 * u))) * v9)
    ]]></literal>
    <justification jstring="[para(19565(a,2),7581(a,1,3,1,2))].">
      <j1 rule="para" parents="19565 7581"/>
    </justification>
  </clause>

  <clause id="19591">
    <literal><![CDATA[
      (x * (a(y,z,a(u,u,w)) * (v5 * v6))) \ ((x * v5) * (a(y,z,a(u,u,w)) * v6)) = a(x,v5,a(y,z,a(u,u,w)) * v6)
    ]]></literal>
    <justification jstring="[para(19566(a,2),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="19566 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19592">
    <literal><![CDATA[
      a(x,y,(a(z,u,a(w,w,v5)) * v6) * v7) = a(x,y,a(z,u,a(w,w,v5)) * (v7 * v6))
    ]]></literal>
    <justification jstring="[para(19566(a,2),5469(a,1,3)),flip(a)].">
      <j1 rule="para" parents="19566 5469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19593">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * (w * v5) = w * (a(y,z,a(x,x,u)) * v5)
    ]]></literal>
    <justification jstring="[para(18945(a,1),19566(a,1,1))].">
      <j1 rule="para" parents="18945 19566"/>
    </justification>
  </clause>

  <clause id="19594">
    <literal><![CDATA[
      a(x,y,y) * (a(z,u,w) * (R(x,y,y) \ v5)) = a(z,u,w) * (x \ v5)
    ]]></literal>
    <justification jstring="[para(19216(a,1),19572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19216 19572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19596">
    <literal><![CDATA[
      a(x,y,a(z,u,T(z,w) \ (v5 \ v6))) = a(x,y,a(z,u,v5 \ (z \ v6)))
    ]]></literal>
    <justification jstring="[para(15480(a,1),19583(a,2,3))].">
      <j1 rule="para" parents="15480 19583"/>
    </justification>
  </clause>

  <clause id="19597">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,w,v5)) * (v6 * v7)) = a(x,y,v6 * (a(z,u,a(w,w,v5)) * v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,5469,a,b,19592,a),flip(a)].">
      <j1 rule="hyper" parents="63 5469 19592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19598">
    <literal><![CDATA[
      x \ (L(R(y,z,u),w,v5) * (L(y,w,v5) \ x)) = L(a(y,z,L(u,w,v5)),y,L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(19034(a,2),18886(a,2,1))].">
      <j1 rule="para" parents="19034 18886"/>
    </justification>
  </clause>

  <clause id="19599">
    <literal><![CDATA[
      a(x,y,L(z,L(u,w,a(x,y,z)) * w,v5)) = a(x,y,L(z,(a(x,y,z) * w) * u,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,19034,a,b,19044,a),flip(a)].">
      <j1 rule="hyper" parents="316 19034 19044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19600">
    <literal><![CDATA[
      a(T(x,y),T(z,u) * (w * (K(u,z) / z)),a(v5,v6,v7)) = a(v5,R(w,z \ 1,z),a(v7,v6,x))
    ]]></literal>
    <justification jstring="[hyper(5558,a,19281,a)].">
      <j1 rule="hyper" parents="5558 19281"/>
    </justification>
  </clause>

  <clause id="19602">
    <literal><![CDATA[
      x \ (L(R(y,z,u),w,v5) * (L(y,w,v5) \ x)) = a(y,z,L(L(u,w,v5),y,L(x,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,19034,a,b,19598,a),flip(a)].">
      <j1 rule="hyper" parents="316 19034 19598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19603">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),x,L(w * u,u,w))) = (w * (u * x)) \ (w * (u * R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14970,a(flip),b,19602,a),flip(a)].">
      <j1 rule="hyper" parents="63 14970 19602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19604">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),x,(u \ 1) \ w)) = (w * (u * x)) \ (w * (u * R(x,y,z)))
    ]]></literal>
    <justification jstring="[para(19516(a,1),19603(a,1,3))].">
      <j1 rule="para" parents="19516 19603"/>
    </justification>
  </clause>

  <clause id="19605">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),x,(u \ 1) * w)) = (w * (u * x)) \ (w * (u * R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19512,a(flip),b,19604,a)].">
      <j1 rule="hyper" parents="63 19512 19604"/>
    </justification>
  </clause>

  <clause id="19606">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * R(z,u,w))) = a(z,u,L(L(w,y,x),z,x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,5768,a(flip),b,19605,a),flip(a)].">
      <j1 rule="hyper" parents="63 5768 19605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19607">
    <literal><![CDATA[
      (x * a(y,z,u)) * a(w,v5,L(y,v6,v7)) = a(y,z,u) * (x * a(w,v5,L(y,v6,v7)))
    ]]></literal>
    <justification jstring="[para(18635(a,1),19033(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18635 19033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19608">
    <literal><![CDATA[
      ((x * y) * a(z,u,w)) * ((x * y) \ x) = x * a(z,u,L(w,x * y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,19114,a(flip),b,19231,a),flip(a)].">
      <j1 rule="hyper" parents="63 19114 19231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19609">
    <literal><![CDATA[
      a(x,y,z) * (a(u,w,L(x,x,a(z,y,v5))) \ v5) = v5 * (a(x,y,z) * (x \ L(x,w,u)))
    ]]></literal>
    <justification jstring="[para(18982(a,1),19356(a,1,2,1,3))].">
      <j1 rule="para" parents="18982 19356"/>
    </justification>
  </clause>

  <clause id="19610">
    <literal><![CDATA[
      a(a(x,x,y),z,(u * w) * a(x,x,x * y)) = a(a(x,x,y),z,w * (u * a(y,x,x)))
    ]]></literal>
    <justification jstring="[hyper(316,a,19410,a(flip),b,19500,a),flip(a)].">
      <j1 rule="hyper" parents="316 19410 19500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19612">
    <literal><![CDATA[
      a(x,y,z) * (a(u,w,L(x,x,a(z,y,v5))) \ v5) = v5 * (a(u,w,x) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(18709(a,1),19609(a,2,2))].">
      <j1 rule="para" parents="18709 19609"/>
    </justification>
  </clause>

  <clause id="19613">
    <literal><![CDATA[
      a(a(x,x,y),z,(u * w) * a(x,x,x * y)) = a(x,x,a(w * (u * a(y,x,x)),z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,19132,a(flip),b,19610,a),flip(a)].">
      <j1 rule="hyper" parents="316 19132 19610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19614">
    <literal><![CDATA[
      a(a(x,x,y),z,a(x,x,y) * (u * w)) = a(x,x,a(w * (u * a(y,x,x)),z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,11730,a(flip),b,19613,a)].">
      <j1 rule="hyper" parents="63 11730 19613"/>
    </justification>
  </clause>

  <clause id="19615">
    <literal><![CDATA[
      a(x,x,a(a(x,x,y) * (z * u),w,y)) = a(x,x,a(u * (z * a(y,x,x)),w,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,19132,a(flip),b,19614,a)].">
      <j1 rule="hyper" parents="63 19132 19614"/>
    </justification>
  </clause>

  <clause id="19616">
    <literal><![CDATA[
      a(x,x,a(y * (z * a(u,x,x)),w,u)) = a(x,x,a(z * y,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19304,a(flip),b,19615,a),flip(a)].">
      <j1 rule="hyper" parents="63 19304 19615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19618">
    <literal><![CDATA[
      a(x,y,L(z \ (x * y),x * y,x * y)) = L(z * (x * y),y,x) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,11178,a(flip),b,18282,a)].">
      <j1 rule="hyper" parents="63 11178 18282"/>
    </justification>
  </clause>

  <clause id="19621">
    <literal><![CDATA[
      L(x,y,z) * (u * L(L(x,w,v5) \ x,x,u)) = x * ((L(x,y,z) * u) / L(T(x,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,6851,a(flip),b,18499,a)].">
      <j1 rule="hyper" parents="63 6851 18499"/>
    </justification>
  </clause>

  <clause id="19623">
    <literal><![CDATA[
      (a(x,y,z) \ (u / z)) * ((u / z) \ a(x,y,z)) = a(u,u * z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,18626,a,b,18594,a),flip(a)].">
      <j1 rule="hyper" parents="316 18626 18594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19624">
    <literal><![CDATA[
      (a(x,y,z) \ (z \ u)) * ((z \ u) \ a(x,y,z)) = a(u,u * z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10484,a(flip),b,19623,a)].">
      <j1 rule="hyper" parents="63 10484 19623"/>
    </justification>
  </clause>

  <clause id="19625">
    <literal><![CDATA[
      a(x * y,x * y,a(z,u,x)) = a(y,y * x,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,17814,a(flip),b,19624,a)].">
      <j1 rule="hyper" parents="63 17814 19624"/>
    </justification>
  </clause>

  <clause id="19626">
    <literal><![CDATA[
      a(x * y,x * y,a(x,z,u)) = a(y,y * x,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,13660,a,b,19625,a)].">
      <j1 rule="hyper" parents="63 13660 19625"/>
    </justification>
  </clause>

  <clause id="19627">
    <literal><![CDATA[
      L(a(x,y,z),x \ u,(x \ u) * a(x,y,z)) = a(u,u * x,a(z,y,x)) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(19626(a,1),17810(a,2,1))].">
      <j1 rule="para" parents="19626 17810"/>
    </justification>
  </clause>

  <clause id="19628">
    <literal><![CDATA[
      L(a(x,y,z),x \ u,(x \ u) * a(x,y,z)) = a(x,y,z) * a(u,u * x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,14470,a(flip),b,19627,a),flip(a)].">
      <j1 rule="hyper" parents="316 14470 19627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19629">
    <literal><![CDATA[
      L(a(x,y,z),x \ u,(x \ u) * a(x,y,z)) = L(a(x,y,z),u * x,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,14593,a(flip),b,19628,a),flip(a)].">
      <j1 rule="hyper" parents="316 14593 19628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19630">
    <literal><![CDATA[
      L(a(x,y,z),x \ u,x \ u) = L(a(x,y,z),u * x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17808,a(flip),b,19629,a)].">
      <j1 rule="hyper" parents="63 17808 19629"/>
    </justification>
  </clause>

  <clause id="19631">
    <literal><![CDATA[
      L(a(x,y,z),x * u,x * u) = L(a(x,y,z),u * x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15778,a(flip),b,19630,a)].">
      <j1 rule="hyper" parents="63 15778 19630"/>
    </justification>
  </clause>

  <clause id="19632">
    <literal><![CDATA[
      a(x,y,L(z,x * u,x * u)) = L(a(x,y,z),u * x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19034,a,b,19631,a)].">
      <j1 rule="hyper" parents="63 19034 19631"/>
    </justification>
  </clause>

  <clause id="19633">
    <literal><![CDATA[
      L(a(x,y,z),u * x,u * x) = L(a(x,y,z),u * x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10844,a,b,19631,a)].">
      <j1 rule="hyper" parents="63 10844 19631"/>
    </justification>
  </clause>

  <clause id="19634">
    <literal><![CDATA[
      a(x,y,L(z,x * u,x * u)) = a(x,y,L(z,u * x,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,19034,a,b,19632,a),flip(a)].">
      <j1 rule="hyper" parents="316 19034 19632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19635">
    <literal><![CDATA[
      L(a(x,y,z),y * x,y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,18220,a(flip),b,19633,a),flip(a)].">
      <j1 rule="hyper" parents="63 18220 19633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19636">
    <literal><![CDATA[
      a(x,y,L(z,y * x,y)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,19034,a,b,19635,a)].">
      <j1 rule="hyper" parents="63 19034 19635"/>
    </justification>
  </clause>

  <clause id="19637">
    <literal><![CDATA[
      a(x,y,L(z \ (x * y),y * x,y)) = L(z * (x * y),y,x) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,19618,a(flip),b,19634,a),flip(a)].">
      <j1 rule="hyper" parents="63 19618 19634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19638">
    <literal><![CDATA[
      L(x * (y * z),z,y) \ (x * (y * z)) = y \ R(y,z,x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19636,a(flip),b,19637,a),flip(a)].">
      <j1 rule="hyper" parents="63 19636 19637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19639">
    <literal><![CDATA[
      L(x * (y * z),z,y) \ (x * (y * z)) = a(y,z,x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,18733,a,b,19638,a),flip(a)].">
      <j1 rule="hyper" parents="316 18733 19638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19640">
    <literal><![CDATA[
      L(x * (y * z),z,y) \ (x * (y * z)) = a(y,z,(y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,18893,a(flip),b,19639,a),flip(a)].">
      <j1 rule="hyper" parents="316 18893 19639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19641">
    <literal><![CDATA[
      a(x,y,(x \ z) * y) = a(x,y,z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(18755,a,19640,a),flip(a)].">
      <j1 rule="hyper" parents="18755 19640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19642">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((z \ (u \ w)) \ w)) = a(x,y,a(u,z,w * (u * z)))
    ]]></literal>
    <justification jstring="[para(19641(a,1),18450(a,2,3))].">
      <j1 rule="para" parents="19641 18450"/>
    </justification>
  </clause>

  <clause id="19643">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) \ (z \ (u \ w))) = a(x,y,a(u,z,w * (u * z)))
    ]]></literal>
    <justification jstring="[para(19641(a,1),19232(a,2,3))].">
      <j1 rule="para" parents="19641 19232"/>
    </justification>
  </clause>

  <clause id="19644">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),w,u)) \ w = u \ ((a(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,19077,a(flip),b,19120,a),flip(a)].">
      <j1 rule="hyper" parents="63 19077 19120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19645">
    <literal><![CDATA[
      L((a(x,y,a(z,u,w)) * v5) \ v6,u,a(x,v5,a(z,y,w))) = v5 \ (v6 * a(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(14470(a,1),19378(a,2,2))].">
      <j1 rule="para" parents="14470 19378"/>
    </justification>
  </clause>

  <clause id="19646">
    <literal><![CDATA[
      L(a(x,y,L(z,u,a(u,w,v5))),a(u,u,v5),w) = a(x,y,z) * a(v5,a(x,y,z),a(u,u,w))
    ]]></literal>
    <justification jstring="[para(19034(a,2),19422(a,1,1))].">
      <j1 rule="para" parents="19034 19422"/>
    </justification>
  </clause>

  <clause id="19647">
    <literal><![CDATA[
      L(x * a(y,y,a(a(z,u,w),x,v5)),u,a(w,y,a(v5,z,y))) = L(x,a(w,u,a(y,y,v5)),z)
    ]]></literal>
    <justification jstring="[para(19132(a,1),19424(a,1,1,2))].">
      <j1 rule="para" parents="19132 19424"/>
    </justification>
  </clause>

  <clause id="19648">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,v6)) * a(w,v6,a(y,v5,L(x,z,u))) = a(v6,a(x,v5,w),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19159,a,b,19431,a)].">
      <j1 rule="hyper" parents="63 19159 19431"/>
    </justification>
  </clause>

  <clause id="19649">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) * a(y,a(w,u,x),L(z,v5,v6)) = a(y,u,a(x,L(z,v5,v6),w))
    ]]></literal>
    <justification jstring="[hyper(139,a,19431,a(flip),b,14470,a)].">
      <j1 rule="hyper" parents="139 19431 14470"/>
    </justification>
  </clause>

  <clause id="19650">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) * K(a(y,u,a(x,L(z,v5,v6),w)) \ 1,a(y,u,a(x,L(z,v5,v6),w)) * a(x,y,a(z,u,L(w,v5,v6)))) = (a(y,a(w,u,x),L(z,v5,v6)) \ a(x,y,a(z,u,L(w,v5,v6)))) * (a(y,u,a(x,L(z,v5,v6),w)) * a(x,y,a(z,u,L(w,v5,v6))))
    ]]></literal>
    <justification jstring="[para(19431(a,1),3196(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="19431 3196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19651">
    <literal><![CDATA[
      a(T(x,y),T(z,u) * (w * (K(u,z) / z)),a(v5,v6,v7)) = a(v5,L(w,z \ 1,z),a(v7,v6,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,11325,a(flip),b,19600,a),flip(a)].">
      <j1 rule="hyper" parents="316 11325 19600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19652">
    <literal><![CDATA[
      x * ((L(x,y,z) * u) / L(T(x,u),w,v5)) = L(x,y,z) * (x * (L(x,w,v5) \ u))
    ]]></literal>
    <justification jstring="[para(13622(a,1),19621(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13622 19621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19653">
    <literal><![CDATA[
      x * ((L(x,y,z) * u) / L(T(x,u),w,v5)) = x * (L(x,y,z) * (L(x,w,v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(316,a,1124,a(flip),b,19652,a),flip(a)].">
      <j1 rule="hyper" parents="316 1124 19652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19654">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,u,w) * v5)) = x * (L(x,u,w) * (L(x,y,z) \ v5))
    ]]></literal>
    <justification jstring="[para(6569(a,1),19653(a,1,2))].">
      <j1 rule="para" parents="6569 19653"/>
    </justification>
  </clause>

  <clause id="19655">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,u,w) * v5) = L(x,u,w) * (L(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(354,a,19654,a),flip(a)].">
      <j1 rule="hyper" parents="354 19654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19658">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((L(1 / x,u,w) \ 1) \ v5)) = x \ (L(x,u,w) * (L(x,y,z) \ v5))
    ]]></literal>
    <justification jstring="[para(19655(a,1),14138(a,2,2))].">
      <j1 rule="para" parents="19655 14138"/>
    </justification>
  </clause>

  <clause id="19660">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((L(1 / x,u,w) \ 1) \ v5)) = ((L(x,y,z) \ v5) / x) * L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,4382,a(flip),b,19658,a),flip(a)].">
      <j1 rule="hyper" parents="316 4382 19658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19661">
    <literal><![CDATA[
      (a(x,y,a(z,z,u)) * w) \ v5 = w \ (v5 * a(x,y,a(z,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19560,a(flip),b,19645,a)].">
      <j1 rule="hyper" parents="63 19560 19645"/>
    </justification>
  </clause>

  <clause id="19662">
    <literal><![CDATA[
      a(x,y,L(L(z,u,a(u,w,v5)),a(u,u,v5),w)) = a(x,y,z) * a(v5,a(x,y,z),a(u,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19034,a,b,19646,a)].">
      <j1 rule="hyper" parents="63 19034 19646"/>
    </justification>
  </clause>

  <clause id="19663">
    <literal><![CDATA[
      L(x * a(y,y,a(z,u,a(w,x,v5))),u,a(v5,y,a(w,z,y))) = L(x,a(v5,u,a(y,y,w)),z)
    ]]></literal>
    <justification jstring="[para(19132(a,1),19647(a,1,1,2,3))].">
      <j1 rule="para" parents="19132 19647"/>
    </justification>
  </clause>

  <clause id="19664">
    <literal><![CDATA[
      T(a(x,a(y,L(z,u,w),a(v5,v6,v7)),a(v5,v7,a(z,v6,L(y,u,w)))) * a(y,L(z,u,w),a(v5,v6,v7)),a(v5,v7,a(z,v6,L(y,u,w)))) = L(a(v5,v7,a(z,v6,L(y,u,w))),a(y,L(z,u,w),a(v5,v6,v7)),x) \ a(v7,a(y,v6,v5),L(z,u,w))
    ]]></literal>
    <justification jstring="[para(19648(a,1),13637(a,2,2))].">
      <j1 rule="para" parents="19648 13637"/>
    </justification>
  </clause>

  <clause id="19665">
    <literal><![CDATA[
      a(T(x,y),T(z,u) * (w * (K(u,z) / z)),a(v5,v6,v7)) = a(v5,L(w,z,z),a(v7,v6,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,12364,a(flip),b,19651,a),flip(a)].">
      <j1 rule="hyper" parents="316 12364 19651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19666">
    <literal><![CDATA[
      a(T(x,y),T(x,z) * (u * (K(z,x) / x)),a(w,v5,v6)) = a(w,u,a(v6,v5,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,19438,a(flip),b,19665,a),flip(a)].">
      <j1 rule="hyper" parents="316 19438 19665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19667">
    <literal><![CDATA[
      a(T(x,y),T(x,z) * (u * (K(z,x) / x)),a(w * (v5 / v6),v7,v8)) = a(w * (v6 \ v5),u,a(v8,v7,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,3150,a(flip),b,19666,a),flip(a)].">
      <j1 rule="hyper" parents="316 3150 19666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19668">
    <literal><![CDATA[
      L(x * 1,y,a(z,u,a(w,v5,u))) = L(x,a(z,y,a(u,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(19545(a,1),19663(a,1,1,2))].">
      <j1 rule="para" parents="19545 19663"/>
    </justification>
  </clause>

  <clause id="19669">
    <literal><![CDATA[
      L(x,a(y,z,a(u,u,w)),v5) = x
    ]]></literal>
    <justification jstring="[hyper(135,a,19544,a(flip),b,19668,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="135 19544 19668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19671">
    <literal><![CDATA[
      (a(x,x,a(y,z,u)) * w) * v5 = w * (a(y,z,a(x,x,u)) * v5)
    ]]></literal>
    <justification jstring="[para(19669(a,1),19279(a,1,2))].">
      <j1 rule="para" parents="19669 19279"/>
    </justification>
  </clause>

  <clause id="19672">
    <literal><![CDATA[
      (x * (a(y,z,a(u,u,w)) * v5)) * v6 = (x * v5) * (a(y,z,a(u,u,w)) * v6)
    ]]></literal>
    <justification jstring="[para(19593(a,1),19671(a,1,1))].">
      <j1 rule="para" parents="19593 19671"/>
    </justification>
  </clause>

  <clause id="19680">
    <literal><![CDATA[
      L(a(x,y,(z \ y) * y) \ u,a(x,y,(z \ y) * y),z) = (u / z) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,13848,a(flip),b,18204,a),flip(a)].">
      <j1 rule="hyper" parents="316 13848 18204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19681">
    <literal><![CDATA[
      L(a(x,y,(z \ y) * y) \ u,z,a(x,y,(z \ y) * y)) = (u / z) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11481,a(flip),b,19680,a)].">
      <j1 rule="hyper" parents="63 11481 19680"/>
    </justification>
  </clause>

  <clause id="19682">
    <literal><![CDATA[
      L(a(x,y,(z \ y) * y) \ u,z,a(x,y,z)) = (u / z) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,18366,a(flip),b,19681,a)].">
      <j1 rule="hyper" parents="63 18366 19681"/>
    </justification>
  </clause>

  <clause id="19683">
    <literal><![CDATA[
      L(a(x,y,z) \ u,z,a(x,y,z)) = (u / z) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(18629(a,1),19682(a,1,1,1))].">
      <j1 rule="para" parents="18629 19682"/>
    </justification>
  </clause>

  <clause id="19684">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),w,u) = a(z,y,y * (x \ y)) \ a(w,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,14986,a(flip),b,18206,a)].">
      <j1 rule="hyper" parents="316 14986 18206"/>
    </justification>
  </clause>

  <clause id="19685">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),L(1 / (1 / y),z,u),w) = T(1 / (a(w,y,L(y,z,u)) / y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10810,a(flip),b,18212,a)].">
      <j1 rule="hyper" parents="63 10810 18212"/>
    </justification>
  </clause>

  <clause id="19687">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),L((1 / y) \ 1,z,u),w) = T(1 / (a(w,y,L(y,z,u)) / y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10835,a(flip),b,19685,a)].">
      <j1 rule="hyper" parents="63 10835 19685"/>
    </justification>
  </clause>

  <clause id="19688">
    <literal><![CDATA[
      L(1 / (K(x,y) / y),L(y,z,u),w) = T(1 / (a(w,y,L(y,z,u)) / y),x)
    ]]></literal>
    <justification jstring="[para(83(a,1),19687(a,1,2,1))].">
      <j1 rule="para" parents="83 19687"/>
    </justification>
  </clause>

  <clause id="19689">
    <literal><![CDATA[
      L(T(x,y),x \ 1,L(z,u,w) * x) = T(1 / (a(z,x,L(x,u,w)) / x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16933,a(flip),b,19688,a)].">
      <j1 rule="hyper" parents="63 16933 19688"/>
    </justification>
  </clause>

  <clause id="19690">
    <literal><![CDATA[
      L(T(x,y),x \ 1,L(z,u,w) * x) = T(L(x,x \ 1,L(x * z,u,w)),y)
    ]]></literal>
    <justification jstring="[para(18426(a,2),19689(a,2,1))].">
      <j1 rule="para" parents="18426 19689"/>
    </justification>
  </clause>

  <clause id="19691">
    <literal><![CDATA[
      L(T(x,y),x \ 1,L(x * z,u,w)) = L(T(x,y),x \ 1,L(z,u,w) * x)
    ]]></literal>
    <justification jstring="[hyper(316,a,25,a,b,19690,a)].">
      <j1 rule="hyper" parents="316 25 19690"/>
    </justification>
  </clause>

  <clause id="19692">
    <literal><![CDATA[
      L(T(x,x \ 1),x \ 1,L(x * y,z,u)) = L(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,7177,a(flip),b,19691,a),flip(a)].">
      <j1 rule="hyper" parents="316 7177 19691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19693">
    <literal><![CDATA[
      (L(x * y,z,u) * (x \ 1)) \ L(x * y,z,u) = L(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,367,a(flip),b,19692,a)].">
      <j1 rule="hyper" parents="63 367 19692"/>
    </justification>
  </clause>

  <clause id="19694">
    <literal><![CDATA[
      L(x,x,L(x * y,z,u)) = L(x,x,x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7862,a(flip),b,19693,a),flip(a)].">
      <j1 rule="hyper" parents="63 7862 19693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19695">
    <literal><![CDATA[
      ((x * L(y,z,u)) * x) \ (x * L(y,z,u)) = (1 / x) * ((x \ 1) * L(x,x,L(x * y,z,u)))
    ]]></literal>
    <justification jstring="[para(19694(a,2),4444(a,2,2,2))].">
      <j1 rule="para" parents="19694 4444"/>
    </justification>
  </clause>

  <clause id="19696">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((R(u,w,w) \ w) \ (z * L(w,w,u)))) = a(x,y,a((w \ 1) \ u,u,z))
    ]]></literal>
    <justification jstring="[para(13109(a,1),18266(a,2,3))].">
      <j1 rule="para" parents="13109 18266"/>
    </justification>
  </clause>

  <clause id="19697">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((R(u,w,w) \ w) \ (z * L(w,w,u)))) = a(x,y,a(w \ u,u,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,12307,a(flip),b,19696,a),flip(a)].">
      <j1 rule="hyper" parents="316 12307 19696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19698">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((R(u,w,w) \ w) \ (z * L(w,w,u)))) = a(x,y,a(w * u,u,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,19392,a(flip),b,19697,a),flip(a)].">
      <j1 rule="hyper" parents="316 19392 19697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19699">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((L(u,w,w) \ w) \ (z * L(w,w,u)))) = a(x,y,a(w * u,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19536,a(flip),b,19698,a)].">
      <j1 rule="hyper" parents="63 19536 19698"/>
    </justification>
  </clause>

  <clause id="19700">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * (((L(x,y,z) \ 1) \ x) * a(u,w,v5)) = L(a(u,w,v5) * x,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,14839,a,b,18457,a),flip(a)].">
      <j1 rule="hyper" parents="316 14839 18457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19701">
    <literal><![CDATA[
      a(x,y,z \ ((u / (w * v5)) * ((w \ 1) \ v5))) = a(x,y,z \ (v5 * (L(v5,w,w) \ u)))
    ]]></literal>
    <justification jstring="[para(18442(a,1),18562(a,1,3,2))].">
      <j1 rule="para" parents="18442 18562"/>
    </justification>
  </clause>

  <clause id="19702">
    <literal><![CDATA[
      a(x,y,z \ ((u / (w * v5)) * (w \ v5))) = a(x,y,z \ (v5 * (L(v5,w,w) \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6690,a(flip),b,19701,a)].">
      <j1 rule="hyper" parents="63 6690 19701"/>
    </justification>
  </clause>

  <clause id="19703">
    <literal><![CDATA[
      a(x,y,z \ (((u * w) \ v5) * (u \ w))) = a(x,y,z \ (w * (L(w,u,u) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5627,a(flip),b,19702,a)].">
      <j1 rule="hyper" parents="63 5627 19702"/>
    </justification>
  </clause>

  <clause id="19704">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * ((w \ u) \ v5))) = a(x,y,z \ (u * (L(u,w,w) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16694,a(flip),b,19703,a)].">
      <j1 rule="hyper" parents="63 16694 19703"/>
    </justification>
  </clause>

  <clause id="19705">
    <literal><![CDATA[
      a(x,y,z \ (((u \ w) \ v5) * (w * u))) = a(x,y,z \ (w * (L(w,u,u) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a,b,19704,a)].">
      <j1 rule="hyper" parents="63 5490 19704"/>
    </justification>
  </clause>

  <clause id="19706">
    <literal><![CDATA[
      a(x,y,z \ (((u \ w) \ v5) * (w * u))) = a(x,y,z \ (a(u,u,w) * v5))
    ]]></literal>
    <justification jstring="[para(18970(a,1),19705(a,2,3,2))].">
      <j1 rule="para" parents="18970 19705"/>
    </justification>
  </clause>

  <clause id="19708">
    <literal><![CDATA[
      ((x * L(y,z,u)) * x) \ (x * L(y,z,u)) = (1 / x) * L((x \ 1) * L(x,x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(16805(a,2),19695(a,2,2))].">
      <j1 rule="para" parents="16805 19695"/>
    </justification>
  </clause>

  <clause id="19709">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x * L(x,y,z)) * a(u,w,v5)) = L(a(u,w,v5) * x,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(10715(a,1),19700(a,1,2,1))].">
      <j1 rule="para" parents="10715 19700"/>
    </justification>
  </clause>

  <clause id="19710">
    <literal><![CDATA[
      ((x * L(x,y,z)) * a(u,w,v5)) * ((x * L(x,y,z)) \ x) = L(a(u,w,v5) * x,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,10716,a,b,19709,a)].">
      <j1 rule="hyper" parents="63 10716 19709"/>
    </justification>
  </clause>

  <clause id="19712">
    <literal><![CDATA[
      ((x * L(y,z,u)) * x) \ (x * L(y,z,u)) = x \ L(x \ L(x,x,x * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,7881,a(flip),b,19708,a),flip(a)].">
      <j1 rule="hyper" parents="316 7881 19708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19713">
    <literal><![CDATA[
      ((x * L(y,z,u)) * x) \ (x * L(y,z,u)) = L(x \ 1,x,L(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,16813,a(flip),b,19712,a),flip(a)].">
      <j1 rule="hyper" parents="316 16813 19712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19714">
    <literal><![CDATA[
      L(x \ 1,x,L(x * y,z,u)) = L(x \ 1,x,x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(379,a,19713,a),flip(a)].">
      <j1 rule="hyper" parents="379 19713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19715">
    <literal><![CDATA[
      L(x \ 1,x,L(x * (x \ y),z,u)) = R((x \ 1) \ y,z,u) \ (R((x \ 1) \ y,z,u) / (1 / (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(316,a,15002,a(flip),b,19714,a),flip(a)].">
      <j1 rule="hyper" parents="316 15002 19714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19716">
    <literal><![CDATA[
      x * a(y,z,L(u,x * L(x,w,v5),L(x,w,v5))) = L(a(y,z,u) * x,x,a(v5,w,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,19608,a(flip),b,19710,a)].">
      <j1 rule="hyper" parents="63 19608 19710"/>
    </justification>
  </clause>

  <clause id="19717">
    <literal><![CDATA[
      x * a(y,z,L(u,a(w,v5,x),L(x,v5,w))) = L(a(y,z,u) * x,x,a(w,v5,x))
    ]]></literal>
    <justification jstring="[para(18898(a,1),19716(a,1,2))].">
      <j1 rule="para" parents="18898 19716"/>
    </justification>
  </clause>

  <clause id="19718">
    <literal><![CDATA[
      L(a(x,y,z) * u,u,a(w,v5,u)) = u * a(x,y,L(z,u,a(w,v5,u)))
    ]]></literal>
    <justification jstring="[para(17828(a,1),19717(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="17828 19717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19719">
    <literal><![CDATA[
      L(a(x,y,z) * u,u,a(w,v5,u)) = R(u,u,a(z,y,a(x,v5,w))) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,19458,a,b,19718,a),flip(a)].">
      <j1 rule="hyper" parents="316 19458 19718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19721">
    <literal><![CDATA[
      L(a(x,y,z) * u,u,a(w,v5,u)) = L(u,u,a(z,y,a(x,v5,w))) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(5264(a,1),19719(a,2,1))].">
      <j1 rule="para" parents="5264 19719"/>
    </justification>
  </clause>

  <clause id="19722">
    <literal><![CDATA[
      x \ R(x,y * (z \ 1),y * z) = 1 * a(x,(z / y) \ 1,1 * ((z / y) \ 1))
    ]]></literal>
    <justification jstring="[para(13974(a,1),18190(a,1,2))].">
      <j1 rule="para" parents="13974 18190"/>
    </justification>
  </clause>

  <clause id="19723">
    <literal><![CDATA[
      1 * a(x,(y / z) \ 1,1 * ((y / z) \ 1)) = a(x,z * (y \ 1),y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5565,a(flip),b,19722,a),flip(a)].">
      <j1 rule="hyper" parents="63 5565 19722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19724">
    <literal><![CDATA[
      1 * a(x,(y / z) \ 1,y / z) = a(x,z * (y \ 1),y * z)
    ]]></literal>
    <justification jstring="[para(18100(a,1),19723(a,1,2))].">
      <j1 rule="para" parents="18100 19723"/>
    </justification>
  </clause>

  <clause id="19725">
    <literal><![CDATA[
      1 * a(x,(y / z) \ 1,z \ y) = a(x,z * (y \ 1),y * z)
    ]]></literal>
    <justification jstring="[para(5477(a,1),19724(a,1,2))].">
      <j1 rule="para" parents="5477 19724"/>
    </justification>
  </clause>

  <clause id="19726">
    <literal><![CDATA[
      1 * a(x,(y \ z) \ 1,y \ z) = a(x,y * (z \ 1),z * y)
    ]]></literal>
    <justification jstring="[para(11241(a,1),19725(a,1,2))].">
      <j1 rule="para" parents="11241 19725"/>
    </justification>
  </clause>

  <clause id="19727">
    <literal><![CDATA[
      a(x,(y \ z) \ 1,y \ z) = a(x,y * (z \ 1),z * y)
    ]]></literal>
    <justification jstring="[hyper(141,a,19726,a)].">
      <j1 rule="hyper" parents="141 19726"/>
    </justification>
  </clause>

  <clause id="19728">
    <literal><![CDATA[
      a(x,y * (z \ 1),z * y) = a(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13870,a(flip),b,19727,a),flip(a)].">
      <j1 rule="hyper" parents="63 13870 19727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19729">
    <literal><![CDATA[
      a(x,y,a(z,u * (w \ 1),w * u)) = a(x,y,a(z,u \ w,u \ w))
    ]]></literal>
    <justification jstring="[para(19727(a,1),8832(a,1,3))].">
      <j1 rule="para" parents="19727 8832"/>
    </justification>
  </clause>

  <clause id="19730">
    <literal><![CDATA[
      a(x,(y \ 1) * z,y * z) = a(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11190,a,b,19728,a)].">
      <j1 rule="hyper" parents="63 11190 19728"/>
    </justification>
  </clause>

  <clause id="19731">
    <literal><![CDATA[
      R(x,(y \ 1) * z,z * y) = x * a(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[para(19730(a,1),6331(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19730 6331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19732">
    <literal><![CDATA[
      R(x,(y \ 1) * z,z * y) = R(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,18732,a,b,19731,a),flip(a)].">
      <j1 rule="hyper" parents="316 18732 19731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19733">
    <literal><![CDATA[
      R(x,y * (z \ 1),y * z) = R(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10737,a,b,19732,a)].">
      <j1 rule="hyper" parents="63 10737 19732"/>
    </justification>
  </clause>

  <clause id="19734">
    <literal><![CDATA[
      R(x,(y \ z) \ 1,y \ z) = R(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13973,a,b,19733,a)].">
      <j1 rule="hyper" parents="63 13973 19733"/>
    </justification>
  </clause>

  <clause id="19735">
    <literal><![CDATA[
      a(x,y,a(z,u \ w,u \ w)) = a(x,y,a(z,w * u,w * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12008,a(flip),b,19729,a),flip(a)].">
      <j1 rule="hyper" parents="63 12008 19729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19736">
    <literal><![CDATA[
      a(x,y \ z,a(u,w,y \ z)) = a(u,w,a(x,z * y,z * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,19142,a,b,19735,a)].">
      <j1 rule="hyper" parents="63 19142 19735"/>
    </justification>
  </clause>

  <clause id="19737">
    <literal><![CDATA[
      a(x,y,a(y,z * u,z * u)) * L(L(u \ T(z,w),y,x) \ (u \ T(z,w)),v5,v6) = a(x,y,L(u \ z,v5,v6))
    ]]></literal>
    <justification jstring="[para(19735(a,1),15527(a,1,1))].">
      <j1 rule="para" parents="19735 15527"/>
    </justification>
  </clause>

  <clause id="19738">
    <literal><![CDATA[
      a(x,y,a(y,z * L(u,w,v5),z * L(u,w,v5))) * L(L(R(u,w,v5) \ z,y,x) \ (R(u,w,v5) \ z),v6,v7) = a(x,y,L(R(u,w,v5) \ z,v6,v7))
    ]]></literal>
    <justification jstring="[para(19735(a,1),15872(a,1,1))].">
      <j1 rule="para" parents="19735 15872"/>
    </justification>
  </clause>

  <clause id="19739">
    <literal><![CDATA[
      a(x,x \ y,a(z,u,x \ y)) = a(z,u,a(y,x * y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,13376,a(flip),b,19736,a),flip(a)].">
      <j1 rule="hyper" parents="316 13376 19736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19740">
    <literal><![CDATA[
      a(x \ y,z,u) * a(u,z,a(y,x * y,x)) = L(a(x \ y,z,u),x \ y,x)
    ]]></literal>
    <justification jstring="[para(19739(a,1),14593(a,1,2))].">
      <j1 rule="para" parents="19739 14593"/>
    </justification>
  </clause>

  <clause id="19741">
    <literal><![CDATA[
      a(x,y * x,a(z,u,y * x)) = a(z,u,a(x,y * x,y))
    ]]></literal>
    <justification jstring="[hyper(34,a,18414,a,b,19740,a)].">
      <j1 rule="hyper" parents="34 18414 19740"/>
    </justification>
  </clause>

  <clause id="19742">
    <literal><![CDATA[
      L(1 * a(x,y,a(z,u * z,u)),z,u) = a(z,u * z,a(u * z,y,x))
    ]]></literal>
    <justification jstring="[para(19741(a,1),14570(a,1,1,2))].">
      <j1 rule="para" parents="19741 14570"/>
    </justification>
  </clause>

  <clause id="19743">
    <literal><![CDATA[
      L(a(x,y,a(z,u * z,u)),z,u) = a(z,u * z,a(u * z,y,x))
    ]]></literal>
    <justification jstring="[para(7(a,1),19742(a,1,1))].">
      <j1 rule="para" parents="7 19742"/>
    </justification>
  </clause>

  <clause id="19744">
    <literal><![CDATA[
      a(L(a(x,y * x,y),x,y),z,u) = a(x,y * x,a(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17737,a,b,19743,a)].">
      <j1 rule="hyper" parents="63 17737 19743"/>
    </justification>
  </clause>

  <clause id="19745">
    <literal><![CDATA[
      a(x,y * x,a(y * x,z,u)) = a(a(x,y * x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6898(a,1),19744(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6898 19744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19746">
    <literal><![CDATA[
      L(x,y * x,a(y * x,z,u)) = x * a(a(x,y * x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,19745,a(flip),b,18787,a),flip(a)].">
      <j1 rule="hyper" parents="139 19745 18787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19748">
    <literal><![CDATA[
      L(a(x,y,z),u * a(x,y,z),a(u * a(x,y,z),w,v5)) = a(x,y,z) * a(a(u,u,a(x,y,z)),w,v5)
    ]]></literal>
    <justification jstring="[para(14836(a,1),19746(a,2,2,1))].">
      <j1 rule="para" parents="14836 19746"/>
    </justification>
  </clause>

  <clause id="19749">
    <literal><![CDATA[
      L(a(x,y,y * ((z \ u) \ y)) \ 1,z \ u,z) = (w * (u \ (z * L(z \ u,y,x)))) / w
    ]]></literal>
    <justification jstring="[para(14398(a,1),18209(a,1,1))].">
      <j1 rule="para" parents="14398 18209"/>
    </justification>
  </clause>

  <clause id="19750">
    <literal><![CDATA[
      L(a(x,y,y * ((z \ u) \ y)) \ 1,z * u,z) = u \ (z * L(z \ u,y,x))
    ]]></literal>
    <justification jstring="[hyper(137,a,18595,a(flip),b,19749,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 18595 19749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19752">
    <literal><![CDATA[
      L(a(x,y,y * ((a(z,u,w) \ (u \ 1)) \ y)) \ 1,u \ a(z,u,w),a(z,u,w)) = (u \ 1) \ (a(z,u,w) * L(a(z,u,w) \ (u \ 1),y,x))
    ]]></literal>
    <justification jstring="[para(18020(a,1),19750(a,1,2))].">
      <j1 rule="para" parents="18020 19750"/>
    </justification>
  </clause>

  <clause id="19753">
    <literal><![CDATA[
      L(x,x * y,a(z,a(u,w,z),v5)) \ (y * a(u,w,a(z,z,v5))) = (x \ y) * a(z,a(u,w,z),v5)
    ]]></literal>
    <justification jstring="[para(18579(a,1),18369(a,1,1))].">
      <j1 rule="para" parents="18579 18369"/>
    </justification>
  </clause>

  <clause id="19754">
    <literal><![CDATA[
      L(x,a(y,z,u),y * L(y,w,v5)) = L(x,y,a(u,z,a(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,17924,a(flip),b,18522,a),flip(a)].">
      <j1 rule="hyper" parents="316 17924 18522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19755">
    <literal><![CDATA[
      x * a(y,z,a(u,a(w,v5,u),x)) = L(x,u,a(y,z,a(u,v5,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18525,a(flip),b,19754,a)].">
      <j1 rule="hyper" parents="63 18525 19754"/>
    </justification>
  </clause>

  <clause id="19756">
    <literal><![CDATA[
      L(x,a(y,z,u),u * L(u,w,v5)) = L(x,u,a(v5,w,a(u,z,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16346,a,b,19755,a)].">
      <j1 rule="hyper" parents="63 16346 19755"/>
    </justification>
  </clause>

  <clause id="19757">
    <literal><![CDATA[
      L(x,a(y,z,u),a(u,w,v5)) = L(x,u,a(v5,w,a(u,z,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19155,a(flip),b,19755,a)].">
      <j1 rule="hyper" parents="63 19155 19755"/>
    </justification>
  </clause>

  <clause id="19758">
    <literal><![CDATA[
      (a(x,y,z) \ a(z,u,w)) * L(v5,z,a(w,u,a(z,y,x))) = a(z,u,w) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(19757(a,1),16166(a,1,2))].">
      <j1 rule="para" parents="19757 16166"/>
    </justification>
  </clause>

  <clause id="19759">
    <literal><![CDATA[
      L(x,a(y,z,u),a(w,v5,y)) = L(x,y,a(w,v5,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18899,a(flip),b,19756,a)].">
      <j1 rule="hyper" parents="63 18899 19756"/>
    </justification>
  </clause>

  <clause id="19760">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,w,v5)) = L(x,y,a(u,z,a(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17145,a(flip),b,19759,a)].">
      <j1 rule="hyper" parents="63 17145 19759"/>
    </justification>
  </clause>

  <clause id="19762">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(316,a,19560,a(flip),b,19760,a),flip(a)].">
      <j1 rule="hyper" parents="316 19560 19760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19784">
    <literal><![CDATA[
      (x * a(y,z,u)) * a(y,w,v5) = x * (a(y,z,u) * a(y,w,v5))
    ]]></literal>
    <justification jstring="[para(19762(a,1),5383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19762 5383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19792">
    <literal><![CDATA[
      (a(x,y,z) \ a(z,u,w)) * v5 = a(z,u,w) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(19560(a,1),19758(a,1,2))].">
      <j1 rule="para" parents="19560 19758"/>
    </justification>
  </clause>

  <clause id="19793">
    <literal><![CDATA[
      (x \ 1) * (a(x,y,a(y,z,u)) * w) = (x \ a(y,y,a(u,z,x))) * w
    ]]></literal>
    <justification jstring="[para(19363(a,1),18949(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19363 18949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19794">
    <literal><![CDATA[
      (x \ 1) * (a(x,y,a(z,u,y)) * w) = (x \ a(y,y,a(z,u,x))) * w
    ]]></literal>
    <justification jstring="[para(13660(a,1),19793(a,1,2,1))].">
      <j1 rule="para" parents="13660 19793"/>
    </justification>
  </clause>

  <clause id="19795">
    <literal><![CDATA[
      (1 / (a(x,x,y) \ ((z / u) * (u * a(x,x,y))))) \ a(x,x,y) = L(a(x,x,y),u,u \ z) * z
    ]]></literal>
    <justification jstring="[para(2276(a,1),18966(a,1,1,2))].">
      <j1 rule="para" parents="2276 18966"/>
    </justification>
  </clause>

  <clause id="19796">
    <literal><![CDATA[
      L(x,a(y,z,x),L(z,u,w)) * L(a(y,z,x) \ 1,u,w) = x * L(x \ L(x,z,y),u,w)
    ]]></literal>
    <justification jstring="[para(19370(a,1),19068(a,1,1))].">
      <j1 rule="para" parents="19370 19068"/>
    </justification>
  </clause>

  <clause id="19797">
    <literal><![CDATA[
      L(x,x,a(y,y,L(z,u,w))) * L(a(z,y,x) \ 1,u,w) = x * L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(17895(a,1),19796(a,1,1))].">
      <j1 rule="para" parents="17895 19796"/>
    </justification>
  </clause>

  <clause id="19798">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ L(z,z,a(y,y,L(x,u,w))) = z * L(z \ L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14675,a(flip),b,19797,a)].">
      <j1 rule="hyper" parents="63 14675 19797"/>
    </justification>
  </clause>

  <clause id="19799">
    <literal><![CDATA[
      L(a(x,y,z),x,y) \ L(z,z,L(x,y,y) \ x) = z * L(z \ L(z,y,x),x,y)
    ]]></literal>
    <justification jstring="[para(14510(a,1),19798(a,1,2,3))].">
      <j1 rule="para" parents="14510 19798"/>
    </justification>
  </clause>

  <clause id="19800">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ L(z,z,L(x,y,y) \ x) = z * L(z \ L(z,y,x),x,y)
    ]]></literal>
    <justification jstring="[para(14606(a,1),19799(a,1,1))].">
      <j1 rule="para" parents="14606 19799"/>
    </justification>
  </clause>

  <clause id="19801">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ L(z,z,a(y,y,x)) = z * L(z \ L(z,y,x),x,y)
    ]]></literal>
    <justification jstring="[para(4952(a,1),19800(a,1,2,3))].">
      <j1 rule="para" parents="4952 19800"/>
    </justification>
  </clause>

  <clause id="19802">
    <literal><![CDATA[
      (R(x,y,z) \ x) * L(z,z,a(y,y,x)) = z * L(z \ L(z,y,x),x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14536,a(flip),b,19801,a)].">
      <j1 rule="hyper" parents="63 14536 19801"/>
    </justification>
  </clause>

  <clause id="19803">
    <literal><![CDATA[
      (R(x,y,z) \ x) * L(z,z,a(y,y,x)) = L(z,y,L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,18536,a(flip),b,19802,a),flip(a)].">
      <j1 rule="hyper" parents="316 18536 19802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19804">
    <literal><![CDATA[
      L(x,y,L(z,z,y)) = (R(z,y,x) \ z) * x
    ]]></literal>
    <justification jstring="[para(18664(a,1),19803(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18664 19803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19805">
    <literal><![CDATA[
      L(x,y,L(z,z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,18904,a,b,19804,a),flip(a)].">
      <j1 rule="hyper" parents="316 18904 19804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19806">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),x,u \ w),u,w) = (w * (u * x)) \ ((w * u) * R(L(x,u,w),y,z))
    ]]></literal>
    <justification jstring="[para(15896(a,1),19517(a,1,1))].">
      <j1 rule="para" parents="15896 19517"/>
    </justification>
  </clause>

  <clause id="19807">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),x,u \ w),u,w) = (w * (u * x)) \ (w * (u * R(x,y,z)))
    ]]></literal>
    <justification jstring="[para(404(a,1),19806(a,2,2))].">
      <j1 rule="para" parents="404 19806"/>
    </justification>
  </clause>

  <clause id="19808">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * R(z,u,w))) = L(L(a(z,u,w),z,y \ x),y,x)
    ]]></literal>
    <justification jstring="[para(18733(a,2),19807(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="18733 19807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19809">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * R(z,u,w))) = L(a(z,u,L(w,z,y \ x)),y,x)
    ]]></literal>
    <justification jstring="[para(19034(a,2),19808(a,2,1))].">
      <j1 rule="para" parents="19034 19808"/>
    </justification>
  </clause>

  <clause id="19810">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * R(z,u,w))) = a(z,u,L(L(w,z,y \ x),y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,19034,a,b,19809,a),flip(a)].">
      <j1 rule="hyper" parents="316 19034 19809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19811">
    <literal><![CDATA[
      a(x,y,L(L(z,x,u \ w),u,w)) = a(x,y,L(L(z,u,w),x,w * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19606,a(flip),b,19810,a),flip(a)].">
      <j1 rule="hyper" parents="63 19606 19810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19813">
    <literal><![CDATA[
      L(x,x * y,a(z,z,a(u,w,v5))) \ (y * a(u,w,a(z,z,v5))) = (x \ y) * a(z,a(u,w,z),v5)
    ]]></literal>
    <justification jstring="[para(18894(a,1),19753(a,1,1,3))].">
      <j1 rule="para" parents="18894 19753"/>
    </justification>
  </clause>

  <clause id="19814">
    <literal><![CDATA[
      (1 / (a(x,x,y) * ((z / u) * (a(x,x,y) \ u)))) \ a(x,x,y) = L(a(x,x,y),u,u \ z) * z
    ]]></literal>
    <justification jstring="[para(14825(a,1),19795(a,1,1,2))].">
      <j1 rule="para" parents="14825 19795"/>
    </justification>
  </clause>

  <clause id="19815">
    <literal><![CDATA[
      L(x,x * y,a(z,z,a(u,w,v5))) \ (y * a(u,w,a(z,z,v5))) = (x \ y) * a(z,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(18894(a,1),19813(a,2,2))].">
      <j1 rule="para" parents="18894 19813"/>
    </justification>
  </clause>

  <clause id="19816">
    <literal><![CDATA[
      x \ (y * a(z,u,a(w,w,v5))) = (x \ y) * a(w,w,a(z,u,v5))
    ]]></literal>
    <justification jstring="[para(19552(a,1),19815(a,1,1))].">
      <j1 rule="para" parents="19552 19815"/>
    </justification>
  </clause>

  <clause id="19817">
    <literal><![CDATA[
      (a(x,y,a(z,z,u)) * w) \ v5 = (w \ v5) * a(z,z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19661,a,b,19816,a)].">
      <j1 rule="hyper" parents="63 19661 19816"/>
    </justification>
  </clause>

  <clause id="19818">
    <literal><![CDATA[
      x \ (y * (z * a(u,w,a(v5,v5,v6)))) = (x \ (y * z)) * a(v5,v5,a(u,w,v6))
    ]]></literal>
    <justification jstring="[para(19567(a,1),19816(a,1,2))].">
      <j1 rule="para" parents="19567 19816"/>
    </justification>
  </clause>

  <clause id="19819">
    <literal><![CDATA[
      (x * (a(y,z,a(u,u,w)) * v5)) \ v6 = ((x * v5) \ v6) * a(u,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[para(19566(a,1),19817(a,1,1))].">
      <j1 rule="para" parents="19566 19817"/>
    </justification>
  </clause>

  <clause id="19820">
    <literal><![CDATA[
      x \ (y * (a(z,u,a(w,w,v5)) * v6)) = (x \ (y * v6)) * a(w,w,a(z,u,v5))
    ]]></literal>
    <justification jstring="[para(2290(a,2),19818(a,1,2,2))].">
      <j1 rule="para" parents="2290 19818"/>
    </justification>
  </clause>

  <clause id="19821">
    <literal><![CDATA[
      a(x,a(y,z,u) * w,w \ a(y,z,u)) = a(x,a(y,z,u) * w,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9926,a(flip),b,18077,a)].">
      <j1 rule="hyper" parents="63 9926 18077"/>
    </justification>
  </clause>

  <clause id="19822">
    <literal><![CDATA[
      a(a(x,y,z),a(u,w,v5) * v6,a(u,w,v5) * v6) \ 1 = a(v6 \ a(u,w,v5),a(u,w,v5) * v6,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(19821(a,1),13734(a,1,1))].">
      <j1 rule="para" parents="19821 13734"/>
    </justification>
  </clause>

  <clause id="19823">
    <literal><![CDATA[
      a(x,y,L(L(z,x,u \ w),u,w)) \ (u \ ((u / x) * R(x,y,z))) = a(z,y,a(w,u * x,x))
    ]]></literal>
    <justification jstring="[para(19810(a,1),18604(a,1,1))].">
      <j1 rule="para" parents="19810 18604"/>
    </justification>
  </clause>

  <clause id="19824">
    <literal><![CDATA[
      a(x,y,L(L(z,x,u \ w),u,w)) \ a(x,y,L(z,x,u)) = a(z,y,a(w,u * x,x))
    ]]></literal>
    <justification jstring="[para(19266(a,1),19823(a,1,2))].">
      <j1 rule="para" parents="19266 19823"/>
    </justification>
  </clause>

  <clause id="19825">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),x,w * u)) \ a(x,y,L(z,x,u)) = a(z,y,a(w,u * x,x))
    ]]></literal>
    <justification jstring="[para(19811(a,1),19824(a,1,1))].">
      <j1 rule="para" parents="19811 19824"/>
    </justification>
  </clause>

  <clause id="19826">
    <literal><![CDATA[
      a(T(x,y),T(x,z) * (u * (K(z,x) / x)),a(w * (K(v5,v6) / v7),v8,v9)) = a(w * (v7 \ 1),u,a(v9,v8,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,4042,a(flip),b,19667,a),flip(a)].">
      <j1 rule="hyper" parents="316 4042 19667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19827">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) * a(y * x,y * x,a(z,z,u)) = L(a(u,z,y \ x) \ 1,y \ x,y)
    ]]></literal>
    <justification jstring="[para(15769(a,1),18188(a,1,2))].">
      <j1 rule="para" parents="15769 18188"/>
    </justification>
  </clause>

  <clause id="19830">
    <literal><![CDATA[
      a(x,y \ L(y,z,x),u) * (w * L(y,a(x \ L(x,x,u),z,y),w)) = w * L(y,z,x \ L(x,x,u))
    ]]></literal>
    <justification jstring="[para(18374(a,2),18437(a,1,1))].">
      <j1 rule="para" parents="18374 18437"/>
    </justification>
  </clause>

  <clause id="19831">
    <literal><![CDATA[
      L(a(x,y,z),u \ w,(u \ w) * v5) * v5 = (v5 / ((u \ 1) \ w)) * (((u \ 1) \ w) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(15762(a,1),18476(a,1,1))].">
      <j1 rule="para" parents="15762 18476"/>
    </justification>
  </clause>

  <clause id="19832">
    <literal><![CDATA[
      (x / ((y \ 1) \ z)) * (((y \ 1) \ z) * a(u,w,v5)) = (x / (y \ z)) * ((y \ z) * a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,18472,a(flip),b,19831,a),flip(a)].">
      <j1 rule="hyper" parents="63 18472 19831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19833">
    <literal><![CDATA[
      (a(x,y,z) * ((u \ 1) \ w)) * (((u \ 1) \ w) \ v5) = (v5 / (u \ w)) * ((u \ w) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5348,a(flip),b,19832,a)].">
      <j1 rule="hyper" parents="63 5348 19832"/>
    </justification>
  </clause>

  <clause id="19834">
    <literal><![CDATA[
      a(x,y,z) \ ((u / (w \ v5)) * ((w \ v5) * a(x,y,z))) = u * a(a(x,y,z),v5 / (w \ 1),u * (v5 / (w \ 1)))
    ]]></literal>
    <justification jstring="[para(19833(a,1),18191(a,1,2))].">
      <j1 rule="para" parents="19833 18191"/>
    </justification>
  </clause>

  <clause id="19835">
    <literal><![CDATA[
      a(x,a(y,x \ z,x),u) * a(y,y,a(u,x,a(x * z,x \ z,x))) = L(y,x \ z,a(u,x,x)) \ y
    ]]></literal>
    <justification jstring="[para(18292(a,1),18619(a,1,1))].">
      <j1 rule="para" parents="18292 18619"/>
    </justification>
  </clause>

  <clause id="19836">
    <literal><![CDATA[
      L(a(x,y,z),u * a(x,y,z),a(u * a(x,y,z),w,v5)) = a(x,y,z) * a(u,a(v5,w,u),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(18303(a,1),19748(a,2,2))].">
      <j1 rule="para" parents="18303 19748"/>
    </justification>
  </clause>

  <clause id="19837">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) * a(y * x,y * x,a(z,z,u)) = a(u,z,x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(316,a,18284,a(flip),b,19827,a),flip(a)].">
      <j1 rule="hyper" parents="316 18284 19827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19843">
    <literal><![CDATA[
      a(x,y \ L(y,z,x),u) * (w * L(y,a(x,a(y,z,x),u),w)) = w * L(y,z,x \ L(x,x,u))
    ]]></literal>
    <justification jstring="[para(18291(a,1),19830(a,1,2,2,2))].">
      <j1 rule="para" parents="18291 19830"/>
    </justification>
  </clause>

  <clause id="19844">
    <literal><![CDATA[
      a(x,y \ L(y,z,x),u) * (w * L(y,a(x,a(y,z,x),u),w)) = w * L(y,z,a(x,x,u))
    ]]></literal>
    <justification jstring="[para(7488(a,1),19843(a,2,2))].">
      <j1 rule="para" parents="7488 19843"/>
    </justification>
  </clause>

  <clause id="19845">
    <literal><![CDATA[
      a(a(x,y,z),u,y) * (w * L(z,a(y,a(z,u,y),x),w)) = w * L(z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(17245(a,1),19844(a,1,1))].">
      <j1 rule="para" parents="17245 19844"/>
    </justification>
  </clause>

  <clause id="19846">
    <literal><![CDATA[
      a(a(x,y,z),u,y) * (w * L(z,z,a(a(x,y,w),u,y))) = w * L(z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(18440(a,1),19845(a,1,2,2))].">
      <j1 rule="para" parents="18440 19845"/>
    </justification>
  </clause>

  <clause id="19848">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * (w * L(y,y,a(a(u,x,w),z,x))) = w * L(y,z,a(x,x,u))
    ]]></literal>
    <justification jstring="[para(18998(a,1),19846(a,1,1))].">
      <j1 rule="para" parents="18998 19846"/>
    </justification>
  </clause>

  <clause id="19849">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * (w * L(y,y,a(x,x,a(w,z,u)))) = w * L(y,z,a(x,x,u))
    ]]></literal>
    <justification jstring="[para(18998(a,1),19848(a,1,2,2,3))].">
      <j1 rule="para" parents="18998 19848"/>
    </justification>
  </clause>

  <clause id="19850">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * (w * y) = w * L(y,z,a(x,x,u))
    ]]></literal>
    <justification jstring="[para(18664(a,1),19849(a,1,2,2))].">
      <j1 rule="para" parents="18664 19849"/>
    </justification>
  </clause>

  <clause id="19851">
    <literal><![CDATA[
      (x * y) * a(z,z,a(y,u,w)) = x * L(y,u,a(z,z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,2290,a(flip),b,19850,a)].">
      <j1 rule="hyper" parents="63 2290 19850"/>
    </justification>
  </clause>

  <clause id="19852">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * L(z,u,a(w,w,v5)))) = L(a(w,w,a(z,u,v5)),y * z,x)
    ]]></literal>
    <justification jstring="[para(19851(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="19851 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19853">
    <literal><![CDATA[
      a(x,a(y,x \ z,x),u) * a(y,y,a(u,z,a(x,x,z))) = L(y,x \ z,a(u,x,x)) \ y
    ]]></literal>
    <justification jstring="[para(18618(a,1),19835(a,1,2,3))].">
      <j1 rule="para" parents="18618 19835"/>
    </justification>
  </clause>

  <clause id="19854">
    <literal><![CDATA[
      a(x,a(y,x \ z,x),u) * a(y,y,a(u,z,a(x,x,z))) = y \ L(y,x \ z,a(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,14060,a(flip),b,19853,a),flip(a)].">
      <j1 rule="hyper" parents="316 14060 19853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19855">
    <literal><![CDATA[
      a(x,a(y,x \ z,x),u) * a(y,y,a(u,z,a(x,x,z))) = a(a(u,x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,18375,a(flip),b,19854,a),flip(a)].">
      <j1 rule="hyper" parents="316 18375 19854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19856">
    <literal><![CDATA[
      a(x,a(y,x \ z,x),u) * a(y,y,a(u,z,a(x,x,z))) = a(a(u,x,y),x * z,x)
    ]]></literal>
    <justification jstring="[hyper(316,a,18584,a(flip),b,19855,a),flip(a)].">
      <j1 rule="hyper" parents="316 18584 19855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19857">
    <literal><![CDATA[
      L(a(x,y,z),u * a(x,y,z),a(u * a(x,y,z),w,v5)) = L(a(x,y,z),u,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,13472,a(flip),b,19836,a),flip(a)].">
      <j1 rule="hyper" parents="316 13472 19836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19858">
    <literal><![CDATA[
      L(a(x,y,z),u,a(u * a(x,y,z),w,v5)) = L(a(x,y,z),u,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14779,a(flip),b,19857,a)].">
      <j1 rule="hyper" parents="63 14779 19857"/>
    </justification>
  </clause>

  <clause id="19859">
    <literal><![CDATA[
      a(x,y,L(z,u,a(u * a(x,y,z),w,v5))) = L(a(x,y,z),u,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19034,a,b,19858,a)].">
      <j1 rule="hyper" parents="63 19034 19858"/>
    </justification>
  </clause>

  <clause id="19860">
    <literal><![CDATA[
      a(x,y,L(z,u,a(u * a(x,y,z),w,v5))) = a(x,y,L(z,u,a(v5,w,u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,19034,a,b,19859,a),flip(a)].">
      <j1 rule="hyper" parents="316 19034 19859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19861">
    <literal><![CDATA[
      a(a(x,L(y \ 1,z,u),w),v5,L(y,z,u)) = a(v5 * (w \ v5),v5,a(y \ 1,y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,13599,a(flip),b,18371,a),flip(a)].">
      <j1 rule="hyper" parents="63 13599 18371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19863">
    <literal><![CDATA[
      a(a(x,L(y \ 1,z,u),w),v5,L(y,z,u)) = a(v5 * (w \ v5),v5,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,12017,a(flip),b,19861,a),flip(a)].">
      <j1 rule="hyper" parents="316 12017 19861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19864">
    <literal><![CDATA[
      a(a(x,L(y \ 1,z,u),w),v5,L(y,z,u)) = a(a(x,y,w),v5,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,18326,a(flip),b,19863,a),flip(a)].">
      <j1 rule="hyper" parents="316 18326 19863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19865">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,L(x,y,z),v5)) = a(a(v5,x,w),u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,14032,a(flip),b,19864,a)].">
      <j1 rule="hyper" parents="63 14032 19864"/>
    </justification>
  </clause>

  <clause id="19866">
    <literal><![CDATA[
      a(a(x,L(y,z,u),w),v5,L(y,z,u)) = a(a(x,y,w),v5,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14012,a,b,19865,a)].">
      <j1 rule="hyper" parents="63 14012 19865"/>
    </justification>
  </clause>

  <clause id="19870">
    <literal><![CDATA[
      a(x,x \ (L(y \ R(y,z,z),u,w) * v5),L(R(y,z,z) \ y,u,w)) = a(x,x * v5,a(y,z,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(17224(a,1),18596(a,1,2,2))].">
      <j1 rule="para" parents="17224 18596"/>
    </justification>
  </clause>

  <clause id="19871">
    <literal><![CDATA[
      (a(x * a(y,z,u),w,v5) * x) * a(y,z,L(u,x,a(v5,w,x))) = R(x * a(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(19860(a,1),19300(a,1,2))].">
      <j1 rule="para" parents="19860 19300"/>
    </justification>
  </clause>

  <clause id="19872">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * v5) * a(x,v5,a(a(z,u,w),y,a(z,u,w) \ v5)) = a(x,y,(a(z,u,w) / v5) \ 1)
    ]]></literal>
    <justification jstring="[para(14403(a,1),19334(a,1,1))].">
      <j1 rule="para" parents="14403 19334"/>
    </justification>
  </clause>

  <clause id="19873">
    <literal><![CDATA[
      a(x,y,(z * ((u \ 1) * (a(u,w,a(v5,v6,w)) * v7))) * v8) = a(x,y,(z * (v7 * L(u,w,a(v5,v6,w)))) * v8)
    ]]></literal>
    <justification jstring="[para(8426(a,1),19391(a,1,3,1,2))].">
      <j1 rule="para" parents="8426 19391"/>
    </justification>
  </clause>

  <clause id="19874">
    <literal><![CDATA[
      R((x \ 1) \ y,z,u) \ (R((x \ 1) \ y,z,u) / (1 / (x \ 1))) = L(x \ 1,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),19715(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 19715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19876">
    <literal><![CDATA[
      R((x \ 1) \ y,z,u) \ (R((x \ 1) \ y,z,u) / x) = L(x \ 1,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(80(a,1),19874(a,1,2,2))].">
      <j1 rule="para" parents="80 19874"/>
    </justification>
  </clause>

  <clause id="19878">
    <literal><![CDATA[
      L((x \ 1) \ y,z,u) \ (L((x \ 1) \ y,z,u) / x) = L(x \ 1,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12972,a(flip),b,19876,a)].">
      <j1 rule="hyper" parents="63 12972 19876"/>
    </justification>
  </clause>

  <clause id="19879">
    <literal><![CDATA[
      L(x \ 1,(x \ 1) \ 1,L(y,z,u) / x) = L(x \ 1,x,L(y / x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12729,a(flip),b,19878,a)].">
      <j1 rule="hyper" parents="63 12729 19878"/>
    </justification>
  </clause>

  <clause id="19880">
    <literal><![CDATA[
      L(x \ 1,(x \ 1) \ 1,L(y,z,u) / x) = L(x \ 1,x,L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,1591,a(flip),b,19879,a),flip(a)].">
      <j1 rule="hyper" parents="316 1591 19879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19881">
    <literal><![CDATA[
      L(x \ 1,(x \ 1) \ 1,x \ L(y,z,u)) = L(x \ 1,x,L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1586,a(flip),b,19880,a)].">
      <j1 rule="hyper" parents="63 1586 19880"/>
    </justification>
  </clause>

  <clause id="19882">
    <literal><![CDATA[
      L(x \ 1,x,L(x \ y,z,u)) = L(x \ 1,x,x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10800,a(flip),b,19881,a),flip(a)].">
      <j1 rule="hyper" parents="63 10800 19881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19884">
    <literal><![CDATA[
      a(x,x,y) * (L(y,x,x) / z) = y * L(z \ 1,z,L(z \ y,x,x))
    ]]></literal>
    <justification jstring="[para(19882(a,2),18999(a,2,2))].">
      <j1 rule="para" parents="19882 18999"/>
    </justification>
  </clause>

  <clause id="19885">
    <literal><![CDATA[
      a(x,x,y) * (L(y,x,x) / z) = y * L(z \ 1,z,z \ y)
    ]]></literal>
    <justification jstring="[para(19475(a,1),19884(a,2,2))].">
      <j1 rule="para" parents="19475 19884"/>
    </justification>
  </clause>

  <clause id="19886">
    <literal><![CDATA[
      a(x,x,y) * (L(y,x,x) / z) = y / z
    ]]></literal>
    <justification jstring="[hyper(316,a,1607,a(flip),b,19885,a),flip(a)].">
      <j1 rule="hyper" parents="316 1607 19885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19888">
    <literal><![CDATA[
      L(x,y,y) \ (L(x,y,y) / z) = x \ (x / z)
    ]]></literal>
    <justification jstring="[hyper(133,a,19886,a(flip),b,18970,a),flip(a)].">
      <j1 rule="hyper" parents="133 19886 18970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19889">
    <literal><![CDATA[
      ((x \ 1) * y) \ (((x \ 1) * y) / z) = (x \ y) \ ((x \ y) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12973,a(flip),b,19888,a)].">
      <j1 rule="hyper" parents="63 12973 19888"/>
    </justification>
  </clause>

  <clause id="19891">
    <literal><![CDATA[
      (x * (y \ 1)) \ ((x * (y \ 1)) / z) = (y \ x) \ ((y \ x) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3069,a,b,19889,a)].">
      <j1 rule="hyper" parents="63 3069 19889"/>
    </justification>
  </clause>

  <clause id="19892">
    <literal><![CDATA[
      a(x,y,z \ (T((u \ w) \ ((u \ w) / v5),v5) * (w * u))) = a(x,y,z \ (v5 \ (w * u)))
    ]]></literal>
    <justification jstring="[para(19891(a,1),9787(a,1,3,2,1,1))].">
      <j1 rule="para" parents="19891 9787"/>
    </justification>
  </clause>

  <clause id="19893">
    <literal><![CDATA[
      a(x,y,z \ (((u \ w) \ ((u \ w) / v5)) * (w * u))) = a(x,y,z \ (v5 \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5600,a(flip),b,19892,a)].">
      <j1 rule="hyper" parents="63 5600 19892"/>
    </justification>
  </clause>

  <clause id="19895">
    <literal><![CDATA[
      a(x,y,z \ (((u \ w) \ (v5 \ (u \ w))) * (w * u))) = a(x,y,z \ (v5 \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10485,a(flip),b,19893,a)].">
      <j1 rule="hyper" parents="63 10485 19893"/>
    </justification>
  </clause>

  <clause id="19897">
    <literal><![CDATA[
      a(x \ a(y,z,u),a(y,z,u) * x,a(w,v5,v6)) = a(a(y,z,u) * x,a(y,z,u) * x,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,13734,a(flip),b,19822,a),flip(a)].">
      <j1 rule="hyper" parents="63 13734 19822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19898">
    <literal><![CDATA[
      (x \ (a(y,z,u) * L(a(y,z,u) \ x,w,v5))) * a(a(y,z,u) * x,a(y,z,u) * x,a(w,w,v5)) = L(a(v5,w,x * a(y,z,u)) \ 1,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(19897(a,1),16430(a,1,2))].">
      <j1 rule="para" parents="19897 16430"/>
    </justification>
  </clause>

  <clause id="19899">
    <literal><![CDATA[
      a(T(x,y),T(x,z) * (u * (K(z,x) / x)),a(w * (K(v5,v6) / v7),v8,v9)) = a(w * v7,u,a(v9,v8,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,13031,a(flip),b,19826,a),flip(a)].">
      <j1 rule="hyper" parents="316 13031 19826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19900">
    <literal><![CDATA[
      a(x,x \ (L(a(y,z,z),u,w) * v5),L(R(y,z,z) \ y,u,w)) = a(x,x * v5,a(y,z,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(2380(a,1),19870(a,1,2,2,1,1))].">
      <j1 rule="para" parents="2380 19870"/>
    </justification>
  </clause>

  <clause id="19901">
    <literal><![CDATA[
      a(x,x \ (a(y,z,L(z,u,w)) * v5),L(R(y,z,z) \ y,u,w)) = a(x,x * v5,a(y,z,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(13562(a,2),19900(a,1,2,2,1))].">
      <j1 rule="para" parents="13562 19900"/>
    </justification>
  </clause>

  <clause id="19902">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * v5) * a(x,v5,a(a(z,u,w),y,a(z,u,w) * v5)) = a(x,y,(a(z,u,w) / v5) \ 1)
    ]]></literal>
    <justification jstring="[para(14403(a,1),19872(a,1,2,3))].">
      <j1 rule="para" parents="14403 19872"/>
    </justification>
  </clause>

  <clause id="19903">
    <literal><![CDATA[
      a(x,y,(z * ((u \ a(w,w,a(v5,v6,u))) * v7)) * v8) = a(x,y,(z * (v7 * L(u,w,a(v5,v6,w)))) * v8)
    ]]></literal>
    <justification jstring="[para(19794(a,1),19873(a,1,3,1,2))].">
      <j1 rule="para" parents="19794 19873"/>
    </justification>
  </clause>

  <clause id="19904">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * v5) * a(x,v5,a(z,u,a(a(z,u,w) * v5,y,w))) = a(x,y,(a(z,u,w) / v5) \ 1)
    ]]></literal>
    <justification jstring="[para(19132(a,1),19902(a,1,2,3))].">
      <j1 rule="para" parents="19132 19902"/>
    </justification>
  </clause>

  <clause id="19905">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * v5) * a(v5,v5,a(x,y,a(w,u,z))) = a(x,y,(a(z,u,w) / v5) \ 1)
    ]]></literal>
    <justification jstring="[para(19377(a,1),19904(a,1,2))].">
      <j1 rule="para" parents="19377 19904"/>
    </justification>
  </clause>

  <clause id="19906">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * v5) * a(v5,v5,a(x,y,a(w,u,z))) = a(x,y,a(z,u,w) / v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,2534,a(flip),b,19905,a),flip(a)].">
      <j1 rule="hyper" parents="316 2534 19905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19907">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * v5) * a(v5,v5,a(x,y,a(w,u,z))) = a(x,y,v5 \ a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5477,a(flip),b,19906,a),flip(a)].">
      <j1 rule="hyper" parents="316 5477 19906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19908">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * v5) * 1 = a(x,y,v5 \ a(z,u,w))
    ]]></literal>
    <justification jstring="[para(19545(a,1),19907(a,1,2))].">
      <j1 rule="para" parents="19545 19907"/>
    </justification>
  </clause>

  <clause id="19910">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(u,w,v5))) = a(x,y,a(v5,w,u) * z)
    ]]></literal>
    <justification jstring="[hyper(135,a,19908,a,b,18674,a),flip(a)].">
      <j1 rule="hyper" parents="135 19908 18674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19913">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (a(u,w,a(z,y,x) * v5) \ v5) = L((x \ L(x,y,z)) \ v5,w,u)
    ]]></literal>
    <justification jstring="[para(19910(a,1),18782(a,1,2,1))].">
      <j1 rule="para" parents="19910 18782"/>
    </justification>
  </clause>

  <clause id="19914">
    <literal><![CDATA[
      (a(x,y,a(z,u,w) * v5) \ v5) * a(z,u,w) = L((w \ L(w,u,z)) \ v5,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,18638,a(flip),b,19913,a)].">
      <j1 rule="hyper" parents="63 18638 19913"/>
    </justification>
  </clause>

  <clause id="19915">
    <literal><![CDATA[
      (a(a(x,y,z) * a(u,w,v5),v6,v7) * a(x,y,z)) * a(u,w,v5) = L((v5 \ L(v5,w,u)) \ a(x,y,z),v6,v7)
    ]]></literal>
    <justification jstring="[para(16062(a,1),19914(a,1,1))].">
      <j1 rule="para" parents="16062 19914"/>
    </justification>
  </clause>

  <clause id="19931">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(x,y,L(z,u,w)) * v5) = a(x,y,z) * v5
    ]]></literal>
    <justification jstring="[para(19762(a,1),19337(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19762 19337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19932">
    <literal><![CDATA[
      a(a(x,x,y),z,u * (a(x,x,y) \ (w \ a(x,x,y)))) = a(x,x,a((w * a(x,x,y)) * (u * a(y,x,x)),z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,19132,a(flip),b,19507,a),flip(a)].">
      <j1 rule="hyper" parents="63 19132 19507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19933">
    <literal><![CDATA[
      a(x,y,a(y,z * u,z * u)) * L(T(z,w) \ (L(u / T(z,w),y,x) \ u),v5,v6) = a(x,y,L(u \ z,v5,v6))
    ]]></literal>
    <justification jstring="[para(13906(a,1),19737(a,1,2,1))].">
      <j1 rule="para" parents="13906 19737"/>
    </justification>
  </clause>

  <clause id="19934">
    <literal><![CDATA[
      a(x,y,z) * ((u / (w \ v5)) * (a(x,y,z) \ (w \ v5))) = u * a(a(x,y,z),v5 / (w \ 1),u * (v5 / (w \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14825,a(flip),b,19834,a)].">
      <j1 rule="hyper" parents="63 14825 19834"/>
    </justification>
  </clause>

  <clause id="19936">
    <literal><![CDATA[
      a(a(x,x,y),z,u * (a(x,x,y) \ (w \ a(x,x,y)))) = a(x,x,a(u * (w * a(x,x,y)),z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,19616,a(flip),b,19932,a),flip(a)].">
      <j1 rule="hyper" parents="316 19616 19932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19937">
    <literal><![CDATA[
      a(x,x,a(y * (z * a(x,x,u)),w,u)) = a(a(x,x,u),w,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(18726(a,1),19936(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="18726 19936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19938">
    <literal><![CDATA[
      a(x,x,a(y * (z * a(x,x,u)),w,u)) = a(a(x,x,u),w,z * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,5529,a(flip),b,19937,a),flip(a)].">
      <j1 rule="hyper" parents="316 5529 19937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19940">
    <literal><![CDATA[
      a(x,x,a(y * (z * a(x,x,u)),w,u)) = a(x,x,a(z * y,w,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,19132,a(flip),b,19938,a),flip(a)].">
      <j1 rule="hyper" parents="316 19132 19938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19941">
    <literal><![CDATA[
      a(x * (y * a(z,z,u)),w,a(u,z,z)) = a(z,z,a(y * x,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19141,a,b,19940,a)].">
      <j1 rule="hyper" parents="63 19141 19940"/>
    </justification>
  </clause>

  <clause id="19942">
    <literal><![CDATA[
      a(x,y,a(y,z * u,z * u)) * L(z \ (L(u / z,y,x) \ u),w,v5) = a(x,y,L(u \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(10616(a,1),19933(a,1,2,1))].">
      <j1 rule="para" parents="10616 19933"/>
    </justification>
  </clause>

  <clause id="19943">
    <literal><![CDATA[
      a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w))) = u * a(a(x,y,z),w / (z \ 1),u * (w / (z \ 1)))
    ]]></literal>
    <justification jstring="[para(6920(a,1),19934(a,1,2,2))].">
      <j1 rule="para" parents="6920 19934"/>
    </justification>
  </clause>

  <clause id="19948">
    <literal><![CDATA[
      a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w))) = u * a(a(x,y,z),w / (z \ 1),u * ((z \ 1) \ w))
    ]]></literal>
    <justification jstring="[para(5481(a,1),19943(a,2,2))].">
      <j1 rule="para" parents="5481 19943"/>
    </justification>
  </clause>

  <clause id="19949">
    <literal><![CDATA[
      a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w))) = u * a(a(x,y,z),w / (z \ 1),(z \ w) * u)
    ]]></literal>
    <justification jstring="[para(6701(a,1),19948(a,2,2))].">
      <j1 rule="para" parents="6701 19948"/>
    </justification>
  </clause>

  <clause id="19950">
    <literal><![CDATA[
      a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w))) = u * a(a(x,y,z),(z \ 1) \ w,(z \ w) * u)
    ]]></literal>
    <justification jstring="[para(11195(a,1),19949(a,2,2))].">
      <j1 rule="para" parents="11195 19949"/>
    </justification>
  </clause>

  <clause id="19951">
    <literal><![CDATA[
      a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w))) = u * a(a(x,y,z),z \ w,(z \ w) * u)
    ]]></literal>
    <justification jstring="[para(15775(a,1),19950(a,2,2))].">
      <j1 rule="para" parents="15775 19950"/>
    </justification>
  </clause>

  <clause id="19952">
    <literal><![CDATA[
      a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w))) = u * a(x,y,a((z \ w) * u,z \ w,z))
    ]]></literal>
    <justification jstring="[para(19132(a,1),19951(a,2,2))].">
      <j1 rule="para" parents="19132 19951"/>
    </justification>
  </clause>

  <clause id="19953">
    <literal><![CDATA[
      a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w))) = u * a(x,y,a((z \ w) * u,z * w,z))
    ]]></literal>
    <justification jstring="[para(19436(a,1),19952(a,2,2))].">
      <j1 rule="para" parents="19436 19952"/>
    </justification>
  </clause>

  <clause id="19954">
    <literal><![CDATA[
      L(L(a(x,y,y),z / y,u),y,L(u * (z / y),z / y,u)) = (u * (a(x,y,y) \ z)) \ (u * ((z / y) * y))
    ]]></literal>
    <justification jstring="[para(7290(a,1),18170(a,1,1,1))].">
      <j1 rule="para" parents="7290 18170"/>
    </justification>
  </clause>

  <clause id="19955">
    <literal><![CDATA[
      L(L(a(x,y,y),y \ z,u),y,L(u * (z / y),z / y,u)) = (u * (a(x,y,y) \ z)) \ (u * ((z / y) * y))
    ]]></literal>
    <justification jstring="[para(10798(a,1),19954(a,1,1))].">
      <j1 rule="para" parents="10798 19954"/>
    </justification>
  </clause>

  <clause id="19956">
    <literal><![CDATA[
      L(a(x,y,L(y,y \ z,u)),y,L(u * (z / y),z / y,u)) = (u * (a(x,y,y) \ z)) \ (u * ((z / y) * y))
    ]]></literal>
    <justification jstring="[para(13562(a,2),19955(a,1,1))].">
      <j1 rule="para" parents="13562 19955"/>
    </justification>
  </clause>

  <clause id="19957">
    <literal><![CDATA[
      (x * (a(y,z,z) \ u)) \ (x * ((u / z) * z)) = a(y,z,L(z,z \ u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,18068,a(flip),b,19956,a),flip(a)].">
      <j1 rule="hyper" parents="63 18068 19956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19959">
    <literal><![CDATA[
      a(x,y,L(y,y \ z,u)) = (u * (a(x,y,y) \ z)) \ (u * z)
    ]]></literal>
    <justification jstring="[para(12(a,1),19957(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 19957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19960">
    <literal><![CDATA[
      a(x,y,L(y,y \ z,u)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,14692,a(flip),b,19959,a),flip(a)].">
      <j1 rule="hyper" parents="316 14692 19959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19961">
    <literal><![CDATA[
      a(x,y,L(y,y * z,u)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),19960(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 19960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19962">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) \ a(x,y,y) = a(y,a(u,y \ z,y),x)
    ]]></literal>
    <justification jstring="[para(19960(a,1),18290(a,1,1))].">
      <j1 rule="para" parents="19960 18290"/>
    </justification>
  </clause>

  <clause id="19964">
    <literal><![CDATA[
      a(x,R(y,y,z),L(R(y,y,z),a(y,y,z) * u,w)) = a(x,R(y,y,z),L(R(y,y,z),y \ u,w))
    ]]></literal>
    <justification jstring="[para(18053(a,1),19961(a,1,3,2))].">
      <j1 rule="para" parents="18053 19961"/>
    </justification>
  </clause>

  <clause id="19965">
    <literal><![CDATA[
      a(x,a(y,x \ z,x),u) = a(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18290,a(flip),b,19962,a),flip(a)].">
      <j1 rule="hyper" parents="63 18290 19962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19966">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * a(y,y,a(u,z,a(x,x,z))) = a(a(u,x,y),x * z,x)
    ]]></literal>
    <justification jstring="[para(19965(a,1),19856(a,1,1))].">
      <j1 rule="para" parents="19965 19856"/>
    </justification>
  </clause>

  <clause id="19967">
    <literal><![CDATA[
      a(a(x,y,z),y * u,y) = a(a(x,y,z),u,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,18503,a(flip),b,19966,a),flip(a)].">
      <j1 rule="hyper" parents="63 18503 19966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19968">
    <literal><![CDATA[
      a(a(x,y,z),u * y,y) = a(a(x,y,z),u,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,11190,a,b,19967,a)].">
      <j1 rule="hyper" parents="63 11190 19967"/>
    </justification>
  </clause>

  <clause id="19969">
    <literal><![CDATA[
      a(x,y * x,a(z,x,u)) = a(a(z,x,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,14010,a(flip),b,19968,a)].">
      <j1 rule="hyper" parents="63 14010 19968"/>
    </justification>
  </clause>

  <clause id="19970">
    <literal><![CDATA[
      a(a(x,y,z),u * (a(y,y,w) \ y),y) = a(a(x,y,z),a(y,y,w) \ u,y)
    ]]></literal>
    <justification jstring="[para(18047(a,1),19968(a,1,2))].">
      <j1 rule="para" parents="18047 19968"/>
    </justification>
  </clause>

  <clause id="19971">
    <literal><![CDATA[
      a(a(x,L(y,z,u),w),v5,L(y,z,u)) = a(a(w,y,x),v5 * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,19865,a(flip),b,19969,a),flip(a)].">
      <j1 rule="hyper" parents="63 19865 19969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19972">
    <literal><![CDATA[
      a(a(x,y,z),u * L(y,w,v5),y) = a(a(z,y,x),u,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,19866,a(flip),b,19971,a),flip(a)].">
      <j1 rule="hyper" parents="63 19866 19971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19974">
    <literal><![CDATA[
      a(a(x,y,z),u * (a(y,y,w) * y),y) = a(a(x,y,z),a(y,y,w) \ u,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14489,a(flip),b,19970,a)].">
      <j1 rule="hyper" parents="63 14489 19970"/>
    </justification>
  </clause>

  <clause id="19975">
    <literal><![CDATA[
      a(a(x,y,z),a(y,y,u) \ w,y) = a(a(x,y,z),w * R(y,y,u),y)
    ]]></literal>
    <justification jstring="[para(7333(a,1),19974(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7333 19974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19976">
    <literal><![CDATA[
      a(a(x,y,z),a(y,y,u) \ w,y) = a(a(x,y,z),w * L(y,y,u),y)
    ]]></literal>
    <justification jstring="[hyper(316,a,12037,a(flip),b,19975,a),flip(a)].">
      <j1 rule="hyper" parents="316 12037 19975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19977">
    <literal><![CDATA[
      a(a(x,y,z),a(y,y,u) \ w,y) = a(a(z,y,x),w,y)
    ]]></literal>
    <justification jstring="[hyper(316,a,19972,a(flip),b,19976,a),flip(a)].">
      <j1 rule="hyper" parents="316 19972 19976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19979">
    <literal><![CDATA[
      a(a(x,y,z),u * a(y,y,w),y) = a(a(z,y,x),u,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14435,a(flip),b,19977,a)].">
      <j1 rule="hyper" parents="63 14435 19977"/>
    </justification>
  </clause>

  <clause id="19980">
    <literal><![CDATA[
      a(x,x,a(y,z * a(x,x,u),w)) = a(a(y,x,w),z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,18998,a(flip),b,19979,a)].">
      <j1 rule="hyper" parents="63 18998 19979"/>
    </justification>
  </clause>

  <clause id="19981">
    <literal><![CDATA[
      a(x,x,a(y,z * a(x,x,u),w)) = a(x,x,a(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,18998,a(flip),b,19980,a),flip(a)].">
      <j1 rule="hyper" parents="316 18998 19980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19982">
    <literal><![CDATA[
      a(x,R(y,y,z),L(L(y,y,z),a(y,y,z) * u,w)) = a(x,R(y,y,z),L(R(y,y,z),y \ u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5953,a(flip),b,19964,a)].">
      <j1 rule="hyper" parents="63 5953 19964"/>
    </justification>
  </clause>

  <clause id="19983">
    <literal><![CDATA[
      a(x,L(y,y,z),L(L(y,y,z),a(y,y,z) * u,w)) = a(x,R(y,y,z),L(R(y,y,z),y \ u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,11325,a(flip),b,19982,a)].">
      <j1 rule="hyper" parents="63 11325 19982"/>
    </justification>
  </clause>

  <clause id="19984">
    <literal><![CDATA[
      a(x,R(y,y,z),L(R(y,y,z),y \ u,w)) = a(x,y,L(y,a(y,y,z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,13574,a(flip),b,19983,a),flip(a)].">
      <j1 rule="hyper" parents="63 13574 19983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19987">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ a(w,v5,v6),w \ 1,w \ 1)) = a(x,y,(w \ a(w,v5,v6)) \ L(w,u,z))
    ]]></literal>
    <justification jstring="[para(17707(a,1),19360(a,1,3))].">
      <j1 rule="para" parents="17707 19360"/>
    </justification>
  </clause>

  <clause id="19988">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ a(w,v5,v6),w,w)) = a(x,y,(w \ a(w,v5,v6)) \ L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7520,a(flip),b,19987,a)].">
      <j1 rule="hyper" parents="63 7520 19987"/>
    </justification>
  </clause>

  <clause id="19990">
    <literal><![CDATA[
      a(x,y,(z \ a(z,u,w)) \ L(z,v5,v6)) = a(x,y,a(v6,v5,z) \ a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14158(a,1),19988(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14158 19988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19991">
    <literal><![CDATA[
      a(x,y,(z \ a(z,u,w)) \ L(z,v5,v6)) = a(x,y,a(v6,v5,z) * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,14403,a(flip),b,19990,a),flip(a)].">
      <j1 rule="hyper" parents="316 14403 19990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19992">
    <literal><![CDATA[
      a(x,y,z * (a(z,u,w) \ L(z,v5,v6))) = a(x,y,a(v6,v5,z) * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(15046(a,1),19991(a,1,3))].">
      <j1 rule="para" parents="15046 19991"/>
    </justification>
  </clause>

  <clause id="19993">
    <literal><![CDATA[
      a(x,y,z * (L(z,u,w) * a(z,v5,v6))) = a(x,y,a(w,u,z) * a(z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,14428,a(flip),b,19992,a)].">
      <j1 rule="hyper" parents="63 14428 19992"/>
    </justification>
  </clause>

  <clause id="19994">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * a(w,v5,v6)) = a(x,y,L(w,u,z) * R(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(18841(a,1),19993(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18841 19993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19995">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * a(w,v5,v6)) = a(x,y,L(w,u,z) * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,7272,a(flip),b,19994,a),flip(a)].">
      <j1 rule="hyper" parents="316 7272 19994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19996">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ L(z,v5,v6)) = a(x,y,a(v6,v5,z) * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,2653,a,b,19995,a)].">
      <j1 rule="hyper" parents="316 2653 19995"/>
    </justification>
  </clause>

  <clause id="19997">
    <literal><![CDATA[
      ((x * (a(y,z,a(u,u,w)) * (v5 * v6))) \ ((x * v5) * v6)) * a(u,u,a(y,z,w)) = a(x,v5,a(y,z,a(u,u,w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,19820,a(flip),b,19591,a)].">
      <j1 rule="hyper" parents="63 19820 19591"/>
    </justification>
  </clause>

  <clause id="19999">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) * a(u,u,a(w,v5,v6))) * a(u,u,a(w,v5,v6)) = a(x,y,a(w,v5,a(u,u,v6)) * z)
    ]]></literal>
    <justification jstring="[para(19819(a,1),19997(a,1,1))].">
      <j1 rule="para" parents="19819 19997"/>
    </justification>
  </clause>

  <clause id="20000">
    <literal><![CDATA[
      (a(x,y,z) * a(u,u,a(w,v5,v6))) * a(u,u,a(w,v5,v6)) = a(x,y,a(w,v5,a(u,u,v6)) * z)
    ]]></literal>
    <justification jstring="[para(14(a,2),19999(a,1,1,1))].">
      <j1 rule="para" parents="14 19999"/>
    </justification>
  </clause>

  <clause id="20001">
    <literal><![CDATA[
      a(x,y,z) * (a(u,u,a(w,v5,v6)) * a(u,u,a(w,v5,v6))) = a(x,y,a(w,v5,a(u,u,v6)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,19784,a(flip),b,20000,a)].">
      <j1 rule="hyper" parents="63 19784 20000"/>
    </justification>
  </clause>

  <clause id="20002">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,w,v5)) * v6) = a(x,y,v6) * 1
    ]]></literal>
    <justification jstring="[para(13998(a,1),20001(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13998 20001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20003">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,w,v5)) * v6) = a(x,y,v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,8,a(flip),b,20002,a),flip(a)].">
      <j1 rule="hyper" parents="316 8 20002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20004">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,a(v5,v5,v6)) * v7)) = a(x,y,z * v7)
    ]]></literal>
    <justification jstring="[hyper(135,a,20002,a(flip),b,19597,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="135 20002 19597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20007">
    <literal><![CDATA[
      a(x,y,a(z,z,a(u,w,v5)) * v6) = a(x,y,v6)
    ]]></literal>
    <justification jstring="[para(18945(a,1),20003(a,1,3,1))].">
      <j1 rule="para" parents="18945 20003"/>
    </justification>
  </clause>

  <clause id="20008">
    <literal><![CDATA[
      a(x,y,L(z,z,a(u,w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(19235(a,1),20003(a,1,3))].">
      <j1 rule="para" parents="19235 20003"/>
    </justification>
  </clause>

  <clause id="20009">
    <literal><![CDATA[
      a(x,y,L(z,u,a(w,v5,u))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(19236(a,1),20003(a,1,3))].">
      <j1 rule="para" parents="19236 20003"/>
    </justification>
  </clause>

  <clause id="20010">
    <literal><![CDATA[
      a(x,y,z * a(u,u,a(w,v5,v6))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(19145(a,1),20003(a,1,3))].">
      <j1 rule="para" parents="19145 20003"/>
    </justification>
  </clause>

  <clause id="20011">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v5))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(19113(a,1),20003(a,1,3))].">
      <j1 rule="para" parents="19113 20003"/>
    </justification>
  </clause>

  <clause id="20013">
    <literal><![CDATA[
      a(x,y,z) * (a(u,w,x) \ v5) = v5 * (a(u,w,x) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(20008(a,1),19612(a,1,2,1))].">
      <j1 rule="para" parents="20008 19612"/>
    </justification>
  </clause>

  <clause id="20014">
    <literal><![CDATA[
      a(x,y,L(L(z,u,a(u,w,v5)),v6,v7)) = a(x,y,L(z,v6,v7))
    ]]></literal>
    <justification jstring="[para(16994(a,2),20009(a,1,3))].">
      <j1 rule="para" parents="16994 20009"/>
    </justification>
  </clause>

  <clause id="20015">
    <literal><![CDATA[
      a(x,y,L(z,u,a(w,w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(19248(a,1),20009(a,1,3))].">
      <j1 rule="para" parents="19248 20009"/>
    </justification>
  </clause>

  <clause id="20017">
    <literal><![CDATA[
      L(a(x,y,z) * u,u,a(w,v5,u)) = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(20009(a,1),19718(a,2,2))].">
      <j1 rule="para" parents="20009 19718"/>
    </justification>
  </clause>

  <clause id="20018">
    <literal><![CDATA[
      (a(x * a(y,z,u),w,v5) * x) * a(y,z,u) = R(x * a(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(20009(a,1),19871(a,1,2))].">
      <j1 rule="para" parents="20009 19871"/>
    </justification>
  </clause>

  <clause id="20019">
    <literal><![CDATA[
      a(x,y,((z * (u \ (z \ u))) * w) \ v5) = a(x,y,w \ (v5 * a(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14808,a(flip),b,20015,a),flip(a)].">
      <j1 rule="hyper" parents="63 14808 20015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20020">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v5)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5101,a(flip),b,20007,a)].">
      <j1 rule="hyper" parents="63 5101 20007"/>
    </justification>
  </clause>

  <clause id="20022">
    <literal><![CDATA[
      a(x,y,z * a(u,u,L(w,v5,v6))) = a(x,y,a(u,u,w) * z)
    ]]></literal>
    <justification jstring="[para(19515(a,1),20007(a,1,3))].">
      <j1 rule="para" parents="19515 20007"/>
    </justification>
  </clause>

  <clause id="20023">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,w,v5)) * v6) = a(x,y,a(z,z,u) * v6)
    ]]></literal>
    <justification jstring="[para(19931(a,1),20007(a,1,3)),flip(a)].">
      <j1 rule="para" parents="19931 20007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20028">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v5))) = a(z,y,a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,19184,a,b,20011,a),flip(a)].">
      <j1 rule="hyper" parents="316 19184 20011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20030">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,w),v5)) = a(x,y,a(z,u,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19524,a,b,20011,a)].">
      <j1 rule="hyper" parents="63 19524 20011"/>
    </justification>
  </clause>

  <clause id="20031">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ v5)) = a(x,y,a(z,u,v5 * w))
    ]]></literal>
    <justification jstring="[para(8606(a,1),20011(a,1,3))].">
      <j1 rule="para" parents="8606 20011"/>
    </justification>
  </clause>

  <clause id="20034">
    <literal><![CDATA[
      a((x \ 1) \ y,z,a(u,w,v5)) = a(x * y,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19327,a(flip),b,20020,a)].">
      <j1 rule="hyper" parents="63 19327 20020"/>
    </justification>
  </clause>

  <clause id="20038">
    <literal><![CDATA[
      a(x,y,a(z,u \ w,v5)) = a(x,y,a(z,u * w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,12004,a(flip),b,20030,a),flip(a)].">
      <j1 rule="hyper" parents="63 12004 20030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20042">
    <literal><![CDATA[
      L(x,x,a(y,z,a(u,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,19721,a(flip),b,20017,a(flip))].">
      <j1 rule="hyper" parents="35 19721 20017"/>
    </justification>
  </clause>

  <clause id="20047">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 \ 1) = v5 \ a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(20042(a,1),11606(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20042 11606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20049">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) = a(x,y,a(v5,w,z \ u))
    ]]></literal>
    <justification jstring="[hyper(316,a,13687,a,b,20031,a)].">
      <j1 rule="hyper" parents="316 13687 20031"/>
    </justification>
  </clause>

  <clause id="20050">
    <literal><![CDATA[
      a(x,y,a(z,u,T(z,w) \ (v5 \ v6))) = a(x,y,a(z,u,(z \ v6) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19596,a,b,20031,a)].">
      <j1 rule="hyper" parents="63 19596 20031"/>
    </justification>
  </clause>

  <clause id="20052">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,L(z,u * w,v5)) = a(x,y,a(v5,u \ w,z))
    ]]></literal>
    <justification jstring="[hyper(316,a,19101,a,b,20038,a)].">
      <j1 rule="hyper" parents="316 19101 20038"/>
    </justification>
  </clause>

  <clause id="20055">
    <literal><![CDATA[
      a(x,L(y,z,u) \ w,a(y,z,u)) = a(y,z,a(x,y * w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19531,a,b,20038,a)].">
      <j1 rule="hyper" parents="63 19531 20038"/>
    </justification>
  </clause>

  <clause id="20057">
    <literal><![CDATA[
      a(x,y,a(z,u * w,L(v5,v6,x))) = a(z,u \ w,a(x,y,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19183,a(flip),b,20038,a),flip(a)].">
      <j1 rule="hyper" parents="63 19183 20038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20062">
    <literal><![CDATA[
      a(x,y,a(z \ u,w,v5)) = a(x,y,a(z * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,13660,a,b,20049,a)].">
      <j1 rule="hyper" parents="316 13660 20049"/>
    </justification>
  </clause>

  <clause id="20068">
    <literal><![CDATA[
      a(x,y,a(z \ (x * u),w,v5)) = a(x,y,a((x \ z) * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19403,a(flip),b,20062,a)].">
      <j1 rule="hyper" parents="63 19403 20062"/>
    </justification>
  </clause>

  <clause id="20075">
    <literal><![CDATA[
      a(x \ y,z,a(u,w,v5)) = a(x * y,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13026,a(flip),b,20034,a)].">
      <j1 rule="hyper" parents="63 13026 20034"/>
    </justification>
  </clause>

  <clause id="20082">
    <literal><![CDATA[
      (x \ 1) * a(y,z,a(u,w,v5)) = x \ a(u,w,a(v5,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,19148,a(flip),b,20047,a)].">
      <j1 rule="hyper" parents="63 19148 20047"/>
    </justification>
  </clause>

  <clause id="20083">
    <literal><![CDATA[
      a(x,y,(z * ((u \ a(w,w,a(v5,v6,v7))) * v8)) * v9) = a(x,y,(z * (a(v7,v6,a(w,w,v5)) * (v8 * u))) * v9)
    ]]></literal>
    <justification jstring="[para(20082(a,1),19590(a,1,3,1,2,1))].">
      <j1 rule="para" parents="20082 19590"/>
    </justification>
  </clause>

  <clause id="20084">
    <literal><![CDATA[
      a(x,y,z * a(u,w,L(w,v5,v6))) = a(x,y,a(w,w,u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,17365,a,b,20022,a)].">
      <j1 rule="hyper" parents="63 17365 20022"/>
    </justification>
  </clause>

  <clause id="20085">
    <literal><![CDATA[
      a(x,y,z * a(u,w,L(L(w,v5,v6),v7,v8))) = a(x,y,a(w,w,L(u,v5,v6)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,17366,a(flip),b,20023,a)].">
      <j1 rule="hyper" parents="63 17366 20023"/>
    </justification>
  </clause>

  <clause id="20086">
    <literal><![CDATA[
      a(x,y \ z,a(u,w,v5)) = a(x,y * z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19183,a(flip),b,20057,a),flip(a)].">
      <j1 rule="hyper" parents="63 19183 20057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20089">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (w * v5)) = a(x,y,w * (v5 * a(u,z,z)))
    ]]></literal>
    <justification jstring="[para(13567(a,1),20084(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13567 20084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20090">
    <literal><![CDATA[
      (a(x,y,z) * (a(u,w,x) \ v5)) \ ((a(u,w,x) \ a(x,y,z)) * (v5 * v6)) = L(K(a(u,w,x) \ a(x,y,z),v5) * v6,v5,a(u,w,x) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(20013(a,2),3299(a,1,1))].">
      <j1 rule="para" parents="20013 3299"/>
    </justification>
  </clause>

  <clause id="20092">
    <literal><![CDATA[
      a(x,y,a((x \ z) * u,w,v5)) = a(x,y,a(z * (x * u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,20062,a(flip),b,20068,a),flip(a)].">
      <j1 rule="hyper" parents="63 20062 20068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20093">
    <literal><![CDATA[
      a(x,y,(a(z,u,u) * w) * v5) = a(x,y,a(u,u,z) * (v5 * w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5623,a,b,20089,a)].">
      <j1 rule="hyper" parents="316 5623 20089"/>
    </justification>
  </clause>

  <clause id="20094">
    <literal><![CDATA[
      a(x,y,(z * a(u,w,w)) * v5) = a(x,y,a(w,w,u) * (v5 * z))
    ]]></literal>
    <justification jstring="[hyper(316,a,5469,a,b,20089,a)].">
      <j1 rule="hyper" parents="316 5469 20089"/>
    </justification>
  </clause>

  <clause id="20095">
    <literal><![CDATA[
      a(x * (y \ z),u,a(y,w,v5)) = a(y,u,a(z * (y * x),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19193,a,b,20092,a)].">
      <j1 rule="hyper" parents="63 19193 20092"/>
    </justification>
  </clause>

  <clause id="20096">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (((w * w) * v5) * v6)) = a(x,y,v5 * (a(u,z,z) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5872,a(flip),b,20093,a),flip(a)].">
      <j1 rule="hyper" parents="63 5872 20093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20097">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (w * (v5 * L(v6,v5,a(u,z,z))))) = a(x,y,((a(u,z,z) * v5) * v6) * w)
    ]]></literal>
    <justification jstring="[para(14054(a,1),20093(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="14054 20093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20098">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,w,v5) * (v6 * v7))) * a(x,u,z) = a(x,u,L(z,y,(a(v5,w,w) * v7) * v6))
    ]]></literal>
    <justification jstring="[para(20093(a,1),19296(a,1,1,3))].">
      <j1 rule="para" parents="20093 19296"/>
    </justification>
  </clause>

  <clause id="20099">
    <literal><![CDATA[
      a(x * a(y,x,a(z,z,u) * (w * v5)),v6,L(v7,y,(a(u,z,z) * v5) * w)) = a(x,v6,L(v7,(a(u,z,z) * v5) * w,y))
    ]]></literal>
    <justification jstring="[para(20093(a,1),19342(a,1,1,2))].">
      <j1 rule="para" parents="20093 19342"/>
    </justification>
  </clause>

  <clause id="20100">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w \ (u \ w))) \ v5)) = a(x,y,a(u,u,w) * (z * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,14771,a,b,20094,a)].">
      <j1 rule="hyper" parents="63 14771 20094"/>
    </justification>
  </clause>

  <clause id="20101">
    <literal><![CDATA[
      a(x,y,L(z,u \ w,v5)) = a(x,y,L(z,u * w,v5))
    ]]></literal>
    <justification jstring="[hyper(38,a,19101,a,b,20052,a)].">
      <j1 rule="hyper" parents="38 19101 20052"/>
    </justification>
  </clause>

  <clause id="20103">
    <literal><![CDATA[
      a(x,R(y,y,z),L(R(y,y,z),y * u,w)) = a(x,y,L(y,a(y,y,z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19984,a(flip),b,20101,a),flip(a)].">
      <j1 rule="hyper" parents="63 19984 20101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20105">
    <literal><![CDATA[
      a(x,y,a(z,u,z \ (w \ v5))) = a(x,y,a(z,u,(z \ v5) * w))
    ]]></literal>
    <justification jstring="[para(113(a,1),20050(a,1,3,3,1))].">
      <j1 rule="para" parents="113 20050"/>
    </justification>
  </clause>

  <clause id="20106">
    <literal><![CDATA[
      a(x,y,a(z,u,(z \ w) * v5)) = a(x,y,a(z,u,z * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(15485(a,1),20105(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15485 20105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20107">
    <literal><![CDATA[
      a(x,y,a((z \ u) * w,v5,z)) = a(x,y,a(z,v5,z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13660,a,b,20106,a)].">
      <j1 rule="hyper" parents="63 13660 20106"/>
    </justification>
  </clause>

  <clause id="20108">
    <literal><![CDATA[
      a(x,y,(z * ((u \ z) * w)) \ (u * L(w,u \ z,u \ z))) = a(x,y,a(u,u * z,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19440,a,b,20107,a)].">
      <j1 rule="hyper" parents="63 19440 20107"/>
    </justification>
  </clause>

  <clause id="20109">
    <literal><![CDATA[
      a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w))) = u * a(x,y,a(z,z * w,z * (u \ w)))
    ]]></literal>
    <justification jstring="[para(20107(a,1),19953(a,2,2))].">
      <j1 rule="para" parents="20107 19953"/>
    </justification>
  </clause>

  <clause id="20110">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ a(u,w,v5),v6,v7) = R(a(u,w,v5) * a(z,y,x),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,19915,a(flip),b,20018,a)].">
      <j1 rule="hyper" parents="63 19915 20018"/>
    </justification>
  </clause>

  <clause id="20113">
    <literal><![CDATA[
      a(x,y,(z * a(u,w,w)) \ v5) = a(x,y,z \ (v5 * a(u,w,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8200,a(flip),b,20019,a)].">
      <j1 rule="hyper" parents="63 8200 20019"/>
    </justification>
  </clause>

  <clause id="20114">
    <literal><![CDATA[
      a(x,y,((z * ((z * u) \ u)) * w) \ v5) = a(x,y,w \ (v5 * a(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7432,a,b,20113,a)].">
      <j1 rule="hyper" parents="63 7432 20113"/>
    </justification>
  </clause>

  <clause id="20115">
    <literal><![CDATA[
      a(x,y,(z * u) * a(w,w,v5)) = a(x,y,u * (a(v5,w,w) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6004,a(flip),b,20096,a)].">
      <j1 rule="hyper" parents="63 6004 20096"/>
    </justification>
  </clause>

  <clause id="20116">
    <literal><![CDATA[
      R(a(x,y,z) * a(u,w,v5),v6,v7) = L(a(x,y,z) * a(u,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(18638(a,1),20110(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18638 20110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20117">
    <literal><![CDATA[
      L(a(x,y,z) * a(u,w,v5),v6,v7) \ (a(x,y,z) * a(u,w,v5)) = v7 \ L(v7,v6,a(x,y,z) * a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(20116(a,1),18911(a,1,1))].">
      <j1 rule="para" parents="20116 18911"/>
    </justification>
  </clause>

  <clause id="20119">
    <literal><![CDATA[
      a(x,y,z * a(u,w,L(L(w,v5,v6),v7,v8))) = a(x,y,a(w,w,u) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,20023,a(flip),b,20085,a),flip(a)].">
      <j1 rule="hyper" parents="316 20023 20085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20121">
    <literal><![CDATA[
      a(x,R(y,y,z),L(L(y,y,z),y * u,w)) = a(x,y,L(y,a(y,y,z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5953,a(flip),b,20103,a)].">
      <j1 rule="hyper" parents="63 5953 20103"/>
    </justification>
  </clause>

  <clause id="20122">
    <literal><![CDATA[
      a(x,L(y,y,z),L(L(y,y,z),y * u,w)) = a(x,y,L(y,a(y,y,z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,11325,a(flip),b,20121,a)].">
      <j1 rule="hyper" parents="63 11325 20121"/>
    </justification>
  </clause>

  <clause id="20123">
    <literal><![CDATA[
      a(x,y,L(y,a(y,y,z) * u,w)) = a(x,y,L(y,y * u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,13574,a(flip),b,20122,a),flip(a)].">
      <j1 rule="hyper" parents="63 13574 20122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20125">
    <literal><![CDATA[
      a(x,y,L(y,a(y,y,z) * u,w)) = a(x,y,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,19961,a(flip),b,20123,a),flip(a)].">
      <j1 rule="hyper" parents="316 19961 20123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20127">
    <literal><![CDATA[
      a(x,y,L(z,u,(a(w,v5,v5) * v6) * v7)) = a(x,y,L(z,u,a(v5,v5,w) * (v7 * v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19296,a(flip),b,20098,a),flip(a)].">
      <j1 rule="hyper" parents="63 19296 20098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20128">
    <literal><![CDATA[
      a(x,y,(z * ((u \ a(w,w,a(v5,v6,v7))) * v8)) * v9) = a(x,y,(z * (v8 * u)) * (a(v7,v6,a(w,w,v5)) * v9))
    ]]></literal>
    <justification jstring="[para(19672(a,1),20083(a,2,3))].">
      <j1 rule="para" parents="19672 20083"/>
    </justification>
  </clause>

  <clause id="20129">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w) * a(v5,v6,v7)) = a(x,y,a(z,u,w) * a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(18755,a,20117,a),flip(a)].">
      <j1 rule="hyper" parents="18755 20117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20130">
    <literal><![CDATA[
      a(x,y,(z * ((u \ a(w,w,a(v5,v6,v7))) * v8)) * v9) = a(x,y,(z * (v8 * u)) * v9)
    ]]></literal>
    <justification jstring="[hyper(316,a,20004,a(flip),b,20128,a),flip(a)].">
      <j1 rule="hyper" parents="316 20004 20128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20132">
    <literal><![CDATA[
      a(x,y,(z * (u * L(w,v5,a(v6,v7,v5)))) * v8) = a(x,y,(z * (u * w)) * v8)
    ]]></literal>
    <justification jstring="[hyper(63,a,19903,a(flip),b,20130,a)].">
      <j1 rule="hyper" parents="63 19903 20130"/>
    </justification>
  </clause>

  <clause id="20134">
    <literal><![CDATA[
      a(x,y,(z * (L(u,w,a(w,v5,v6)) * v7)) * v8) = a(x,y,(z * (v7 * u)) * v8)
    ]]></literal>
    <justification jstring="[hyper(63,a,17026,a,b,20132,a)].">
      <j1 rule="hyper" parents="63 17026 20132"/>
    </justification>
  </clause>

  <clause id="20135">
    <literal><![CDATA[
      a(x,y,z * (u * (w * L(v5,v6,a(v7,v7,v8))))) = a(x,y,(u * (w * v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,19286,a(flip),b,20134,a)].">
      <j1 rule="hyper" parents="63 19286 20134"/>
    </justification>
  </clause>

  <clause id="20137">
    <literal><![CDATA[
      a(x,y,z * (u * (w * L(v5,v6,a(v7,v8,v8))))) = a(x,y,(u * (w * v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9692,a,b,20135,a)].">
      <j1 rule="hyper" parents="63 9692 20135"/>
    </justification>
  </clause>

  <clause id="20139">
    <literal><![CDATA[
      a(x,y,((a(z,u,u) * w) * v5) * v6) = a(x,y,(v6 * (w * v5)) * a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,20097,a(flip),b,20137,a)].">
      <j1 rule="hyper" parents="63 20097 20137"/>
    </justification>
  </clause>

  <clause id="20141">
    <literal><![CDATA[
      a(x,y,((a(z,u,u) * w) * v5) * v6) = a(x,y,(w * v5) * (a(z,u,u) * v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,20115,a(flip),b,20139,a),flip(a)].">
      <j1 rule="hyper" parents="316 20115 20139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20142">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,w) * v5)) * v6) = a(x,y,(v5 * z) * (a(u,w,w) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,5542,a,b,20141,a)].">
      <j1 rule="hyper" parents="63 5542 20141"/>
    </justification>
  </clause>

  <clause id="20143">
    <literal><![CDATA[
      a(x,y,(z * u) * (a(w,v5,v5) * (u \ K(a(w,v5,v5) * z,u)))) = a(x,y,R(a(w,v5,v5) * z,u,u))
    ]]></literal>
    <justification jstring="[para(6271(a,1),20142(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6271 20142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20144">
    <literal><![CDATA[
      a(x,y,(z * u) * (a(w,v5,v5) * (u \ K(a(w,v5,v5) * z,u)))) = a(x,y,L(a(w,v5,v5) * z,u,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5746,a(flip),b,20143,a),flip(a)].">
      <j1 rule="hyper" parents="316 5746 20143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20145">
    <literal><![CDATA[
      a(x,y,(z * u) * (a(w,v5,v5) * (u \ K(z,u)))) = a(x,y,L(a(w,v5,v5) * z,u,u))
    ]]></literal>
    <justification jstring="[para(5278(a,1),20144(a,1,3,2,2,2))].">
      <j1 rule="para" parents="5278 20144"/>
    </justification>
  </clause>

  <clause id="20147">
    <literal><![CDATA[
      a(x,y,(z * u) * (T(u,z) \ a(w,v5,v5))) = a(x,y,L(a(w,v5,v5) * z,u,u))
    ]]></literal>
    <justification jstring="[para(18953(a,1),20145(a,1,3,2))].">
      <j1 rule="para" parents="18953 20145"/>
    </justification>
  </clause>

  <clause id="20148">
    <literal><![CDATA[
      a(x,y,(z * u) * (T(u,z) * a(w,v5,v5))) = a(x,y,L(a(w,v5,v5) * z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18972,a(flip),b,20147,a)].">
      <j1 rule="hyper" parents="63 18972 20147"/>
    </justification>
  </clause>

  <clause id="20149">
    <literal><![CDATA[
      a(x,y,(z * u) * (z * a(w,v5,v5))) = a(x,y,L(a(w,v5,v5) * u,z,z))
    ]]></literal>
    <justification jstring="[para(6260(a,1),20148(a,1,3))].">
      <j1 rule="para" parents="6260 20148"/>
    </justification>
  </clause>

  <clause id="20151">
    <literal><![CDATA[
      a(x * (a(y,x,x) * (z \ (x * a(y,x,x)))),L(x,x,y),a(u,w,v5)) = z \ L(z,x * a(y,x,x),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,13070,a(flip),b,18243,a)].">
      <j1 rule="hyper" parents="63 13070 18243"/>
    </justification>
  </clause>

  <clause id="20152">
    <literal><![CDATA[
      a((x \ (y * a(z,y,y))) * L(y,y,z),L(y,y,z),a(u,w,v5)) = x \ L(x,y * a(z,y,y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,18248,a(flip),b,20151,a)].">
      <j1 rule="hyper" parents="63 18248 20151"/>
    </justification>
  </clause>

  <clause id="20153">
    <literal><![CDATA[
      a((x \ (y * a(z,y,y))) * L(y,y,z),L(y,y,z),a(u,w,v5)) = x \ L(x,L(y,y,z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(15727(a,1),20152(a,2,2))].">
      <j1 rule="para" parents="15727 20152"/>
    </justification>
  </clause>

  <clause id="20154">
    <literal><![CDATA[
      a((x \ (y * a(z,y,y))) * L(y,y,z),L(y,y,z),a(u,w,v5)) = a(x,L(y,y,z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,18787,a(flip),b,20153,a),flip(a)].">
      <j1 rule="hyper" parents="316 18787 20153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20155">
    <literal><![CDATA[
      a((a(x,y,y) * (z \ y)) * L(y,y,x),L(y,y,x),a(u,w,v5)) = a(z,L(y,y,x),a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(18903(a,1),20154(a,1,1,1))].">
      <j1 rule="para" parents="18903 20154"/>
    </justification>
  </clause>

  <clause id="20156">
    <literal><![CDATA[
      a(a(x,y,y) * ((z \ y) * L(y,y,x)),L(y,y,x),a(u,w,v5)) = a(z,L(y,y,x),a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(6870(a,1),20155(a,1,1))].">
      <j1 rule="para" parents="6870 20155"/>
    </justification>
  </clause>

  <clause id="20157">
    <literal><![CDATA[
      a((x \ y) * y,L(y,y,z),a(u,w,v5)) = a(x,L(y,y,z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(18054(a,1),20156(a,1,1))].">
      <j1 rule="para" parents="18054 20156"/>
    </justification>
  </clause>

  <clause id="20158">
    <literal><![CDATA[
      a(x * (y \ x),z,a(u,L(x,x,w),v5)) = a(y,L(x,x,w),a(v5,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19209,a,b,20157,a)].">
      <j1 rule="hyper" parents="63 19209 20157"/>
    </justification>
  </clause>

  <clause id="20160">
    <literal><![CDATA[
      a(x * (y \ x),z,a(u,x,L(w,x,v5))) = a(y,L(x,x,v5),a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19524,a(flip),b,20158,a)].">
      <j1 rule="hyper" parents="63 19524 20158"/>
    </justification>
  </clause>

  <clause id="20161">
    <literal><![CDATA[
      a(x,L(y,y,z),a(u,w,v5)) = a(x,y,a(L(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19282,a(flip),b,20160,a),flip(a)].">
      <j1 rule="hyper" parents="63 19282 20160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20162">
    <literal><![CDATA[
      a(x,L(y,y,z),a(u,w,v5)) = a(x,y,a(u,w,L(v5,y,z)))
    ]]></literal>
    <justification jstring="[hyper(316,a,19380,a(flip),b,20161,a),flip(a)].">
      <j1 rule="hyper" parents="316 19380 20161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20164">
    <literal><![CDATA[
      a(x,y \ (y / (z \ 1)),a(u,w,v5)) = a(x,z,a(u,w,L(v5,z,y)))
    ]]></literal>
    <justification jstring="[para(1447(a,1),20162(a,1,2))].">
      <j1 rule="para" parents="1447 20162"/>
    </justification>
  </clause>

  <clause id="20166">
    <literal><![CDATA[
      a(x,y \ ((z \ 1) \ y),a(u,w,v5)) = a(x,z,a(u,w,L(v5,z,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11209,a(flip),b,20164,a)].">
      <j1 rule="hyper" parents="63 11209 20164"/>
    </justification>
  </clause>

  <clause id="20167">
    <literal><![CDATA[
      a(x,y \ (z \ y),a(u,w,v5)) = a(x,z,a(u,w,L(v5,z,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18559,a(flip),b,20166,a)].">
      <j1 rule="hyper" parents="63 18559 20166"/>
    </justification>
  </clause>

  <clause id="20175">
    <literal><![CDATA[
      a(x * a(y,x,a(z,z,u) * (w * v5)),v6,L(v7,y,a(z,z,u) * (w * v5))) = a(x,v6,L(v7,(a(u,z,z) * v5) * w,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,20127,a(flip),b,20099,a)].">
      <j1 rule="hyper" parents="63 20127 20099"/>
    </justification>
  </clause>

  <clause id="20191">
    <literal><![CDATA[
      a(x,y,L(z,(a(u,w,w) * v5) * v6,v7)) = a(x,y,L(z,a(w,w,u) * (v6 * v5),v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,19342,a(flip),b,20175,a),flip(a)].">
      <j1 rule="hyper" parents="63 19342 20175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20203">
    <literal><![CDATA[
      a(x,y,L(((z \ u) / z) * L(z,w,L(v5,v5,w)),w,a(z,z,v5))) = a(x,y,L(v5 \ R(v5,w,z),z,w) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(18062(a,1),18490(a,1,3,3))].">
      <j1 rule="para" parents="18062 18490"/>
    </justification>
  </clause>

  <clause id="20204">
    <literal><![CDATA[
      a(x,y,L((z \ (z \ u)) * L(z,w,L(v5,v5,w)),w,a(z,z,v5))) = a(x,y,L(v5 \ R(v5,w,z),z,w) \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5717,a(flip),b,20203,a)].">
      <j1 rule="hyper" parents="63 5717 20203"/>
    </justification>
  </clause>

  <clause id="20206">
    <literal><![CDATA[
      a(x,y,L(z * (L(z,u,L(w,w,u)) \ (z \ v5)),u,a(z,z,w))) = a(x,y,L(w \ R(w,u,z),z,u) \ (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,13627,a(flip),b,20204,a)].">
      <j1 rule="hyper" parents="63 13627 20204"/>
    </justification>
  </clause>

  <clause id="20207">
    <literal><![CDATA[
      a(x,y,L(L(z,u,L(w,w,u)) \ v5,u,a(z,z,w))) = a(x,y,L(w \ R(w,u,z),z,u) \ (z \ v5))
    ]]></literal>
    <justification jstring="[para(1130(a,1),20206(a,1,3,1))].">
      <j1 rule="para" parents="1130 20206"/>
    </justification>
  </clause>

  <clause id="20208">
    <literal><![CDATA[
      a(x,y,L(L(z,u,L(w,w,u)) \ v5,u,a(z,z,w))) = a(x,y,L(R(w,u,z) \ w,z,u) * (z \ v5))
    ]]></literal>
    <justification jstring="[para(17225(a,1),20207(a,2,3))].">
      <j1 rule="para" parents="17225 20207"/>
    </justification>
  </clause>

  <clause id="20209">
    <literal><![CDATA[
      a(x,y,L(L(z,u,L(w,w,u)) \ v5,u,a(z,z,w))) = a(x,y,L(w * L(w,u,z),z,u) * (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,17374,a(flip),b,20208,a),flip(a)].">
      <j1 rule="hyper" parents="316 17374 20208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20210">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),w,u) * (w \ v5)) = a(x,y,L(L(w,u,z) \ v5,u,a(w,w,z)))
    ]]></literal>
    <justification jstring="[para(19805(a,1),20209(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="19805 20209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20211">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ v5,u,a(z,z,w))) = a(x,y,a(z,u,L(w,z,u)) * (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19028,a(flip),b,20210,a),flip(a)].">
      <j1 rule="hyper" parents="63 19028 20210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20212">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ v5,u,a(z,z,w))) = a(x,y,a(z,u,w) * (z \ v5))
    ]]></literal>
    <justification jstring="[para(18860(a,1),20211(a,2,3,1))].">
      <j1 rule="para" parents="18860 20211"/>
    </justification>
  </clause>

  <clause id="20213">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * (z \ v5)) = a(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,20015,a(flip),b,20212,a),flip(a)].">
      <j1 rule="hyper" parents="63 20015 20212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20215">
    <literal><![CDATA[
      a((x \ 1) \ (a(y,y,z) \ u),x,a(y,y,z)) * (a(y,y,z) \ u) = T((u / (x \ a(y,y,z))) * (x \ 1),a(y,y,z))
    ]]></literal>
    <justification jstring="[para(15743(a,1),18965(a,1,1))].">
      <j1 rule="para" parents="15743 18965"/>
    </justification>
  </clause>

  <clause id="20216">
    <literal><![CDATA[
      a((x \ 1) * (a(y,y,z) \ u),x,a(z,y,y)) * (a(y,y,z) \ u) = T((u / (x \ a(y,y,z))) * (x \ 1),a(y,y,z))
    ]]></literal>
    <justification jstring="[para(20075(a,1),20215(a,1,1))].">
      <j1 rule="para" parents="20075 20215"/>
    </justification>
  </clause>

  <clause id="20217">
    <literal><![CDATA[
      a((x \ 1) * (y * a(z,z,u)),x,a(u,z,z)) * (a(z,z,u) \ y) = T((y / (x \ a(z,z,u))) * (x \ 1),a(z,z,u))
    ]]></literal>
    <justification jstring="[para(14963(a,1),20216(a,1,1))].">
      <j1 rule="para" parents="14963 20216"/>
    </justification>
  </clause>

  <clause id="20218">
    <literal><![CDATA[
      a(x,x,a(y * (z \ 1),z,u)) * (a(x,x,u) \ y) = T((y / (z \ a(x,x,u))) * (z \ 1),a(x,x,u))
    ]]></literal>
    <justification jstring="[para(19941(a,1),20217(a,1,1))].">
      <j1 rule="para" parents="19941 20217"/>
    </justification>
  </clause>

  <clause id="20219">
    <literal><![CDATA[
      T((x / (y \ a(z,z,u))) * (y \ 1),a(z,z,u)) = a(z,z,a(y \ x,y,u)) * (a(z,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(18094(a,1),20218(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="18094 20218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20220">
    <literal><![CDATA[
      T((x / (y \ a(z,z,u))) * (y \ 1),a(z,z,u)) = a(z,z,a(x * y,y,u)) * (a(z,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(18260(a,1),20219(a,2,1))].">
      <j1 rule="para" parents="18260 20219"/>
    </justification>
  </clause>

  <clause id="20221">
    <literal><![CDATA[
      T((x / (y \ a(z,z,u))) * (y \ 1),a(z,z,u)) = a(z,z,L(u,y,x * y)) \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,19433,a(flip),b,20220,a),flip(a)].">
      <j1 rule="hyper" parents="316 19433 20220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20222">
    <literal><![CDATA[
      T((x / (y \ a(z,z,u))) * (y \ 1),a(z,z,u)) = (x / y) * (a(z,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(316,a,19400,a(flip),b,20221,a),flip(a)].">
      <j1 rule="hyper" parents="316 19400 20221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20223">
    <literal><![CDATA[
      T(x * ((a(y,y,z) * x) \ u),a(y,y,z)) = (u / x) * (a(y,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(18964(a,1),20222(a,1,1))].">
      <j1 rule="para" parents="18964 20222"/>
    </justification>
  </clause>

  <clause id="20224">
    <literal><![CDATA[
      (x / y) * (a(z,z,u) \ y) = y * ((a(z,z,u) * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(2294,a,20223,a),flip(a)].">
      <j1 rule="hyper" parents="2294 20223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20226">
    <literal><![CDATA[
      (1 / (a(x,x,y) * (z * ((a(x,x,y) * z) \ u)))) \ a(x,x,y) = L(a(x,x,y),z,z \ u) * u
    ]]></literal>
    <justification jstring="[para(20224(a,1),19814(a,1,1,2,2))].">
      <j1 rule="para" parents="20224 19814"/>
    </justification>
  </clause>

  <clause id="20227">
    <literal><![CDATA[
      L(a(x,x,y),z,z \ u) * u = a(x,x,y) * (a(x,x,y) * (z * ((a(x,x,y) * z) \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18735,a(flip),b,20226,a),flip(a)].">
      <j1 rule="hyper" parents="63 18735 20226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20228">
    <literal><![CDATA[
      L(a(x,x,y),z,z \ u) * u = y * (L(L(y,x,x),x,x) \ (z * ((a(x,x,y) * z) \ u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,19451,a(flip),b,20227,a),flip(a)].">
      <j1 rule="hyper" parents="316 19451 20227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20229">
    <literal><![CDATA[
      L(a(x,x,y),z,z \ u) * u = y * (y \ (z * ((a(x,x,y) \ z) \ u)))
    ]]></literal>
    <justification jstring="[para(17575(a,1),20228(a,2,2))].">
      <j1 rule="para" parents="17575 20228"/>
    </justification>
  </clause>

  <clause id="20230">
    <literal><![CDATA[
      L(a(x,x,y),z,z \ u) * u = z * ((a(x,x,y) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(316,a,10,a(flip),b,20229,a),flip(a)].">
      <j1 rule="hyper" parents="316 10 20229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20232">
    <literal><![CDATA[
      (x / y) * (y * a(z,z,u)) = y * ((a(z,z,u) \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2435,a(flip),b,20230,a)].">
      <j1 rule="hyper" parents="63 2435 20230"/>
    </justification>
  </clause>

  <clause id="20233">
    <literal><![CDATA[
      (a(x,x,y) * z) * (z \ u) = z * ((a(x,x,y) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5348,a(flip),b,20232,a)].">
      <j1 rule="hyper" parents="63 5348 20232"/>
    </justification>
  </clause>

  <clause id="20234">
    <literal><![CDATA[
      (a(x,x,y) * z) * (z \ (z * u)) = z * L(a(x,x,y) * u,a(x,x,y),z)
    ]]></literal>
    <justification jstring="[para(16145(a,2),20233(a,2,2))].">
      <j1 rule="para" parents="16145 20233"/>
    </justification>
  </clause>

  <clause id="20235">
    <literal><![CDATA[
      x * L(a(y,y,z) * u,a(y,y,z),x) = (a(y,y,z) * x) * u
    ]]></literal>
    <justification jstring="[hyper(539,a,20234,a),flip(a)].">
      <j1 rule="hyper" parents="539 20234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20237">
    <literal><![CDATA[
      (x * ((a(y,y,z) * u) * w)) / T(x * u,L(a(y,y,z) * w,a(y,y,z),u)) = L(L(a(y,y,z) * w,a(y,y,z),u),u,x)
    ]]></literal>
    <justification jstring="[para(20235(a,1),4365(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="20235 4365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20238">
    <literal><![CDATA[
      R(x,y \ z,L(y \ z,(y \ z) / (1 / y),(y \ z) / (1 / y))) = R(x,y \ z,L(y,y \ 1,z) * ((1 / y) \ (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(316,a,4683,a(flip),b,19014,a),flip(a)].">
      <j1 rule="hyper" parents="316 4683 19014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20239">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * (L(L(a(z,u,u),w,v5),v6,v7) * (R(z,u,u) \ v8))) = a(x,y,(z \ v8) * L(a(z,u,L(u,w,v5)),v6,v7))
    ]]></literal>
    <justification jstring="[para(13562(a,2),19220(a,2,3,2,1))].">
      <j1 rule="para" parents="13562 19220"/>
    </justification>
  </clause>

  <clause id="20240">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * u) \ z))) \ z = ((z / (u * w)) * u) * L(L(w,u,u \ (w \ z)),y,x)
    ]]></literal>
    <justification jstring="[para(14927(a,1),19268(a,1,1))].">
      <j1 rule="para" parents="14927 19268"/>
    </justification>
  </clause>

  <clause id="20241">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * u) \ z))) \ z = (L(w,y,x) * u) * ((w * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(316,a,16533,a(flip),b,20240,a),flip(a)].">
      <j1 rule="hyper" parents="316 16533 20240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20242">
    <literal><![CDATA[
      (x * ((a(y,y,z) * u) * w)) / T(x * u,a(y,y,z) * w) = L(L(a(y,y,z) * w,a(y,y,z),u),u,x)
    ]]></literal>
    <justification jstring="[para(4304(a,1),20237(a,1,2))].">
      <j1 rule="para" parents="4304 20237"/>
    </justification>
  </clause>

  <clause id="20244">
    <literal><![CDATA[
      L(L(a(x,x,y) * z,a(x,x,y),u),u,w) = (w * ((a(x,x,y) * u) * z)) / T(w * u,z)
    ]]></literal>
    <justification jstring="[para(5239(a,1),20242(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5239 20242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20245">
    <literal><![CDATA[
      L(L(a(x,x,y) * z,a(x,x,y),T(u,w)),T(u,w),w) = (w * ((a(x,x,y) * T(u,w)) * z)) / T(u * w,z)
    ]]></literal>
    <justification jstring="[para(114(a,1),20244(a,2,2,1))].">
      <j1 rule="para" parents="114 20244"/>
    </justification>
  </clause>

  <clause id="20247">
    <literal><![CDATA[
      L(L(a(x,x,y) * z,a(x,x,y),u),T(u,w),w) = (w * ((a(x,x,y) * T(u,w)) * z)) / T(u * w,z)
    ]]></literal>
    <justification jstring="[para(1581(a,1),20245(a,1,1))].">
      <j1 rule="para" parents="1581 20245"/>
    </justification>
  </clause>

  <clause id="20248">
    <literal><![CDATA[
      L(L(a(x,x,y) * z,a(x,x,y),u),u,w) = (w * ((a(x,x,y) * T(u,w)) * z)) / T(u * w,z)
    ]]></literal>
    <justification jstring="[hyper(10874,a,20247,a)].">
      <j1 rule="hyper" parents="10874 20247"/>
    </justification>
  </clause>

  <clause id="20251">
    <literal><![CDATA[
      L(L(a(x,x,y) * z,a(x,x,y),u),u,w) = (w * (T(u * a(x,x,y),w) * z)) / T(u * w,z)
    ]]></literal>
    <justification jstring="[para(5332(a,2),20248(a,2,1,2,1))].">
      <j1 rule="para" parents="5332 20248"/>
    </justification>
  </clause>

  <clause id="20252">
    <literal><![CDATA[
      R(x,y \ z,L(y \ z,(y \ z) / (1 / y),(y \ z) / (1 / y))) = R(x,y \ z,y * ((1 / L(y,y \ 1,z)) \ (y \ z)))
    ]]></literal>
    <justification jstring="[para(14854(a,1),20238(a,2,3))].">
      <j1 rule="para" parents="14854 20238"/>
    </justification>
  </clause>

  <clause id="20253">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * (L(L(a(z,u,u),w,v5),v6,v7) * (R(z,u,u) \ v8))) = a(x,y,(z \ v8) * a(z,u,L(L(u,w,v5),v6,v7)))
    ]]></literal>
    <justification jstring="[para(13557(a,2),20239(a,2,3,2))].">
      <j1 rule="para" parents="13557 20239"/>
    </justification>
  </clause>

  <clause id="20254">
    <literal><![CDATA[
      R(x,y \ z,L(y \ z,(y \ z) / (1 / y),(y \ z) / (1 / y))) = R(x,y \ z,y * ((L(y,y \ 1,z) \ 1) \ (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(316,a,4761,a(flip),b,20252,a),flip(a)].">
      <j1 rule="hyper" parents="316 4761 20252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20255">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * (L(L(a(z,u,u),w,v5),v6,v7) * (R(z,u,u) \ v8))) = a(x,y,a(u,u,z) * (z \ v8))
    ]]></literal>
    <justification jstring="[hyper(316,a,20119,a(flip),b,20253,a),flip(a)].">
      <j1 rule="hyper" parents="316 20119 20253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20257">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * (L(L(a(z,u,u),w,v5),v6,v7) * (R(z,u,u) \ v8))) = a(x,y,L(z,u,u) \ v8)
    ]]></literal>
    <justification jstring="[para(18968(a,1),20255(a,2,3))].">
      <j1 rule="para" parents="18968 20255"/>
    </justification>
  </clause>

  <clause id="20258">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * (L(a(z,u,L(u,w,v5)),v6,v7) * (R(z,u,u) \ v8))) = a(x,y,L(z,u,u) \ v8)
    ]]></literal>
    <justification jstring="[para(13562(a,2),20257(a,1,3,2,1,1))].">
      <j1 rule="para" parents="13562 20257"/>
    </justification>
  </clause>

  <clause id="20259">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * (a(z,u,L(L(u,w,v5),v6,v7)) * (R(z,u,u) \ v8))) = a(x,y,L(z,u,u) \ v8)
    ]]></literal>
    <justification jstring="[para(13557(a,2),20258(a,1,3,2,1))].">
      <j1 rule="para" parents="13557 20258"/>
    </justification>
  </clause>

  <clause id="20260">
    <literal><![CDATA[
      a(x,y,a(z,u,L(L(u,w,v5),v6,v7)) * (z \ v8)) = a(x,y,L(z,u,u) \ v8)
    ]]></literal>
    <justification jstring="[para(19594(a,1),20259(a,1,3))].">
      <j1 rule="para" parents="19594 20259"/>
    </justification>
  </clause>

  <clause id="20261">
    <literal><![CDATA[
      a(x,y,L(z,u,L(L(u,w,v5),v6,v7)) \ v8) = a(x,y,L(z,u,u) \ v8)
    ]]></literal>
    <justification jstring="[hyper(63,a,20213,a(flip),b,20260,a)].">
      <j1 rule="hyper" parents="63 20213 20260"/>
    </justification>
  </clause>

  <clause id="20263">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w) \ v5,z,z) \ (L(z,v6,v7) * v5)) = a(x,y,L(z,v6,v7) \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17192,a(flip),b,20261,a),flip(a)].">
      <j1 rule="hyper" parents="63 17192 20261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20265">
    <literal><![CDATA[
      a(x,y,(z * L(u,w,v5)) \ (L(u,v6,v7) * z)) = a(x,y,L(u,v6,v7) \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,13970,a(flip),b,20263,a)].">
      <j1 rule="hyper" parents="63 13970 20263"/>
    </justification>
  </clause>

  <clause id="20266">
    <literal><![CDATA[
      a(x,y,(z * L(u,w,v5)) \ (L(u,v6,v7) * z)) = a(x,y,a(v5,w,u) * a(u,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(316,a,19996,a(flip),b,20265,a),flip(a)].">
      <j1 rule="hyper" parents="316 19996 20265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20267">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * a(w,z,u)) = a(x,y,a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19408,a(flip),b,20266,a),flip(a)].">
      <j1 rule="hyper" parents="63 19408 20266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20269">
    <literal><![CDATA[
      R(x,y \ z,L(y \ z,(y \ z) / (1 / y),(y \ z) / (1 / y))) = R(x,y \ z,(L(y,y \ 1,z) \ (y \ z)) * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,11089,a(flip),b,20254,a),flip(a)].">
      <j1 rule="hyper" parents="316 11089 20254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20270">
    <literal><![CDATA[
      R(x,y \ z,L(y \ z,(y \ z) / (1 / y),(y \ z) / (1 / y))) = R(x,y \ z,(y \ (L(y,y \ 1,z) \ z)) * y)
    ]]></literal>
    <justification jstring="[para(1137(a,1),20269(a,2,3,1))].">
      <j1 rule="para" parents="1137 20269"/>
    </justification>
  </clause>

  <clause id="20271">
    <literal><![CDATA[
      R(x,y \ z,L(y \ z,(y \ z) / (1 / y),(y \ z) / (1 / y))) = R(x,y \ z,(y \ T(z * (1 / y),y)) * y)
    ]]></literal>
    <justification jstring="[para(3679(a,1),20270(a,2,3,1,2))].">
      <j1 rule="para" parents="3679 20270"/>
    </justification>
  </clause>

  <clause id="20272">
    <literal><![CDATA[
      R(x,y \ z,L(y \ z,(y \ z) / (1 / y),(y \ z) / (1 / y))) = R(x,y \ z,(y \ (z * (1 / y))) * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,10267,a(flip),b,20271,a),flip(a)].">
      <j1 rule="hyper" parents="316 10267 20271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20274">
    <literal><![CDATA[
      R(x,y \ z,L(y \ z,(y \ z) / (1 / y),(y \ z) / (1 / y))) = R(x,y \ z,z * (1 / y))
    ]]></literal>
    <justification jstring="[hyper(316,a,4677,a(flip),b,20272,a),flip(a)].">
      <j1 rule="hyper" parents="316 4677 20272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20276">
    <literal><![CDATA[
      R(x,y \ z,L(y \ z,(y \ z) / (1 / y),(y \ z) / (1 / y))) = R(x,y \ z,z * y)
    ]]></literal>
    <justification jstring="[hyper(316,a,1709,a(flip),b,20274,a),flip(a)].">
      <j1 rule="hyper" parents="316 1709 20274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20277">
    <literal><![CDATA[
      L(a(x,y,z),u,u * w) * (a(w,v5,v6) \ (a(w,v5,v6) / w)) = (((a(w,v5,v6) / w) / a(w,v5,v6)) / u) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(11617(a,1),18474(a,1,1))].">
      <j1 rule="para" parents="11617 18474"/>
    </justification>
  </clause>

  <clause id="20278">
    <literal><![CDATA[
      (((a(x,y,z) / x) / a(x,y,z)) / u) * (u * a(x,w,v5)) = L(a(x,w,v5),u,u) * (a(x,y,z) \ (a(x,y,z) / x))
    ]]></literal>
    <justification jstring="[para(18455(a,1),20277(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18455 20277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20279">
    <literal><![CDATA[
      (((a(x,y,z) / x) / a(x,y,z)) / u) * (u * a(x,w,v5)) = L(a(x,w,v5),u,u) * (1 / x)
    ]]></literal>
    <justification jstring="[para(8427(a,1),20278(a,2,2))].">
      <j1 rule="para" parents="8427 20278"/>
    </justification>
  </clause>

  <clause id="20280">
    <literal><![CDATA[
      (((a(x,y,z) / x) / a(x,y,z)) / u) * (u * a(x,w,v5)) = L(a(x,w,v5),u,u) / x
    ]]></literal>
    <justification jstring="[hyper(316,a,8503,a(flip),b,20279,a),flip(a)].">
      <j1 rule="hyper" parents="316 8503 20279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20282">
    <literal><![CDATA[
      (L(a(x,y,z),u,u) / x) \ (a(x,y,z) / x) = a(u \ (1 / x),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(20280(a,1),8435(a,1,1))].">
      <j1 rule="para" parents="20280 8435"/>
    </justification>
  </clause>

  <clause id="20283">
    <literal><![CDATA[
      (x \ L(a(x,y,z),u,u)) \ (x \ a(x,y,z)) = a(u \ (1 / x),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9195,a(flip),b,20282,a)].">
      <j1 rule="hyper" parents="63 9195 20282"/>
    </justification>
  </clause>

  <clause id="20285">
    <literal><![CDATA[
      a(x \ (1 / y),x,a(y,z,u)) = a(x,x,(a(y,z,u) \ y) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16465,a(flip),b,20283,a),flip(a)].">
      <j1 rule="hyper" parents="63 16465 20283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20286">
    <literal><![CDATA[
      a(x \ (1 / y),x,a(y,z,u)) = a(x,x,y * (y * a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,14409,a(flip),b,20285,a),flip(a)].">
      <j1 rule="hyper" parents="316 14409 20285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20287">
    <literal><![CDATA[
      a(x \ (1 / y),x,a(y,z,u)) = a(x,x,L(a(y,z,u),y,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,5810,a(flip),b,20286,a),flip(a)].">
      <j1 rule="hyper" parents="316 5810 20286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20288">
    <literal><![CDATA[
      a(x \ (1 / y),x,a(y,z,u)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,20020,a(flip),b,20287,a),flip(a)].">
      <j1 rule="hyper" parents="316 20020 20287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20290">
    <literal><![CDATA[
      a((1 / x) * y,y,a(z,u,x)) = a(y,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18252,a(flip),b,20288,a)].">
      <j1 rule="hyper" parents="63 18252 20288"/>
    </justification>
  </clause>

  <clause id="20292">
    <literal><![CDATA[
      a((x \ 1) * y,y,a(z,u,x)) = a(y,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,3117,a(flip),b,20290,a)].">
      <j1 rule="hyper" parents="63 3117 20290"/>
    </justification>
  </clause>

  <clause id="20293">
    <literal><![CDATA[
      a(x * y,x,a(z,u,y)) = a(x,x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13030,a(flip),b,20292,a)].">
      <j1 rule="hyper" parents="63 13030 20292"/>
    </justification>
  </clause>

  <clause id="20294">
    <literal><![CDATA[
      a(T(x,y),T(x,z) * (u * (K(z,x) / x)),a(u * (K(w,v5) / x),v6,v7)) = a(u,u,a(x,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,19899,a,b,20293,a)].">
      <j1 rule="hyper" parents="63 19899 20293"/>
    </justification>
  </clause>

  <clause id="20295">
    <literal><![CDATA[
      a(T(x,y),T(x,z) * (u * (K(z,x) / x)),a(u * (x \ 1),w,v5)) = a(u,u,a(x,w,v5))
    ]]></literal>
    <justification jstring="[para(338(a,1),20294(a,1,3,1,2))].">
      <j1 rule="para" parents="338 20294"/>
    </justification>
  </clause>

  <clause id="20296">
    <literal><![CDATA[
      a(T(x,y),T(x,z) * (u * (K(z,x) / x)),a(x * u,w,v5)) = a(u,u,a(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,12312,a(flip),b,20295,a)].">
      <j1 rule="hyper" parents="63 12312 20295"/>
    </justification>
  </clause>

  <clause id="20297">
    <literal><![CDATA[
      a(T(x,y),T(x,z) * (u * (x \ K(z,x))),a(x * u,w,v5)) = a(u,u,a(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,11215,a(flip),b,20296,a)].">
      <j1 rule="hyper" parents="63 11215 20296"/>
    </justification>
  </clause>

  <clause id="20298">
    <literal><![CDATA[
      a(T(x,y),T(x,z) * (u * (x \ 1)),a(x * u,w,v5)) = a(u,u,a(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,11259,a(flip),b,20297,a)].">
      <j1 rule="hyper" parents="63 11259 20297"/>
    </justification>
  </clause>

  <clause id="20300">
    <literal><![CDATA[
      a(x * y,z,a(u,T(x,w) * (y * x),T(x,v5))) = a(y,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19140,a(flip),b,20298,a)].">
      <j1 rule="hyper" parents="63 19140 20298"/>
    </justification>
  </clause>

  <clause id="20301">
    <literal><![CDATA[
      a(x * y,z,a(u,T(x,w) * (y * x),x)) = a(y,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(113(a,1),20300(a,1,3,3))].">
      <j1 rule="para" parents="113 20300"/>
    </justification>
  </clause>

  <clause id="20302">
    <literal><![CDATA[
      a(x * y,z,a(u,x * (y * x),x)) = a(y,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(113(a,1),20301(a,1,3,2,1))].">
      <j1 rule="para" parents="113 20301"/>
    </justification>
  </clause>

  <clause id="20303">
    <literal><![CDATA[
      a(x * y,z,a(u,L(y,x,x),x)) = a(y,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12007,a(flip),b,20302,a)].">
      <j1 rule="hyper" parents="63 12007 20302"/>
    </justification>
  </clause>

  <clause id="20304">
    <literal><![CDATA[
      a(x * y,z,a(u,y,x)) = a(y,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20030,a(flip),b,20303,a)].">
      <j1 rule="hyper" parents="63 20030 20303"/>
    </justification>
  </clause>

  <clause id="20307">
    <literal><![CDATA[
      a(x * y,z,u) * a(y,y,a(x,z,u)) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(20304(a,1),19331(a,1,2))].">
      <j1 rule="para" parents="20304 19331"/>
    </justification>
  </clause>

  <clause id="20308">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) * a(y,y,a(v5,w,a(u,z,x))) = a((y \ 1) \ x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(19154(a,1),20307(a,1,2,3))].">
      <j1 rule="para" parents="19154 20307"/>
    </justification>
  </clause>

  <clause id="20309">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) * a(y,y,a(v5,w,a(u,z,x))) = a(y \ x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,13026,a(flip),b,20308,a),flip(a)].">
      <j1 rule="hyper" parents="316 13026 20308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20310">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) * 1 = a(y \ x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(19545(a,1),20309(a,1,2))].">
      <j1 rule="para" parents="19545 20309"/>
    </justification>
  </clause>

  <clause id="20312">
    <literal><![CDATA[
      a(x * (y * z),u,a(z,w,v5)) = a(z,w,a(y \ (z \ x),u,v5))
    ]]></literal>
    <justification jstring="[hyper(135,a,20310,a,b,19419,a(flip))].">
      <j1 rule="hyper" parents="135 20310 19419"/>
    </justification>
  </clause>

  <clause id="20315">
    <literal><![CDATA[
      a(x * (y * z),u,a(z,w,v5)) = a(z,w,a(y * (z \ x),u,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,20062,a(flip),b,20312,a),flip(a)].">
      <j1 rule="hyper" parents="316 20062 20312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20316">
    <literal><![CDATA[
      (a(x,y,z) * ((u / (w * z)) * ((a(x,y,z) \ w) * z))) \ u = a(z,y,a(w * (z \ u),w * z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,18254,a,b,20315,a)].">
      <j1 rule="hyper" parents="63 18254 20315"/>
    </justification>
  </clause>

  <clause id="20319">
    <literal><![CDATA[
      L(a(x,y,z),u,w * (a(x,y,z) * u)) * w = (w / (a(x,y,z) * u)) * ((u * a(x,y,z)) * T(a(x,y,z),u))
    ]]></literal>
    <justification jstring="[para(14781(a,1),18475(a,1,1))].">
      <j1 rule="para" parents="14781 18475"/>
    </justification>
  </clause>

  <clause id="20320">
    <literal><![CDATA[
      L(a(x,y,z),u,w * (a(x,y,z) * u)) * w = (w / (a(x,y,z) * u)) * ((u * a(x,y,z)) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(2286(a,1),20319(a,2,2,2))].">
      <j1 rule="para" parents="2286 20319"/>
    </justification>
  </clause>

  <clause id="20322">
    <literal><![CDATA[
      L(a(x,y,z),u,w * (a(x,y,z) * u)) * w = (w / (a(x,y,z) * u)) * (z * (L(L(z,y,x),y,x) \ u))
    ]]></literal>
    <justification jstring="[para(14726(a,1),20320(a,2,2))].">
      <j1 rule="para" parents="14726 20320"/>
    </justification>
  </clause>

  <clause id="20323">
    <literal><![CDATA[
      L(a(x,y,z),u,w * (a(x,y,z) * u)) * w = u * ((a(x,y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(316,a,16102,a(flip),b,20322,a),flip(a)].">
      <j1 rule="hyper" parents="316 16102 20322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20324">
    <literal><![CDATA[
      L(a(x,y,z),u,(u * a(x,y,z)) * w) * w = u * ((a(x,y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(2391(a,2),20323(a,1,1))].">
      <j1 rule="para" parents="2391 20323"/>
    </justification>
  </clause>

  <clause id="20325">
    <literal><![CDATA[
      L(a(x,y,(z \ y) * y),z,(z * a(x,y,(z \ y) * y)) * u) * u = z * (L(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(18108(a,2),20324(a,2,2,1))].">
      <j1 rule="para" parents="18108 20324"/>
    </justification>
  </clause>

  <clause id="20326">
    <literal><![CDATA[
      L(a(x,y,(z \ y) * y),z,(L(1 / z,y,x) \ 1) * u) * u = z * (L(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(18158(a,1),20325(a,1,1,3,1))].">
      <j1 rule="para" parents="18158 20325"/>
    </justification>
  </clause>

  <clause id="20327">
    <literal><![CDATA[
      L(a(x,y,(z \ y) * y),z,L((1 / z) \ 1,y,x) * u) * u = z * (L(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(17180(a,2),20326(a,1,1))].">
      <j1 rule="para" parents="17180 20326"/>
    </justification>
  </clause>

  <clause id="20328">
    <literal><![CDATA[
      L(a(x,y,(z \ y) * y),z,L(z,y,x) * u) * u = z * (L(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(83(a,1),20327(a,1,1,3,1,1))].">
      <j1 rule="para" parents="83 20327"/>
    </justification>
  </clause>

  <clause id="20329">
    <literal><![CDATA[
      L(a(x,y,z),z,L(z,y,x) * u) * u = z * (L(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(18629(a,1),20328(a,1,1,1))].">
      <j1 rule="para" parents="18629 20328"/>
    </justification>
  </clause>

  <clause id="20330">
    <literal><![CDATA[
      a(a(x,x,y),L(y,x,x) * z,L(u,z,L(y,x,x))) = (y * (z * u)) \ ((y * z) * L(u,z,L(y,x,x)))
    ]]></literal>
    <justification jstring="[para(18969(a,1),19000(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18969 19000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20332">
    <literal><![CDATA[
      a(a(x,x,y),L(y,x,x) * z,L(u,z,L(y,x,x))) = (y * (z * u)) \ (y * (z * L(u,z,a(x,x,y))))
    ]]></literal>
    <justification jstring="[para(19468(a,1),20330(a,2,2))].">
      <j1 rule="para" parents="19468 20330"/>
    </justification>
  </clause>

  <clause id="20333">
    <literal><![CDATA[
      L(a(x,x,a(y,z,u)),z * y,u) = a(a(x,x,u),L(u,x,x) * z,L(y,z,L(u,x,x)))
    ]]></literal>
    <justification jstring="[hyper(316,a,19852,a(flip),b,20332,a)].">
      <j1 rule="hyper" parents="316 19852 20332"/>
    </justification>
  </clause>

  <clause id="20334">
    <literal><![CDATA[
      a(a(x,x,y),L(y,x,x) * z,L(u,z,L(y,x,x))) = a(x,x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15243,a(flip),b,20333,a),flip(a)].">
      <j1 rule="hyper" parents="63 15243 20333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20336">
    <literal><![CDATA[
      a(x,x,a(L(y,z,L(u,x,x)),L(u,x,x) * z,u)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19132,a(flip),b,20334,a)].">
      <j1 rule="hyper" parents="63 19132 20334"/>
    </justification>
  </clause>

  <clause id="20337">
    <literal><![CDATA[
      a(x,x,a(y,L(z,x,x) * u,L(z,u,L(z,x,x)))) = a(x,x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19380,a(flip),b,20336,a)].">
      <j1 rule="hyper" parents="63 19380 20336"/>
    </justification>
  </clause>

  <clause id="20338">
    <literal><![CDATA[
      a(x,x,a(y,L(z,x,x) * u,L(z,u,z))) = a(x,x,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(7995(a,1),20337(a,1,3,3))].">
      <j1 rule="para" parents="7995 20337"/>
    </justification>
  </clause>

  <clause id="20339">
    <literal><![CDATA[
      a(x,x,a(y,L(z,x,x) * u,z)) = a(x,x,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(5574(a,1),20338(a,1,3))].">
      <j1 rule="para" parents="5574 20338"/>
    </justification>
  </clause>

  <clause id="20341">
    <literal><![CDATA[
      a(x,L(y,z,z) \ u,a(y,z,z)) = a(z,z,a(x,u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,19535,a,b,20339,a)].">
      <j1 rule="hyper" parents="63 19535 20339"/>
    </justification>
  </clause>

  <clause id="20343">
    <literal><![CDATA[
      a(x,y,a(z,x * u,y)) = a(y,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,20055,a(flip),b,20341,a)].">
      <j1 rule="hyper" parents="63 20055 20341"/>
    </justification>
  </clause>

  <clause id="20344">
    <literal><![CDATA[
      a(x,x * y,a(z,z,u)) = a(z,z,a(u,y * a(z,z,u),x))
    ]]></literal>
    <justification jstring="[hyper(63,a,19012,a(flip),b,20343,a)].">
      <j1 rule="hyper" parents="63 19012 20343"/>
    </justification>
  </clause>

  <clause id="20345">
    <literal><![CDATA[
      a(x,x * y,a(z,z,u)) = a(z,z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,19981,a(flip),b,20344,a),flip(a)].">
      <j1 rule="hyper" parents="316 19981 20344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20347">
    <literal><![CDATA[
      a(x,y,a(L(z,z,u) * (L(z,z,u) * (w \ L(z,z,u))),L(z,z,u),u)) = a(x,y,(L(z,z,u) \ w) * ((u / (z \ 1)) \ (u * w)))
    ]]></literal>
    <justification jstring="[para(6441(a,1),18244(a,1,3))].">
      <j1 rule="para" parents="6441 18244"/>
    </justification>
  </clause>

  <clause id="20348">
    <literal><![CDATA[
      a(x,y,a(z,L(u,u,z),L(u,u,z) * (L(u,u,z) * (w \ L(u,u,z))))) = a(x,y,(L(u,u,z) \ w) * ((z / (u \ 1)) \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13660,a,b,20347,a)].">
      <j1 rule="hyper" parents="63 13660 20347"/>
    </justification>
  </clause>

  <clause id="20349">
    <literal><![CDATA[
      a(x,y,a(z,L(u,u,z),u * (L(L(u,u,z),u,z) * (w \ L(u,u,z))))) = a(x,y,(L(u,u,z) \ w) * ((z / (u \ 1)) \ (z * w)))
    ]]></literal>
    <justification jstring="[para(17085(a,1),20348(a,1,3,3))].">
      <j1 rule="para" parents="17085 20348"/>
    </justification>
  </clause>

  <clause id="20350">
    <literal><![CDATA[
      a(x,y,a(z,L(u,u,z),u * (u * (w \ L(L(L(u,u,z),u,z),u,z))))) = a(x,y,(L(u,u,z) \ w) * ((z / (u \ 1)) \ (z * w)))
    ]]></literal>
    <justification jstring="[para(13349(a,1),20349(a,1,3,3,2))].">
      <j1 rule="para" parents="13349 20349"/>
    </justification>
  </clause>

  <clause id="20351">
    <literal><![CDATA[
      a(x,y,a(z,L(u,u,z),L(w \ L(L(L(u,u,z),u,z),u,z),u,u))) = a(x,y,(L(u,u,z) \ w) * ((z / (u \ 1)) \ (z * w)))
    ]]></literal>
    <justification jstring="[para(5810(a,1),20350(a,1,3))].">
      <j1 rule="para" parents="5810 20350"/>
    </justification>
  </clause>

  <clause id="20352">
    <literal><![CDATA[
      a(x,y,a(z,L(u,u,z),L(w \ L(u,u,z),u,u))) = a(x,y,(L(u,u,z) \ w) * ((z / (u \ 1)) \ (z * w)))
    ]]></literal>
    <justification jstring="[para(10043(a,1),20351(a,1,3))].">
      <j1 rule="para" parents="10043 20351"/>
    </justification>
  </clause>

  <clause id="20353">
    <literal><![CDATA[
      a(x,y,a(z,L(u,u,z),w \ L(u,u,z))) = a(x,y,(L(u,u,z) \ w) * ((z / (u \ 1)) \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20011,a(flip),b,20352,a)].">
      <j1 rule="hyper" parents="63 20011 20352"/>
    </justification>
  </clause>

  <clause id="20355">
    <literal><![CDATA[
      a(x,y,a(z,L(u,u,z),w \ L(u,u,z))) = a(x,y,(L(u,u,z) \ w) * (((u \ 1) \ z) \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5643,a(flip),b,20353,a),flip(a)].">
      <j1 rule="hyper" parents="316 5643 20353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20357">
    <literal><![CDATA[
      a(x,y,a(z,L(u,u,z),w \ L(u,u,z))) = a(x,y,(L(u,u,z) \ w) * ((u \ z) \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,12483,a(flip),b,20355,a),flip(a)].">
      <j1 rule="hyper" parents="316 12483 20355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20358">
    <literal><![CDATA[
      a(x,y,a(z,L(u,u,z),w * L(u,u,z))) = a(x,y,(L(u,u,z) \ w) * ((u \ z) \ (z * w)))
    ]]></literal>
    <justification jstring="[para(18890(a,1),20357(a,1,3))].">
      <j1 rule="para" parents="18890 20357"/>
    </justification>
  </clause>

  <clause id="20359">
    <literal><![CDATA[
      a(x,y,(L(z,z,u) \ w) * ((z \ u) \ (u * w))) = a(x,y,a(w \ L(z,z,u),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19402,a(flip),b,20358,a),flip(a)].">
      <j1 rule="hyper" parents="63 19402 20358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20360">
    <literal><![CDATA[
      a(x,y,((z \ u) \ (u * w)) \ (L(z,z,u) \ w)) = a(x,y,a(w \ L(z,z,u),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12486,a,b,20359,a)].">
      <j1 rule="hyper" parents="63 12486 20359"/>
    </justification>
  </clause>

  <clause id="20361">
    <literal><![CDATA[
      a(x,y,((z \ u) \ (u * w)) \ (L(z,z,u) \ w)) = a(x,y,a(u,z,w * L(z,z,u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,19518,a(flip),b,20360,a),flip(a)].">
      <j1 rule="hyper" parents="316 19518 20360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20362">
    <literal><![CDATA[
      a(x,y,((z \ u) \ (u * w)) \ (L(z,z,u) \ w)) = a(x,y,a(u,z,w * z))
    ]]></literal>
    <justification jstring="[para(19022(a,1),20361(a,2,3))].">
      <j1 rule="para" parents="19022 20361"/>
    </justification>
  </clause>

  <clause id="20363">
    <literal><![CDATA[
      a(x,y,R(z,z,z * (((u * (w / v5)) * v6) * v7)) * (((u * (v5 \ w)) * v6) * v7)) = a(x,y,z \ (((u * (w / v5)) * v6) * v7))
    ]]></literal>
    <justification jstring="[hyper(316,a,5803,a(flip),b,18180,a),flip(a)].">
      <j1 rule="hyper" parents="316 5803 18180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20365">
    <literal><![CDATA[
      a(x,y,R(z,z,z * (((u * (w \ v5)) * v6) * v7)) * (((u * (w \ v5)) * v6) * v7)) = a(x,y,z \ (((u * (v5 / w)) * v6) * v7))
    ]]></literal>
    <justification jstring="[para(15660(a,1),20363(a,1,3,1))].">
      <j1 rule="para" parents="15660 20363"/>
    </justification>
  </clause>

  <clause id="20366">
    <literal><![CDATA[
      a(x,y,(z * z) * (z \ (((u * (w \ v5)) * v6) * v7))) = a(x,y,z \ (((u * (v5 / w)) * v6) * v7))
    ]]></literal>
    <justification jstring="[para(18155(a,1),20365(a,1,3))].">
      <j1 rule="para" parents="18155 20365"/>
    </justification>
  </clause>

  <clause id="20367">
    <literal><![CDATA[
      a(x,y,z \ (((u * (w / v5)) * v6) * v7)) = a(x,y,z \ (((u * (v5 \ w)) * v6) * v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,5803,a(flip),b,20366,a),flip(a)].">
      <j1 rule="hyper" parents="63 5803 20366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20369">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) \ L(a(x,y,a(z,u,y)),w,v5)) * L(x,y,a(z,u,y)) = x * (a(x,y,a(z,u,y)) * a(z,u,a(y,a(v5,w,y),x)))
    ]]></literal>
    <justification jstring="[hyper(316,a,8412,a(flip),b,18546,a),flip(a)].">
      <j1 rule="hyper" parents="316 8412 18546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20387">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) \ L(a(x,y,a(z,u,y)),w,v5)) * L(x,y,a(z,u,y)) = x * a(y,a(z,u,y),L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(18523(a,1),20369(a,2,2))].">
      <j1 rule="para" parents="18523 20369"/>
    </justification>
  </clause>

  <clause id="20388">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) \ L(a(x,y,a(z,u,y)),w,v5)) * L(x,y,a(z,u,y)) = L(x,a(z,u,y),L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,16255,a(flip),b,20387,a),flip(a)].">
      <j1 rule="hyper" parents="316 16255 20387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20389">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) \ L(a(x,y,a(z,u,y)),w,v5)) * L(x,y,a(z,u,y)) = L(x,y,a(z,u,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,19084,a(flip),b,20388,a),flip(a)].">
      <j1 rule="hyper" parents="316 19084 20388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20390">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) \ a(L(a(z,u,y),w,v5),y,x)) * L(x,y,a(z,u,y)) = L(x,y,a(z,u,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(17737(a,2),20389(a,1,1,2))].">
      <j1 rule="para" parents="17737 20389"/>
    </justification>
  </clause>

  <clause id="20391">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) \ a(y,a(z,u,y),L(x,w,v5))) * L(x,y,a(z,u,y)) = L(x,y,a(z,u,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(17763(a,1),20390(a,1,1,2))].">
      <j1 rule="para" parents="17763 20390"/>
    </justification>
  </clause>

  <clause id="20392">
    <literal><![CDATA[
      (a(x,a(y,z,x),L(u,w,v5)) * a(u,x,a(y,z,x))) * L(u,x,a(y,z,x)) = L(u,x,a(y,z,L(x,w,v5)))
    ]]></literal>
    <justification jstring="[para(14470(a,1),20391(a,1,1))].">
      <j1 rule="para" parents="14470 20391"/>
    </justification>
  </clause>

  <clause id="20393">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,z),v5)) * L(v5,z,a(x,y,z)) = L(v5,z,a(x,y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[para(18519(a,1),20392(a,1,1))].">
      <j1 rule="para" parents="18519 20392"/>
    </justification>
  </clause>

  <clause id="20394">
    <literal><![CDATA[
      a(x,y,a(z,z,a(u,w,v5))) * L(v5,z,a(x,y,z)) = L(v5,z,a(x,y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[para(18894(a,1),20393(a,1,1,3))].">
      <j1 rule="para" parents="18894 20393"/>
    </justification>
  </clause>

  <clause id="20395">
    <literal><![CDATA[
      L(x,y,a(z,u,L(y,w,v5))) = 1 * L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(19542(a,1),20394(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19542 20394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20397">
    <literal><![CDATA[
      L(a(x,y,z) \ (L(z,u,w) \ v5),z,a(x,y,z)) = (a(x,y,z) * L(z,u,w)) \ v5
    ]]></literal>
    <justification jstring="[hyper(131,a,20395,a(flip),b,19085,a(flip))].">
      <j1 rule="hyper" parents="131 20395 19085"/>
    </justification>
  </clause>

  <clause id="20399">
    <literal><![CDATA[
      ((L(x,y,z) \ u) / x) * L(x,w,v5) = (a(v5,w,x) * L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,19683,a(flip),b,20397,a)].">
      <j1 rule="hyper" parents="63 19683 20397"/>
    </justification>
  </clause>

  <clause id="20400">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((L(1 / x,u,w) \ 1) \ v5)) = (a(w,u,x) * L(x,y,z)) \ v5
    ]]></literal>
    <justification jstring="[hyper(63,a,19660,a,b,20399,a)].">
      <j1 rule="hyper" parents="63 19660 20399"/>
    </justification>
  </clause>

  <clause id="20401">
    <literal><![CDATA[
      L(a(x,y,y * ((z \ (a(u,z,w) \ 1)) \ y)) \ 1,z \ a(u,z,w),a(u,z,w)) = (z \ 1) \ (a(u,z,w) * L(a(u,z,w) \ (z \ 1),y,x))
    ]]></literal>
    <justification jstring="[para(18021(a,1),19752(a,1,1,1,3,2,1))].">
      <j1 rule="para" parents="18021 19752"/>
    </justification>
  </clause>

  <clause id="20402">
    <literal><![CDATA[
      L(a(x,y,((z \ a(u,z,w)) \ y) * y) \ 1,z \ a(u,z,w),a(u,z,w)) = (z \ 1) \ (a(u,z,w) * L(a(u,z,w) \ (z \ 1),y,x))
    ]]></literal>
    <justification jstring="[para(6748(a,1),20401(a,1,1,1))].">
      <j1 rule="para" parents="6748 20401"/>
    </justification>
  </clause>

  <clause id="20403">
    <literal><![CDATA[
      L(a(x,y,((z * a(u,z,w)) \ y) * y) \ 1,z \ a(u,z,w),a(u,z,w)) = (z \ 1) \ (a(u,z,w) * L(a(u,z,w) \ (z \ 1),y,x))
    ]]></literal>
    <justification jstring="[para(17713(a,1),20402(a,1,1,1))].">
      <j1 rule="para" parents="17713 20402"/>
    </justification>
  </clause>

  <clause id="20404">
    <literal><![CDATA[
      L(a(x,y,((z * a(u,z,w)) \ y) * y) \ 1,z,a(u,z,w)) = (z \ 1) \ (a(u,z,w) * L(a(u,z,w) \ (z \ 1),y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,18023,a(flip),b,20403,a)].">
      <j1 rule="hyper" parents="63 18023 20403"/>
    </justification>
  </clause>

  <clause id="20405">
    <literal><![CDATA[
      L(a(x,y,((z * a(u,z,w)) \ y) * y) \ 1,z,a(u,z,w)) = (z \ 1) \ (a(u,z,w) * L(z \ (a(u,z,w) \ 1),y,x))
    ]]></literal>
    <justification jstring="[para(18021(a,1),20404(a,2,2,2,1))].">
      <j1 rule="para" parents="18021 20404"/>
    </justification>
  </clause>

  <clause id="20406">
    <literal><![CDATA[
      L(a(x,y,((z * a(u,z,w)) \ y) * y) \ 1,z,a(u,z,w)) = (z \ 1) \ (a(u,z,w) \ L(z \ a(u,z,w),y,x))
    ]]></literal>
    <justification jstring="[para(14749(a,1),20405(a,2,2))].">
      <j1 rule="para" parents="14749 20405"/>
    </justification>
  </clause>

  <clause id="20408">
    <literal><![CDATA[
      a(x,y,a(y,z * L(u,w,v5),z * L(u,w,v5))) * L(z \ (L(L(u,w,v5) / z,y,x) \ L(u,w,v5)),v6,v7) = a(x,y,L(R(u,w,v5) \ z,v6,v7))
    ]]></literal>
    <justification jstring="[para(13907(a,1),19738(a,1,2,1))].">
      <j1 rule="para" parents="13907 19738"/>
    </justification>
  </clause>

  <clause id="20409">
    <literal><![CDATA[
      (a(x,y,z) * (a(u,w,x) \ v5)) \ (a(x,y,z) * (a(u,w,x) \ (v5 * v6))) = L(K(a(u,w,x) \ a(x,y,z),v5) * v6,v5,a(u,w,x) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(19792(a,1),20090(a,1,2))].">
      <j1 rule="para" parents="19792 20090"/>
    </justification>
  </clause>

  <clause id="20423">
    <literal><![CDATA[
      a(x,y,L(R(z,u,w) \ v5,v6,v7)) = a(x,y,L(L(z,u,w) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,19942,a(flip),b,20408,a),flip(a)].">
      <j1 rule="hyper" parents="63 19942 20408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20424">
    <literal><![CDATA[
      a(x,x \ (a(y,z,L(z,u,w)) * v5),L(L(y,z,z) \ y,u,w)) = a(x,x * v5,a(y,z,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19901,a(flip),b,20423,a),flip(a)].">
      <j1 rule="hyper" parents="63 19901 20423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20425">
    <literal><![CDATA[
      a(x,x \ (a(y,z,L(z,u,w)) * v5),a(z,z,L(y,u,w))) = a(x,x * v5,a(y,z,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(11874(a,1),20424(a,1,3))].">
      <j1 rule="para" parents="11874 20424"/>
    </justification>
  </clause>

  <clause id="20426">
    <literal><![CDATA[
      a(x,x * (a(y,z,L(z,u,w)) * v5),a(z,z,L(y,u,w))) = a(x,x * v5,a(y,z,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18583,a(flip),b,20425,a)].">
      <j1 rule="hyper" parents="63 18583 20425"/>
    </justification>
  </clause>

  <clause id="20427">
    <literal><![CDATA[
      a(x,x * y,a(z,u,L(u,w,v5))) = a(u,u,a(x,a(z,u,L(u,w,v5)) * y,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20345,a(flip),b,20426,a),flip(a)].">
      <j1 rule="hyper" parents="63 20345 20426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20428">
    <literal><![CDATA[
      a(x,x * y,a(z,u,L(u,w,v5))) = a(z,u,a(x,y,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,19522,a(flip),b,20427,a),flip(a)].">
      <j1 rule="hyper" parents="316 19522 20427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20429">
    <literal><![CDATA[
      a(x,x * y,a(z,u,u)) = a(z,u,a(x,y,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19578,a(flip),b,20428,a)].">
      <j1 rule="hyper" parents="63 19578 20428"/>
    </justification>
  </clause>

  <clause id="20430">
    <literal><![CDATA[
      a(x,x * y,a(z,u,u)) = a(z,u,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,20011,a(flip),b,20429,a),flip(a)].">
      <j1 rule="hyper" parents="316 20011 20429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20432">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * (a(x,y,y) * (z \ u)) = z \ (u * a(x,y,y))
    ]]></literal>
    <justification jstring="[para(20430(a,1),18597(a,1,1))].">
      <j1 rule="para" parents="20430 18597"/>
    </justification>
  </clause>

  <clause id="20433">
    <literal><![CDATA[
      (x \ y) * a(z,u,L(u,y,x)) = x \ (y * a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19515,a(flip),b,20432,a)].">
      <j1 rule="hyper" parents="63 19515 20432"/>
    </justification>
  </clause>

  <clause id="20434">
    <literal><![CDATA[
      (x \ (y * (a(y,z,a(u,w,w)) \ z))) * a(u,w,L(w,y * (a(y,z,a(u,w,w)) \ z),x)) = x \ (y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[para(8531(a,1),20433(a,2,2))].">
      <j1 rule="para" parents="8531 20433"/>
    </justification>
  </clause>

  <clause id="20435">
    <literal><![CDATA[
      (x \ (y * (z * a(y,z,a(u,w,w))))) * a(u,w,L(w,y * (a(y,z,a(u,w,w)) \ z),x)) = x \ (y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[para(14468(a,1),20434(a,1,1,2,2))].">
      <j1 rule="para" parents="14468 20434"/>
    </justification>
  </clause>

  <clause id="20436">
    <literal><![CDATA[
      (x \ (L(y,z,a(u,w,w)) * z)) * a(u,w,L(w,y * (a(y,z,a(u,w,w)) \ z),x)) = x \ (y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[para(13764(a,1),20435(a,1,1,2))].">
      <j1 rule="para" parents="13764 20435"/>
    </justification>
  </clause>

  <clause id="20437">
    <literal><![CDATA[
      (x \ (L(y,z,a(u,w,w)) * z)) * a(u,w,L(w,y * (z * a(y,z,a(u,w,w))),x)) = x \ (y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[para(14468(a,1),20436(a,1,2,3,2,2))].">
      <j1 rule="para" parents="14468 20436"/>
    </justification>
  </clause>

  <clause id="20438">
    <literal><![CDATA[
      (x \ (L(y,z,a(u,w,w)) * z)) * a(u,w,L(w,L(y,z,a(u,w,w)) * z,x)) = x \ (y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[para(13764(a,1),20437(a,1,2,3,2))].">
      <j1 rule="para" parents="13764 20437"/>
    </justification>
  </clause>

  <clause id="20439">
    <literal><![CDATA[
      (x \ (L(y,z,a(u,w,w)) * z)) * a(u,w,L(w,(a(u,w,w) * z) * y,x)) = x \ (y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[para(19599(a,1),20438(a,1,2))].">
      <j1 rule="para" parents="19599 20438"/>
    </justification>
  </clause>

  <clause id="20440">
    <literal><![CDATA[
      (x \ (L(y,z,a(u,w,w)) * z)) * a(u,w,L(w,a(w,w,u) * (y * z),x)) = x \ (y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[para(20191(a,1),20439(a,1,2))].">
      <j1 rule="para" parents="20191 20439"/>
    </justification>
  </clause>

  <clause id="20441">
    <literal><![CDATA[
      (x \ (L(y,z,a(u,w,w)) * z)) * a(u,w,L(w,y * z,x)) = x \ (y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[para(20125(a,1),20440(a,1,2))].">
      <j1 rule="para" parents="20125 20440"/>
    </justification>
  </clause>

  <clause id="20443">
    <literal><![CDATA[
      (a(x,y,z) * (u * a(w,v5,x))) \ (a(x,y,z) * ((u * v6) * a(w,v5,x))) = L(K(a(w,v5,x) \ a(x,y,z),u) * v6,u,a(w,v5,x) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17392,a(flip),b,20409,a)].">
      <j1 rule="hyper" parents="63 17392 20409"/>
    </justification>
  </clause>

  <clause id="20444">
    <literal><![CDATA[
      L(K(a(x,y,z) \ a(z,u,w),v5) * v6,v5,a(x,y,z) \ a(z,u,w)) = L(L(v6,v5,a(x,y,z)),v5 * a(x,y,z),a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,2511,a(flip),b,20443,a),flip(a)].">
      <j1 rule="hyper" parents="63 2511 20443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20445">
    <literal><![CDATA[
      L(K(a(x,y,z) \ 1,u) * w,u,a(x,y,z) \ a(z,v5,v6)) = L(L(w,u,a(x,y,z)),u * a(x,y,z),a(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(5287(a,1),20444(a,1,1,1))].">
      <j1 rule="para" parents="5287 20444"/>
    </justification>
  </clause>

  <clause id="20446">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y * a(z,u,w),a(w,v5,v6)) = L(1 * x,y,a(z,u,w) \ a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(4998(a,1),20445(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4998 20445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20448">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y * a(z,u,w),a(w,v5,v6)) = L(x,y,a(z,u,w) \ a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(7(a,1),20446(a,2,1))].">
      <j1 rule="para" parents="7 20446"/>
    </justification>
  </clause>

  <clause id="20450">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y * a(z,u,w),a(w,v5,v6)) = L(x,y,a(z,u,w) * a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,16972,a(flip),b,20448,a),flip(a)].">
      <j1 rule="hyper" parents="316 16972 20448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20451">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),a(z,u,w) * y,a(w,v5,v6)) = L(x,y,a(z,u,w) * a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,10797,a,b,20450,a)].">
      <j1 rule="hyper" parents="63 10797 20450"/>
    </justification>
  </clause>

  <clause id="20453">
    <literal><![CDATA[
      a(x,y,L(a(z,u,u) * T(w \ v5,u \ (z \ (u \ z))),w,w)) = a(x,y,a(u,u,z) * ((u \ (z \ (u \ z))) \ (v5 * (w \ (u \ (z \ (u \ z)))))))
    ]]></literal>
    <justification jstring="[hyper(316,a,20149,a(flip),b,19457,a)].">
      <j1 rule="hyper" parents="316 20149 19457"/>
    </justification>
  </clause>

  <clause id="20454">
    <literal><![CDATA[
      a(x,y,L(T((z \ u) * a(w,v5,v5),v5 \ (w \ (v5 \ w))),z,z)) = a(x,y,a(v5,v5,w) * ((v5 \ (w \ (v5 \ w))) \ (u * (z \ (v5 \ (w \ (v5 \ w)))))))
    ]]></literal>
    <justification jstring="[para(5332(a,2),20453(a,1,3,1))].">
      <j1 rule="para" parents="5332 20453"/>
    </justification>
  </clause>

  <clause id="20455">
    <literal><![CDATA[
      a(x,y,L((z \ u) * a(w,v5,v5),z,z)) = a(x,y,a(v5,v5,w) * ((v5 \ (w \ (v5 \ w))) \ (u * (z \ (v5 \ (w \ (v5 \ w)))))))
    ]]></literal>
    <justification jstring="[hyper(63,a,5503,a(flip),b,20454,a)].">
      <j1 rule="hyper" parents="63 5503 20454"/>
    </justification>
  </clause>

  <clause id="20456">
    <literal><![CDATA[
      a(x,y,L((z \ u) * a(w,v5,v5),z,z)) = a(x,y,a(v5,v5,w) * (a(v5,v5,w) * (u * (z \ (v5 \ (w \ (v5 \ w)))))))
    ]]></literal>
    <justification jstring="[hyper(316,a,20100,a(flip),b,20455,a),flip(a)].">
      <j1 rule="hyper" parents="316 20100 20455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20458">
    <literal><![CDATA[
      a(x,y,L((z \ u) * a(w,v5,v5),z,z)) = a(x,y,w * (L(L(w,v5,v5),v5,v5) \ (u * (z \ (v5 \ (w \ (v5 \ w)))))))
    ]]></literal>
    <justification jstring="[para(14699(a,1),20456(a,2,3))].">
      <j1 rule="para" parents="14699 20456"/>
    </justification>
  </clause>

  <clause id="20459">
    <literal><![CDATA[
      a(x,y,L((z \ u) * a(w,v5,v5),z,z)) = a(x,y,w * (w \ (u * (z \ (v5 \ (w \ (v5 \ w)))))))
    ]]></literal>
    <justification jstring="[hyper(316,a,14064,a(flip),b,20458,a),flip(a)].">
      <j1 rule="hyper" parents="316 14064 20458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20461">
    <literal><![CDATA[
      a(x,y,L((z \ u) * a(w,v5,v5),z,z)) = a(x,y,u * (z \ (v5 \ (w \ (v5 \ w)))))
    ]]></literal>
    <justification jstring="[para(10(a,1),20459(a,2,3))].">
      <j1 rule="para" parents="10 20459"/>
    </justification>
  </clause>

  <clause id="20462">
    <literal><![CDATA[
      a(x,y,L((z \ u) * a(w,v5,v5),z,z)) = a(x,y,u * (z * a(w,v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(316,a,19409,a(flip),b,20461,a),flip(a)].">
      <j1 rule="hyper" parents="316 19409 20461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20487">
    <literal><![CDATA[
      L(a(x,y,z * a(u,w,v5)) \ 1,z,a(u,w,v5)) = a(x,y,z \ a(u,w,v5)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,19837,a(flip),b,19898,a),flip(a)].">
      <j1 rule="hyper" parents="63 19837 19898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20488">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ (((x \ ((x * y) * z)) / z) \ a(x,y,z)),u,w) = (y \ 1) * (z \ ((x \ ((x * y) * z)) * L((x \ ((x * y) * z)) \ z,u,w)))
    ]]></literal>
    <justification jstring="[para(5189(a,1),18195(a,2,2))].">
      <j1 rule="para" parents="5189 18195"/>
    </justification>
  </clause>

  <clause id="20489">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ (((x \ ((x * y) * z)) / z) \ a(x,y,z)),u,w) = (y \ 1) * (z \ (x \ (((x * y) * L((x * y) \ x,u,w)) * z)))
    ]]></literal>
    <justification jstring="[para(1540(a,1),20488(a,2,2,2))].">
      <j1 rule="para" parents="1540 20488"/>
    </justification>
  </clause>

  <clause id="20490">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ (((x \ ((x * y) * z)) / z) \ a(x,y,z)),u,w) = (y \ 1) * (z \ (x \ ((x * (y * L(y \ 1,u,w))) * z)))
    ]]></literal>
    <justification jstring="[para(777(a,1),20489(a,2,2,2,2,1))].">
      <j1 rule="para" parents="777 20489"/>
    </justification>
  </clause>

  <clause id="20491">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ (((x \ ((x * y) * z)) / z) \ a(x,y,z)),u,w) = (y \ 1) * (z \ (x \ ((x * (y \ L(y,u,w))) * z)))
    ]]></literal>
    <justification jstring="[para(1064(a,1),20490(a,2,2,2,2,1,2))].">
      <j1 rule="para" parents="1064 20490"/>
    </justification>
  </clause>

  <clause id="20492">
    <literal><![CDATA[
      (x \ 1) * (y \ (z \ ((z * (x \ L(x,u,w))) * y))) = a(z,x,y) * L(a(z,x,y) \ (x \ 1),u,w)
    ]]></literal>
    <justification jstring="[para(18184(a,1),20491(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="18184 20491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20493">
    <literal><![CDATA[
      (x \ 1) * (y \ (z \ ((z * (x \ L(x,u,w))) * y))) = a(z,x,y) * L(x \ (a(z,x,y) \ 1),u,w)
    ]]></literal>
    <justification jstring="[para(18021(a,1),20492(a,2,2,1))].">
      <j1 rule="para" parents="18021 20492"/>
    </justification>
  </clause>

  <clause id="20495">
    <literal><![CDATA[
      (x \ 1) * (y \ (z \ ((z * (x \ L(x,u,w))) * y))) = a(z,x,y) \ L(x \ a(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,14749,a(flip),b,20493,a),flip(a)].">
      <j1 rule="hyper" parents="316 14749 20493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20496">
    <literal><![CDATA[
      (x \ 1) * L(L(x \ L(x,y,z),u,w),w,u) = a(w,x,u) \ L(x \ a(w,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(13527(a,1),20495(a,1,2))].">
      <j1 rule="para" parents="13527 20495"/>
    </justification>
  </clause>

  <clause id="20497">
    <literal><![CDATA[
      a(x,y,z) \ L(y \ a(x,y,z),u,w) = y \ L(L(y \ L(y,u,w),z,x),x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5171,a(flip),b,20496,a),flip(a)].">
      <j1 rule="hyper" parents="63 5171 20496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20498">
    <literal><![CDATA[
      L(a(x,y,((z * a(u,z,w)) \ y) * y) \ 1,z,a(u,z,w)) = (z \ 1) \ (z \ L(L(z \ L(z,y,x),w,u),u,w))
    ]]></literal>
    <justification jstring="[para(20497(a,1),20406(a,2,2))].">
      <j1 rule="para" parents="20497 20406"/>
    </justification>
  </clause>

  <clause id="20499">
    <literal><![CDATA[
      L(a(x,y,((z * a(u,z,w)) \ y) * y) \ 1,z,a(u,z,w)) = L((z \ 1) \ (z \ L(z \ L(z,y,x),w,u)),u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,1000,a,b,20498,a),flip(a)].">
      <j1 rule="hyper" parents="316 1000 20498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20500">
    <literal><![CDATA[
      L(a(x,y,((z * a(u,z,w)) \ y) * y) \ 1,z,a(u,z,w)) = L(L(z \ L(z,y,x),w,u),u,w)
    ]]></literal>
    <justification jstring="[para(1740(a,1),20499(a,2,1))].">
      <j1 rule="para" parents="1740 20499"/>
    </justification>
  </clause>

  <clause id="20501">
    <literal><![CDATA[
      L(a(x,y,z * a(u,z,w)) \ 1,z,a(u,z,w)) = L(L(z \ L(z,y,x),w,u),u,w)
    ]]></literal>
    <justification jstring="[para(18629(a,1),20500(a,1,1,1))].">
      <j1 rule="para" parents="18629 20500"/>
    </justification>
  </clause>

  <clause id="20502">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),w,u) = a(z,y,x \ a(w,x,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,20487,a(flip),b,20501,a),flip(a)].">
      <j1 rule="hyper" parents="63 20487 20501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20503">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),w,u) = a(z,y,x * a(w,x,u)) \ 1
    ]]></literal>
    <justification jstring="[para(18019(a,1),20502(a,2,1))].">
      <j1 rule="para" parents="18019 20502"/>
    </justification>
  </clause>

  <clause id="20504">
    <literal><![CDATA[
      a(x,y,y * (z \ y)) \ a(u,z \ L(z,y,x),w) = a(x,y,z * a(u,z,w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,19684,a(flip),b,20503,a)].">
      <j1 rule="hyper" parents="63 19684 20503"/>
    </justification>
  </clause>

  <clause id="20505">
    <literal><![CDATA[
      a(x,y,z) \ a(u,z \ L(z,y,x),w) = a(x,y,z * a(u,z,w)) \ 1
    ]]></literal>
    <justification jstring="[para(18628(a,1),20504(a,1,1))].">
      <j1 rule="para" parents="18628 20504"/>
    </justification>
  </clause>

  <clause id="20506">
    <literal><![CDATA[
      a(x,y,z) \ a(u,a(x,y,z),w) = a(x,y,z * a(u,z,w)) \ 1
    ]]></literal>
    <justification jstring="[para(18695(a,1),20505(a,1,2))].">
      <j1 rule="para" parents="18695 20505"/>
    </justification>
  </clause>

  <clause id="20507">
    <literal><![CDATA[
      a(x,y,z) * (u * a(w,a(x,y,z),v5)) = (a(x,y,z * a(v5,z,w)) \ 1) \ u
    ]]></literal>
    <justification jstring="[para(20506(a,1),17874(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20506 17874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20508">
    <literal><![CDATA[
      a(x,y,z) * a(u,a(x,y,z),w) = a(x,y,z * a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(34,a,14394,a(flip),b,20507,a),flip(a)].">
      <j1 rule="hyper" parents="34 14394 20507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20509">
    <literal><![CDATA[
      a(x,y,L(L(z,u,a(u,w,v5)),a(u,u,v5),w)) = a(x,y,z * a(a(u,u,w),z,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19662,a,b,20508,a)].">
      <j1 rule="hyper" parents="63 19662 20508"/>
    </justification>
  </clause>

  <clause id="20510">
    <literal><![CDATA[
      a(x,y,L(L(z,u,a(u,w,v5)),a(u,u,v5),w)) = a(x,y,z * a(u,u,a(v5,z,w)))
    ]]></literal>
    <justification jstring="[para(19132(a,1),20509(a,2,3,2))].">
      <j1 rule="para" parents="19132 20509"/>
    </justification>
  </clause>

  <clause id="20511">
    <literal><![CDATA[
      a(x,y,z * a(u,u,a(w,z,v5))) = a(x,y,L(z,a(u,u,w),v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,20014,a(flip),b,20510,a),flip(a)].">
      <j1 rule="hyper" parents="63 20014 20510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20513">
    <literal><![CDATA[
      a(x,y,L(z,a(u,u,w),v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,20010,a(flip),b,20511,a),flip(a)].">
      <j1 rule="hyper" parents="63 20010 20511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20515">
    <literal><![CDATA[
      a(x,y,L(z,a(u,w,w),v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(16124(a,1),20513(a,1,3))].">
      <j1 rule="para" parents="16124 20513"/>
    </justification>
  </clause>

  <clause id="20517">
    <literal><![CDATA[
      a(x,y,((z * (u / (z * u))) * w) \ v5) = a(x,y,a(u,z,z) * (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,18001,a(flip),b,20515,a),flip(a)].">
      <j1 rule="hyper" parents="63 18001 20515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20519">
    <literal><![CDATA[
      a(x,y,((z * ((z * u) \ u)) * w) \ v5) = a(x,y,a(u,z,z) * (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,10666,a(flip),b,20517,a)].">
      <j1 rule="hyper" parents="63 10666 20517"/>
    </justification>
  </clause>

  <clause id="20520">
    <literal><![CDATA[
      a(x,y,z \ (u * a(w,v5,v5))) = a(x,y,a(w,v5,v5) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20114,a(flip),b,20519,a)].">
      <j1 rule="hyper" parents="63 20114 20519"/>
    </justification>
  </clause>

  <clause id="20521">
    <literal><![CDATA[
      a(x,y,z \ (a(u,u,w) * v5)) = a(x,y,a(w,u,u) * (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,12450,a,b,20520,a)].">
      <j1 rule="hyper" parents="63 12450 20520"/>
    </justification>
  </clause>

  <clause id="20522">
    <literal><![CDATA[
      a(x,y,z \ (((u \ w) \ v5) * (w * u))) = a(x,y,a(w,u,u) * (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,19706,a,b,20521,a)].">
      <j1 rule="hyper" parents="63 19706 20521"/>
    </justification>
  </clause>

  <clause id="20523">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * (w \ (v5 \ (u \ z)))) = a(x,y,w \ (v5 \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19895,a(flip),b,20522,a),flip(a)].">
      <j1 rule="hyper" parents="63 19895 20522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20529">
    <literal><![CDATA[
      (L(x,y,z) \ (u * L(u \ L(x,y,z),w,v5))) * (R(v6,v7,v8) * L(R(x,y,z) \ u,a(v5,w,R(x,y,z) \ u),R(v6,v7,v8))) = L(R(x,y,z) \ u,w,v5) * R(T(v6,x \ u),v7,v8)
    ]]></literal>
    <justification jstring="[para(12654(a,1),18434(a,1,1))].">
      <j1 rule="para" parents="12654 18434"/>
    </justification>
  </clause>

  <clause id="20530">
    <literal><![CDATA[
      (L(x,y,z) \ (u * L(u \ L(x,y,z),w,v5))) * (R(v6,v7,v8) * L(R(x,y,z) \ u,a(v5,w,L(x,y,z) \ u),R(v6,v7,v8))) = L(R(x,y,z) \ u,w,v5) * R(T(v6,x \ u),v7,v8)
    ]]></literal>
    <justification jstring="[para(9541(a,1),20529(a,1,2,2,2))].">
      <j1 rule="para" parents="9541 20529"/>
    </justification>
  </clause>

  <clause id="20531">
    <literal><![CDATA[
      (L(x,y,z) \ (u * L(u \ L(x,y,z),w,v5))) * (R(v6,v7,v8) * L(R(x,y,z) \ u,a(v5,w,L(x,y,z) \ u),L(v6,v7,v8))) = L(R(x,y,z) \ u,w,v5) * R(T(v6,x \ u),v7,v8)
    ]]></literal>
    <justification jstring="[para(4628(a,1),20530(a,1,2,2))].">
      <j1 rule="para" parents="4628 20530"/>
    </justification>
  </clause>

  <clause id="20532">
    <literal><![CDATA[
      (L(x,y,z) \ (u * L(u \ L(x,y,z),w,v5))) * (L(x,y,z) * L(L(x,y,z) \ u,a(v5,w,L(x,y,z) \ u),L(x,y,z))) = L(R(x,y,z) \ u,w,v5) * R(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(16434(a,1),20531(a,1,2))].">
      <j1 rule="para" parents="16434 20531"/>
    </justification>
  </clause>

  <clause id="20533">
    <literal><![CDATA[
      L(R(x,y,z) \ u,w,v5) * R(T(x,x \ u),y,z) = L(x,y,z) * L(L(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,18436,a(flip),b,20532,a),flip(a)].">
      <j1 rule="hyper" parents="63 18436 20532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20534">
    <literal><![CDATA[
      R(x,y,z) * L(R(x,y,z) \ u,w,v5) = L(x,y,z) * L(L(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,4576,a(flip),b,20533,a)].">
      <j1 rule="hyper" parents="63 4576 20533"/>
    </justification>
  </clause>

  <clause id="20535">
    <literal><![CDATA[
      L(x / T(y,z),y,y) * L(L(x / T(y,z),y,y) \ u,w,v5) = (x * (T(y,z) \ 1)) * L(R(x / T(y,z),y,y) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(5209(a,1),20534(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5209 20534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20536">
    <literal><![CDATA[
      L(x / T(y,z),y,y) * L(L(x / T(y,z),y,y) \ u,w,v5) = (x * (T(y,z) \ 1)) * L((x * (T(y,z) \ 1)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(5209(a,1),20535(a,2,2,1,1))].">
      <j1 rule="para" parents="5209 20535"/>
    </justification>
  </clause>

  <clause id="20537">
    <literal><![CDATA[
      L(x / T(y,z),y,y) * L(L(x / T(y,z),y,y) \ u,w,v5) = x * ((T(y,z) \ 1) * L((T(y,z) \ 1) \ (x \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,879,a(flip),b,20536,a),flip(a)].">
      <j1 rule="hyper" parents="316 879 20536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20538">
    <literal><![CDATA[
      L(x / T(y,z),y,y) * L(L(x / T(y,z),y,y) \ u,w,v5) = x * (T(y,z) * L(T(y,z) \ (x \ u),w,v5))
    ]]></literal>
    <justification jstring="[para(1350(a,1),20537(a,2,2))].">
      <j1 rule="para" parents="1350 20537"/>
    </justification>
  </clause>

  <clause id="20539">
    <literal><![CDATA[
      L(x / T(y,z),y,y) * L(L(x / T(y,z),y,y) \ u,w,v5) = x * (y * L(y \ (x \ u),w,v5))
    ]]></literal>
    <justification jstring="[para(4868(a,1),20538(a,2,2))].">
      <j1 rule="para" parents="4868 20538"/>
    </justification>
  </clause>

  <clause id="20541">
    <literal><![CDATA[
      T(a(x,a(y,L(z,u,w),a(v5,v6,v7)),a(v5,v7,a(z,v6,L(y,u,w)))) * a(y,L(z,u,w),a(v5,v6,v7)),a(v5,v7,a(z,v6,L(y,u,w)))) = a(v5,v7,a(z,v6,L(L(y,u,w),a(y,L(z,u,w),a(v5,v6,v7)),x))) \ a(v7,a(y,v6,v5),L(z,u,w))
    ]]></literal>
    <justification jstring="[para(19079(a,2),19664(a,2,1))].">
      <j1 rule="para" parents="19079 19664"/>
    </justification>
  </clause>

  <clause id="20542">
    <literal><![CDATA[
      T(a(x,a(y,L(z,u,w),a(v5,v6,v7)),a(v5,v7,a(z,v6,L(y,u,w)))) * a(y,L(z,u,w),a(v5,v6,v7)),a(v5,v7,a(z,v6,L(y,u,w)))) = a(v5,v7,a(z,v6,L(L(y,u,w),L(z,u,w),a(x,y,a(v5,v6,v7))))) \ a(v7,a(y,v6,v5),L(z,u,w))
    ]]></literal>
    <justification jstring="[para(19454(a,1),20541(a,2,1,3,3))].">
      <j1 rule="para" parents="19454 20541"/>
    </justification>
  </clause>

  <clause id="20543">
    <literal><![CDATA[
      T(a(x,a(y,L(z,u,w),a(v5,v6,v7)),a(v5,v7,a(z,v6,L(y,u,w)))) * a(y,L(z,u,w),a(v5,v6,v7)),a(v5,v7,a(z,v6,L(y,u,w)))) = a(z,v6,a(L(y,u,w),v7,v5)) \ a(v7,a(y,v6,v5),L(z,u,w))
    ]]></literal>
    <justification jstring="[para(19384(a,1),20542(a,2,1))].">
      <j1 rule="para" parents="19384 20542"/>
    </justification>
  </clause>

  <clause id="20544">
    <literal><![CDATA[
      T(a(x,a(y,L(z,u,w),a(v5,v6,v7)),a(v5,v7,a(z,v6,L(y,u,w)))) * a(y,L(z,u,w),a(v5,v6,v7)),a(v5,v7,a(z,v6,L(y,u,w)))) = a(z,v6,a(y,v7,L(v5,u,w))) \ a(v7,a(y,v6,v5),L(z,u,w))
    ]]></literal>
    <justification jstring="[para(19305(a,1),20543(a,2,1,3))].">
      <j1 rule="para" parents="19305 20543"/>
    </justification>
  </clause>

  <clause id="20546">
    <literal><![CDATA[
      T(a(x,a(y,L(z,u,w),a(v5,v6,v7)),a(v5,v7,a(z,v6,L(y,u,w)))) * a(y,L(z,u,w),a(v5,v6,v7)),a(v5,v7,a(z,v6,L(y,u,w)))) = a(v7,a(y,v6,v5),L(z,u,w)) * a(z,v6,a(y,v7,L(v5,u,w)))
    ]]></literal>
    <justification jstring="[hyper(316,a,14470,a(flip),b,20544,a),flip(a)].">
      <j1 rule="hyper" parents="316 14470 20544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20547">
    <literal><![CDATA[
      T(a(x,L(y,z,u),a(w,v5,v6)) * a(L(x,z,u),v5,a(y,v6,a(v7,a(x,L(y,z,u),a(w,v5,v6)),w))),a(w,v6,a(y,v5,L(x,z,u)))) = a(v6,a(x,v5,w),L(y,z,u)) * a(y,v5,a(x,v6,L(w,z,u)))
    ]]></literal>
    <justification jstring="[para(19278(a,1),20546(a,1,1))].">
      <j1 rule="para" parents="19278 20546"/>
    </justification>
  </clause>

  <clause id="20548">
    <literal><![CDATA[
      T(a(x,L(y,z,u),a(w,v5,v6)) * 1,a(w,v6,a(y,v5,L(x,z,u)))) = a(v6,a(x,v5,w),L(y,z,u)) * a(y,v5,a(x,v6,L(w,z,u)))
    ]]></literal>
    <justification jstring="[para(15239(a,1),20547(a,1,1,2))].">
      <j1 rule="para" parents="15239 20547"/>
    </justification>
  </clause>

  <clause id="20549">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,v6)) * a(w,z,a(y,x,L(u,v5,v6))) = a(y,L(w,v5,v6),a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(135,a,2273,a(flip),b,20548,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="135 2273 20548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20551">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) * K(a(y,u,a(x,L(z,v5,v6),w)) \ 1,a(y,u,a(x,L(z,v5,v6),w)) * a(x,y,a(z,u,L(w,v5,v6)))) = (a(x,y,a(z,u,L(w,v5,v6))) * a(L(z,v5,v6),a(x,u,w),y)) * (a(y,u,a(x,L(z,v5,v6),w)) * a(x,y,a(z,u,L(w,v5,v6))))
    ]]></literal>
    <justification jstring="[para(14414(a,1),19650(a,2,1))].">
      <j1 rule="para" parents="14414 19650"/>
    </justification>
  </clause>

  <clause id="20552">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) * K(a(y,u,a(x,L(z,v5,v6),w)) \ 1,a(y,u,a(x,L(z,v5,v6),w)) * a(x,y,a(z,u,L(w,v5,v6)))) = (a(x,y,a(z,u,L(w,v5,v6))) * a(z,a(x,u,w),L(y,v5,v6))) * (a(y,u,a(x,L(z,v5,v6),w)) * a(x,y,a(z,u,L(w,v5,v6))))
    ]]></literal>
    <justification jstring="[para(16248(a,1),20551(a,2,1,2))].">
      <j1 rule="para" parents="16248 20551"/>
    </justification>
  </clause>

  <clause id="20553">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) * K(a(y,u,a(x,L(z,v5,v6),w)) \ 1,a(y,u,a(x,L(z,v5,v6),w)) * a(x,y,a(z,u,L(w,v5,v6)))) = (a(x,y,a(z,u,L(w,v5,v6))) * a(z,a(x,u,w),L(y,v5,v6))) * a(y,a(w,u,x),L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(19431(a,1),20552(a,2,2))].">
      <j1 rule="para" parents="19431 20552"/>
    </justification>
  </clause>

  <clause id="20554">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) * K(a(y,u,a(x,L(z,v5,v6),w)) \ 1,a(y,u,a(x,L(z,v5,v6),w)) * a(x,y,a(z,u,L(w,v5,v6)))) = a(z,a(x,u,w),L(y,v5,v6)) * (a(x,y,a(z,u,L(w,v5,v6))) * a(y,a(w,u,x),L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(316,a,19607,a(flip),b,20553,a),flip(a)].">
      <j1 rule="hyper" parents="316 19607 20553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20555">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) * K(a(y,u,a(x,L(z,v5,v6),w)) \ 1,a(y,u,a(x,L(z,v5,v6),w)) * a(x,y,a(z,u,L(w,v5,v6)))) = a(z,a(x,u,w),L(y,v5,v6)) * a(y,u,a(x,L(z,v5,v6),w))
    ]]></literal>
    <justification jstring="[para(19649(a,1),20554(a,2,2))].">
      <j1 rule="para" parents="19649 20554"/>
    </justification>
  </clause>

  <clause id="20556">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,v6)) * a(w,z,a(y,L(x,v5,v6),u)) = a(y,w,a(x,z,L(u,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5032,a(flip),b,20555,a),flip(a)].">
      <j1 rule="hyper" parents="63 5032 20555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20558">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,v6)) * a(w,z,a(y,x,L(u,v5,v6))) = a(y,w,a(x,z,L(u,v5,v6)))
    ]]></literal>
    <justification jstring="[para(19524(a,1),20556(a,1,2))].">
      <j1 rule="para" parents="19524 20556"/>
    </justification>
  </clause>

  <clause id="20559">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,v6)) = a(x,y,a(v6,v5,L(w,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20549,a(flip),b,20558,a)].">
      <j1 rule="hyper" parents="63 20549 20558"/>
    </justification>
  </clause>

  <clause id="20561">
    <literal><![CDATA[
      a(x,y * (z * y),a(u,w,v5)) = a(x,z,a(v5,w,L(u,y,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15787,a,b,20559,a)].">
      <j1 rule="hyper" parents="63 15787 20559"/>
    </justification>
  </clause>

  <clause id="20563">
    <literal><![CDATA[
      a(x,((y \ 1) * z) \ u,a(w,v5,L(v6,z * y,z * y))) = a(x,u * (z * y),a(v6,v5,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17941,a(flip),b,20559,a),flip(a)].">
      <j1 rule="hyper" parents="63 17941 20559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20566">
    <literal><![CDATA[
      a(x,y * (z * y),a(u,w,v5)) = a(v5,z,a(x,w,u))
    ]]></literal>
    <justification jstring="[hyper(316,a,20028,a(flip),b,20561,a),flip(a)].">
      <j1 rule="hyper" parents="316 20028 20561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20568">
    <literal><![CDATA[
      a(x,((y \ 1) * z) \ u,a(w,v5,v6)) = a(w,u * (z * y),a(v6,v5,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,20028,a(flip),b,20563,a)].">
      <j1 rule="hyper" parents="63 20028 20563"/>
    </justification>
  </clause>

  <clause id="20570">
    <literal><![CDATA[
      a(x,y \ (z \ y),a(u,w,v5)) = a(u,y * (z * y),a(v5,w,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,15767,a(flip),b,20568,a)].">
      <j1 rule="hyper" parents="63 15767 20568"/>
    </justification>
  </clause>

  <clause id="20571">
    <literal><![CDATA[
      a(x,y \ (z \ y),a(u,w,v5)) = a(x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(316,a,20566,a(flip),b,20570,a),flip(a)].">
      <j1 rule="hyper" parents="316 20566 20570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20575">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,y,v5))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,20167,a(flip),b,20571,a)].">
      <j1 rule="hyper" parents="63 20167 20571"/>
    </justification>
  </clause>

  <clause id="20582">
    <literal><![CDATA[
      L(x,y,z) * a(u,y,a(w,v5,x)) = L(L(x,y,z),y,a(w,v5,u))
    ]]></literal>
    <justification jstring="[para(20575(a,1),19223(a,1,2))].">
      <j1 rule="para" parents="20575 19223"/>
    </justification>
  </clause>

  <clause id="20583">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(z,w,u)) = x * a(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19508,a(flip),b,20582,a),flip(a)].">
      <j1 rule="hyper" parents="63 19508 20582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20584">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(z,w,u)) = x * a(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,30,a,b,20583,a)].">
      <j1 rule="hyper" parents="63 30 20583"/>
    </justification>
  </clause>

  <clause id="20585">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),a(z,u,w) * y,a(w,z,u)) = x * a(u,a(x,a(z,u,w) * y,w),z)
    ]]></literal>
    <justification jstring="[para(17101(a,1),20584(a,1,1))].">
      <j1 rule="para" parents="17101 20584"/>
    </justification>
  </clause>

  <clause id="20586">
    <literal><![CDATA[
      x * a(y,a(x,a(z,y,u) * w,u),z) = L(x,w,a(z,y,u) * a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,20451,a(flip),b,20585,a),flip(a)].">
      <j1 rule="hyper" parents="63 20451 20585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20587">
    <literal><![CDATA[
      x * a(y,a(x,z * a(u,y,w),u),w) = L(x,z,a(w,y,u) * a(u,w,y))
    ]]></literal>
    <justification jstring="[para(16575(a,1),20586(a,1,2,2))].">
      <j1 rule="para" parents="16575 20586"/>
    </justification>
  </clause>

  <clause id="20588">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w) * a(w,z,u)) = a(z,a(w,y * a(w,u,z),x),u)
    ]]></literal>
    <justification jstring="[hyper(133,a,20587,a(flip),b,14127,a)].">
      <j1 rule="hyper" parents="133 20587 14127"/>
    </justification>
  </clause>

  <clause id="20589">
    <literal><![CDATA[
      a(x,a(y,z * a(y,u,x),w),u) = a(w,z,a(x,u,y) * a(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20129,a(flip),b,20588,a),flip(a)].">
      <j1 rule="hyper" parents="63 20129 20588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20590">
    <literal><![CDATA[
      a(x,a(y,z * a(u,w,x),u),w) = a(y,z,a(x,w,u) * a(u,x,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,13658,a,b,20589,a)].">
      <j1 rule="hyper" parents="63 13658 20589"/>
    </justification>
  </clause>

  <clause id="20591">
    <literal><![CDATA[
      a(x,a(y,z * a(u,w,x),u),w) = a(y,z,a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,20267,a(flip),b,20590,a),flip(a)].">
      <j1 rule="hyper" parents="316 20267 20590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20592">
    <literal><![CDATA[
      a(x,y,a(z,x,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,5418,a(flip),b,20591,a),flip(a)].">
      <j1 rule="hyper" parents="63 5418 20591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20596">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,20592,a,b,19191,a),flip(a)].">
      <j1 rule="hyper" parents="134 20592 19191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20597">
    <literal><![CDATA[
      a(a(x,y,z),u,y) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,20592,a,b,13738,a),flip(a)].">
      <j1 rule="hyper" parents="134 20592 13738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20600">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,19188,a,b,20592,a)].">
      <j1 rule="hyper" parents="63 19188 20592"/>
    </justification>
  </clause>

  <clause id="20601">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,19154,a,b,20592,a)].">
      <j1 rule="hyper" parents="63 19154 20592"/>
    </justification>
  </clause>

  <clause id="20602">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,19142,a,b,20592,a)].">
      <j1 rule="hyper" parents="63 19142 20592"/>
    </justification>
  </clause>

  <clause id="20603">
    <literal><![CDATA[
      a(a(x,y,z),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,19137,a,b,20592,a)].">
      <j1 rule="hyper" parents="63 19137 20592"/>
    </justification>
  </clause>

  <clause id="20615">
    <literal><![CDATA[
      a(a(x,y,y),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,14012,a,b,20596,a)].">
      <j1 rule="hyper" parents="63 14012 20596"/>
    </justification>
  </clause>

  <clause id="20627">
    <literal><![CDATA[
      L(x,y,a(z,x,u)) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,20597,a)].">
      <j1 rule="hyper" parents="52 20597"/>
    </justification>
  </clause>

  <clause id="20634">
    <literal><![CDATA[
      x \ a(y,y,a(z,u,w)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,20600,a,b,10,a)].">
      <j1 rule="hyper" parents="133 20600 10"/>
    </justification>
  </clause>

  <clause id="20653">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) = w \ w
    ]]></literal>
    <justification jstring="[hyper(316,a,67,a,b,20601,a),flip(a)].">
      <j1 rule="hyper" parents="316 67 20601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20654">
    <literal><![CDATA[
      L(a(x,y,z),z,u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(52,a,20601,a)].">
      <j1 rule="hyper" parents="52 20601"/>
    </justification>
  </clause>

  <clause id="20666">
    <literal><![CDATA[
      L(a(x,y,z),x,u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(52,a,20602,a)].">
      <j1 rule="hyper" parents="52 20602"/>
    </justification>
  </clause>

  <clause id="20670">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,20603,a)].">
      <j1 rule="hyper" parents="52 20603"/>
    </justification>
  </clause>

  <clause id="20676">
    <literal><![CDATA[
      L(x,y,a(z,u,u)) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,20615,a)].">
      <j1 rule="hyper" parents="52 20615"/>
    </justification>
  </clause>

  <clause id="20680">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,19254,a,b,20627,a)].">
      <j1 rule="hyper" parents="63 19254 20627"/>
    </justification>
  </clause>

  <clause id="20697">
    <literal><![CDATA[
      (a(x,y,z) * L(z,u,w)) \ v5 = a(x,y,z) \ (L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,20397,a(flip),b,20670,a)].">
      <j1 rule="hyper" parents="63 20397 20670"/>
    </justification>
  </clause>

  <clause id="20698">
    <literal><![CDATA[
      (x / y) * L(y,z,u) = a(u,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,19683,a(flip),b,20670,a)].">
      <j1 rule="hyper" parents="63 19683 20670"/>
    </justification>
  </clause>

  <clause id="20699">
    <literal><![CDATA[
      L(x,y,L(z,u,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,19467,a(flip),b,20670,a)].">
      <j1 rule="hyper" parents="63 19467 20670"/>
    </justification>
  </clause>

  <clause id="20700">
    <literal><![CDATA[
      (x * L(y,z,u)) * a(u,z,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(63,a,18719,a(flip),b,20670,a)].">
      <j1 rule="hyper" parents="63 18719 20670"/>
    </justification>
  </clause>

  <clause id="20710">
    <literal><![CDATA[
      a(x,x,y) * (z * u) = z * (a(x,x,y) * u)
    ]]></literal>
    <justification jstring="[para(20670(a,1),19263(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20670 19263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20722">
    <literal><![CDATA[
      R(x,y,a(z,u,u)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,5371,a,b,20676,a)].">
      <j1 rule="hyper" parents="63 5371 20676"/>
    </justification>
  </clause>

  <clause id="20733">
    <literal><![CDATA[
      (a(x,x,y) * z) * u = a(x,x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(20676(a,1),17009(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="20676 17009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20735">
    <literal><![CDATA[
      (a(x,x,y) * z) / u = a(x,x,y) * (z / u)
    ]]></literal>
    <justification jstring="[para(20676(a,1),17002(a,1,2))].">
      <j1 rule="para" parents="20676 17002"/>
    </justification>
  </clause>

  <clause id="20737">
    <literal><![CDATA[
      (x \ (y * z)) * a(u,w,L(w,y * z,x)) = x \ (y * (z * a(u,w,w)))
    ]]></literal>
    <justification jstring="[para(20676(a,1),20441(a,1,1,2,1))].">
      <j1 rule="para" parents="20676 20441"/>
    </justification>
  </clause>

  <clause id="20770">
    <literal><![CDATA[
      (a(x,y,z) \ u) * z = u * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(20680(a,1),19412(a,1,2))].">
      <j1 rule="para" parents="20680 19412"/>
    </justification>
  </clause>

  <clause id="20773">
    <literal><![CDATA[
      x \ (y * a(z,u,u)) = (x \ y) * a(z,u,u)
    ]]></literal>
    <justification jstring="[para(20722(a,1),492(a,1,1))].">
      <j1 rule="para" parents="20722 492"/>
    </justification>
  </clause>

  <clause id="20776">
    <literal><![CDATA[
      a(x,y,L(y,z * u,w)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,20052,a,b,20653,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 20052 20653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20789">
    <literal><![CDATA[
      x * (L(x,y,z) \ u) = a(z,y,x) * u
    ]]></literal>
    <justification jstring="[para(20654(a,1),20329(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20654 20329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20796">
    <literal><![CDATA[
      a(x,y,L(z,x,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,19034,a,b,20666,a)].">
      <j1 rule="hyper" parents="63 19034 20666"/>
    </justification>
  </clause>

  <clause id="20818">
    <literal><![CDATA[
      L(x,y,(z \ 1) * u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17031,a(flip),b,20699,a),flip(a)].">
      <j1 rule="hyper" parents="63 17031 20699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20832">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,L(z,x,u)) = a(z,y,a(w,u * x,x))
    ]]></literal>
    <justification jstring="[para(20796(a,1),19825(a,1,1))].">
      <j1 rule="para" parents="20796 19825"/>
    </justification>
  </clause>

  <clause id="20835">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,19110,a,b,20634,a),flip(a)].">
      <j1 rule="hyper" parents="39 19110 20634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20844">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * (w * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5825,a,b,20835,a)].">
      <j1 rule="hyper" parents="63 5825 20835"/>
    </justification>
  </clause>

  <clause id="20847">
    <literal><![CDATA[
      a(x,y,L(z,u * w,w * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5557,a,b,20835,a)].">
      <j1 rule="hyper" parents="63 5557 20835"/>
    </justification>
  </clause>

  <clause id="20848">
    <literal><![CDATA[
      a(x,y,(z \ u) * a(w,v5,v5)) = a(x,y,u * (z * a(w,v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20462,a(flip),b,20835,a),flip(a)].">
      <j1 rule="hyper" parents="63 20462 20835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20851">
    <literal><![CDATA[
      a(x,y,z \ u) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8606,a(flip),b,20835,a)].">
      <j1 rule="hyper" parents="63 8606 20835"/>
    </justification>
  </clause>

  <clause id="20852">
    <literal><![CDATA[
      a(x,y,z \ u) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8605,a(flip),b,20835,a)].">
      <j1 rule="hyper" parents="63 8605 20835"/>
    </justification>
  </clause>

  <clause id="20855">
    <literal><![CDATA[
      R(x,y,L(z,u,u)) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(138,a,20835,a(flip),b,18821,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="138 20835 18821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20883">
    <literal><![CDATA[
      a(x,y \ z,z * y) \ x = (x / (z \ y)) / (1 / (z \ y))
    ]]></literal>
    <justification jstring="[para(20851(a,1),13871(a,1,1))].">
      <j1 rule="para" parents="20851 13871"/>
    </justification>
  </clause>

  <clause id="20901">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * (w \ (v5 \ (u \ z)))) = a(x,y,w * (v5 \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20523,a,b,20852,a)].">
      <j1 rule="hyper" parents="63 20523 20852"/>
    </justification>
  </clause>

  <clause id="20902">
    <literal><![CDATA[
      (x \ (y * L(y \ (z * x),u,w))) \ T(z,x) = a(w,u,z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,19018,a,b,20852,a)].">
      <j1 rule="hyper" parents="63 19018 20852"/>
    </justification>
  </clause>

  <clause id="20903">
    <literal><![CDATA[
      T(x * (y * L(y \ (x \ z),u,w)),v5) \ T(z,v5) = a(w,u,z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,19017,a,b,20852,a)].">
      <j1 rule="hyper" parents="63 19017 20852"/>
    </justification>
  </clause>

  <clause id="20905">
    <literal><![CDATA[
      a(x,y,z \ (u * L(w \ v5,v5,v5))) = a(x,y,z * (u * (L(w,v5,v5) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12544,a,b,20852,a)].">
      <j1 rule="hyper" parents="63 12544 20852"/>
    </justification>
  </clause>

  <clause id="20908">
    <literal><![CDATA[
      a(x,y,((z \ u) \ (u * w)) * (L(z,z,u) \ w)) = a(x,y,a(u,z,w * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,20362,a(flip),b,20852,a),flip(a)].">
      <j1 rule="hyper" parents="63 20362 20852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20909">
    <literal><![CDATA[
      a(x,y,(z * u) * ((L(u,w,w) \ w) \ (z * L(w,w,u)))) = a(x,y,a(w * u,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19699,a(flip),b,20852,a),flip(a)].">
      <j1 rule="hyper" parents="63 19699 20852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20910">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) * (z \ (u \ w))) = a(x,y,a(u,z,w * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19643,a(flip),b,20852,a),flip(a)].">
      <j1 rule="hyper" parents="63 19643 20852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20911">
    <literal><![CDATA[
      a(x,y,(z * u) * ((z \ (u \ w)) \ w)) = a(x,y,a(u,z,w * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19642,a(flip),b,20852,a),flip(a)].">
      <j1 rule="hyper" parents="63 19642 20852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20913">
    <literal><![CDATA[
      a(x,y,z * (u \ (((u \ a(w,v5,w)) * v6) * z))) = a(x,y,L(L(v6,u,z),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12467,a(flip),b,20852,a),flip(a)].">
      <j1 rule="hyper" parents="63 12467 20852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20914">
    <literal><![CDATA[
      a(x,y,((z * u) * w) * ((w * u) * z)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6132,a(flip),b,20852,a),flip(a)].">
      <j1 rule="hyper" parents="63 6132 20852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20932">
    <literal><![CDATA[
      a(x,y,z * (u * ((w * u) \ z))) \ z = (L(w,y,x) * u) * ((w * u) \ z)
    ]]></literal>
    <justification jstring="[para(20852(a,1),20241(a,1,1))].">
      <j1 rule="para" parents="20852 20241"/>
    </justification>
  </clause>

  <clause id="20935">
    <literal><![CDATA[
      R(x,y,L(z,u,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(316,a,18731,a,b,20855,a),flip(a)].">
      <j1 rule="hyper" parents="316 18731 20855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20940">
    <literal><![CDATA[
      R(x,y \ z,y \ z) = R(x,y \ z,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,20276,a(flip),b,20935,a),flip(a)].">
      <j1 rule="hyper" parents="63 20276 20935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20966">
    <literal><![CDATA[
      (a(x,y,z) \ u) / z = a(x,y,z) \ (u / z)
    ]]></literal>
    <justification jstring="[hyper(136,a,20698,a(flip),b,20770,a)].">
      <j1 rule="hyper" parents="136 20698 20770"/>
    </justification>
  </clause>

  <clause id="20967">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,y,x) \ u) = z \ u
    ]]></literal>
    <justification jstring="[hyper(35,a,4409,a(flip),b,20770,a),flip(a)].">
      <j1 rule="hyper" parents="35 4409 20770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20974">
    <literal><![CDATA[
      (a(x,y,z) * ((u / (w * z)) * (w * L(z,y,x)))) \ u = a(z,y,a(w * (z \ u),w * z,x))
    ]]></literal>
    <justification jstring="[para(20770(a,1),20316(a,1,1,2,2))].">
      <j1 rule="para" parents="20770 20316"/>
    </justification>
  </clause>

  <clause id="20986">
    <literal><![CDATA[
      a(x,y,z) * ((L(1 / z,u,w) \ 1) \ v5) = (a(w,u,z) * L(z,y,x)) \ v5
    ]]></literal>
    <justification jstring="[hyper(63,a,20400,a(flip),b,20789,a),flip(a)].">
      <j1 rule="hyper" parents="63 20400 20789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21002">
    <literal><![CDATA[
      a(x,y,z \ L(u,w,v5 \ v6)) = a(x,y,z \ L(u,w,v6 * v5))
    ]]></literal>
    <justification jstring="[para(20818(a,1),10682(a,1,3,2))].">
      <j1 rule="para" parents="20818 10682"/>
    </justification>
  </clause>

  <clause id="21016">
    <literal><![CDATA[
      (a(x,x,y) * z) * u = z * (a(x,x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(316,a,20710,a(flip),b,20733,a),flip(a)].">
      <j1 rule="hyper" parents="316 20710 20733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21017">
    <literal><![CDATA[
      T(x * a(y,y,z),u) * w = a(y,y,z) * (T(x,u) * w)
    ]]></literal>
    <justification jstring="[para(5332(a,2),20733(a,1,1))].">
      <j1 rule="para" parents="5332 20733"/>
    </justification>
  </clause>

  <clause id="21018">
    <literal><![CDATA[
      (x * (a(y,y,z) * u)) / w = a(y,y,z) * ((x * u) / w)
    ]]></literal>
    <justification jstring="[para(20710(a,1),20735(a,1,1))].">
      <j1 rule="para" parents="20710 20735"/>
    </justification>
  </clause>

  <clause id="21023">
    <literal><![CDATA[
      R(x,(y \ z) \ 1,y \ z) = R(x,z \ y,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,19734,a,b,20940,a)].">
      <j1 rule="hyper" parents="63 19734 20940"/>
    </justification>
  </clause>

  <clause id="21024">
    <literal><![CDATA[
      (a(x,x,y) \ (1 / y)) * L(((a(x,x,y) \ 1) / y) \ z,u,w) = L(y \ 1,x,x) * L((y \ (a(x,x,y) \ 1)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(20966(a,1),6298(a,1,1))].">
      <j1 rule="para" parents="20966 6298"/>
    </justification>
  </clause>

  <clause id="21026">
    <literal><![CDATA[
      L(x,a(y,y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,10626,a,b,21016,a(flip))].">
      <j1 rule="hyper" parents="35 10626 21016"/>
    </justification>
  </clause>

  <clause id="21040">
    <literal><![CDATA[
      (x * (T(y * a(z,z,u),x) * w)) / T(y * x,w) = L(a(z,z,u) * w,y,x)
    ]]></literal>
    <justification jstring="[para(21026(a,1),20251(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21026 20251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21042">
    <literal><![CDATA[
      a(x,y,z \ (((u * (1 / (w / v5))) * (v5 \ w)) * v6)) = a(x,y,z \ (R(u,w \ v5,v5 * w) * v6))
    ]]></literal>
    <justification jstring="[para(21023(a,1),10758(a,2,3,2,1))].">
      <j1 rule="para" parents="21023 10758"/>
    </justification>
  </clause>

  <clause id="21043">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w / (v5 \ v6)) / (1 / (v5 \ v6))))) = a(x,y,z \ (u \ (w * a(w,v6 \ v5,v5 * v6))))
    ]]></literal>
    <justification jstring="[para(20883(a,1),14405(a,1,3,2,2))].">
      <j1 rule="para" parents="20883 14405"/>
    </justification>
  </clause>

  <clause id="21044">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w / (v5 \ v6)) / (1 / (v5 \ v6))))) = a(x,y,z \ (u * (a(w,v6 \ v5,v5 * v6) * w)))
    ]]></literal>
    <justification jstring="[para(20883(a,1),14411(a,1,3,2,2))].">
      <j1 rule="para" parents="20883 14411"/>
    </justification>
  </clause>

  <clause id="21045">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * ((z * w) * u)) = a(x,y,a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5542,a,b,20914,a)].">
      <j1 rule="hyper" parents="63 5542 20914"/>
    </justification>
  </clause>

  <clause id="21048">
    <literal><![CDATA[
      a(x,y,z \ L(u,w,v5 * v6)) = a(x,y,z * L(u,w,v6 \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,20852,a(flip),b,21002,a),flip(a)].">
      <j1 rule="hyper" parents="63 20852 21002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21050">
    <literal><![CDATA[
      a(x,y,z * L(u,w,v5 \ v6)) = a(x,y,z * L(u,w,v6 * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,20852,a(flip),b,21048,a),flip(a)].">
      <j1 rule="hyper" parents="63 20852 21048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21051">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * L(w,u * z,z * u)) = a(x,y,((u \ z) * w) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13199,a(flip),b,21050,a),flip(a)].">
      <j1 rule="hyper" parents="63 13199 21050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21052">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,z) = a(z,y,a(w,u * x,x))
    ]]></literal>
    <justification jstring="[para(20796(a,1),20832(a,1,2))].">
      <j1 rule="para" parents="20796 20832"/>
    </justification>
  </clause>

  <clause id="21054">
    <literal><![CDATA[
      a(x,y,a(z,u * w,w)) = a(w,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,19102,a(flip),b,21052,a),flip(a)].">
      <j1 rule="hyper" parents="63 19102 21052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21057">
    <literal><![CDATA[
      a(x,x * y,a(z,u,w)) = a(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19185,a,b,21054,a)].">
      <j1 rule="hyper" parents="63 19185 21054"/>
    </justification>
  </clause>

  <clause id="21058">
    <literal><![CDATA[
      a(x,y,a(z,u * x,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19164,a,b,21054,a)].">
      <j1 rule="hyper" parents="63 19164 21054"/>
    </justification>
  </clause>

  <clause id="21060">
    <literal><![CDATA[
      a(x,y,a(z,z * u,w)) = a(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,19141,a(flip),b,21057,a)].">
      <j1 rule="hyper" parents="63 19141 21057"/>
    </justification>
  </clause>

  <clause id="21061">
    <literal><![CDATA[
      x \ (y * (z * a(u,w,w))) = (x \ (y * z)) * a(u,w,w)
    ]]></literal>
    <justification jstring="[para(20776(a,1),20737(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20776 20737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21062">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (w * v5)) * a(v6,w,w))) = a(x,y,z \ (u \ (v5 * L(w,w,v6))))
    ]]></literal>
    <justification jstring="[para(21061(a,1),18565(a,1,3,2))].">
      <j1 rule="para" parents="21061 18565"/>
    </justification>
  </clause>

  <clause id="21064">
    <literal><![CDATA[
      a(x,y,z * (u * L(w \ v5,v5,v5))) = a(x,y,z * (u * (L(w,v5,v5) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20852,a(flip),b,20905,a)].">
      <j1 rule="hyper" parents="63 20852 20905"/>
    </justification>
  </clause>

  <clause id="21065">
    <literal><![CDATA[
      a(x,y,z) * ((L(1 / z,u,w) \ 1) \ v5) = a(w,u,z) \ (L(z,y,x) \ v5)
    ]]></literal>
    <justification jstring="[hyper(316,a,20697,a(flip),b,20986,a),flip(a)].">
      <j1 rule="hyper" parents="316 20697 20986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21067">
    <literal><![CDATA[
      (x * (a(y,y,z) * (T(u,x) * w))) / T(u * x,w) = L(a(y,y,z) * w,u,x)
    ]]></literal>
    <justification jstring="[para(21017(a,1),21040(a,1,1,2))].">
      <j1 rule="para" parents="21017 21040"/>
    </justification>
  </clause>

  <clause id="21068">
    <literal><![CDATA[
      a(x,x,y) * ((z * (T(u,z) * w)) / T(u * z,w)) = L(a(x,x,y) * w,u,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21018,a(flip),b,21067,a)].">
      <j1 rule="hyper" parents="63 21018 21067"/>
    </justification>
  </clause>

  <clause id="21069">
    <literal><![CDATA[
      L(a(x,x,y) * z,u,w) = a(x,x,y) * L(z,u,w)
    ]]></literal>
    <justification jstring="[para(4364(a,2),21068(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4364 21068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21071">
    <literal><![CDATA[
      a(x,y,L(a(z,z,u) * w,v5,v6)) = a(x,y,a(u,z,z) * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(21069(a,2),8680(a,2,3)),flip(a)].">
      <j1 rule="para" parents="21069 8680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21073">
    <literal><![CDATA[
      a(x,y,L(a(z,z,u) * w,z * u,u * z)) = a(x,y,((z \ u) * w) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21071,a,b,21051,a)].">
      <j1 rule="hyper" parents="63 21071 21051"/>
    </justification>
  </clause>

  <clause id="21074">
    <literal><![CDATA[
      a(x,y,(z \ (u \ (w * v5))) * a(v6,w,w)) = a(x,y,z \ (u \ (v5 * L(w,w,v6))))
    ]]></literal>
    <justification jstring="[para(20773(a,1),21062(a,1,3))].">
      <j1 rule="para" parents="20773 21062"/>
    </justification>
  </clause>

  <clause id="21075">
    <literal><![CDATA[
      a(x,y,((z \ u) * w) * (z * u)) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,20847,a(flip),b,21073,a),flip(a)].">
      <j1 rule="hyper" parents="63 20847 21073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21077">
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * (v5 * a(v6,u,u))) = a(x,y,v5 \ (z \ (w * L(u,u,v6))))
    ]]></literal>
    <justification jstring="[hyper(63,a,20848,a(flip),b,21074,a)].">
      <j1 rule="hyper" parents="63 20848 21074"/>
    </justification>
  </clause>

  <clause id="21078">
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * (v5 * a(v6,u,u))) = a(x,y,v5 * (z \ (w * L(u,u,v6))))
    ]]></literal>
    <justification jstring="[hyper(316,a,20852,a(flip),b,21077,a),flip(a)].">
      <j1 rule="hyper" parents="316 20852 21077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21079">
    <literal><![CDATA[
      (a(x,y,z) * ((u / (w * z)) * (w * L(z,y,x)))) \ u = a(z,y,a(w * (z \ u),w,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,21058,a(flip),b,20974,a),flip(a)].">
      <j1 rule="hyper" parents="316 21058 20974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21081">
    <literal><![CDATA[
      a(x,y,z \ (((u * (1 / (w / v5))) * (v5 \ w)) * v6)) = a(x,y,z \ (L(u,w \ v5,v5 * w) * v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,12133,a(flip),b,21042,a),flip(a)].">
      <j1 rule="hyper" parents="316 12133 21042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21082">
    <literal><![CDATA[
      a(x,y,z \ (((u * ((w / v5) \ 1)) * (v5 \ w)) * v6)) = a(x,y,z \ (L(u,w \ v5,v5 * w) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,20367,a(flip),b,21081,a)].">
      <j1 rule="hyper" parents="63 20367 21081"/>
    </justification>
  </clause>

  <clause id="21083">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w \ v5) * (v6 * (v5 / w))))) = a(x,y,z \ (L(v6,v5 \ w,w * v5) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11856,a(flip),b,21082,a)].">
      <j1 rule="hyper" parents="63 11856 21082"/>
    </justification>
  </clause>

  <clause id="21084">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w \ v5) * (v6 * (w \ v5))))) = a(x,y,z \ (L(v6,v5 \ w,w * v5) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5777,a(flip),b,21083,a)].">
      <j1 rule="hyper" parents="63 5777 21083"/>
    </justification>
  </clause>

  <clause id="21085">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w \ v5,w \ v5) * v6)) = a(x,y,z \ (L(u,v5 \ w,w * v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,6794,a(flip),b,21084,a)].">
      <j1 rule="hyper" parents="63 6794 21084"/>
    </justification>
  </clause>

  <clause id="21086">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w \ v5,v5 * w) * v6)) = a(x,y,z \ (L(u,v5 * w,v5 * w) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,17592,a(flip),b,21085,a),flip(a)].">
      <j1 rule="hyper" parents="63 17592 21085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21087">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w * v5,w * v5) * v6)) = a(x,y,z * (L(u,v5 \ w,w * v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,20852,a(flip),b,21086,a),flip(a)].">
      <j1 rule="hyper" parents="63 20852 21086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21088">
    <literal><![CDATA[
      a(x,y,z * (L(u,w \ v5,v5 * w) * v6)) = a(x,y,z * (L(u,v5 * w,v5 * w) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,20852,a(flip),b,21087,a),flip(a)].">
      <j1 rule="hyper" parents="63 20852 21087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21089">
    <literal><![CDATA[
      a(x,y,z * (L(u,w \ v5,w * v5) * v6)) = a(x,y,z * (L(u,v5 * w,v5 * w) * v6))
    ]]></literal>
    <justification jstring="[para(1668(a,1),21088(a,1,3,2,1))].">
      <j1 rule="para" parents="1668 21088"/>
    </justification>
  </clause>

  <clause id="21090">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w / (v5 \ v6)) / (1 / (v5 \ v6))))) = a(x,y,z \ (u \ R(w,v6 \ v5,v5 * v6)))
    ]]></literal>
    <justification jstring="[para(18732(a,2),21043(a,2,3,2,2))].">
      <j1 rule="para" parents="18732 21043"/>
    </justification>
  </clause>

  <clause id="21091">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w / (v5 \ v6)) / (1 / (v5 \ v6))))) = a(x,y,z \ (u \ L(w,v6 \ v5,v5 * v6)))
    ]]></literal>
    <justification jstring="[hyper(316,a,12124,a(flip),b,21090,a),flip(a)].">
      <j1 rule="hyper" parents="316 12124 21090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21092">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((1 / (w \ v5)) \ (v6 / (w \ v5))))) = a(x,y,z \ (u \ L(v6,v5 \ w,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5606,a(flip),b,21091,a)].">
      <j1 rule="hyper" parents="63 5606 21091"/>
    </justification>
  </clause>

  <clause id="21093">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w \ v5) \ (v6 / ((w \ v5) \ 1))))) = a(x,y,z \ (u \ L(v6,w \ v5,v5 * w)))
    ]]></literal>
    <justification jstring="[para(14153(a,1),21092(a,1,3,2,2))].">
      <j1 rule="para" parents="14153 21092"/>
    </justification>
  </clause>

  <clause id="21094">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w \ v5) \ (((w \ v5) \ 1) \ v6)))) = a(x,y,z \ (u \ L(v6,w \ v5,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5920,a(flip),b,21093,a)].">
      <j1 rule="hyper" parents="63 5920 21093"/>
    </justification>
  </clause>

  <clause id="21095">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(w,v5 \ v6,v5 \ v6))) = a(x,y,z \ (u \ L(w,v5 \ v6,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12125,a(flip),b,21094,a)].">
      <j1 rule="hyper" parents="63 12125 21094"/>
    </justification>
  </clause>

  <clause id="21096">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(w,(v5 \ v6) * (v5 * v5),(v5 \ 1) \ v6))) = a(x,y,z \ (u \ L(w,v5 \ v6,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13050,a,b,21095,a)].">
      <j1 rule="hyper" parents="63 13050 21095"/>
    </justification>
  </clause>

  <clause id="21097">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w / (v5 \ v6)) / (1 / (v5 \ v6))))) = a(x,y,z \ (u * R(w,v6 \ v5,v5 * v6)))
    ]]></literal>
    <justification jstring="[para(18731(a,2),21044(a,2,3,2,2))].">
      <j1 rule="para" parents="18731 21044"/>
    </justification>
  </clause>

  <clause id="21098">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w / (v5 \ v6)) / (1 / (v5 \ v6))))) = a(x,y,z \ (u * L(w,v6 \ v5,v5 * v6)))
    ]]></literal>
    <justification jstring="[hyper(316,a,12129,a(flip),b,21097,a),flip(a)].">
      <j1 rule="hyper" parents="316 12129 21097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21099">
    <literal><![CDATA[
      a(x,y,z \ (u * ((1 / (w \ v5)) \ (v6 / (w \ v5))))) = a(x,y,z \ (u * L(v6,v5 \ w,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,5599,a(flip),b,21098,a)].">
      <j1 rule="hyper" parents="63 5599 21098"/>
    </justification>
  </clause>

  <clause id="21100">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w \ v5) \ (v6 / ((w \ v5) \ 1))))) = a(x,y,z \ (u * L(v6,w \ v5,v5 * w)))
    ]]></literal>
    <justification jstring="[para(14153(a,1),21099(a,1,3,2,2))].">
      <j1 rule="para" parents="14153 21099"/>
    </justification>
  </clause>

  <clause id="21101">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w \ v5) \ ((w \ v5) \ v6)))) = a(x,y,z \ (u * L(v6,w \ v5,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7982,a(flip),b,21100,a)].">
      <j1 rule="hyper" parents="63 7982 21100"/>
    </justification>
  </clause>

  <clause id="21102">
    <literal><![CDATA[
      a(x,y,z \ (u * L(w,v5 \ v6,v5 \ v6))) = a(x,y,z \ (u * L(w,v5 \ v6,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11752,a(flip),b,21101,a)].">
      <j1 rule="hyper" parents="63 11752 21101"/>
    </justification>
  </clause>

  <clause id="21103">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(w,(v5 \ 1) \ v6,(v5 \ 1) \ v6))) = a(x,y,z \ (u \ L(w,v5 \ v6,v6 * v5)))
    ]]></literal>
    <justification jstring="[para(10965(a,1),21096(a,1,3,2,2))].">
      <j1 rule="para" parents="10965 21096"/>
    </justification>
  </clause>

  <clause id="21104">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(w,v5 \ v6,v6 * v5))) = a(x,y,z \ (u \ L(w,v5 * v6,v6 * v5)))
    ]]></literal>
    <justification jstring="[para(14239(a,1),21103(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="14239 21103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21105">
    <literal><![CDATA[
      a(x,y,z \ (u \ L(w,v5 * v6,v6 * v5))) = a(x,y,z * (u \ L(w,v5 \ v6,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20852,a(flip),b,21104,a),flip(a)].">
      <j1 rule="hyper" parents="63 20852 21104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21106">
    <literal><![CDATA[
      a(x,y,z * (u \ L(w,v5 \ v6,v6 * v5))) = a(x,y,z * (u \ L(w,v5 * v6,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20852,a(flip),b,21105,a),flip(a)].">
      <j1 rule="hyper" parents="63 20852 21105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21107">
    <literal><![CDATA[
      a(x,y,z * (u \ L(L(w,v5 \ v6,v6 * v5),v5 * v6,v6 * v5))) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14083,a(flip),b,21106,a),flip(a)].">
      <j1 rule="hyper" parents="63 14083 21106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21108">
    <literal><![CDATA[
      a(x,y,z * (u \ L(w,v5 \ v6,v5 * v6))) = a(x,y,z * (u \ L(w,v5 * v6,v6 * v5)))
    ]]></literal>
    <justification jstring="[para(1668(a,1),21106(a,1,3,2,2))].">
      <j1 rule="para" parents="1668 21106"/>
    </justification>
  </clause>

  <clause id="21109">
    <literal><![CDATA[
      L(1 / x,y,y) * L(((a(y,y,x) \ 1) / x) \ z,u,w) = L(x \ 1,y,y) * L((x \ (a(y,y,x) \ 1)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(4955(a,1),21024(a,1,1))].">
      <j1 rule="para" parents="4955 21024"/>
    </justification>
  </clause>

  <clause id="21110">
    <literal><![CDATA[
      L(1 / x,y,y) * L((a(y,y,x) \ (1 / x)) \ z,u,w) = L(x \ 1,y,y) * L((x \ (a(y,y,x) \ 1)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(20966(a,1),21109(a,1,2,1,1))].">
      <j1 rule="para" parents="20966 21109"/>
    </justification>
  </clause>

  <clause id="21111">
    <literal><![CDATA[
      L(x \ 1,y,y) * L((x \ (a(y,y,x) \ 1)) \ z,u,w) = L(1 / x,y,y) * L(L(1 / x,y,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(4955(a,1),21110(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4955 21110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21112">
    <literal><![CDATA[
      L(1 / x,y,y) * L(L(1 / x,y,y) \ z,u,w) = L(x \ 1,y,y) * L(L(x \ 1,y,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(5094(a,1),21111(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5094 21111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21113">
    <literal><![CDATA[
      L(1 / x,y,y) * L(L(1 / x,y,y) \ z,u,w) = L(x,y,y) * L(L(x,y,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(316,a,12858,a(flip),b,21112,a),flip(a)].">
      <j1 rule="hyper" parents="316 12858 21112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21114">
    <literal><![CDATA[
      (x * a(y,y,x)) * L((L(1 / x,y,y) \ 1) \ z,u,w) = L(x,y,y) * L(L(x,y,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6587,a,b,21113,a)].">
      <j1 rule="hyper" parents="63 6587 21113"/>
    </justification>
  </clause>

  <clause id="21115">
    <literal><![CDATA[
      x * (a(y,y,x) * L((L(1 / x,y,y) \ 1) \ z,u,w)) = L(x,y,y) * L(L(x,y,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18741,a(flip),b,21114,a)].">
      <j1 rule="hyper" parents="63 18741 21114"/>
    </justification>
  </clause>

  <clause id="21116">
    <literal><![CDATA[
      x * L(a(y,y,x) * ((L(1 / x,y,y) \ 1) \ z),u,w) = L(x,y,y) * L(L(x,y,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(21069(a,2),21115(a,1,2))].">
      <j1 rule="para" parents="21069 21115"/>
    </justification>
  </clause>

  <clause id="21117">
    <literal><![CDATA[
      x * L(a(y,y,x) \ (L(x,y,y) \ z),u,w) = L(x,y,y) * L(L(x,y,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(21065(a,1),21116(a,1,2,1))].">
      <j1 rule="para" parents="21065 21116"/>
    </justification>
  </clause>

  <clause id="21118">
    <literal><![CDATA[
      L(x,y,y) * L(L(x,y,y) \ z,u,w) = x * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(20967(a,1),21117(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20967 21117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21119">
    <literal><![CDATA[
      (x / T(y,z)) * L((x / T(y,z)) \ u,w,v5) = x * (y * L(y \ (x \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,20539,a(flip),b,21118,a),flip(a)].">
      <j1 rule="hyper" parents="63 20539 21118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21122">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ z,u,w) = y * (x * L(x \ (y \ z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,11744,a(flip),b,21119,a)].">
      <j1 rule="hyper" parents="63 11744 21119"/>
    </justification>
  </clause>

  <clause id="21123">
    <literal><![CDATA[
      T(x * (y * L(y \ (x \ z),u,w)),y) = y \ (x * L(x \ (z * y),u,w))
    ]]></literal>
    <justification jstring="[para(21122(a,1),7600(a,1,1))].">
      <j1 rule="para" parents="21122 7600"/>
    </justification>
  </clause>

  <clause id="21124">
    <literal><![CDATA[
      (x \ (y * L(y \ (z * x),u,w))) \ T(z,x) = a(w,u,z * (y * x))
    ]]></literal>
    <justification jstring="[para(21123(a,1),20903(a,1,1))].">
      <j1 rule="para" parents="21123 20903"/>
    </justification>
  </clause>

  <clause id="21125">
    <literal><![CDATA[
      a(x,y,z * (u \ w)) = a(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20902,a(flip),b,21124,a)].">
      <j1 rule="hyper" parents="63 20902 21124"/>
    </justification>
  </clause>

  <clause id="21126">
    <literal><![CDATA[
      a(x,y,z * (u \ w)) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(316,a,5491,a,b,21125,a),flip(a)].">
      <j1 rule="hyper" parents="316 5491 21125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21127">
    <literal><![CDATA[
      a(x,y,z * (u / w)) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5481,a,b,21125,a)].">
      <j1 rule="hyper" parents="63 5481 21125"/>
    </justification>
  </clause>

  <clause id="21129">
    <literal><![CDATA[
      a(x,y,z * (u \ L(w,v5 * v6,v6 * v5))) = a(x,y,z * (L(w,v5 \ v6,v5 * v6) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21108,a(flip),b,21125,a)].">
      <j1 rule="hyper" parents="63 21108 21125"/>
    </justification>
  </clause>

  <clause id="21130">
    <literal><![CDATA[
      a(x,y,z * ((((u \ a(w,v5,w)) * v6) * z) * u)) = a(x,y,L(L(v6,u,z),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20913,a(flip),b,21125,a),flip(a)].">
      <j1 rule="hyper" parents="63 20913 21125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21131">
    <literal><![CDATA[
      a(x,y,(z * u) * (w * (z \ (u \ w)))) = a(x,y,a(u,z,w * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20911,a(flip),b,21125,a),flip(a)].">
      <j1 rule="hyper" parents="63 20911 21125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21132">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) * ((u \ w) * z)) = a(x,y,a(u,z,w * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20910,a(flip),b,21125,a),flip(a)].">
      <j1 rule="hyper" parents="63 20910 21125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21133">
    <literal><![CDATA[
      a(x,y,(z * u) * ((z * L(w,w,u)) * (L(u,w,w) \ w))) = a(x,y,a(w * u,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,20909,a(flip),b,21125,a),flip(a)].">
      <j1 rule="hyper" parents="63 20909 21125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21134">
    <literal><![CDATA[
      a(x,y,((z \ u) \ (u * w)) * (w * L(z,z,u))) = a(x,y,a(u,z,w * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,20908,a(flip),b,21125,a),flip(a)].">
      <j1 rule="hyper" parents="63 20908 21125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21136">
    <literal><![CDATA[
      a(x,y,(z * ((u \ z) * w)) \ (u * L(w,u \ z,u \ z))) = a(x,y,a(u,u * z,u * (z * w)))
    ]]></literal>
    <justification jstring="[para(21125(a,1),20108(a,2,3))].">
      <j1 rule="para" parents="21125 20108"/>
    </justification>
  </clause>

  <clause id="21137">
    <literal><![CDATA[
      a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w))) = u * a(x,y,a(z,z * w,z * (w * u)))
    ]]></literal>
    <justification jstring="[para(21125(a,1),20109(a,2,2,3))].">
      <j1 rule="para" parents="21125 20109"/>
    </justification>
  </clause>

  <clause id="21138">
    <literal><![CDATA[
      a(x,y,z \ (u \ w)) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,20852,a,b,21126,a)].">
      <j1 rule="hyper" parents="63 20852 21126"/>
    </justification>
  </clause>

  <clause id="21140">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * (w * (v5 \ (u \ z)))) = a(x,y,w * (v5 \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20901,a(flip),b,21126,a),flip(a)].">
      <j1 rule="hyper" parents="63 20901 21126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21141">
    <literal><![CDATA[
      a(x,y,z * ((u * (w * w)) * v5)) = a(x,y,(u \ v5) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6737,a(flip),b,21126,a),flip(a)].">
      <j1 rule="hyper" parents="63 6737 21126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21144">
    <literal><![CDATA[
      a(x,y,z * ((u * w) / v5)) = a(x,y,z * (v5 * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,5796,a(flip),b,21127,a),flip(a)].">
      <j1 rule="hyper" parents="316 5796 21127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21145">
    <literal><![CDATA[
      a(x,y,(z \ u) * w) = a(x,y,(u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5996,a(flip),b,21141,a),flip(a)].">
      <j1 rule="hyper" parents="63 5996 21141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21147">
    <literal><![CDATA[
      a(x,y,z * (u * (w * u))) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5480,a(flip),b,21144,a),flip(a)].">
      <j1 rule="hyper" parents="63 5480 21144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21149">
    <literal><![CDATA[
      a(x,y,z * L(u,w,w)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5942,a(flip),b,21147,a)].">
      <j1 rule="hyper" parents="63 5942 21147"/>
    </justification>
  </clause>

  <clause id="21153">
    <literal><![CDATA[
      a(x,y,(z * u) * L(L(w,u,z),v5,v5)) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(100(a,1),21149(a,2,3))].">
      <j1 rule="para" parents="100 21149"/>
    </justification>
  </clause>

  <clause id="21154">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,v5,v5))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(403(a,1),21153(a,1,3))].">
      <j1 rule="para" parents="403 21153"/>
    </justification>
  </clause>

  <clause id="21156">
    <literal><![CDATA[
      a(x,y,z * (L(u,w,w) * v5)) = a(x,y,z * (v5 * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5491,a,b,21154,a)].">
      <j1 rule="hyper" parents="63 5491 21154"/>
    </justification>
  </clause>

  <clause id="21157">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ v5))) = a(x,y,z * (u * (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9022,a(flip),b,21154,a)].">
      <j1 rule="hyper" parents="63 9022 21154"/>
    </justification>
  </clause>

  <clause id="21159">
    <literal><![CDATA[
      a(x,y,z * (u * (z * (w * u)))) \ z = (L(w,y,x) * u) * ((w * u) \ z)
    ]]></literal>
    <justification jstring="[para(21157(a,1),20932(a,1,1))].">
      <j1 rule="para" parents="21157 20932"/>
    </justification>
  </clause>

  <clause id="21160">
    <literal><![CDATA[
      a(x,y,(z * ((u * z) * w)) * w) = a(x,y,L(L(u,z,w),w,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13215,a(flip),b,21130,a)].">
      <j1 rule="hyper" parents="63 13215 21130"/>
    </justification>
  </clause>

  <clause id="21161">
    <literal><![CDATA[
      a(x,y,z * (u * (z * (w * u)))) = a(x,y,L(L(w,u,z),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5666,a(flip),b,21160,a)].">
      <j1 rule="hyper" parents="63 5666 21160"/>
    </justification>
  </clause>

  <clause id="21162">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),w,u)) \ w = (L(z,y,x) * u) * ((z * u) \ w)
    ]]></literal>
    <justification jstring="[para(21161(a,1),21159(a,1,1))].">
      <j1 rule="para" parents="21161 21159"/>
    </justification>
  </clause>

  <clause id="21163">
    <literal><![CDATA[
      (L(x,y,z) * u) * ((x * u) \ w) = u \ ((a(z,y,x) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,19644,a(flip),b,21162,a),flip(a)].">
      <j1 rule="hyper" parents="63 19644 21162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21164">
    <literal><![CDATA[
      (x / (y * z)) * (y * L(z,u,w)) = y \ ((a(w,u,z) \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,16531,a,b,21163,a)].">
      <j1 rule="hyper" parents="63 16531 21163"/>
    </justification>
  </clause>

  <clause id="21165">
    <literal><![CDATA[
      (a(x,y,z) * (u \ ((a(x,y,z) \ u) * w))) \ w = a(z,y,a(u * (z \ w),u,x))
    ]]></literal>
    <justification jstring="[para(21164(a,1),21079(a,1,1,2))].">
      <j1 rule="para" parents="21164 21079"/>
    </justification>
  </clause>

  <clause id="21167">
    <literal><![CDATA[
      a(x,y,a(z * (x \ u),z,w)) = L(u,a(x,y,w),z) \ u
    ]]></literal>
    <justification jstring="[para(16149(a,1),21165(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16149 21165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21168">
    <literal><![CDATA[
      a(x,y,a(z * (x \ u),z,w)) = a(z,a(x,y,w),u)
    ]]></literal>
    <justification jstring="[hyper(316,a,18626,a,b,21167,a),flip(a)].">
      <j1 rule="hyper" parents="316 18626 21167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21171">
    <literal><![CDATA[
      a(x,y,(z * u) * ((z * L(w,w,u)) * L(u \ w,w,w))) = a(x,y,a(w * u,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21064,a,b,21133,a)].">
      <j1 rule="hyper" parents="63 21064 21133"/>
    </justification>
  </clause>

  <clause id="21172">
    <literal><![CDATA[
      a(x,y,(z * u) * ((z * L(w,w,u)) * (u \ w))) = a(x,y,a(w * u,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21154,a(flip),b,21171,a)].">
      <j1 rule="hyper" parents="63 21154 21171"/>
    </justification>
  </clause>

  <clause id="21174">
    <literal><![CDATA[
      a(x,y,z * (u \ L(w,v5 * v6,v6 * v5))) = a(x,y,z * (L(w,v6 * v5,v6 * v5) * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,21089,a(flip),b,21129,a),flip(a)].">
      <j1 rule="hyper" parents="316 21089 21129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21175">
    <literal><![CDATA[
      a(x,y,z * (u \ L(w,v5 * v6,v6 * v5))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(316,a,21156,a(flip),b,21174,a),flip(a)].">
      <j1 rule="hyper" parents="316 21156 21174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21177">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,v5 \ v6,v6 * v5))) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21107,a(flip),b,21175,a),flip(a)].">
      <j1 rule="hyper" parents="63 21107 21175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21178">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,v5 \ v6,v6 * v5))) = a(x,y,(w * u) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,21145,a(flip),b,21177,a),flip(a)].">
      <j1 rule="hyper" parents="316 21145 21177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21180">
    <literal><![CDATA[
      a(x,y,(z * ((u \ z) * w)) \ (u * L(w,u \ z,z * u))) = a(x,y,a(u,u * z,u * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21102,a(flip),b,21136,a)].">
      <j1 rule="hyper" parents="63 21102 21136"/>
    </justification>
  </clause>

  <clause id="21181">
    <literal><![CDATA[
      a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w))) = u * a(z,y,a(z * (w * u),w,x))
    ]]></literal>
    <justification jstring="[para(21060(a,1),21137(a,2,2))].">
      <j1 rule="para" parents="21060 21137"/>
    </justification>
  </clause>

  <clause id="21182">
    <literal><![CDATA[
      a(x,y,(z * ((u \ z) * w)) * (u * L(w,u \ z,z * u))) = a(x,y,a(u,u * z,u * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20852,a(flip),b,21180,a)].">
      <j1 rule="hyper" parents="63 20852 21180"/>
    </justification>
  </clause>

  <clause id="21183">
    <literal><![CDATA[
      a(x,y,(z * ((u \ z) * w)) * (u * L(w,u \ z,z * u))) = a(u,y,a(u * (z * w),z,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,21060,a(flip),b,21182,a),flip(a)].">
      <j1 rule="hyper" parents="316 21060 21182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21184">
    <literal><![CDATA[
      a(x,y,(z * u) * (w * ((u \ w) * z))) = a(u,y,a(u * (w * z),w,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,21178,a(flip),b,21183,a)].">
      <j1 rule="hyper" parents="63 21178 21183"/>
    </justification>
  </clause>

  <clause id="24414">
    <literal><![CDATA[
      a(x,y,(z \ u) \ ((z * u) \ w)) = a(x,y,(u * z) * (w * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(316,a,12151,a(flip),b,21138,a),flip(a)].">
      <j1 rule="hyper" parents="316 12151 21138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24416">
    <literal><![CDATA[
      a(x,y,((z * (u * T(u \ (z \ w),v5))) * u) * (v6 * (u \ (z * (u * T(u \ (z \ w),v5)))))) = a(x,y,T(z * T(z \ (w / u),v5),u) \ ((u * (z * (u * T(u \ (z \ w),v5)))) \ v6))
    ]]></literal>
    <justification jstring="[para(1391(a,1),24414(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1391 24414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24419">
    <literal><![CDATA[
      a(x,y,((z * (u * T(u \ (z \ w),v5))) * u) * (v6 * (u \ (z * (u * T(u \ (z \ w),v5)))))) = a(x,y,(z * T(z \ (w / u),v5)) \ ((u * (z * (u * T(u \ (z \ w),v5)))) \ v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,5492,a(flip),b,24416,a),flip(a)].">
      <j1 rule="hyper" parents="316 5492 24416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24421">
    <literal><![CDATA[
      a(x,y,((z * (u * T(u \ (z \ w),v5))) * u) * (v6 * (u \ (z * (u * T(u \ (z \ w),v5)))))) = a(x,y,(z * (z \ (w / u))) \ ((u * (z * (u * T(u \ (z \ w),v5)))) \ v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,5677,a(flip),b,24419,a),flip(a)].">
      <j1 rule="hyper" parents="316 5677 24419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24423">
    <literal><![CDATA[
      a(x,y,((z * (u * T(u \ (z \ w),v5))) * u) * (v6 * (u \ (z * (u * T(u \ (z \ w),v5)))))) = a(x,y,(w / u) \ ((u * (z * (u * T(u \ (z \ w),v5)))) \ v6))
    ]]></literal>
    <justification jstring="[para(10(a,1),24421(a,2,3,1))].">
      <j1 rule="para" parents="10 24421"/>
    </justification>
  </clause>

  <clause id="24424">
    <literal><![CDATA[
      a(x,y,((z * (u * T(u \ (z \ w),v5))) * u) * (v6 * (u \ (z * (u * T(u \ (z \ w),v5)))))) = a(x,y,(u \ w) \ ((u * (z * (u * T(u \ (z \ w),v5)))) \ v6))
    ]]></literal>
    <justification jstring="[hyper(316,a,5546,a(flip),b,24423,a),flip(a)].">
      <j1 rule="hyper" parents="316 5546 24423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24426">
    <literal><![CDATA[
      a(x,y,((z * (u * T(u \ (z \ w),v5))) * u) * (v6 * T(z * T(z \ (w / u),v5),u))) = a(x,y,(u \ w) \ ((u * (z * (u * T(u \ (z \ w),v5)))) \ v6))
    ]]></literal>
    <justification jstring="[para(1391(a,1),24424(a,1,3,2,2))].">
      <j1 rule="para" parents="1391 24424"/>
    </justification>
  </clause>

  <clause id="24427">
    <literal><![CDATA[
      a(x,y,(z * (u * T(u \ (w / v5),v6))) * ((u * (v5 * T(v5 \ (u \ w),v6))) * v5)) = a(x,y,(v5 \ w) \ ((v5 * (u * (v5 * T(v5 \ (u \ w),v6)))) \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5651,a(flip),b,24426,a)].">
      <j1 rule="hyper" parents="63 5651 24426"/>
    </justification>
  </clause>

  <clause id="24429">
    <literal><![CDATA[
      a(x,y,(z * (u * (z * (z \ (u \ w))))) * (v5 * (u * T(u \ (w / z),v6)))) = a(x,y,(z \ w) \ ((z * (u * (z * T(z \ (u \ w),v6)))) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,11757,a(flip),b,24427,a)].">
      <j1 rule="hyper" parents="63 11757 24427"/>
    </justification>
  </clause>

  <clause id="24431">
    <literal><![CDATA[
      a(x,y,(z \ u) \ ((z * (w * (z * T(z \ (w \ u),v5)))) \ v6)) = a(x,y,(z * u) * (v6 * (w * T(w \ (u / z),v5))))
    ]]></literal>
    <justification jstring="[para(76(a,1),24429(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="76 24429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24432">
    <literal><![CDATA[
      a(x,y,(z \ u) \ ((z * (w * (z * T(z \ (w \ u),v5)))) \ v6)) = a(x,y,((w * (w \ (u / z))) * v6) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,6051,a(flip),b,24431,a),flip(a)].">
      <j1 rule="hyper" parents="316 6051 24431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24434">
    <literal><![CDATA[
      a(x,y,(z \ u) \ ((z * (w * (z * T(z \ (w \ u),v5)))) \ v6)) = a(x,y,((u / z) * v6) * (z * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),24432(a,2,3,1,1))].">
      <j1 rule="para" parents="10 24432"/>
    </justification>
  </clause>

  <clause id="24435">
    <literal><![CDATA[
      a(x,y,(z \ u) \ ((z * (w * (z * T(z \ (w \ u),v5)))) \ v6)) = a(x,y,((z \ u) * v6) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(316,a,5547,a(flip),b,24434,a),flip(a)].">
      <j1 rule="hyper" parents="316 5547 24434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24437">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((z * (w * (z * T(z \ (w \ u),v5)))) \ v6)) = a(x,y,((z \ u) * v6) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20852,a(flip),b,24435,a)].">
      <j1 rule="hyper" parents="63 20852 24435"/>
    </justification>
  </clause>

  <clause id="24438">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((z * (w * (z * T(z \ (w \ u),v5)))) \ v6)) = a(x,y,a(z,z,u) * v6)
    ]]></literal>
    <justification jstring="[hyper(316,a,21075,a(flip),b,24437,a),flip(a)].">
      <j1 rule="hyper" parents="316 21075 24437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24439">
    <literal><![CDATA[
      a(x,y,(z \ u) * (w * (z * (v5 * (z * T(z \ (v5 \ u),v6)))))) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21125,a(flip),b,24438,a)].">
      <j1 rule="hyper" parents="63 21125 24438"/>
    </justification>
  </clause>

  <clause id="24440">
    <literal><![CDATA[
      a(x,y,(z * (u * (w * (u * (u \ (w \ v5)))))) * (u \ v5)) = a(x,y,a(u,u,v5) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6365,a(flip),b,24439,a)].">
      <j1 rule="hyper" parents="63 6365 24439"/>
    </justification>
  </clause>

  <clause id="24441">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * (u \ w)) = a(x,y,a(u,u,w) * z)
    ]]></literal>
    <justification jstring="[para(76(a,1),24440(a,1,3,1,2,2))].">
      <j1 rule="para" parents="76 24440"/>
    </justification>
  </clause>

  <clause id="24442">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * (w * u)) = a(x,y,a(u,u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21125,a(flip),b,24441,a)].">
      <j1 rule="hyper" parents="63 21125 24441"/>
    </justification>
  </clause>

  <clause id="24443">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,20844,a(flip),b,24442,a),flip(a)].">
      <j1 rule="hyper" parents="63 20844 24442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24448">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8680,a,b,24443,a)].">
      <j1 rule="hyper" parents="63 8680 24443"/>
    </justification>
  </clause>

  <clause id="24450">
    <literal><![CDATA[
      a(x,y,z * (u * a(w,v5,v5))) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,20089,a(flip),b,24443,a)].">
      <j1 rule="hyper" parents="63 20089 24443"/>
    </justification>
  </clause>

  <clause id="24455">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ v5))) = a(x,y,z * (u \ (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21140,a(flip),b,24448,a),flip(a)].">
      <j1 rule="hyper" parents="63 21140 24448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24459">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * L(v5,v5,v6)))) = a(x,y,(u \ (v5 * w)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21078,a(flip),b,24450,a)].">
      <j1 rule="hyper" parents="63 21078 24450"/>
    </justification>
  </clause>

  <clause id="24460">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,w,v5))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(20700(a,1),24450(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="20700 24450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24461">
    <literal><![CDATA[
      a(x,y,((z \ u) \ (u * w)) * (w * z)) = a(x,y,a(u,z,w * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21134,a(flip),b,24460,a),flip(a)].">
      <j1 rule="hyper" parents="63 21134 24460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24463">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * v5))) = a(x,y,z * ((v5 \ w) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21125,a(flip),b,24455,a),flip(a)].">
      <j1 rule="hyper" parents="63 21125 24455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24464">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) * v5)) = a(x,y,z * ((w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,21125,a(flip),b,24463,a),flip(a)].">
      <j1 rule="hyper" parents="63 21125 24463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24465">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) * ((w * u) * z)) = a(x,y,a(u,z,w * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21132,a(flip),b,24464,a),flip(a)].">
      <j1 rule="hyper" parents="63 21132 24464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24467">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * L(v5,v5,v6)))) = a(x,y,((v5 * w) * u) * z)
    ]]></literal>
    <justification jstring="[hyper(316,a,21145,a(flip),b,24459,a),flip(a)].">
      <j1 rule="hyper" parents="316 21145 24459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24469">
    <literal><![CDATA[
      a(x,y,((z * u) * (w \ z)) * (u * w)) = a(x,y,a(z,w,u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,21145,a(flip),b,24461,a)].">
      <j1 rule="hyper" parents="63 21145 24461"/>
    </justification>
  </clause>

  <clause id="24470">
    <literal><![CDATA[
      a(x,y,z * ((u * L(w,w,v5)) * v6)) = a(x,y,((w * u) * v6) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21125,a(flip),b,24467,a)].">
      <j1 rule="hyper" parents="63 21125 24467"/>
    </justification>
  </clause>

  <clause id="24471">
    <literal><![CDATA[
      a(x,y,((z * u) * (w \ z)) * (u * w)) = a(x,y,a(z * w,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21172,a(flip),b,24470,a),flip(a)].">
      <j1 rule="hyper" parents="63 21172 24470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24473">
    <literal><![CDATA[
      a(x,y,a(z * u,u,w)) = a(x,y,a(z,u,w * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,24469,a(flip),b,24471,a),flip(a)].">
      <j1 rule="hyper" parents="63 24469 24471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24475">
    <literal><![CDATA[
      a(x,y,a(z * u,z,w)) = a(x,y,a(u,z,w * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8927,a,b,24473,a)].">
      <j1 rule="hyper" parents="63 8927 24473"/>
    </justification>
  </clause>

  <clause id="24476">
    <literal><![CDATA[
      a(x,y,a(x \ z,u,w * u)) = a(u,a(x,y,w),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21168,a(flip),b,24475,a),flip(a)].">
      <j1 rule="hyper" parents="63 21168 24475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24479">
    <literal><![CDATA[
      a(x,y,a(x * z,u,w * u)) = a(u,a(x,y,w),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,20062,a(flip),b,24476,a)].">
      <j1 rule="hyper" parents="63 20062 24476"/>
    </justification>
  </clause>

  <clause id="24480">
    <literal><![CDATA[
      x * a(y,z,a(y * x,u,w * u)) = L(x,a(y,z,w),u)
    ]]></literal>
    <justification jstring="[hyper(139,a,24479,a,b,16195,a)].">
      <j1 rule="hyper" parents="139 24479 16195"/>
    </justification>
  </clause>

  <clause id="24481">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * ((z * w) * u)) = a(x,y,a(w,u,z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21145,a(flip),b,24465,a)].">
      <j1 rule="hyper" parents="63 21145 24465"/>
    </justification>
  </clause>

  <clause id="24482">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (z * u))) = a(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21045,a(flip),b,24481,a),flip(a)].">
      <j1 rule="hyper" parents="63 21045 24481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24483">
    <literal><![CDATA[
      a(x,y,(z * u) * (w * (z \ (u \ w)))) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21131,a,b,24482,a)].">
      <j1 rule="hyper" parents="63 21131 24482"/>
    </justification>
  </clause>

  <clause id="24486">
    <literal><![CDATA[
      a(x,y,(z * u) * (w * ((u \ w) * z))) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21157,a(flip),b,24483,a)].">
      <j1 rule="hyper" parents="63 21157 24483"/>
    </justification>
  </clause>

  <clause id="24487">
    <literal><![CDATA[
      a(x,y,a(x * (z * u),z,w)) = a(w,y,a(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21184,a(flip),b,24486,a)].">
      <j1 rule="hyper" parents="63 21184 24486"/>
    </justification>
  </clause>

  <clause id="24488">
    <literal><![CDATA[
      a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w))) = u * a(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[para(24487(a,1),21181(a,2,2))].">
      <j1 rule="para" parents="24487 21181"/>
    </justification>
  </clause>

  <clause id="24489">
    <literal><![CDATA[
      a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w))) = L(u,y,a(w,z,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,19223,a(flip),b,24488,a),flip(a)].">
      <j1 rule="hyper" parents="316 19223 24488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25292">
    <literal><![CDATA[
      (a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w)))) \ u = a(u * (z \ w),z * w,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,18253,a,b,20086,a)].">
      <j1 rule="hyper" parents="63 18253 20086"/>
    </justification>
  </clause>

  <clause id="25298">
    <literal><![CDATA[
      (a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w)))) \ u = a(z,z * w,a(w * (z * u),y,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,20095,a(flip),b,25292,a),flip(a)].">
      <j1 rule="hyper" parents="316 20095 25292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25299">
    <literal><![CDATA[
      (a(x,y,z) * ((u / (z \ w)) * (z \ (a(x,y,z) \ w)))) \ u = a(z,y,a(w * (z * u),w,x))
    ]]></literal>
    <justification jstring="[hyper(316,a,21057,a(flip),b,25298,a),flip(a)].">
      <j1 rule="hyper" parents="316 21057 25298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25300">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),z,w)) = L(u,y,a(z,x,w)) \ u
    ]]></literal>
    <justification jstring="[para(24489(a,1),25299(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24489 25299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25301">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),z,w)) = a(a(z,x,w),y,u)
    ]]></literal>
    <justification jstring="[hyper(316,a,18626,a,b,25300,a),flip(a)].">
      <j1 rule="hyper" parents="316 18626 25300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25302">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),z,w)) = a(z,x,a(u,y,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,19132,a(flip),b,25301,a),flip(a)].">
      <j1 rule="hyper" parents="316 19132 25301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25303">
    <literal><![CDATA[
      a(x,y,a(x * z,u,w * u)) = a(u,x,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,24475,a(flip),b,25302,a)].">
      <j1 rule="hyper" parents="63 24475 25302"/>
    </justification>
  </clause>

  <clause id="25305">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,24479,a(flip),b,25303,a)].">
      <j1 rule="hyper" parents="63 24479 25303"/>
    </justification>
  </clause>

  <clause id="25306">
    <literal><![CDATA[
      x * a(y,z,a(x,u,w)) = L(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(25303(a,1),24480(a,1,2))].">
      <j1 rule="para" parents="25303 24480"/>
    </justification>
  </clause>

  <clause id="25315">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(316,a,13660,a,b,25305,a),flip(a)].">
      <j1 rule="hyper" parents="316 13660 25305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25331">
    <literal><![CDATA[
      x * a(y,z,a(x,u,w)) = L(x,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[para(25305(a,1),16198(a,1,2))].">
      <j1 rule="para" parents="25305 16198"/>
    </justification>
  </clause>

  <clause id="25371">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,w,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(34,a,25306,a,b,25331,a)].">
      <j1 rule="hyper" parents="34 25306 25331"/>
    </justification>
  </clause>

  <clause id="25377">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(x,w,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(316,a,25315,a,b,25371,a)].">
      <j1 rule="hyper" parents="316 25315 25371"/>
    </justification>
  </clause>

  <clause id="25426">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,25377,a,b,19448,a),flip(a)].">
      <j1 rule="hyper" parents="134 25377 19448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25460">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,25426,a,b,13738,a),flip(a)].">
      <j1 rule="hyper" parents="134 25426 13738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25461">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("aa1")
    ]]></attribute>
    <justification jstring="[resolve(25460,a,64,a)].">
      <j1 rule="resolve" parents="25460 64"/>
    </justification>
  </clause>

</proof>

</proofs>
